NOVEL SOLAR CELL CONCEPTS
Dissertation zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.) an der Universität Konstanz Fachbereich Physik
vorgelegt von
Jan Christoph Goldschmidt
Fraunhofer Institut für Solare Energiesysteme (ISE) Freiburg
September 2009 Dissertation der Universität Konstanz Tag der mündlichen Prüfung: 16.11.2009
Referent/in: Prof. Gerhard Willeke Referent/in: Prof. Thomas Dekorsy 1 Table of contents
1 Table of contents...... i 2 Motivation and Introduction ...... 1 2.1 Motivation ...... 1 2.1.1 Why it is essential to transform the global energy system?...... 1 2.1.2 Why photovoltaics?...... 1 2.1.3 Why new concepts for higher efficiencies?...... 2 2.1.4 Photon management for full spectrum utilization ...... 3 2.2 Main objectives of this work ...... 4 2.3 Structure of this Work ...... 5 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts...... 7 3.1 A short theory of solar cells...... 7 3.1.1 Thermodynamic efficiency limits ...... 7 3.1.2 Generating chemical energy...... 8 3.1.3 Extracting useful energy...... 10 3.1.4 The pn-structure ...... 13 3.2 Novel solar cell concepts...... 17 3.2.1 Thermophotovoltaic Systems...... 17 3.2.2 Hot carrier solar cells ...... 17 3.2.3 Tandem solar cells...... 18 3.2.4 Intermediate band-gap solar cells...... 18 3.2.5 Photon management...... 19 4 Fluorescent Concentrators...... 21 4.1 Introduction to fluorescent concentrators ...... 21 4.1.1 The working principle of fluorescent concentrators...... 21 4.1.2 The factors that determine the efficiency of fluorescent concentrator systems ...... 23 4.1.3 Fluorescent concentrator system design...... 26
i 1 Table of contents
4.1.4 Materials for fluorescent collectors ...... 30 4.1.5 Fluorescence...... 31 4.2 Theoretical description of fluorescent concentrators ...... 36 4.2.1 Maximum concentration and Stokes shift ...... 36 4.2.2 Thermodynamic model of the fluorescent concentrator ...... 39 4.2.3 Photonic structures ...... 43 4.3 Optical characterization of fluorescent concentrator materials ...... 48 4.3.1 Photoluminescence measurements ...... 48 4.3.2 Characterizing the light guiding of fluorescent concentrators ...... 56 4.3.3 Measuring the angular distribution of the guided light...... 74 4.3.4 Short summary of the optical characterization ...... 77 4.4 Simulating fluorescent concentrators...... 79 4.4.1 Monte Carlo simulation...... 80 4.4.2 The used model ...... 81 4.4.3 Results of simple model ...... 87 4.4.4 Improvements of model...... 90 4.4.5 Conclusions from simulation...... 100 4.5 Fluorescent concentrator systems ...... 101 4.5.1 Solar cells for fluorescent concentrator systems...... 101 4.5.2 Systems with different materials ...... 103 4.5.3 Systems with silicon bottom cells ...... 110 4.5.4 The effect of photonic structures...... 115 4.5.5 The influence of system size on collection efficiency ...... 120 4.6 The future of fluorescent concentrators ...... 128 4.6.1 The “Nano-Fluko” concept...... 129
ii 1 Table of contents
5 Upconversion...... 133 5.1 Introduction to upconversion...... 133 5.2 The potential of upconversion and ways to increase upconversion efficiency...... 135 5.2.1 The potential of upconversion...... 135 5.2.2 Definition of upconversion efficiency...... 136 5.2.3 Upconversion efficiencies achieved so far ...... 137 5.2.4 Spectral concentration...... 137 5.2.5 An advanced system design for spectral concentration...... 138 5.2.6 Enhancing upconversion efficiency by plasmon resonances...... 140 5.3 Upconversion mechanisms and their theoretical description ...... 142 5.3.1 Absorption and emission...... 144 5.3.2 Migration of excitation energy...... 148 5.3.3 Multi-phonon relaxation...... 151 5.3.4 Intensity dependence of upconversion ...... 152 5.4 Suitable materials for upconversion...... 156 5.4.1 Theoretical aspects of the energy spectrum of trivalent erbium ...... 157 5.5 Optical material characterization ...... 161 5.5.1 Absorption measurements...... 161 5.5.2 The Kubelka-Munk theory...... 163 5.5.3 Absorption coefficient and Einstein coefficients...... 164 5.5.4 Time-resolved photoluminescence...... 167 5.5.5 Intensity dependent upconversion photoluminescence...... 176 5.5.6 Calibrated photoluminescence measurements...... 179 5.5.7 Optical properties of luminescent nanocrystalline quantum dots (NQD)...... 185 5.6 Simulating upconversion ...... 188 5.6.1 The rate equation model...... 189 5.6.2 Input parameters...... 194
iii 1 Table of contents
5.6.3 Simulation results...... 197 5.7 Upconversion systems ...... 204 5.7.1 Used solar cells and experimental setup...... 204 5.7.2 Applying the upconverter to the solar cell...... 206 5.7.3 External quantum efficiency with different upconverter samples...... 207 5.7.4 Upconversion solar cell system under concentrated sunlight...... 211 5.8 Conclusions and outlook on the application of upconverting materials to silicon solar cells...... 220 6 Summary...... 225 6.1 Fluorescent concentrators ...... 225 6.2 Upconversion...... 228 7 Deutsche Zusammenfassung...... 231 7.1 Fluoreszenzkonzentratoren ...... 231 7.2 Hochkonversion...... 234 8 References...... 237 9 Appendix...... 249 9.1 Abbreviations...... 249 9.2 Glossary...... 250 9.3 Physical Constants...... 261 10 Author’s Publications...... 263 10.1 Refereed journal papers ...... 263 10.2 Conference papers...... 264 10.3 Oral presentations ...... 267 10.4 Patents...... 268 10.5 Other publications...... 269 11 Curriculum vitae ...... 271 12 Acknowledgements...... 273
iv 2 Motivation and Introduction
2.1 Motivation
2.1.1 Why it is essential to transform the global energy system? The global energy system is based on the primary energy sources oil, coal and gas predominantly. Burning these fossil fuels releases carbon dioxide and other emissions, ultimately resulting in climate change. Global climate protection is the supreme challenge that makes it necessary to transform energy systems worldwide. Also, at the local and regional levels, mining, transport, storage, and usage of fossil and nuclear fuels destroy or put at risk complete ecosystems and human health. Therefore the persisting patterns of energy usage jeopardize the natural basis of life. The global energy resources are limited and distributed unevenly. This causes geostrategic conflict and makes a forced end to our current energy usage inevitable. About two billion people have no access to modern energy sources. They are therefore cut off from any chance to overcome their poverty. All this leaves humanity with the challenge to drastically change the global energy system and to orient it towards sustainable ecolo- gical and social criteria [1]. Such criteria are the mitigation of climate change, conser- vation of nature and ecosystems such as oceans, rivers and soil, and the reduction of air pollution. A sufficient food supply for everybody must always be more important than energy production. Everybody should have affordable access to modern energy sources. Everybody should be able to use energy without endangering one’s health and should live without fear of risks associated with the energy system. As control over energy sources has always meant political power, reshaping our energy systems also presents a chance for more democracy and a more just distribution of power [2]. While searching for solutions, all of these criteria should be considered. There is no benefit in solving one problem while worsening another one at the same time.
2.1.2 Why photovoltaics? An increase in energy productivity and a switch to new renewable energy sources are the two main pillars of the necessary transformation in global energy systems. Among the new renewable energy sources, solar energy has the most important role to play. The sustainably usable potential of solar energy appears to be virtually unlimited in comparison to the world energy demand. Other renewable energy sources like wind energy, water power, and biomass originate from solar energy, but their sustainably usable potential is not sufficient to meet the global energy demand [1]. The technology
1 2 Motivation and Introduction likely to succeed in bringing solar energy to the people in developed as well as in developing countries is photovoltaics, the direct conversion of solar radiation into electric power. The modular character of the technology allows for the construction of power plants in any size. Photovoltaic devices, also known as solar cells, can serve as a power source in consumer products or be interconnected in modules as power plants of varying size: small island-systems to power houses or villages, mainly in developing countries are just as possible as grid-connected systems on residential housing in industrial countries or huge power plants in the megawatt range. The absence of moving parts makes the systems reliable and enables system lifetimes exceeding 25 years. Additionally, solar cells convert diffuse radiation into electricity as well, so they can harvest solar energy efficiently in middle and even northern Europe. Of all energy technologies, photovoltaics have the steepest learning curve. That is, no energy technology is getting cheaper faster. On average, a doubling in the cumulated installed power capacity of photovoltaic systems results in a 20% reduction in production costs. Together with the enormous market growth [3], this leads to a fast reduction in costs. Already now, levelized electricity costs from photovoltaics can compete with peak load prices in southern Europe [4]. Around 2015 or earlier, grid-parity will be reached in middle Europe [4]. Then the electricity from a roof-mounted photovoltaic system will cost about the same as the end consumer pays for electricity. However, prices are still high at the moment. To reach grid parity and to continue the expected development beyond 2015, continuous innovation is necessary.
2.1.3 Why new concepts for higher efficiencies? Crystalline silicon is the dominant material in the production of solar cells. It is non- toxic and abundant. At the moment the material costs for silicon in the required purity dominate the costs for solar cell production. Therefore, alternative production techno- logies, such as thin-film solar cells or innovative silicon-wafer based concepts appear attractive. But also for new technologies, maturing production technologies will lead to a situation in which the material costs dominate. In the end, it will be the wafer, the glazing, or the substrate for thin-film technologies which sets the limit for further cost reduction. The only way to overcome this limit is to increase the efficiency of the solar cells. A higher efficiency increases the amount of electricity produced from one unit of material. This reduces the electricity costs and the amount of resources needed to meet our energy needs. Current innovations are mainly focused on production technologies. The underlying working principle of the solar cells remains unchanged. However, to achieve substantially higher efficiencies, novel solar cell concepts are needed that also address the working principle and which overcome fundamental limits.
2 2.1 Motivation
2.1.4 Photon management for full spectrum utilization Most solar cells today are made from silicon, and therefore from one semiconductor material with one band-gap. These solar cells do not use the full solar spectrum (see Fig. 2.1). Photons which have energies below the band-gap of the semiconductor are not absorbed. The energy of photons which exceeds the band-gap is converted into heat, and is therefore lost as well [5]. As more than 55% of the energy is lost by these mechanisms, it is obvious that new concepts for higher efficiencies have to make better use of the energy contained in the solar spectrum.
Fig. 2.1: Illustration of the principal losses incurred by a silicon solar cell. Photons with energies below the band-gap are transmitted straight through the device. Around 20% of the incident energy is lost this way. The energy of photons exceeding the band-gap is converted into heat. These thermalization losses account for around 35% of the incident energy. To achieve high efficiencies, novel concepts are needed to reduce these losses.
Several concepts are being discussed to overcome these fundamental efficiency- limiting problems. Most of these novel concepts require complex new solar cell structures and many are rather theoretical concepts than working devices. An alternative approach is photon management. Photon management means splitting or modifying of the solar spectrum before the photons are absorbed in the solar cells in such a way that the energy of the solar spectrum is used more efficiently. The solar cells themselves remain fairly unchanged, and well-established solar cell technologies can be used. This gives the concepts high realization potential. Because of these advantages, this work will deal with different concepts of photon management.
3 2 Motivation and Introduction
2.2 Main objectives of this work
The role of this work is to find and explore promising fields in the wide landscape of novel solar cell concepts. The main objectives are to increase the understanding of the concepts, investigate the materials on which the concepts are based, to realize complete systems, and to further develop the concepts to a point where their perspective and potential becomes clear.
In this work, I concentrated on two concepts from the fields of photon management that appeared to be especially promising: fluorescent concentrators and upconversion. Both rely on luminescent materials. Luminescent materials absorb light independently from the direction of incidence. Therefore, in principle these concepts are able to use diffuse light as well. This is a big advantage to many other concepts for photon management, which rely on selective mirrors, filters, diffraction gratings, or similar, and which usually only work under direct sunlight. Both concepts share important aspects in theory as well as in technological issues, e.g. the need for a matrix material for the luminescent material, and they can be combined in one system as we will see later on.
Fluorescent concentrators are a concept well known since the late 1970s [6, 7] to concentrate both direct and diffuse radiation without tracking systems. In a fluorescent collector, a luminescent material embedded in a transparent matrix absorbs sunlight and emits radiation with a different wavelength. Total internal reflection traps most of the emitted light and guides it to the edges of the fluorescent collector. Solar cells, optically coupled to the edges, convert this light into electricity. Fluorescent concentrators were investigated intensively in the early 1980s [8, 9]. Research at that time aimed at cutting costs by using the concentrator to reduce the need for expensive solar cells. After 20 years, there has been considerable progress in the development of solar cells and luminescent materials, and new concepts have been developed.
In this work, several new ideas will be combined into one advanced concept for a fluorescent concentrator system design. The key features are a stack of different fluorescent concentrators to use the full solar spectrum, spectrally matched solar cells, and photonic structures that increase the fraction of light guided to the edges of the concentrator. To understand and to develop the different components, and finally to realize systems with all of these features is the main objective of my work on fluorescent concentrators within the frame of this PhD thesis.
Upconversion of photons with energies below the band-gap is a promising approach to overcome the losses caused by the transmission of these photons [10]. An upconverter
4 2.3 Structure of this Work generates one high-energy photon out of at least two low-energy photons. This high- energy photon can then create a free charge carrier in the solar cell.
In combination with a second luminescent material, the spectral range of upconverted photons can be increased. In this work, an advanced system design for such a combination is developed. The main objectives are to characterize the materials involved, to develop a theoretical model of the upconverter and to realize systems with the relevant components.
2.3 Structure of this Work
In this chapter 2, the motivation and topic of this work is introduced.
In chapter 3, I will outline fundamental theoretical concepts regarding the conversion of solar radiation into electric energy. I will restrict my presentation to very fundamental aspects that are necessary to understand how novel solar cell concepts help to increase the efficiency of solar cells and photovoltaic systems.
Chapter 4 deals with fluorescent concentrators. At the beginning, I will introduce the general working principle of fluorescent concentrators and review the results achieved so far. Following this, I will present the results from optical characterization of fluorescent concentrator materials and a method to characterize the light guiding behavior of fluorescent concentrators that I developed in the context of this work. To test different hypotheses that could explain the results of the optical characterization, a Monte-Carlo simulation of the concentrator’s light guiding is developed. Finally, investigations on complete systems of fluorescent concentrators and solar cells are presented. This includes systems with different collector materials and spectrally matched solar cells, as well as systems with photonic structures that increase light guiding efficiency.
Chapter 5 deals with upconversion. At the beginning, I will highlight by which mechanisms upconversion can occur and will introduce the theoretical concepts describing upconversion. I will discuss which materials are suitable as upconverter and show results of extensive optical characterization of the investigated erbium doped
NaYF4. This includes absorption measurements, time and intensity resolved photoluminescence measurements, and calibrated photoluminescence measurements to directly measure upconversion efficiency. Based on the experimental results and the theory, a simulation tool that models the upconversion dynamics is developed. Finally, experimental investigations on systems with upconverting material attached to silicon solar cells will be presented.
5 2 Motivation and Introduction
Chapter 6 will summarize and conclude the results of this work, the summary can be found in German in chapter 7. The referenced publications, abbreviations, a glossary, the used physical constants, the list of the author’s publications, a CV, and the acknowledgements are located at the end of the work.
6 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts
In this chapter, I will outline fundamental theoretical concepts about the conversion of solar radiation into electric energy, in short: the theory of solar cells. In this work, solar cells are used in systems that apply photon management. The processing and optimization of the solar cells is of minor importance. Consequently, I will restrict my presentation to very fundamental aspects that are necessary to understand how novel solar cell concepts help to increase the efficiency of solar cells or photovoltaic systems. I will start from general thermodynamic considerations and will describe which conditions result in which efficiency limits. In the following, I will show how some of these limits can be overcome by novel solar cell concepts. This presentation is based on the discussions in [5, 11, 12] where detailed information can be found.
3.1 A short theory of solar cells
3.1.1 Thermodynamic efficiency limits A photovoltaic device converts solar radiation into electric energy. Solar radiation is nothing more than heat radiation emitted by the sun. With heat, entropy is always associated, while electricity is entropy-free. Therefore, in the conversion process, the entropy must be released to the surroundings in the form of heat. This should happen at a lower temperature, so that not all the received energy is lost in this process. An idealized way of this process of receiving energy that contains entropy, dissipation of entropy, and generating entropy-free work is the Carnot cycle. With TS being the temperature of the sun and T0 the ambient temperature, the Carnot efficiency K is
T0 K 1 . (3.1) TS
With TS = 6000 K and T0 = 300 K this efficiency is very high and exceeds 95%. The Carnot efficiency is the fundamental limit for all thermodynamic processes, and since the limit is a direct result of the second law of thermodynamics, it cannot be overcome. However, the Carnot efficiency is a very theoretical limit. It relies on isentropic processes that generate no extra entropy. Unfortunately, these processes are infinitely slow so the working power of a Carnot engine is infinitesimally small.
7 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts
The Carnot efficiency does not consider that energy is re-radiated from the converter to the sun. Considering the radiation emitted from the converter leads to a maximum possible efficiency of 93.3% [13]. This is the so-called Landsberg limit.
A model of a solar cell system that is a little bit more realistic is an absorber that receives solar radiation and powers a heat engine that works with the Carnot efficiency. When the temperature of the absorber TA equals TS the efficiency is zero, because the absorber would emit as much energy as it receives. When TA = T0 the efficiency would be zero as well, for there would be no temperature difference to drive the heat engine. Between these extremes, for an ideal temperature an efficiency of 85.4% can be achieved [12]. This efficiency can be increased to 86.8% if an absorber for each wavelength is used, which is operated at its individual ideal temperature. Even such an ideal system suffers losses from the emission of radiation. If this emission is re-directed to another ideal system, of which the emission is again re-directed to yet another system and so on, the Landsberg limit can be reached [14]. However, this requires breaking time symmetry. For this purpose circulators are needed that accept radiation from one direction while emitting it in a different direction [12]. There are different proposals for how such a system could be realized; probably the easiest to imagine is a rotating mirror.
3.1.2 Generating chemical energy Up to now, I have not considered the internal structure of the photovoltaic device. In a heat engine, one usually has some kind of gas that absorbs energy and performs work during expansion. Most solar cells are realized from semiconductor materials. In a semiconductor, the electrons and holes play the role of the working gas. Directly after absorption, the electrons in the conduction band and the holes in the valence band have the same energy distribution as the absorbed photons and the electron ensemble has the same temperature as the sun. In consequence, the higher energy states are relatively frequently populated. The electron ensemble cools down fast (in around 10-12 s) to the ambient room temperature by phonon interaction with the ion lattice, so that lower energy levels are now populated more frequently. The changes in the energy distribution are sketched in Fig. 3.1.
8 3.1 A short theory of solar cells
Fig. 3.1: Directly after absorption, the electrons in the conduction band and the holes in the valence band have the same energy distribution as the absorbed photons. In 10-12 s the electrons and holes cool down to the ambient temperature. For the population of the energy levels dne/dEe and dnh/dEh this means that the population is shifted to lower energies. After the cooling, the concentration of electrons and holes is still higher than in equilibrium. To describe this non-equilibrium situation, two Fermi distributions are necessary. The idea for this picture was taken from [5].
The cooling does not change the electron or hole concentration. Therefore, the concentration of both is higher than in equilibrium with the ambient temperature. To describe this non-equilibrium situation, two (quasi-)Fermi distributions are necessary: one for the electrons in the conduction band, and one for the holes in the valence band.
The Fermi energy of the electrons in the conduction band EFC can be identified as the electrochemical potential Ke of the electrons [5], and the Fermi energy of the holes in the valence band EFV can be identified as minus one times the electrochemical potential Kh of the holes. Consequently, the difference of the Fermi energies equals the sum of the electrochemical potentials:
EFC - EFV = Ke + Kh = Pe + Ph =: Peh (3.2)
Because of the opposite charges of electron and hole, the sum of their electrochemical potentials equals the sum of their chemical potentials [5]. The final consequence is that the splitting of the Fermi energies equals the chemical potential of electrons and holes. The splitting of the Fermi energies, and therefore the chemical potential, has been a result of the generation of extra carriers by photon absorption and subsequent cooling. Because of the band-gap, no complete equilibrium is reached and an electronically excited state remains: the heat or thermal energy contained in the thermal solar radiation has been converted into chemical energy.
9 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts
It is illustrative to consider the case without a band-gap like in a metal. The absorbed photons do not generate extra free carriers, as they only excite electrons within the band to higher energies. Directly after absorption, the electron temperature is also increased, but after the cooling equilibrium is reached, because concentration had not changed. Therefore, no chemical energy is generated.
3.1.3 Extracting useful energy As we have seen in the previous section, in a semiconductor solar energy is converted into chemical energy. This happens without any special structure, such as a pn- junction. Nevertheless, to use this energy we have to extract the electrons and holes, together with their energy from the semiconductor. In this section, I will show which aspects are important for the extraction of useful energy independent from any special structure.
The chemical potential Peh is the amount of energy that can be extracted with one electron-hole pair. Therefore, multiplying this amount with the particle flux per illuminated area of extracted electron-hole pairs jeh gives the extracted power density pext:
. pext = jeh Peh (3.3)
The particle flux jeh that can be extracted from an illuminated semiconductor is given by the difference of the rates of generation geh and recombination reh (in this case the rates are defined per area):
jeh = geh - reh. (3.4)
In an idealized case, only radiative recombination occurs, so the recombination rate equals the emission of photons from the semiconductor.
The number of emitted photons per time, per area, per unit solid angle, and per frequency interval is given by the generalized Planck’s law [5]
22 n QQ )(2 1 , p,Q TB ,, PQ 2 QD c § h PQ · (3.5) exp¨ ¸ 1 © BTk ¹ where Qis the frequency of the photons, T the temperature of the emitter, µ the chemical potential within the emitter (which has to be identified with Peh in this case), n(Q) is the refractive index into which the emission takes place, D Q is the absorption coefficient, c the speed of light in vacuum, h the Planck constant and kB the Boltzmann
10 3.1 A short theory of solar cells
constant. With this definition, Bp,Q cos(T) dA dQ d: is the number of photons emitted from the surface element dA in the frequency range of Qto Q +dQ into the solid angle d: into the direction given by the polar angle T and an azimuth angle I.
For the efficiency of a solar cell, especially two features of the generalized Planck’s law are important: the dependence on the chemical potential and the influence of the solid angle in which radiation is emitted.
To increase the extracted power jeh*Peh a high chemical potential in the semiconductor seems beneficial. On the other hand, following equation (3.5) a high chemical potential means high emission of photons. Therefore, a high chemical potential decreases the extracted current. For a maximum chemical potential POC, all photons are emitted, so the extractable current is zero. As a result, although the chemical potential is at its maximum, no power is extracted. The contrary situation is achieved when all the electron-hole pairs are extracted. Since there are no excess carriers left in the semiconductor, the chemical potential is zero in this case. Again, the extracted power is zero. In between, there is a point where the extracted power is at its maximum (see Fig. 3.2).
If the -1 in the denominator of equation (3.5) is neglected, for monochromatic irradiation and emission equations (3.4) and (3.5) can be combined to § P · ¨ eh ¸ . eheh constgj exp¨ ¸ (3.6) © BTk ¹
The structure of equation (3.6) is quite similar to that of the IV-characteristic of a pn- junction solar cell, if the electrochemical potential is identified with the voltage of the solar cell. From this derivation, it becomes clear that the exponential current voltage characteristic is not a result of the pn-junction, but a fundamental consequence of the balance between generation and recombination of electrons and holes.
This is still true even when the dominant recombination mechanism is not radiative recombination. Recombination can be interpreted as a reaction with the electron and the hole being the educts. Whether such a reaction does occur is governed by the chemical potential of both in comparison to the chemical potential of the product of the reaction. In semiconductors, the chemical potential depends approximately exponentially on the concentration [15] of the electrons and holes, which is the case for most educts in chemical reactions. In a standard silicon solar cell, the current voltage characteristic is mainly determined by processes in the region close to the pn-junction. In this so-called space charge region, the recombination rate depends on the product of
11 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts the concentration of holes and electrons, which is again equivalent to an exponential dependency on the chemical potential of the electron-hole pairs [15]. So we can state more generally, that the extraction of useful energy is described by three cases: first, maximum extraction that reduces the chemical potential to zero; second, the maximum chemical potential in the case where there is no extraction but maximum recombination; and third, the range in between. The height of the chemical potential determines the extent of the recombination in the most cases with an approximately exponential relation and therefore the remaining number of charge carriers that can be extracted.
Fig. 3.2: Illustration of how the extracted current jeh and the extracted power depend on the sum of chemical potentials of the electrons and holes in the semiconductor Peh [11]. At Peh = POC all photons are emitted, so the extractable current is zero. Therefore the extracted power jeh*Peh is zero as well. At Peh = 0 the extracted current is at its maximum jSC, because the radiative recombination is at its minimum. Nevertheless, because of Peh = 0 the extracted power is again zero. In between, a maximum power point (MPP) exists, at which the extracted power reaches its maximum jmpp*Pmpp (indicated as blue rectangle).
Without any special means, a semiconductor emits into a complete hemisphere. In contrast, the solid angle of the sun, from which radiation is received, is very small. Concentration with lenses or mirrors increases this solid angle. The maximum concentration is reached when radiation is received from the complete hemisphere.
Equation (3.5), with T = Ts and P = 0, describes as well the absorbed photon flux
12 3.1 A short theory of solar cells received from the sun and therefore the generation rate [11]. It is obvious that an expanded solid angle, from which radiation is received, increases the generation rate geh. Because the concentration of electrons and holes rises, the chemical potential is also higher with concentration. In consequence, more power jeh*Peh can be extracted and the efficiency increases. An alternative approach with the same result is to narrow the solid angle in which radiation is emitted. With a narrower solid angle of emission, the losses due to radiative recombination are smaller and the extracted current, the chemical potential, and consequently the extracted power are higher.
We have seen that only from the generalized Planck’s law an exponential current/chemical potential characteristics with a maximum power point can be derived, and the effect of concentration can be explained. Now the question arises of how exactly the electrons are extracted from the semiconductor and how the chemical energy is converted into electric energy. For this purpose, electrons and holes have to be extracted at different points of the semiconductor. If these two points are connected over an electric load, the difference in the electrochemical potential of the electrons and the holes drives a current through the load and work is performed. One structure that is able to separate electrons and holes is the pn-structure of common semiconductor solar cells.
3.1.4 The pn-structure A pn-structure consists of one p- and one n-doped region. Without illumination, in the p-doped region, the concentration of holes is higher than in intrinsic material, therefore the Fermi energy is close to the valence band edge. In the n-doped region, the electron concentration is higher and the Fermi energy is close to the conduction band edge. Illumination creates excess carriers, so both the electron and the hole concentration increases. As mentioned before, this situation is described with two Fermi distributions and therefore also two Fermi levels. This is the so-called splitting of the Fermi levels. The relative effect of the increase in charge carrier concentration is more pronounced for the minority charge carriers in each region, i.e. for the holes in the n-doped region and the electrons in the p-doped region. Consequently, the Fermi level of the majority charge carriers hardly moves, while the Fermi level of the minority charge carriers is at a distinctly different position than the common Fermi energy of the non-illuminated case.
In section 3.1.2, it was shown that the Fermi level can be identified with the electro- chemical potential of the respective kind of charge carrier (considering the sign of its charge). Gradients in this electrochemical potential cause the charge carriers to flow in a certain direction. For instance, the particle flux density of the electrons is [11]
13 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts
jeh = - ne/q me grad(EFC), (3.7) with ne being the electron concentration, q the elementary charge and me the mobility of the electrons. The particle flux density of the holes can be calculated accordingly but the different sign of the charge must be considered.
In equation (3.7), the carrier concentration plays an important role. Usually, the concentration of the majority carriers is higher by orders of magnitude than the minority carrier concentration. Therefore, the total charge current density J
J = - q je + q jh, (3.8) can be mainly attributed to the flow of the majority charge carriers in the respective region. Additionally, at the interface between metal contact and semiconductor, a lot of recombination occurs and in the metal itself no separate Fermi levels exist. Therefore, at the contacts the charge carriers have the same concentration as under the equilibrium without illumination. Because of these two facts, only the electro-chemical potentials of the majority carriers at the contact points determine the current through an external load. The difference of these two potentials is the voltage of the solar cell Vcell that can be measured externally between the two contacts of a solar cell.
Fig. 3.3: The pn-structure of common semiconductor solar cells under illumination. This figure shows the solar cell under short circuit conditions. Because of the short circuit, the electrochemical potentials of the majority carriers at the contact points are on the same level. The light-induced Fermi level splitting results into a large gradient of the Fermi levels across the pn- junction. This gradient causes a large current to flow. Because of their different charges, the electrons move to the contacts of the n-doped region, while the holes move to the contact of the p-doped region. The charge carriers are effectively separated. Because the external voltage is zero, no work is performed
14 3.1 A short theory of solar cells
If the two contacts are connected without any resistance (short circuit conditions), then the two electrochemical potentials EFC and EFV at the contact points are on the same level (see Fig. 3.3). Since the illumination has induced a splitting of the Fermi levels, a large gradient within the Fermi levels exists across the pn-junction. Following equation (3.7), this results into a large current. Further away from the junction, because of the higher charge carrier concentrations a smaller gradient of the Fermi levels is sufficient to maintain the same current. Because of their different charges, the electrons move to the contact of the n-region and the holes to the contact of the p-region. This constitutes a successful separation of electrons and holes. The resulting charge carrier density is designated short circuit current density JSC. Under short circuit conditions, no energy is extracted. As with the discussion of the chemical potential, without an external voltage, the product of current and voltage is zero.
To drive a current through a load and to perform work, a voltage difference - that is a difference between the electrochemical potentials of the majority carriers at the contact points - is necessary. As visible in Fig. 3.4, this reduces the gradient of the Fermi levels within the solar cell and therefore the extracted current. If the voltage is further increased to the open circuit voltage VOC so that the gradient is zero, no current flows (Fig. 3.5).
Fig. 3.4: Illuminated pn-structure of a solar cell under working point conditions. The electrochemical potentials of the majority carriers at the contact points determine the current through an external load. The difference of these two potentials is the voltage of the solar cell Vcell that can be measured externally between the two contacts of a solar cell. When this potential difference drives a current through the external load, work is performed. In comparison to Fig. 3.3 the internal gradient of the Fermi levels is reduced so the resulting current is smaller.
15 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts
Fig. 3.5: Illuminated pn-structure under open circuit conditions. At the open circuit voltage VOC the gradients of the electrochemical potentials across the pn- junction are zero and no current is flowing.
The maximum efficiency of a solar cell with one pn-junction has been calculated in [16] and also in [11]. Under the assumption that only radiative recombination occurs, the efficiency limit is 33% for an optimum band-gap of 1.3 eV under illumination with non-concentrated light and an AM1.5g spectral distribution. The band-gap of silicon is 1.12eV and therefore the achievable efficiency is very close to the optimum value. Experimentally, an efficiency of 24.7% [17] has been reached so far for a silicon solar cell under non-concentrated sunlight.
These values are considerably lower than the efficiency limits presented in the beginning of this chapter. The reason for this is that energy is lost in the cooling of the electrons and that photons are transmitted that have an energy below the band-gap, as it was visualized in Fig. 2.1. For a silicon solar cell, about 20% of the incident energy is lost because low-energy photons are not absorbed. The thermalization losses are specified to be around 35% of the incident energy. This value is calculated under the assumption that all electrons thermalize to the energy of the band-gap. As we have seen in this chapter, the energy distribution of the electrons has an average above the band-gap (Fig. 3.1). However, it is not the band-gap that determines the voltage, but the splitting of the Fermi levels. Additionally, to extract current, the voltage must be reduced in order to enable a current flow. So even under idealized conditions, the unavoidable losses are even higher.
In conclusion, the band-gap that played an important role in converting heat into chemical energy is also a source of fundamental losses. Therefore, most novel concepts deal with the question of how these losses associated with the band-gap can be overcome.
16 3.2 Novel solar cell concepts
3.2 Novel solar cell concepts
3.2.1 Thermophotovoltaic Systems A system design that resembles the idealized system, with an absorber that powers a Carnot engine (section 3.1.1), is the thermophotovoltaic system [18, 19]. In a thermo- photovoltaic system, the sun heats an absorber. The heated absorber then radiates energy to a solar cell. A filter can be placed between absorber and solar cell that trans- mits only monochromatic radiation and is reflective otherwise. In this way, the solar cell is illuminated monochromatically. With the right band-gap, the solar cell converts the monochromatic radiation very efficiently. The radiation that is reflected by the filter heats the absorber and therefore is not lost. Also the photons emitted from the solar cell are either reflected back to the solar cell, or transmitted by the filter and used by the absorber. Since the photons emitted from the solar cell are not lost, it is not necessary to operate the solar cell at its maximum power point. The solar cell can be operated with a higher voltage close to open circuit conditions [11]. In consequence, the efficiency limit of 85.4% presented in section 3.1.1 can be achieved theoretically.
In practice the achieved efficiencies are very low and no system has been commercialized yet [20]. The reasons for this, among others, are that very high concentration is needed and that very high absorber temperatures are necessary for reasonable efficiencies, posing a serious challenge for material development.
3.2.2 Hot carrier solar cells Another system design that avoids thermalization losses is the hot carrier cell. The idea is to extract the energy of the hot electron and hole ensembles before they cool down by interacting with the lattice [12, 21]. As mentioned before, the time scale in which thermalization usually takes place is 10-12s and is therefore very short. Since the carriers have a finite velocity, they hardly can travel a reasonable distance to the contacts in this time. Therefore, phonon interaction must be slowed down in a hot carrier solar cell. There are possibilities discussed to achieve this by nano-structuring the device such that the phonon spectrum is modified and a phonon bottleneck created [22].
In the metal contact, the charge carriers are thermalized at the lattice temperature. Therefore the charge carriers in the metal must be prevented from interacting with the hot carriers in the solar cell. This could be achieved with energy-selective contacts, through which the hot carriers are extracted [21]. It becomes clear that the hot carrier solar cell is a very demanding system design. Accordingly, no hot carrier solar cells have yet been successfully realized.
17 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts
3.2.3 Tandem solar cells In contrast to the rather theoretical aforementioned concepts, tandem solar cells are an already established concept to reduce the band-gap associated losses. The general idea is to combine solar cells with different band-gaps in one stack, such that each solar cell uses a different part of the solar spectrum efficiently. The solar cell with the highest band-gap must be placed on top of the stack. It absorbs all high-energy photons and transmits the photons with energies below its band-gap. Under the top cell, the solar cell with the second highest band-gap is placed and so on. Theoretically, a stack of an infinite number of solar cells could reach a maximum efficiency of 86.8% for direct sunlight [12].
In practice, three to four different solar cells are stacked on top of each other. With a system of three solar cells, the highest confirmed efficiency of 41.1% for a photovoltaic system was reached under 454 suns concentration [23]. Such tandem cells are usually made by growing several solar cells made from III-V compound semiconductors on top of each other. Therefore the solar cells are forced to be connected in series, with a tunnel diode between each pair of cells. Since in a series connection, the current through all cells must be the same, the cell with the lowest current limits the performance of the stack. Another disadvantage of this concept is that the needed cell structures are very complex and expensive to fabricate. Therefore, tandem solar cells are only used in conjunction with concentrating systems in terrestrial applications.
3.2.4 Intermediate band-gap solar cells In a tandem solar cell, stacking different solar cells on top of each other creates different energy thresholds for the absorption of photons. An alternative approach realizes different energy thresholds within one solar cell by creating an intermediate band [24, 25]. The general idea is that a half-filled band located between valence and conduction bands creates the opportunity for lower energy photons to be absorbed. An electron can reach the conduction band by the absorption of two photons using the intermediate band as stepping-stone. On the other hand, the high-energy photons do not lose most of their energy due to thermalization as they only thermalize to the conduction band edge. A problem is that the intermediate band also creates more opportunities for recombination losses, so in practice no improvement of the solar cell performance has yet been achieved with this concept.
18 3.2 Novel solar cell concepts
3.2.5 Photon management Most of the presented novel concepts require complex new solar cell structures. An alternative approach is photon management. Photon management means splitting or modifying the solar spectrum before the photons are absorbed in the solar cells, such that the energy of the solar spectrum is used more efficiently. The solar cells themselves remain fairly unchanged, and well-established solar cell technologies can be used giving the concepts high realization potential. Because of these advantages, this work will deal with different concepts of photon management.
3.2.5.1 Spectrum splitting The high efficiencies of tandem solar cells show that by utilizing different parts of the solar spectrum with different solar cells high efficiencies can be achieved. In tandem solar cells the transmission of the upper cells determines which spectrum is used by the lower solar cells. Using selective mirrors, filters, diffraction gratings, prism etc. the solar spectrum can be split and the different parts of the spectrum can be directed to different solar cells in a more active way. The advantage is that the stack configuration of tandem solar cells is avoided. This results into a greater freedom in the choice of material from which the solar cells are produced and a greater freedom in the way the solar cells are interconnected, and a series connection is no longer inevitable. However, most of these concepts are very complex and use only direct radiation.
A special way to realize spectrum splitting is the concept of fluorescent concentrators [7], which will be discussed in detail in the following chapter 4. Fluorescent concentrators combine spectrum splitting with concentration and are able to utilize diffuse light as well. However, we will also see in this work that fluorescent concentrators are better suited to reduce cost via concentration and the use of cheap materials than to achieve high efficiencies.
3.2.5.2 Quantum cutting We have seen before that the energy of the incident photons in excess of the conduction band edge is transformed into heat. These losses could be reduced significantly, if more than one free charge carrier was generated by a high-energy photon. The idea of quantum cutting, which is sometimes called down conversion as well, is to transform one high-energy photon into two lower energy photons, which still have sufficient energy to generate free carriers. A system of one single junction solar cell and a quantum cutting material with one intermediate level has a theoretical efficiency limit of 39.6% [26]. The problem of this concept is that some kind of luminescent material that performs the down conversion has to be placed in front of
19 3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts the solar cell. Any parasitic absorption or reflection of this material affects the solar cells performance negatively.
3.2.5.3 Upconversion Upconversion of photons with energies below the band-gap is a promising approach overcoming the losses due to the transmission of these photons. An upconverter generates one high-energy photon out of at least two low-energy photons. For most materials, this involves an intermediate energy level, which is excited by the absorption of the first photon. From this level, a higher excited state can be reached after the absorption of the second photon. If the electron returns directly to the ground state via radiative recombination, one high-energy photon is emitted. Depending on the energy levels involved, this high-energy photon can create a free charge carrier in the solar cell. An additional upconverter pushes the theoretical efficiency limit for a silicon solar cell with an upconverter illuminated by non-concentrated light up to 40.2% [10].
A big advantage of upconversion is that the upconverter can be placed at the back of the solar cell, as the sub-band-gap photons are transmitted through the solar cell. In this configuration, the upconverter does not interfere negatively with the solar cell performance. All improvements are real gain, since they come on top of the original performance of the solar cell. Upconversion can be used in conjunction with classical silicon solar cells. Therefore, upconversion addresses the fundamental problem of transmission losses, while still retaining the advantages of silicon photovoltaic devices. The concept of upconversion will be investigated in detail in chapter 5 of this work.
20 4 Fluorescent Concentrators
This chapter deals with fluorescent concentrators. At the beginning, I will introduce the general working principle of fluorescent concentrators and review the results achieved so far. In the following, I will present the results from optical characterization of fluorescent concentrator materials and a method to characterize the light guiding behavior of fluorescent concentrators that I developed in the context of this work. Based on the optical characterization a Monte-Carlo simulation of the concentrator’s light guiding is developed. Finally, experimental results are presented of a complete system of fluorescent concentrators and solar cells. This includes systems with different collector materials and spectrally matched solar cells, as well as systems with photonic structures that increase light collection efficiency.
4.1 Introduction to fluorescent concentrators
4.1.1 The working principle of fluorescent concentrators Fluorescent concentrators are a special type of light concentrating device. The underlying principle was first used in scintillation counters [27, 28] and then their application to concentrate solar radiation was proposed in the late 1970s [6, 7]. In a fluorescent collector, a luminescent material embedded in a transparent matrix absorbs sunlight and emits radiation with a different wavelength. Total internal reflection traps most of the emitted light and guides it to the edges of the collector (Fig. 4.1). Solar cells optically coupled to the edges convert this light into electricity.
Different configurations are possible as well: The luminescent material can be applied in a film on a transparent slab [29] and solar cells can also be coupled to the bottom of the collector [30]. The fluorescent concentrator has many different names, e.g. luminescent collector or organic solar concentrator. All kinds of luminescent materials can be used in a fluorescent concentrator: fluorescent materials that show a Stokes shift of the emission to longer wavelengths; phosphorescent materials; upconverters that emit one high-energy photon after the absorption of at least two low-energy photons; and quantum-cutting materials that emit two low-energy photons after the absorption of one high-energy photon.
21 4 Fluorescent Concentrators
Fig. 4.1: Principle of a fluorescent concentrator. A luminescent material in a matrix absorbs incoming sunlight (E1) and emits radiation with a different energy (E2). Total internal reflection traps most of the emitted light and guides it to solar cells optically coupled to the edges. Emitted light that impinges on the internal surface with an angle steeper than the critical angle șc is lost due to the escape cone of total internal reflection. A part of the emitted light is also reabsorbed, which can be followed by re-emission.
This work is based on fluorescent materials. Therefore, I will use the term fluorescent concentrator for the overall concept. For clarity, fluorescent collector will identify the collector plate without attached solar cells and fluorescent concentrator system will refer to a system constructed from a collector plate with solar cells attached. In graphs the abbreviation fluko will be used to describe collector or concentrator systems, whereas the meaning will be clear from the context.
Fluorescent concentrators are able to concentrate both direct and diffuse radiation. A geometric concentration is achieved, if the area of the solar cell at the edges is smaller than the illuminated front surface of the collector, i.e. when the area from which light is collected is larger than the solar cell area. If the solar cell is illuminated with a higher intensity than it would be in direct sunlight, a real concentration is achieved. For real concentration, high geometric concentration, as well as high collection efficiency is necessary. The ability to concentrate diffuse radiation presents a great advantage for the application of fluorescent concentrators in temperate climates, such as in middle Europe, or in indoor applications with relatively high fractions of diffuse radiation. Additionally, fluorescent concentrators do not require tracking systems that follow the path of the sun, in contrast to concentrator systems that use lenses or mirrors. This facilitates, for instance, the integration of fluorescent concentrators in buildings.
22 4.1 Introduction to fluorescent concentrators
Fluorescent concentrators were investigated intensively in the early 1980s [8, 9]. Research at that time aimed at cutting costs by using the concentrator to reduce the need for expensive solar cells. After 20 years of progress in the development of solar cells and luminescent materials, and with new concepts, several groups such as those of Refs. [20, 30-46] are currently reinvestigating the potential of fluorescent concentrators.
4.1.2 The factors that determine the efficiency of fluorescent concentrator systems Several factors determine the efficiency of a fluorescent concentrator system. Most of these factors are wavelength dependent. By integrating over the respective relevant spectrum, a description of the overall system efficiency with a set of efficiencies for individual processes is possible [47, 48]. The important parameters are:
Ktrans,front Transmission of the front surface in respect to the solar spectrum
Kabs Absorption efficiency of the luminescent material due to its absorption spectrum with respect to the transmitted solar spectrum
QE Quantum efficiency of the luminescent material
Kstok “Stokes efficiency”; (1-Kstok) is the energy loss due to the Stokes shift
Ktrap Fraction of the emitted light that is trapped by total internal reflection
Kreabs Efficiency of light guiding limited by self-absorption of luminescent
material, (1-Kreabs) is the energy loss due to reabsorption
Kmat “Matrix efficiency”; (1-Kmat) is the loss caused by scattering or absorption in the matrix.
Ktref Efficiency of light guiding by total internal reflection
Kcoup Efficiency of the optical coupling of solar cell and fluorescent collector
Kcell Efficiency of the solar cell under illumination with the edge emission of the fluorescent collector
The overall system efficiency can be calculated from the single parameters via . Ksystem K Kabstrans QEK K K K K K Kcellcouptrefmatreabstrapstok (4.1)
Several aspects are of importance for the different efficiencies:
23 4 Fluorescent Concentrators
The transmission of the front surface is determined by its reflection R(Oinc). This is usually the Fresnel reflection, which is
2 § n Oinc 1· R O ¨ ¸ (4.2) © n Oinc 1¹ for normal incidence and the surface between a medium with refractive index of one and a medium with refractive index n(Oinc). The reflection of typical materials is in the range of 4% for one surface. Special layers or structures applied to the front can reduce or increase reflection. Interestingly, an antireflection coating that reduces the Fresnel reflection does not affect the total internal reflection. This can be understood by considering that total internal reflection is an effect strongly linked to refraction. Total internal reflection occurs when the light from inside the high index material impinges on the surface with an angle sufficiently shallow that the light would be refracted back into the medium again. As the antireflection coating does not change the refraction, total internal reflection is not affected either.
The absorption spectrum Abs(Oinc) determines the absorption efficiency. A large fraction of the solar spectrum is lost, because many luminescent materials only absorb a narrow spectral region. The absorption range of typical fluorescent organic dyes is only about 200 nm in width.
The quantum efficiency QE of the luminescent material is defined as the ratio of emitted photons to the number of the absorbed photons. For organic dyes the fluorescent quantum efficiency can exceed 95%.
The energy of the emitted photons is usually different from the energy of the absorbed photons. For most luminescent materials, a Stokes shift to lower energy occurs. This means that the emitted photons possess less energy than the absorbed ones. Therefore the wavelength of the emitted photons Oemit is different from the wavelength of the incident photons Oinc. As we will see in section 4.2, this Stokes shift is of critical importance to the ability of the fluorescent concentrator to concentrate light.
The luminescent material emits light isotropically in a first approximation. All light that impinges on the internal surface with an angle smaller than the critical angle
Tc(Oemit) leaves the collector and is lost (Fig. 4.1). The critical angle is given by § 1 · ¨ ¸ . c OT arcsin¨ ¸ (4.3) © n Oemit ¹
24 4.1 Introduction to fluorescent concentrators
This effect is also called the escape cone of total internal reflection. The light which impinges with greater angles is totally internally reflected. Integration gives a fraction
2 trap OK 1 n Oemit (4.4) of the emitted photon flux that is trapped in the collector [49]. For PMMA (Polymethylmethacrylate) with n = 1.5, this results in a trapped fraction of around 74%, which means that a fraction of 26% is lost after every emission process. The 26% account for the losses through both surfaces. An attached mirror does not change this number, as with a mirror the light leaves the collector through the front surface after being reflected.
The absorption spectrum and the emission spectrum overlap. For principal reasons, absorption must be possible in the spectral region where emission occurs. Therefore, part of the emitted light is reabsorbed. Again, the energy loss due to a quantum efficiency smaller than one occurs, and again radiation is lost into the escape cone.
Realistic matrix materials are not perfectly transparent. They absorb light and they scatter light so it leaves the collector.
Total internal reflection is a loss-free process. However, the surface of the fluorescent collector is not perfect. Minor roughness at the surface causes light to leave the collector, because locally the light hits the uneven surface with a steep angle. Fingerprints and scratches can seriously harm the efficiency of the light guiding.
The fluorescent collector and the solar cell have to be optically coupled. Otherwise, reflection losses occur at the interface between collector and air and again at the interface air to solar cell. However, the optical coupling can also cause losses: Light can be scattered away from the solar cell or parasitic absorption can occur.
Finally, the solar cell has to convert the radiation it receives from the collector into electricity. Again, a whole set of parameters determine this process, ranging from reflection and transparency losses, to thermalization and electrical losses.
This description is not very relevant for actually calculating the efficiency of fluorescent concentrator systems, because some of the involved efficiencies are neither easy to calculate nor directly accessible by measurement. Nevertheless, this description illustrates very well the effects that affect the efficiency of fluorescent concentrator systems.
25 4 Fluorescent Concentrators
4.1.3 Fluorescent concentrator system design Many system designs have been proposed for efficient and economic fluorescent concentrator systems. Probably the most fundamental one was the concept to stack several collector plates [7]. With different dyes in each plate, different parts of the spectrum can be utilized (see Fig. 4.2). At each fluorescent collector, a solar cell can be attached, which is optimized for the spectrum emitted from the collector. With this spectrum splitting, high efficiencies can be achieved in principle. The stack design with the matched solar cells at the edges provides a high degree of freedom for cell interconnection. Therefore, there is no forced series connection like in tandem cell concepts, which causes current limitation problems. Additionally, no tunnel diodes are necessary.
Fig. 4.2: Concept of stacked fluorescent concentrators, as presented in [7]. (a) The different collectors C1-C3 are connected with different solar cells S1-S3. In each collector, a different dye is incorporated. The absorption and emission (shaded) spectra of the different dyes are shown in (b). With a proper alignment of the absorption and emission properties, the recycling of photons lost from one collector in another collector is possible. It is important that an air gap between the different collectors is maintained so that each spectral range of light is guided in one collector by total internal reflection and does not get lost in adjacent collectors.
The possibilities to realize systems in this configuration were limited during the first research campaign in the 1980s because the range of solar cell materials with different band-gaps was very limited. The situation has improved considerably in the interim, so in Chapter 4.5 a detailed investigation of stack systems with spectrally matched solar cells will be presented.
26 4.1 Introduction to fluorescent concentrators
Fig. 4.2 shows mirrors at some of the edges of the collector plate as well. If some edges are not covered with solar cells, but with reflectors, the geometric concentration is increased. This can be beneficial for the costs of the fluorescent concentrator system, as solar cells are usually the most expensive component of the system. However, the reflection on mirrors is not free of losses. Therefore, it should be kept to a minimum and the emitted light should reach the solar cells with as few reflections on mirrors as possible. For this purpose, an isosceles and rectangular triangular shape of the fluorescent collector is beneficial [7]. With solar cells at the hypotenuse and the two other sides covered with mirrors, only two reflections are necessary at most until the emitted light hits a solar cell.
A reflector underneath the collector increases the collection efficiency as well. It reflects transmitted light back into the collector and creates a second chance for absorption. When a white reflector instead of a mirror is used, light can also be scattered and redirected towards the solar cells. Both for reflectors underneath the collector and for mirrors at the edges, it is beneficial to maintain an air gap between collector and reflector. In this configuration, the reflection of the reflector comes on top of total internal reflection. However, with an air gap the diffuse reflector does not change the direction of light emitted into the escape cone to directions that are subject to total internal reflection. The reason for this is that due to refraction, the light that leaves the collector is already distributed over a complete hemisphere, even before it hits the diffuse reflector. This is not changed by diffuse reflection. So consequently, when the light enters the collector again, it is refracted into exactly the angles of the escape cone.
Another idea to increase the geometric concentration was proposed in [50]. The angular range of the edge emission of the fluorescent concentrator is limited by the critical angle of total internal reflection. Therefore, a further concentration is possible until the divergence reaches the full hemisphere. Compound parabolic concentrators, which are attached to the edges, are one possibility for this purpose.
As mentioned before, no luminescent materials that are active in the infrared and show high quantum efficiency, high stability, and broad absorption have been developed so far. Therefore, a range of designs were proposed to utilize the infrared radiation. The infrared light transmitted through the collector could be used by a thermal collector. It was also suggested to use an upconverter to convert the transmitted radiation into light that could be collected by the fluorescent collector [48]. The transmitted light can also be used to grow plants in a greenhouse [51]. Another option will be investigated in this work: the bottom of the fluorescent collector can be covered with silicon solar cells (or
27 4 Fluorescent Concentrators another low band-gap material), while solar cells made from a high band-gap material are attached to the edges (Section 4.5.3). In this way, spectrum splitting is achieved. High-energy photons are absorbed in the fluorescent collector and a large fraction of their energy is used by the solar cells at the edges. The remaining photons are not lost, but utilized by the silicon solar cells.
Besides the losses due to an incomplete utilization of the full solar spectrum, the escape cone of total internal reflection is the most important loss mechanism. The loss of around 26% does not only occur once, but after every reabsorption and re-emission. However, the Stokes shift between absorption and emission opens the opportunity to reduce these losses significantly: a selective reflector, which transmits all the light in the absorption range of the luminescent material and reflects the emitted light, would trap nearly all the emitted light inside the collector [52]. As we will discuss in section 4.2, it is not possible to trap all the light inside the collector due to fundamental reasons. The concept is illustrated in Fig. 4.3.
Fig. 4.3: A selective reflector, realized as a photonic structure, reduces the escape cone losses. The photonic structure acts as a band stop reflection filter. It allows light in the absorption range of the dyes to enter the collectors, but reflects light in the emission range.
In [34] hot mirrors were proposed to serve as selective reflectors and in [30] photonic structures. In this work, photonic structures and their effect on fluorescent concentrators will be investigated in detail. Sections 4.2 and 4.2.3 document theoretical considerations and in section 4.5.4 experimental results are presented.
28 4.1 Introduction to fluorescent concentrators
An alternative to selective reflectors is to modify the emission characteristic of the dyes in such a way that emission occurs predominantly into favorable directions. This can be achieved with an orientation of dye molecules which show a distinct angular characteristic in their emissions depending on their position. This can be achieved with liquid crystals and an efficiency increase has been reported [38]. However, this approach requires the production of new collector plates and was therefore beyond the scope of this PhD thesis.
The presented ideas can be combined into an advanced concept for a fluorescent concentrator system design. The key features are a stack of different fluorescent concentrators to use the full solar spectrum, spectrally matched solar cells, and photonic structures that increase the fraction of light guided to the edges of the concentrator. To understand and to realize the different components and finally systems with all these features has been the main objective of my work on fluorescent concentrators within the frame of this PhD thesis.
Fig. 4.4: Advanced fluorescent concentrator system design. The full spectrum can be used with a stack of fluorescent collectors with different dyes. The stack configuration allows for ‘‘recycling’’ of emitted photons that are lost in one collector but can be absorbed in another one. The escape cone of total internal reflection is a principal efficiency-limiting problem. A photonic structure helps to minimize these losses. The photonic structure acts as a band-stop reflection filter. It allows light in the absorption range of the dyes to enter the concentrator, but reflects light in the emission range. Therefore a larger amount of light is trapped in the concentrator and guided to the solar cells at the edges.
29 4 Fluorescent Concentrators
4.1.4 Materials for fluorescent collectors Many of the parameters described in the section 4.1.2 are related to the materials used for the fluorescent collector, and especially to the luminescent material. Therefore, a lot of research has been conducted to find materials for efficient fluorescent collectors.
Fig. 4.5: A selection of fluorescent concentrator materials, based on organic dyes that were produced during the first research campaign in the 1980s and that are still among the most efficient fluorescent concentrator materials.
Organic dyes were the dominant luminescent material in the first research campaign in the 1980s [8, 9, 29, 47, 51, 53-56]. They were applied both distributed in a transparent matrix material and as a thin layer on a transparent slab of material. The research of this time resulted in fluorescent dyes with high fluorescent quantum efficiencies above 95% and good stability. Fig. 4.5 shows a photograph of a selection of fluorescent concentrator materials produced during that time. Today, these fluorescent dyes are commercially available and therefore also used in recent works [37, 39, 40, 57, 58]. Until now, the highest reported efficiencies as presented in this work and in [40, 46] were reached with systems based on organic dyes.
However, high quantum efficiency is only achieved in the visible range of the spectrum, while efficiency remains low in the infrared. In [47] it is shown that these low quantum efficiencies have fundamental reasons that are difficult to overcome. Another problem of the organic dyes is the large overlap between absorption and emission spectra. This results in reabsorption and re-emission with the associated losses. Research has therefore been conducted to increase the Stokes shift of the organic dyes. One option is to use energy transfer from one absorbing dye to another emitting dye [59, 60]. Another option is to use phosphorescence instead of
30 4.1 Introduction to fluorescent concentrators fluorescence [60]. Phosphorescence is associated with a larger Stokes shift, but also with lower quantum efficiency (see section 4.1.5). There have also been attempts to increase overall efficiency by bringing metal nanoparticles close to the dyes, in order to increase absorption and luminescence due to plasmonic resonances [61, 62].
Because of the instability of organic materials, especially under ultraviolet radiation, inorganic materials have been investigated as well. Promising inorganic materials are glasses and glass ceramics doped with rare earth ions like ND3+ and Yb3+, or other metal ions like Cr3+ [63-66]. The advantages to these approaches are high stability and a high refraction index of the glasses, which increases the trapped fraction of light. One big disadvantage is the narrow absorption bands of the luminescent materials. Additionally, these material systems turned out to be quite complex and costly to fabricate.
With the development of nanotechnology, luminescent nanocrystalline quantum dots (NQD) have become of interest for luminescent concentrators. The most frequently used materials are CdS, CdSe and ZnS quantum dots [41, 42, 67-69]. One big advantage of the NQD is that absorption and emission properties can be tuned by the size and composition of the nanocrystals. Additionally, the NQD feature a broad absorption range. However, the achieved quantum efficiencies are lower than those of organic dyes, especially if the NQD are incorporated into polymer matrixes.
This work focuses on system designs and not on materials development. Therefore, it was sufficient to use old material produced in the first research campaign in the 1980s at Fraunhofer ISE [8, 47, 51, 53, 55]. The fluorescent collectors consist of PMMA (Polymethylmethacrylate) doped with organic dyes produced from BASF [9]. The used dyes are perylene derivates. The precise chemical structures, however, were not published by BASF. Despite the age of the samples, excellent results could be achieved from this material, as we will see in this work.
4.1.5 Fluorescence This work will be based on fluorescent organic dyes. Therefore, a short introduction into fluorescence will be given in this section, which is based mainly on [70].
The emission of a photon due to the transition of an electronic system from a higher energetic state to a lower energetic state is called luminescence. If the excitation is the result of the absorption of another photon, the luminescence is called photoluminescence. Fluorescence is a special form of photoluminescence. In the case of fluorescence, the photon is emitted directly after absorption and the energy of the emitted photons is lower than the energy of the absorbed photon. The difference
31 4 Fluorescent Concentrators between the energy of absorption and emission is called the Stokes shift. Phosphorescence is a different type of photoluminescence, characterized by a time delay between absorption and emission.
Fig. 4.6: Energy diagram that illustrates the three processes involved in fluorescence: absorption of a photon, vibrational relaxation, and emission of a photon. The excitation usually starts from the electronic ground state (S0) and the lowest vibrational level (v0=0). The absorption of a photon excites the molecule to higher electronic and vibrational levels. Vibrational relaxation to the lowest vibrational level of the excited electronic state occurs before emission of a photon and the return of the molecule to the ground state. The vibronic transitions during absorption and emission happen so fast that the nuclear distances of the atoms in the molecule cannot adjust. That is why the transitions are represented as vertical lines. The probability of a transition is determined by the overlap of the vibrational wave function (Franck-Condon principle).
32 4.1 Introduction to fluorescent concentrators
In organic fluorescent dyes, the fluorescence is caused by the transitions between electronic states of rather complex organic molecules. The energy states of the molecule are determined by its electronic states, the vibrational modes of the molecule, and by its rotational modes. The electronic state determines the distribution of negative charge and the overall molecular geometry. The different electronic states depend on the total electron energy and the symmetry of various electron spin states. Each electronic state is further subdivided into a number of vibrational and rotational energy levels. The difference in energy between two neighboring electronic states usually corresponds to the energy of photons in the ultraviolet and visible spectral range. For comparison, the difference of the vibrational states corresponds to the near-infrared and the difference of the rotational states to the far infrared and the microwave range. In the frame of this work, only the electronic states and the vibrational modes are relevant.
Fluorescence involves three important processes: absorption of a photon, vibrational relaxation, and emission of a photon. They are illustrated in Fig. 4.6.
At room temperature, most molecules are in their ground state (S0) and also at the lowest vibrational level (v0=0). In consequence, most excitation processes originate from this level. The excitation by an incoming photon happens in femtoseconds (10 -15s), which is the time necessary for a photon to travel the distance of a single wavelength. For most organic molecules, the ground state is an electronic singlet state, which means that all electrons are spin-paired (have opposite spins). Normally, the excitation of a molecule takes place without a change in electron spin-pairing, so the excited state is also a singlet (S1).
Light in the visible or ultraviolet range usually excites higher vibrational levels of the excited electron level (v1>0). After the absorption of the photon several processes can occur, but most likely is relaxation to the lowest vibrational energy level of the first excited state (v1=0). This process is called vibrational relaxation. This relaxation takes picoseconds or less. The excess vibrational energy is dissipated as heat. Because of this relaxation, emission spectra are generally independent of the excitation wavelength, which is known as the Kasha rule. However, there are also materials that show exceptions to this rule.
After a relatively long period of nanoseconds, a photon is emitted and the molecule returns to its ground state. As mentioned before, the excitation started from the ground state to higher vibrational levels of the excited electronic state, and then energy was dissipated as heat during relaxation. Finally, during emission of the photon the molecule does not necessarily return directly into the ground state and the lowest
33 4 Fluorescent Concentrators vibrational level. It is likely that directly after the emission the molecule is at a higher vibrational level of the electronic ground state and relaxes subsequently to lower vibrational levels. In consequence, the energy of the emitted photon is lower than that of the absorbed photon, which results in the Stokes shift.
During absorption and emission, the electronic energy and the vibrational energy change simultaneously. Those simultaneous changes are called vibronic transitions. The probability of the vibronic transitions, and therefore the shape of the absorption and the emission spectra, is determined by the overlap of the vibrational wave functions of the states involved in the transition: the larger the overlap, the more likely is the transition (see also Fig. 4.6). This rule is also known as the Franck-Condon principle.
Fig. 4.7: Jablonski Energy Diagram showing the different energy states of a molecule and the possible transitions between them. In addition to Fig. 4.6, internal conversion from higher excited singlet states (S2), intersystem crossing to triplet states (T1), and phosphorescence are depicted as well.
34 4.1 Introduction to fluorescent concentrators
Several other relaxation pathways compete with the fluorescence emission. They are illustrated in Fig. 4.7. One process is that the excited state energy is dissipated non- radiatively as heat. Alternatively, intersystem crossing can occur, which causes phosphorescence. During intersystem crossing the energy is transferred from the electronic singlet state to a triplet state. Because spin conversion is necessary for this transition, it is relatively unlikely. The transition from the excited triplet state to the singlet ground state by emission of a photon is forbidden by spin selection rules. However, due to several effects it becomes possible, but rate constants remain small. In consequence, the excited triplet state can be long-lived and the emission can occur long after the absorption of a photon.
As discussed extensively e.g. in [47], the non-radiative processes become more likely for a small energy difference between ground state and excited state, while the radiative transitions become less frequent. In consequence, the quantum efficiency of dyes emitting at longer wavelengths and especially in the infrared is lower for principal reasons.
4.1.5.1 Angular anisotropy of fluorescence When a fluorescent molecule absorbs an incident photon, the excitation arises from an interaction between the oscillating electric field of the incoming radiation and the transition dipole moment created by the electronic state of the molecular orbitals. The molecules preferentially absorb photons that have an electric field vector aligned parallel to the molecule’s absorption transition dipole moment. The fluorescence emission occurs in a plane that is defined by the direction of the emission transition dipole moment. The directions of the transition dipole moments are determined by the molecular structure. Because of changes in the molecular structure due to the excitation, the directions of absorption and emission can differ. Rotation of the molecule further depolarizes the emission in respect to the excitation vector. The molecule’s size and the rigidity of the molecule’s environment therefore determine how strongly the direction of the emission is coupled to the direction of excitation. In the case of fluorescent concentrators, the light impinges from one direction onto the fluorescent concentrator. Therefore the polarization vectors are aligned in one plane. The matrix material of fluorescent concentrators, in which the molecules are embedded, is a rather rigid polymer. In consequence, an angular anisotropy of the emission remains, which is subsequently reduced by reabsorption.
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4.2 Theoretical description of fluorescent concentrators
4.2.1 Maximum concentration and Stokes shift The ability to as well concentrate diffuse radiation sets the fluorescent concentrator apart from all other types of concentrators. Systems utilizing only geometrical optics cannot concentrate diffuse light. For a discussion of this difference, the concept of étendue and its links with entropy are very helpful. Therefore, I will briefly introduce the concept of étendue at this point.
The étendue dH of a light beam being received from a solid angle d: by an infinitesimal surface element dA can be defined as
H cosT :dAdd , (4.5) with ș being the angle between the surface normal of dA and the incident light. The definition of étendue usually does not consider the refractive index and is therefore, strictly speaking, only useful for systems in vacuum. In media with a refractive index unequal to one, the changes of the solid angle due to refraction have to be considered. To calculate the étendue H from the perspective of an extended receiving system, an integration must be performed over the receiving area Ainc and over the solid angle :inc from which radiation is received: H cosT :dAd . ³ ³ (4.6) Ainc :inc
The étendue can also be calculated from the perspective of an emitting system. In this case, the integration has to be performed over the emitting area Aemit and over the solid angle :emit in which radiation is emitted. For light incident from a cone, with șinc being half of the opening angle, and a flat, not tilted illuminated area Ainc (see Fig. 4.8) the étendue can be calculated to be
2 sin TSH Aincinc . (4.7)
From the definition and this result, the étendue can be understood as a measure of how “spread out” a light beam is in terms of angular divergence and illuminated or emitting area.
36 4.2 Theoretical description of fluorescent concentrators
Fig. 4.8: Illustration of the conservation of étendue. The étendue is a measure of how “spread out” a light beam is in terms of angular divergence and illuminated or emitting area. In a system utilizing only geometrical optics, the étendue cannot be decreased. That is, if the area from which light is emitted Aemit is smaller than the receiving area Ainc, the angular divergence of the emitted light must be larger than the divergence of the incoming light.
The étendue is closely linked to entropy. If an optical system increases the étendue, entropy is generated. Following Markvart in [71], if Hinc is the étendue of the incident beam and Hemit the étendue of the emitted beam, the entropy per photon V that is generated is
H emit V kB ln . (4.8) H inc
A conservative system does not generate entropy, so in a conservative system the étendue is constant. If there are no other sources of entropy, the étendue cannot be reduced, because the entropy cannot decrease. That is, any concentration with geometrical optics that decreases the illuminated area must increase the angular divergence. Because for diffuse radiation angular divergence is already at its maximum, diffuse radiation cannot be concentrated with a system using only geometrical optics.
As a fluorescent concentrator is able to concentrate diffuse radiation, there must be another source of entropy. This source of entropy can be found in the Stokes shift. The dissipation of part of the excitation energy as heat generates entropy and leads to photon emission at longer wavelengths. Therefore, the extent of the Stokes shift determines the maximum concentration that is achievable with a fluorescent concentrator.
37 4 Fluorescent Concentrators
This relationship between Stokes shift and concentration has been theoretically described in [72]. The theoretical model considers two distinct photon fields: one that is incident on the fluorescent collector and one that is emitted from the collector. The entropy change 'V1 associated with the loss of a photon from the incident Bose field is § 8 n QS 22 · 'V k ¨1ln inc ¸ , 1 B ¨ 2 ¸ (4.9) © Fc Q ,, incp ¹ where Fp,Q, inc is the flux of photons (i.e. photons per unit time) per unit area, per unit bandwidth, and per 4S solid angle of the incident field. The other parameters are the frequency of the photon Qinc, the speed of light c, and the refractive index n [72].
The emission of a photon with the frequency Qemit increases the entropy of the emitted field. Additionally, due to the Stokes shift the energy h (Qinc - Qemit) is dissipated as heat at the ambient temperature T. The entropy generated from these two processes is § 8 n 22 · h QQQS 'V k ¨1ln emit ¸ inc emit , 2 B ¨ 2 ¸ (4.10) © Fc Q ,, emitp ¹ T with the parameters defined for the emission corresponding to the parameters of the incident field.
According to the second law of thermodynamics, it must be
V 1 ' 'V 2 t0 . (4.11)
In the argument of the logarithm in (4.9) and (4.10) the 1 can be neglected under illumination with sunlight and for frequencies in the visible spectral range. With this approximation and the equations (4.9)-(4.11), the concentration ratio C can be calculated to be
2 F Q ,, emitp Q § h QQ · C : d emit exp¨ inc emit ¸ . 2 ¨ ¸ (4.12) F Q ,, incp Q inc © B Tk ¹
Fig. 4.9 illustrates these results. The maximum possible concentration has been calculated with equation (4.12) for three different wavelengths of the incident light. It becomes obvious that from an entropic point of view, higher concentrations can be achieved for shorter wavelengths than for longer wavelengths. For short wavelengths, the maximum concentration is very high and constitutes no practical limit. For longer
38 4.2 Theoretical description of fluorescent concentrators wavelengths, however, a sufficiently large Stokes shift is necessary in order to avoid limitations for principal reasons.
The fact that there is a maximum concentration has one more consequence: When the maximum concentration is reached, increasing the collector area will not increase the output at the edges of the concentrator. Already before the maximum concentration is reached, increasing the collector area of a large concentrator will not increase the output in the same way as increasing the area of smaller collector. In consequence, the light collection efficiency of fluorescent collectors decreases with increasing size.
Fig. 4.9: Illustration of the maximum concentration from an entropic point of view. For short wavelengths, very high concentrations are theoretically possible. For longer wavelengths, a large Stokes shift is necessary to avoid limitations.
4.2.2 Thermodynamic model of the fluorescent concentrator The picture of an incident and an emitted light field that was introduced by Yablonovitch in [72] has been subsequently developed into a thermodynamic model of fluorescent concentrators e.g. [41-43, 73, 74]. This model was successfully used to describe fluorescent concentrators based on luminescent quantum dots. To include the more complex spectral characteristics of organic materials, a stack of different materials and features like diffuse reflectors and photonic structures proved to be difficult. Therefore, I will not use this model to actually calculate characteristics of any system presented in this work, but will rely on ray tracing simulations that will be
39 4 Fluorescent Concentrators presented in chapter 4.4. Nevertheless, I will attempt to present a phenomenological thermodynamic model in this section, which brings together the main ideas of different theoretical discussions, that offers valuable insight into the working principles of fluorescent concentrators, and will be helpful later on in this work.
The incident light field with the intensity Binc excites the ensemble of fluorescent molecules in the collector out of equilibrium with the ambient temperature T. Because of the fast thermal equilibration among the vibrational substates of the electronically excited state, the electrons cool down very fast to the ambient temperature. But as the molecule remains nonetheless in an electronically excited state, the electrons have a chemical potential µ > 0, just as in an illuminated semiconductor. The chemical potential is a measure of how many fluorescent molecules are excited. Similar to the discussion in section 3.1, the emission of the ensemble of the fluorescent molecules is described by the generalized Planck’s law. The number of emitted photons per time, per area, per unit solid angle, and per frequency interval is 2 2n2 1 Q emit , B Q ,, emitp emit T,, PQ 2 QD emit c § h emit PQ · (4.13) exp¨ ¸ 1 © BTk ¹ where D Qemit is the absorption coefficient.
Part of the emitted light is lost due to the escape cone of total internal reflection, but most of the light is trapped and guided in the collector to its edges. In consequence, the molecules are illuminated not only by the incident field but also by the emitted and trapped light. The higher the combined intensity Bint is at a point of the collector, the higher is the chemical potential, and in turn also the emission of light. The chemical potential is not constant throughout the collector. For instance, close to the front surface, the chemical potential is higher because the fluorescent molecules are excited from the full incident field. Further away from the surface, part of the incident light has been absorbed and therefore intensity is lower.
40 4.2 Theoretical description of fluorescent concentrators
Fig. 4.10: Illustration of the main ideas of the thermodynamic model. Incident radiation with the intensity Binc excites the ensemble of fluorescent molecules in the fluorescent collector. The fraction of excited molecules is described by the chemical potential µ of the molecule ensemble. The fluorescent molecules emit radiation with the intensity Bemit which depends on the chemical potential. The trapped fraction of the emitted light and the incident light combine to the internal intensity Bint. This internal intensity again determines the chemical potential. As the internal intensity is not constant throughout the collector, the chemical potential varies as well.
This picture can explain why there is a maximum possible concentration. The larger the collector is, the more photons from the incident field are collected. Thus, the intensity of the trapped light field that travels towards the edges also increases. This increases the chemical potential, and consequently, the emission of light as well. The maximum concentration is reached when the chemical potential has become so high that the emitted light lost in the escape cone equals the incident field. The limit obtained from this consideration is stricter than the limit presented in equation (4.12) [72].
The link of the maximum concentration with the Stokes shift and the problematic of reabsorption can be understood considering a simple model system that features an absorption region and an emission region (see Fig. 4.11) [30]. The absorption coefficient Dabs in the absorption region is much higher than in the emission region with an absorption coefficient Demit.
41 4 Fluorescent Concentrators
Fig. 4.11: Idealized model of the absorption and emission characteristics of a fluorescent concentrator [30]. In the absorption region the absorption coefficient Dabs is high, while in the emission region the coefficient Demit is much smaller. Following Kirchoff’s law, the emission coefficient equals the absorption coefficient. Nevertheless, emission in the emission region is much higher, because the generalized Planck’s law favors emissions at lower energies. A bandstop reflection filter that reflects in the emission region can increase efficiency and the maximum possible concentration considerably.
As described by Kirchoff’s law, the absorption and emissions coefficients are equal. In spite of Dabs>Demit, the emission in the emission region is much larger than in the absorption region, because of the energy dependency of the generalized Planck’s law, which states that in this regime the emission at lower energies is considerably more likely than at higher energies. Hence, the larger the Stokes shift, that is the bigger the energy difference E2 - E1, the less frequent is the emission in the absorption range relative to the emission in the emission range. With less light being emitted in the absorption range, reabsorption becomes less likely. Because each reabsorption and re- emission again causes escape cone losses, with less reabsorption the escape cone losses are reduced as well. Less escape cone losses mean that a higher internally guided field and a higher chemical potential is possible until the emitted light lost in the escape cone equals the incident field. In consequence, a higher maximum concentration is possible.
42 4.2 Theoretical description of fluorescent concentrators
Because absorption and emission are linked by Kirchhoff’s law, it is not possible to eliminate reabsorption entirely. Additionally, without reabsorption the excitation of the molecules would be completely independent from the emitted light. This would allow for an infinite concentration, which is a clear contradiction of the second law of thermodynamics.
However, it is possible to reduce the escape cone losses and therefore to increase the maximum possible concentration with the addition of a band stop filter. The band stop filter should reflect in the emission range, but should transmit in the absorption range. The desirable reflection band is sketched in Fig. 4.11. Like this, only the small amount of light emitted in the absorption region can be subjected to escape cone losses. Again, this means that a higher internally guided field and a higher chemical potential is possible until the emitted light lost in the escape cone equals the incident field. In [30] it was shown that the maximum efficiency of a fluorescent concentrator system with such a band stop filter equals the Shockley-Queisser limit of a solar cell with a band- gap similar to that of the cut-off wavelength E2 of the band stop filter.
4.2.3 Photonic structures The term photonic structure describes optical elements that show distinct energy or angular selective characteristics and rely on structures in the order of magnitude of the wavelength of the considered light. As described in the introduction and the previous section, spectrally selectively reflective structures have the potential to increase the efficiency of fluorescent concentrators significantly. Later on in this work, we will also see how such structures can be used for photon management in the context of upconversion. The structures used in this work were obtained from external sources. Nevertheless, I will give a short theoretical introduction of the source of their unique properties, which is mainly based on the work presented in [75].
Photonic crystals are a special type of photonic structure. In a photonic crystal, the refractive index varies periodically. The period length of this variation must be on the order of magnitude of the wavelength of the light that should be affected. The number of directions in which the refractive index is varied determines the periodicity of the photonic crystal (Fig. 4.12). For instance, in a one-dimensional photonic crystal the refractive index varies only in one direction, while it is constant in the other two directions. Such a 1D crystal can be described as planes with different refractive indices stacked upon each other.
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Fig. 4.12: Photonic crystals with different dimensions. In these examples two different refractive indices n1 and n2 are ordered in one to three different directions, resulting in 1D – 3D photonic crystals. For a photonic crystal, the periodic variation of the refractive index is important. They can be formed with more than two different refractive indices as well, and also the function describing the spatial distribution can be varied. The concept underlying this picture was taken from [76].
Photonic crystals show exceptional optical properties, including the spectral and angular selectivity, necessary for the concepts presented in this work. Natural examples of photonic crystals are found in butterfly wings, in the sting of the sea mouse, or in the iridescent play of colors in several gems.
Bykov described photonic crystals in 1972 for the first time [77]. In 1987 Yablonovitch [78] and John [79] independently calculated their optical properties. A summary of the field of photonic crystals can be found in [76]. In a classical crystal, the periodic potential of the crystal ions interacts with the electrons. In a photonic crystal, it is the refractive index, and consequently the dielectric function, that varies periodically. The periodic variation of the dielectric function affects the propagation of electromagnetic waves in a similar way, as the periodic potential in a crystal lattice affects the electron motion. Consequently, in analogy to the electronic band structure, a band structure for the photons in a photonic crystal can be calculated. The band structure is obtained from the dispersion relation of the photons under the influence of diffraction in the photonic crystal with a periodic dielectric function. The band structure describes the allowed and forbidden energy states of the photons. Like in a semiconductor with an electronic band-gap, bands of forbidden energy states that form a photonic band-gap can occur in a photonic crystal.
In the energy range of the photonic band-gap, no propagation of light within the photonic crystal is possible. Therefore, a photonic crystal with a photonic band-gap is completely reflective for light in the respective energy range. One can distinguish between a complete band-gap and a pseudogap. In a complete band-gap the
44 4.2 Theoretical description of fluorescent concentrators propagation of light is forbidden in all crystallographic directions, whereas in a pseudogap the propagation of light is only forbidden in certain crystallographic directions. A common representation of the band structure shows the allowed energy regions in the momentum-space reduced to the first Brillouin zone. An example for a photonic band structure is given in Fig. 4.13. The band structure diagram shows a closed path in the Brillouin zone that includes all points of high symmetry.
Fig. 4.13: Band structure (left) and first Brillouin zone (right) of a face centered cubic (fcc) photonic crystal (opal) with a lattice constant a [80]. The band structure is plotted against the normalized frequency a/O The band structure is scalable with the frequency. A photonic crystal with twice the lattice constant will show the same characteristic for half the frequency of the light. In the band structure a complete band (red) and one exemplary pseudogap in *–L direction (blue) are shown. The band structure was calculated using the MIT photonic bands program [81] for an inverted opal with the refractive index contrast 3.5:1.
4.2.3.1 One-dimensional photonic crystals In this work, mainly one-dimensional photonic crystals were used. A structure that can be classified as a 1D photonic crystal, but that has been known considerably longer than the idea of photonic crystals, is the distributed Bragg reflector (DBR). A DBR consists of two layers, A and B, with the refractive index nA and nB that are ordered periodically in the scheme ABAB… This structure shows a high reflectance for normal incidence at the wavelength O0, if the thicknesses of the layers dA and dB fulfill the condition that O 0 , i=A,B. di (4.14) 4 ni
45 4 Fluorescent Concentrators
Every surface in this structure reflects light. Because of the special thickness of each layer, the reflected light interferes constructively for light with the wavelength O0. The result is high reflectance for this special wavelength. More layers increase the reflectance. The structure of the DBR and its reflection characteristic are visualized in Fig. 4.14.
Not only light with the design frequency Q0 = c/O0 experiences constructive interference and therefore high reflection, but also all odd multiples of this frequency 3Q0 , 5Q0 , 7Q0 and so on. They are called the harmonic reflection peaks. The applications in this work require high reflection in a single spectral region and high transmission otherwise. Therefore the harmonic reflections are detrimental.
Fig. 4.14: Refractive index profile (left) and reflection spectrum (right) of a distributed Bragg mirror. The presented profile is designed for high reflection at O0 = 1000nm [75]. Reflection peaks occur for the design frequency Q0 and the odd multiples of this frequency 3Q0 , 5Q0 , 7Q0 and so on.
The problem of the harmonics can be overcome by non-binary refractive index profiles. A sinusoidal refractive index profile shows no harmonics. Only a single reflection peak remains, but this peak usually features some side lobes. Such structures are called Rugate filters. Optimized Rugate filters [82] show only one single reflection peak for a certain wavelength and almost no other reflections. The characteristics of an optimized Rugate filter are shown in Fig. 4.15. Such optimized Rugate filters that were produced at the company mso-jena [83] were used throughout this work as photonic structures.
46 4.2 Theoretical description of fluorescent concentrators
Fig. 4.15: Refractive index profile (left) and calculated reflection spectrum (right) of an optimized Rugate filter [75]. This filter shows only a single reflectance peak and very low reflection otherwise.
4.2.3.2 Two- and three-dimensional photonic structures No two-dimensional photonic crystals were used in this work, but a special type of 3D photonic crystal was tested as a band reflection filter on a fluorescent concentrator system. The investigated 3D photonic crystal was an opal. The opal consists of spheres ordered in a closest package. Opals can be produced by a self-organizing process [84]. First, monodisperse spheres are produced with colloidal chemistry. Common sphere materials are PMMA or SiO2. Subsequently, the dispersed colloids can be assembled into ordered structures by different techniques, including vertical deposition by lifting the substrate out of suspension of dispersed colloids, or the slow drying of a colloidal dispersion on a flat substrate. The advantage of the opal structure is that it has the potential to be easy to produce on a large scale. On the other hand, the ordering in these colloidal crystals critically determines their properties. The higher the ordering, the more distinct is the Bragg reflectance and the lower is the rate of diffuse scattering.
47 4 Fluorescent Concentrators
4.3 Optical characterization of fluorescent concentrator materials
In this chapter, I will discuss different optical methods for characterizing fluorescent concentrator materials and the results obtained. I will start with photoluminescence measurements. The fluorescence of the dyes is the fundamental property that enables the construction of fluorescent concentrators. Additionally, the photoluminescence spectrum will be important for a correct interpretation of the following measurements, the simulation of fluorescent collector and complete systems, and for the design of fluorescent concentrator systems.
Secondly, I will present measurements performed with spectrophotometers. This includes classical reflection and transmission measurements. However, the interpretation of the results is not trivial for samples that show fluorescence and have light guiding properties. Additionally, the most interesting characteristic to be tested is the ability of the collectors to guide light to their edges, where the solar cells are mounted. This ability depends on a large set of parameters, such as the absorption and the quantum efficiency of the dyes, the optical properties of the matrix material, the surface quality, and geometric dimensions of the collector plate. Hence, measurements of absorption spectra and the photoluminescence alone are not sufficient to assess the spectral collection efficiency. Therefore, I will present a novel method to determine this ability spectrally resolved with transmission, reflection measurements using a spectrophotometer and an integrating sphere, and with one measurement where the sample is mounted in the center of the integrating sphere.
Finally, I will present a method for measuring the angular distribution of the light guided in the fluorescent collector.
4.3.1 Photoluminescence measurements The photoluminescence (PL) spectrum is a very fundamental property of the fluorescent material. In this work, I measured the photoluminescence directly on samples of the materials from which the fluorescent collectors were realized. That is, I investigated PMMA samples that were doped with different organic dyes. As mentioned before, these materials were produced during the first research campaign in the 1980s at our institute and were stored in the dark since. The investigated samples were 2 cm x 2 cm in size. Measuring the fluorescence directly on the later collector material has the advantage that the PL spectrum is determined under realistic conditions. The energy states, and therefore the PL spectrum depend e.g. on the
48 4.3 Optical characterization of fluorescent concentrator materials chemical surroundings of the dyes. Additionally, a rigid environment affects the vibrational levels differently than a liquid solvent. Therefore, only measurements on the used material system yield data that are actually relevant for the fluorescence concentrator systems, be they for simulation purposes or for system design (e.g. the question which solar cell should be attached to the edges).
When measuring the PL on the collector material, several issues have to be taken into account. Because the collector should preferably absorb the incoming light completely, the dye concentration is relatively high. Hence, reabsorption will occur and alter the shape of the PL spectrum. Therefore, to investigate the effect of reabsorption was one objective of the PL measurements. Related to the question of reabsorption is the difference between the spectrum that could be measured at the edges of the fluorescent collector and at its front or back surface. The spectrum at the edges will illuminate the solar cells and is therefore relevant for the system design. The spectrum emitted at the back or the front has experienced less reabsorption, because the path length through the collector is considerably shorter. In consequence, it is more similar to the spectrum actually emitted from the dye and thus important e.g. for determining the input data for the collector simulation. In conclusion, the PL spectrum was measured both at the edges and at the back of the collector (see Fig. 4.16).
Another important question was whether the PL spectrum is really independent from the excitation wavelength. In following measurements of the collection efficiency (section 4.3.2), and also on fluorescent concentrator systems (section 4.5), a wavelength dependency occurred, and the question arose whether this could be linked to a wavelength dependency of the PL spectrum. Therefore PL spectra were measured with two different excitation wavelengths.
4.3.1.1 Setup for photoluminescence measurements The samples were illuminated with monochromatic light. For this purpose, a manually operated monochromator with a single grating was used to select single wavelengths from the light of a Xenon lamp. Because the monochromator was originally designed for the NIR, the second order peak was used for the illumination of the samples. Peaks of higher order were blocked with a Schott WG360 filter. The excitation peak was around 10 nm wide (FWHM). The emitted light was collected with a collimator and guided to spectrometer with an optical fiber. The collimator was placed either at one edge of the sample (position 1) or at the back (position 2), see also Fig. 4.16. The PL spectra were measured with a MCDP 1000 diode array spectrometer from Otsuka.
49 4 Fluorescent Concentrators
Fig. 4.16: Setup for the photoluminescence measurements. The samples were illuminated with monochromatic light. The emitted light was collected with a collimator and guided to a spectrometer with an optical fiber. The collimator was placed either at one edge of the sample (position 1) or at the back (position 2.) The PL spectra were measured with a MCDP 1000 diode array spectrometer from Otsuka.
4.3.1.2 Results of photoluminescence measurements Fig. 4.17 shows a comparison between the normalized PL spectra measured at the edge (position 1) and at the back (position 2) of a collector made from the material BA241. Furthermore, also the absorption spectrum is shown, which will be discussed in the following section. The sample was 2 cm x 2 cm in size and 3.2 mm thick. The excitation was at Oinc= 490 nm. During the measurement at the back, a Schott OG 530 filter was placed between sample and collimator to block the excitation peak. The transmission of the filter was taken into account in the data analysis.
The spectrum measured at the back is somewhat similar to a mirrored spectrum of the absorption. This is expected from theory. Usually the vibrational levels in the electronically excited state are quite similar to the vibrational level of the ground state, both in the energy spacing and in the shape of the wave functions. Therefore, the overlap between the lowest vibrational level (v0=0) in the electronic ground state (S0), from which the excitation starts, and the higher vibrational levels (v1>0) of the electronically excited state (S1) is quite similar to the overlap of the lowest vibrational level (v1=0) of the electronically excited state (S1) and the higher vibrational levels
(v0>0) of the electronic ground state (S0) (see also Fig. 4.6). Therefore, the PL spectrum should have the mirrored shape of the absorption spectrum. This is also known as the mirror rule [70].
50 4.3 Optical characterization of fluorescent concentrator materials
In the spectrum measured at the edge, the peak that is visible in the back measurement at Oemit= 546 nm appears only as a little kink in the falling edge of the peak at
Oemit= 575 nm. This is the effect of reabsorption. The dye shows significant absorption at 546 nm already. As the light has to travel some distance from the excitation in the middle of the sample to the edge, most of the light emitted at this wavelength is absorbed and emitted at different wavelengths. The differences at higher wavelengths are considered to be measurement artifacts. The background noise level was considerably higher relative to the PL spectrum in the measurements at the back and occurred to be increasing at longer wavelengths. Because of the normalization, this background appears amplified.
Fig. 4.17: Comparison between the normalized PL spectra measured at the edge (position 1) and at the back (position 2) of a collector made from the material BA241. Also the absorption spectrum is shown. The spectrum measured at the back is reasonably similar to a mirrored spectrum of the absorption. The reason behind this is the similarity between the vibrational levels in the electronically excited state to the vibrational level of the electronic ground state. The spectrum measured at the edge shows the effect of re-absorption: the peak that is visible in the back measurement at 546 nm appears only as a little kink in the falling edge of the peak at 575 nm, because the dye already shows significant absorption at 546 nm.
Fig. 4.18 shows a comparison of the normalized PL spectra measured at the edge for two different excitation wavelengths for three different materials. The samples were excited at Oinc= 490 nm and at Oinc= 440 nm. No significant differences are visible for the different excitation wavelengths.
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Fig. 4.18: Comparison of the normalized PL spectra measured at the edge for two different excitation wavelengths for three different materials. No significant differences are visible for the different excitation wavelengths.
In Fig. 4.19, the normalized PL spectra measured at the back of three samples made from the material BA241 are presented. The samples are made from the exact same material, but two samples were thinned to a thickness of 2 mm and 1 mm, respectively.
The excitation was at Oinc= 490 nm. Again, the excitation peak was blocked with a Schott OG530 filter between sample and collimator. The relative height of the peaks at
Oemit= 546 nm and Oemit= 575 nm changes considerably with the thickness. For the thickest sample, both peaks have nearly the same height, but the peak at Oemit= 575 nm is still a little bit higher. With decreasing thickness, the Oemit= 546 nm peak rises and is clearly the highest peak at 1 mm thickness. Again, this is a clear sign of the re- absorption. From the measurements we can conclude two things: first, in the spectrum emitted from the dye, the peak at Oemit= 546 nm peak is much more pronounced than the Oemit= 575 nm. Second, the distance, in which nearly all the light emitted at the shorter wavelengths is reabsorbed, is only a few millimeters.
52 4.3 Optical characterization of fluorescent concentrator materials
Fig. 4.19: PL spectra measured at the back of three samples made from the same material BA241, but with three different thicknesses. The excitation was at Oinc= 490 nm. The spectra were normalized such that the peaks at Oemit= 546 nm have the same heights. The relative height of the peaks at Oemit= 546 nm and Oemit= 575 nm changes considerably with the thickness. For the thickest sample, both peaks have nearly the same height. With decreasing thickness, the Oemit= 546 nm peak becomes relatively higher and is clearly the highest peak at 1 mm thickness. This is a clear hint that re-absorption changes the shape of the spectrum within a few millimeters.
The dependence of the excitation wavelength on the PL spectrum was measured as well at the back. Fig. 4.20 shows the results for the 3.2 mm thick sample made from
BA241. The samples were excited at Oinc= 490 nm and at Oinc= 440 nm. Again, the excitation peak was blocked with a filter between the sample and the collimator. A
Schott OG530 filter was used during excitation with Oinc= 490 nm and a GG455 filter for the Oinc= 440 nm measurement. The transmission spectra of the filters were considered in the evaluation of the data.
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Fig. 4.20: Comparison of the normalized PL spectra measured at the back for two different excitation wavelengths, at Oinc= 490 nm and Oinc= 440 nm. The measured sample was made from BA241 and 3.2 mm thick. The relative height of the peaks at Oemit= 546 nm and Oemit= 575 nm changes considerably with the excitation.
Clear differences between the two measurements are visible. Part of these differences can be attributed to the fact that the total height of the signal was considerably lower during excitation with Oinc= 440 nm, for the absorption at Oinc= 440 nm is lower than at
Oinc= 490 nm. In consequence, after normalization of the spectra, the Oinc= 440 nm spectrum shows a higher background that again increases to longer wavelengths. Independent from the background, the relative peak heights change significantly with the excitation wavelength. The nearly similar heights of the peaks at Oemit= 546 nm and
Oemit=575 nm change to a clear domination of the Oemit=546 nm peak under excitation with Oinc= 440 nm. Several effects could explain this correlation between shorter wavelength excitation and shorter wavelength emission. One factor could be the lower absorption for the Oinc= 440 nm excitation. With strong absorption, most of the light is absorbed and therefore emitted close to the front. With less absorption, the absorption and consequently the emission profile is more evenly distributed over the depths of the collector. Hence, on average the emitted light has to travel only a shorter distance to the back and the detector. This would result in lower re-absorption and therefore a relatively higher peak at Oemit=546 nm, because this peak is strongly influenced by re- absorption. If this effect was dominant, the differences between the two excitations
54 4.3 Optical characterization of fluorescent concentrator materials should be less pronounced for the thinner samples. Fig. 4.21 shows the results of the same measurement for the 1 mm thick BA241 sample. Although the effects of the background are even stronger, it is still visible that the relative peak heights change considerably. Under excitation with Oinc= 440 nm, the peak at Oemit=570 nm is hardly visible. Therefore, the different absorption cannot be the only factor. Another explanation could be that the excitation at Oinc= 440 nm excites higher energy levels, from which direct transitions to the ground state are also possible. These higher energy levels could be either higher vibrational states of the first electronically excited level that show a large overlap with states of the electronic ground state, or higher electronically excited levels (S2). From Fig. 4.21 it appears reasonable that most of the first emission actually involves these higher energy states, and that the peak at
Oemit=570 nm is only the result of re-absorption and subsequent emission, at least for excitation at Oinc= 440 nm. The different possibilities will be discussed again in detail in the simulation chapter (4.4), where the different assumptions will be tested in a Monte-Carlo model.
Fig. 4.21: Comparison of the normalized PL spectra measured at the back for two different excitation wavelengths, at Oinc= 490 nm and Oinc= 440 nm. The measured sample was made from BA241 and 1 mm thick. Also for this thickness, the relative height of the peaks at Oemit=546 nm and Oemit=575 nm changes considerably with the excitation.
55 4 Fluorescent Concentrators
4.3.2 Characterizing the light guiding of fluorescent concentrators The development of new material systems for fluorescent concentrators requires the testing of a wide range of materials with a fast method. The most important characteristic to be tested is the ability of the collectors to guide light to their edges, where the solar cells are mounted. For the construction of advanced systems with several collectors in one stack, such as in [40, 46, 85], this information is required with spectral resolution. In this work, the spectrally resolved information about the ability of the fluorescent collector to guide light to the edges will be designated “spectral collection efficiency” KS(Oinc). It is defined as the ratio of the number of photons that leave the collector through the edges Nedge(Oinc) under monochromatic excitation with
Oinc, to the number of photons incident Ninc(Oinc): N O incedge OK incS : (4.15) N Oincinc
Several parameters determine this spectral collection efficiency, such as the absorption and the quantum efficiency of the dyes, the optical properties of the matrix material, the surface quality, and the geometric dimensions of the collector plate. Hence, measurements of the absorption spectra and the photoluminescence alone are not sufficient to assess the spectral collection efficiency.
In this section, I present a method to determine the spectral collection efficiency with transmission, reflection and centermount measurements using a spectrophotometer and an integrating sphere. The method was developed during the work for this PhD-thesis and represents considerable progress to existing methods. Moreover, additional information such as the escape cone losses can be obtained from the measurements.
First, I will briefly discuss alternative methods. Then I will discuss the important features of the used spectrophotometer. Subsequently, I will introduce the concept of the method and show qualitative results. Reasonably similar samples can be compared without requiring any corrections. For fully quantitative results on an absolute scale, for samples with large Stokes shifts and/or very different properties, additional corrections must be applied. Therefore, I will discuss the necessary corrections and compare the results with EQE measurements. In the last part, I will present which information in addition to the spectral collection efficiency can be obtained with the method.
56 4.3 Optical characterization of fluorescent concentrator materials
4.3.2.1 Common methods to determine the spectral collection efficiency In the past, measurements on systems consisting of a fluorescent collector with a solar cell attached to its edges were used to determine the collection efficiency of fluorescent concentrators, e.g. [41]. From external quantum efficiency (EQE) measurements, the spectral collection efficiency KS(Oinc) can be determined, if the EQE of the solar cell in use is known. However, the results are sensitive to the optical coupling of solar cell and fluorescent concentrator. For the comparison of different samples, the varying properties of the solar cells add uncertainty. Moreover, this method is quite laborious and therefore not very well suited to test a wide range of material. Usually, the excitation during the EQE measurements is point like. This is a problem, because the collection efficiency is strongly dependent on the position, as I will show in chapter 4.5. So also the relevance of the EQE based method is limited.
I first presented my method in [32]. In the meantime Currie et al. presented a method that used an integrating sphere as well [60]. In their method, the samples are placed inside an integrating sphere and two measurements are performed. In the second measurement, the emission from the edges is blocked with ink or tape. However, in that case obtaining the information necessary for the corrections is not possible. Additionally, with black edges, no further use of the samples is possible and therefore also no direct comparison with system measurements can be performed.
4.3.2.2 Working principle of a spectrophotometer In this work, the spectral collection efficiency is determined with three measurements with an integrating sphere and a spectrophotometer. A Cary500i UV-Vis-NIR Spectrophotometer from Varian Inc. was used for the reflection and transmission measurements. For the centermount measurements, the samples were placed inside the integrating sphere. Therefore, a larger Cary5000i UV-Vis-NIR Spectrophotometer from the same company was used.
Fig. 4.22 shows the schematic setup of the spectrophotometers. The spectrophotometers contain several different light sources, in order to cover a wide spectral range. A double-monochromator selects a specific excitation wavelength Oinc. The monochromatic beam is split by a reflecting chopper into a sample beam and a reference beam.
The sample beam interacts with the sample, and depending on the measurement, different fractions of light reflected, transmitted or absorbed and re-emitted from the sample are collected from the integrating sphere and detected.
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Fig. 4.22: Setup of a spectrophotometer. A double-monochromator selects a specific excitation wavelength. The monochromatic beam is split by a reflecting chopper into a sample beam and a reference beam. The sample beam interacts with the sample, and depending on the measurement, different fractions of light reflected, transmitted or absorbed and re-emitted are collected from the integrating sphere and detected. For reflection measurements, the sample is mounted tilted by an angle D=4° so that the direct reflection does not leave the sphere, but is also detected. The detection does not discriminate different wavelengths. That is, photons with all wavelengths are detected. In consequence, all data is given as a ratio of the number of photons (regardless of which wavelength) detected under the monochromatic excitation with Oinc to the number of photons incident at the wavelength Oinc. The reference beam enters the integrating sphere without interacting with the sample. The signal recorded during the measurement is the ratio of the signal from the sample beam and the signal from the reference beam. In this way, fluctuations of the excitation intensity are compensated. Additionally, a baseline correction was performed for all measurements.
The reference beam enters the integrating sphere without interacting with the sample. The signal recorded during the measurement is the ratio of the signal from the sample beam and the signal from the reference beam. This compensates for fluctuations in the excitation intensity. Additionally, a baseline correction was performed for all measurements. These baseline corrections take into account the varying sensitivity of the setup for different wavelengths. The baseline corrections will be discussed in more detail in section 4.3.2.4. Because of the fluorescence and the Stokes shift, the case is a little bit more complex than for standard measurements.
58 4.3 Optical characterization of fluorescent concentrator materials
The detection does not discriminate between different wavelengths. This means that photons with all wavelengths are detected. In consequence, all data is given as a ratio of the number of photons detected, regardless of their wavelength Nmes(Oinc) under excitation with Oinc, to the number of photons incident Ninc(Oinc). The number of photons detected Nmes(Oinc) can be described as
N O N , dOOO incmes ³ mes inc (4.16) all swavelength with Nmes(OOinc) being the number of photons that have a wavelength Othat are detected under excitation with Oinc. So finally, the recorded data can be expressed as
N , dOOO ³ mes inc all swavelength (4.17) Data Oincmes N Oincinc
4.3.2.3 The general concept of measuring the light guiding For the first measurement, the sample is located at the transmission sample port of the integrating sphere of the spectrophotometer (Fig. 4.23a). I will designate the result of this measurement Tmes(Oinc). The second measurement is performed with the sample at the reflection port (Fig. 4.23b), giving Rmes(Oinc). For the third measurement, the sample is placed inside the integrating sphere with a centermount (Fig. 4.23c), from which one obtains Cmes(Oinc).
Fig. 4.24 shows the data from all three measurements for one sample. The sample was made from the already introduced material BA241, 3.2 mm thick and 2 cm x 2 cm in size. In figure Fig. 4.24, the transmission drops in the absorption range of the dye at around 500 nm. The reflection is roughly 8% over a broad spectral region, which corresponds to the Fresnel reflection at the front and back surface. The reflection appears to be higher in the absorption region of the dye. This is because the reflection measurement also detects light that is emitted into the escape cone of total internal reflection and leaves the sample at its front surface. The centermount measurement shows that parasitic absorption in the matrix material is low, but that losses occur in the absorption region of the dye.
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Fig. 4.23: Three measurements are performed with an integrating sphere setup to determine the spectral collection efficiency KS(Oinc) of the fluorescent concentrator. At first, standard transmission Tmes(Oinc) (a) and reflection Rmes(Oinc) measurements (b) are performed. The light that is detected is shown as bold arrows, the light not detected as thinner arrows. As the sample is outside the integrating sphere during the first two measurements, especially light that leaves the fluorescent concentrator at the edges is not detected. The third measurement is performed with the sample mounted in the center of the integrating sphere (c). This measurement yields Cmes Oinc), which is one minus the total absorption Absmes(Oinc).
Fig. 4.24: The data collected with the transmission, reflection and centermount measurements of a sample from the material BA241. From this data, the spectral collection efficiency is calculated. The effect of the dye’s absorption is clearly visible in the transmission and centermount measurements. The increased reflection is a result of the dye’s emission into the escape cone of total internal reflection.
60 4.3 Optical characterization of fluorescent concentrator materials
From this data, one can determine the spectral collection efficiency KS(Oinc), which is the fraction of photons that leaves the collector at the edges in respect to the number of photons incident. With the sample inside the integrating sphere during the third measurement, all photons are detected that are not absorbed and their energy transformed into heat. This measurement therefore yields
Cmes(Oinc)= 1 - Absmes(Oinc). (4.18)
Of particular interest is the fact that the light leaving the edges is also detected.
In contrast, during the first two measurements, the sample is outside the integrating sphere. Hence, light that leaves the collector sample at its edges is not detected. For standard transmission T and reflection R measurements, 1 – T - R yields the absorption Abs of the sample. However, this is not true in our case, because the light that leaves the collector at the edges KS(Oinc) is neither absorbed nor detected in Tmes(Oinc) or
Rmes(Oinc). It has to be considered additionally. Therefore, it is
1 - Tmes(Oinc) - Rmes(Oinc) - KS(Oinc) = Absmes(Oinc). (4.19)
Combining equation (4.18) and (4.19) the spectral collection efficiency can be calculated with
KS(Oinc) = Cmes(Oinc) - Tmes(Oinc) - Rmes(Oinc) . (4.20)
I performed these measurements on samples from more than 20 different materials, a task that would have meant tremendous effort with other methods. All samples were 2 cm x 2 cm in size. Fig. 4.25 shows the spectral collection efficiency for a representative set of samples with relatively high efficiencies. The figure shows the efficiency of two samples with the same dye but different thickness (BA241 3.2mm and 8.3mm). With increasing thickness, Ks(Oinc) increases up to a maximum spectral collection efficiency of 60% for specific wavelengths. In a thicker sample, more light is absorbed. Another effect that might contribute to the increase in efficiency is that fewer reflection events at the surfaces are needed in a thicker sample before the light reaches the edges. Fig. 4.25 also shows the results for samples with different dyes. In order to compare different materials, the geometric dimensions of the samples must be the same, as KS(Oinc) is dependent upon size and the ratio between length and thickness. As mentioned before, all samples were 2 cm x 2 cm in size and these samples were all 3.1 mm thick. A trend becomes obvious that collection efficiency decreases for materials that are active at longer wavelengths.
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Fig. 4.25: The spectral collection efficiency Ks(Oinc) of a representative set of different materials. All samples were 2 cm x 2 cm. The figure shows the efficiency of two samples with the same dye but different thickness (BA241 3.2mm and 8.3mm). With increasing thickness, Ks(Oinc) increases as well. The spectral collection efficiency reaches up to 60%. The graph also shows the results for samples with different dyes. These samples were all 3.1 mm thick. Collection efficiency tends to decrease for materials that are active at longer wavelengths.
Fig. 4.25 shows a spectral collection efficiency of 1-2% in the spectral region above 600 nm for the thinner BA241 sample. This can be considered an artifact from the uncertainties of the measurement in combination with the performed calculations. To obtain the data, several sets of spectral data have to be added or subtracted from each other. A small relative error in the transmission or centermount measurements that show high signals in this region could lead to that 1% absolute error. Nevertheless, the collection efficiency in the absorption region of the dye is of primary interest. In that region, relative errors remain small.
In the presented way, the method is already a fast and easy way to assess and compare the ability of concentrators made from different materials. As we will see later on in this work (chapter 4.5), I also fabricated complete fluorescent concentrator systems with attached solar cells from materials tested with this method [46]. Indeed, the samples that had been the most promising ones based on the results of the new method also achieved the highest system efficiencies. The spectral information obtained
62 4.3 Optical characterization of fluorescent concentrator materials proved to be very helpful for the decision regarding which materials should be combined in one stack.
However, the results are not yet fully quantitative, and care must be taken when comparing samples with significantly differing properties. This is especially true when the materials are active in very different regions of the spectrum and for large Stokes shifts, as I will show in the next section.
4.3.2.4 Correcting for Stokes shift effects The spectral data presented in the previous section was obtained from measurements with a spectrophotometer and an integrating sphere. While obtaining these measurements, a standard baseline correction is performed. For the transmission measurement, the signal with no sample is recorded as 100% baseline. The signal during each measurement of a sample is then compared to the baseline signal to obtain the transmission data. For the baseline of the reflection measurements, the signal with a standard reference is recorded. The reflection of this standard reference is known, so by comparing the signal with the sample to the baseline and taking into account the reference’s reflection, the reflection data of the sample can be obtained. The reflection of the fluorescent concentrator has both specular and diffuse parts. I chose a diffuse standard reference made from Polytetrafluoroethylene (PTFE).
The standard baseline corrections are usually completely sufficient. However, a problem occurs when investigating fluorescent concentrators. Because of the Stokes shift, the emitted light has a different wavelength Oemit than the light impinging on the sample with a wavelength Oinc. On the other hand, the baseline value used for the calculation of the result is, by default, the value for the wavelength of the incident light. Under standard conditions, the resulting data is calculated via
Data(Oinc)=Signal(Oinc)/Baseline(Oinc). (4.21)
With this standard procedure, the signal from the emitted light with Oemit would be divided by a baseline value for a different wavelength Oinc:
Data’(Oinc)=Signal(Oemit)/Baseline(Oinc). (4.22)
Therefore, we must correct the outcome of the standard procedure via Baseline O Signal O Baseline O Signal O Data O Data' O inc emit inc emit corr inc (4.23) Baseline Oemit Baseline Oinc Baseline Oemit Baseline Oemit to obtain the correct data.
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Fig. 4.26: This graph highlights the problems associated with the Stokes-shift and the baseline correction. It shows 1 - Tmes(Oinc) - Rmes(Oinc) of the sample BA241 3.2mm, which one could call “apparent absorption”. This data indicates very well in which spectral region the dye absorbs. The graph also presents the photoluminescence spectrum recorded at the edges of the fluorescent concentrator. The excitation was at 497 nm. Additionally, the baseline scans for transmission and centermount measurements and the baseline scan for the reflection measurement divided by the reflection of the standard reference are shown. It becomes obvious that calculating the data with the baseline value for the wavelength of the absorbed light leads to mistakes, as the baseline is different in the absorption and emission regions.
As we can see from Fig. 4.26, light is not emitted at a single wavelength Oemit, but over a whole wavelength range. Consequently, we need the weighted average value for the baseline in the emission range of the dye. This can be calculated by
³ PL O Baseline dOO Emission Range Baselineav (4.24) ³ dPL OO Emission Range , and finally the correction is
64 4.3 Optical characterization of fluorescent concentrator materials
Baseline Oinc . Data Oinccorr Data' Oinc (4.25) Baselineav
In the case of the reflection measurements, the measured baseline divided by the reflection of the standard reference must be used instead of only the baseline in this correction.
4.3.2.5 Calculating the emitted fraction The correction of the data need only be applied to the part of the light that has been emitted by the dye, as this is the only part for which a Stokes shift occurs. Consequently, it is necessary to separate in the measurement data the fraction that is transmitted or reflected without interaction with the dye from the fraction which has interacted with the dye and stems from an emission process.
For the reflection measurement, a good assumption is that the diffuse fraction results primarily out of the approximately isotropic emission process. Therefore, we should be able to calculate the fraction of emitted light detected during the reflection measurement Remit(Oinc) from measurements of the diffuse reflection Rdiffuse(Oinc). I checked this hypothesis by measuring the diffuse reflection from a reference sample without a dye Rdiffuse,ref(Oinc). Indeed, the diffuse reflection independent of the dye was very small. So Remit (Oinc) determined via
Remit(Oinc) = Rdiffuse(Oinc) - Rdiffuse, ref(Oinc) (4.26) is very close to Rdiffuse(Oinc). The results of the calculation of the emitted fraction can be seen in Fig. 4.27. In a similar way, the fraction of emitted light detected during the reflection measurement Temit(Oinc) can be calculated from the diffuse fraction of the transmitted light of the sample (see also Fig. 4.27). I determined this diffuse fraction through a comparison of the direct transmission with the total transmission measured with the integrating sphere.
The case is a little bit more complicated for the emitted fraction detected during the centermount measurement. As given in equation (4.18), the data of the centermount measurement Cmes(Oinc) is equal to 1 - Absmes(Oinc). The absorption of the matrix material Absmatrix(Oinc) and the absorption of the dye Absdye(Oinc) contribute to the total absorption. A part of the absorbed light is re-emitted and leaves the sample, which is the fraction Cemit(Oinc) that we need. Cmes(Oinc) can be expressed as
C Oincmes 1 Absmatrix Oinc Abs Oincdye C Oincemit (4.27)
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The term 1 - Absmatrix(Oinc) can be identified with the data obtained from a centermount measurement of a reference sample Cref(Oinc), which yields the expression
C Oincemit C Oincmes C Oincref Abs Oincdye (4.28) to calculate the emitted fraction. The absorption of the dye Absdye(Oinc), which is needed for this calculation, can be derived from the already available data via
Abs Oincdye T Oincref Oincmes TT Oincemit R Oincref R Oincmes R Oincemit (4.29)
Please note that for calculating the emitted fraction in the centermount measurement, to which we wish to apply the correction, Absdye(Oinc) must be calculated with the uncorrected Temit(Oinc) and Remit(Oinc). Fig. 4.27 shows the emitted fractions for the different measurements. The absorption of the dye is shown in Fig. 4.32 and will be discussed in more detail in a following section.
Fig. 4.27: The fraction of photons which is emitted by the dye inside the collector and detected during the three measurements. Please note that all data is given relative to the number of photons incident on the sample. The presented correction must be applied to these data. One can see that the emitted fraction is lower for the transmission measurement than for the reflection measurement. More light is absorbed, and consequently emitted, close to the front surface. To be detected in the transmission measurement, this emitted light must traverse the fluorescent collector. Along the way, re- absorption reduces the amount that actually leaves the collector. These losses do not occur in the same strength for the light to be detected during the reflection measurement. Hence, the emitted and detected fraction is higher in the reflection measurement.
66 4.3 Optical characterization of fluorescent concentrator materials
4.3.2.6 Calculating the corrected spectral collection efficiency
With all this corrected data, the correct spectral collection efficiency KS(Oinc) can be calculated with equation (4.20). Having calculated all the emitted fractions, there is also a faster way:
K , Oinccorrs C , Oinccorremit T , Oinccorremit R , Oinccorremit (4.30)
A comparison between the corrected and the uncorrected data is shown in Fig. 4.28. The effect should be more pronounced for larger Stokes shifts or spectral regions, where the baseline varies more strongly.
Fig. 4.28: Comparison of the spectral collection efficiency with and without the described correction. With the correction, the values are higher than without. This can be explained as follows: in the emission region of the dye, the sensitivity of the detector in the integrating sphere is lower than in the absorption region. This is why the baseline is lower in the emission region, as can be seen in Fig. 4.26. This has not been taken into account in the uncorrected measurement and is now corrected.
4.3.2.7 Comparison between spectral collection efficiency and external quantum efficiency measurements To test the new method, I compared the results with external quantum efficiency measurements (EQE). The EQE was measured for a system with a 2 cm x 2 cm fluorescent concentrator (BA241, 3.2mm thick) with four attached GaInP solar cells. The solar cells and the complete systems of fluorescent collector and solar cells will be
67 4 Fluorescent Concentrators discussed in detail in chapter 4.5. At this point, I will treat the EQE measurement simply as an alternative method to determine the spectral collection efficiency. In contrast to chapter 4.5, I placed a black absorber underneath the fluorescent concentrator. In this way, light that has passed the collector is absorbed and cannot enter the collector again.
The EQE measurement gives the ratio of electrons collected at the contacts of the solar cells to the photons impinging on the system. I denote the result of the EQE measurement of the system of fluorescent collector and solar cell EQEsystem(Oinc). The spectral collection efficiency KS(Oinc) is the result of optical measurements. To compare both results, one has to calculate which result of the external quantum efficiency one could expect based on the optical measurements. This “predicted” value is denoted
EQEsystem,optical (Oinc). In our case, the solar cells are illuminated by the light emitted from the dye molecules (Fig. 4.29). So one has to take into account the average external quantum efficiency encountered by the emitted light. The resulting relation is
dEQEPL OOO ''' ³ cell . EQEsystem, optical inc OKO incs (4.31) ³ dPL OO ''
Fig. 4.29: The external quantum efficiency EQEcell(Oinc) of one GaInP solar cell and the photoluminescence spectrum PL(Oemit) of the dye BA241.
68 4.3 Optical characterization of fluorescent concentrator materials
Fig. 4.30 shows the measured EQEsystem(Oinc) of the system in comparison to the
EQEsystem,optical(Oinc) calculated with equation (4.31) from the optically measured spectral collection efficiency. Apparently, the measured EQEsystem(Oinc) is considerably lower than the one calculated from the optical measurement. There is yet another effect that must be considered: The external quantum efficiency depends on the position of the measurement spot on the fluorescent concentrator, as we will see in chapter 4.5. Losses like re-absorption of the emitted light by the dye and parasitic absorption in the matrix material depend on the length of the path of the emitted light within the concentrator. Therefore, the distance of the excitation spot from the solar cells at the edges affects the measured efficiency significantly. As the dyes emit the light approximately isotropically, the average distance to the solar cell is important and not the direct way (see Fig. 4.31).
Fig. 4.30: Comparison of the measured EQEsystem(Oinc) of the system in comparison to the EQEsystem,optical(Oinc) calculated from the optically measured spectral collection efficiency. Also, the measured EQEsystem,corr(Oinc) scaled by a factor of 1.13 to consider the position dependency of the EQE is shown. The scaled EQEsystem,corr(Oinc) and EQEsystem,optical(Oinc) from the optical measurement agree very well, considering uncertainties of the measurements and the corrections applied.
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Fig. 4.31: Illustration of the average distance of the excitation spot from the solar cells at the edges. Because the dye emits isotropically, the average distance is considerably longer than the direct path to the closest solar cell. The average distance is longest in the middle of the sample. For a 2 cm x 2 cm sample the average distance from the center is 1.12 cm. Close to the corner it is about 0.7 cm and even directly at a corner the average distance is still 0.56 cm.
The presented EQEsystem(Oinc) was measured in the middle of the sample where efficiency is the lowest with an excitation point of a few mm. For an excitation in the middle of the sample, the average distance in the horizontal direction to a solar cell at one of the edges is about 1.12 cm [45]. The data presented in [45] shows that for 44% of the area of the fluorescent concentrator, the average path is between 0.98 cm and
1.12 cm. For this 44% we can use the EQEsystem(Oinc) measured in the middle to be a good estimate for the local EQE.
Another 34% have an average path between 0.84 cm and 0.98 cm. As we ill see in chapter 4.5, the EQE in the absorption region of the dye in 0.5 cm distance to the solar cell (direct way) is about 16% higher than in 1 cm (direct way) distance. Therefore, it is reasonable to expect a 16% higher efficiency for the aforementioned 34% fraction of the area.
The remaining 22% have a shorter average distance to a solar cell. The measured EQE in 0.25 cm distance (direct way) was 34% higher than in 1 cm distance.
A weighted average with these values yields a correction factor of 1.13 to consider the position dependency of the EQE measurement. An accordingly scaled graph of
EQEsystem,corr(Oinc) is also shown in Fig. 4.30. The agreement with the EQEsystem,optical derived from the optical measurement is much better than without the scaling.
70 4.3 Optical characterization of fluorescent concentrator materials
The remaining differences are small, and the agreement very good considering the measurement uncertainty of about 1-2% absolute for the individual optical measurements and of 3% relative for the measurement of the EQE. Naturally, the corrections applied add uncertainty as well. Especially critical is the influence of the photoluminescence spectra. As we have seen before, the spectrum is heavily influenced by re-absorption. In addition to the effects discussed in section 4.3.1, we have to consider also a position dependency. Due to re-absorption, the spectrum leaving the edges also depends on how close the excitation was to the edges. If the peak at shorter wavelengths is not fully lost due to re-absorption, additional wavelength dependencies will occur. All this is a bigger problem for the EQE measurement than for the optical method: The baseline of the optical system does not vary strongly in the emission range, while the EQE decreases strongly above 600 nm. Considering the complexity, the last correction for the position dependency of the EQE has to be considered as fairly rough.
Nonetheless, the satisfactory agreement between measured EQEsystem,corr(Oinc) and
EQEsystem,optical(Oinc) from the optical measurement achieved in spite of all these problems can be seen as a good validation of the method proposed. Furthermore, it has become obvious that determining the spectral collection efficiency via the electrically measured EQE contains a considerable amount of uncertainties and problems and requires significant corrections. Consequently, the proposed new method provides more reliable results.
4.3.2.8 Collateral information from the measurements Much data has been measured and calculated to determine the corrected spectral collection efficiency. This data can be used to gain some additional information about the fluorescent collector. One byproduct of the correction presented in the previous section was the fraction of the incident light that is absorbed by the dye Absdye(Oinc)
(Fig. 4.32). This result could not be derived simply via 1-T(Oinc)-R(Oinc) because some of the absorbed light is reemitted. The absorption coefficient of the dye inside the host material could give information on whether the dye was affected by the embedding process. It also presents valuable input data for simulations of the fluorescent concentrators, e.g. [86]. Care must be taken, because the data is given as the fraction of the light incident on the concentrator. So to calculate the absorption coefficient, the reflection at the front surface must be taken into account (see also section 4.4.2.2).
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Fig. 4.32: The fraction of the incident light which is absorbed by the dye within the material BA241. The slab was 3.2 mm thick. The correction does not affect the absorption data significantly.
Another very important result which can be directly derived from the generated data is the escape cone loss. As I already showed in Fig. 4.1, emitted light that impinges on the surface with angles steeper than the critical angle Tc is lost, due to the escape cone of total internal reflection. In section 4.3.2.5 I have calculated the emitted fraction detected during the centermount measurement Cemit(Oinc), which corresponds to the total amount of light emitted in any direction. I also calculated the fraction of light emitted and detected during the reflection measurement Remit(Oinc) and the transmission measurement Temit(Oinc). This corresponds to the fraction of light lost due to the escape cone through the front and the back surface. So via
R Oincemit T Oincemit Escape Oinc (4.32) C Oincemit one can calculate the fraction that is lost due to the escape cone of total internal reflection. The results can be seen in Fig. 4.33.
72 4.3 Optical characterization of fluorescent concentrator materials
Fig. 4.33: The fraction of emitted light that is lost due the escape cone of total internal reflection. The value predicted theoretically under ideal conditions is 26%.
Interestingly, the escape cone losses are not constant. They tend to be lower for smaller wavelengths. This is surprising considering the results of the photoluminescence measurements. There, under excitation with shorter wavelengths shorter wavelengths were also emitted. These shorter wavelengths are more prone to re-absorption, which would increase the escape cone losses. A possible explanation for this occurrence could be that for higher energy photons that are absorbed, more thermal relaxation occurs before a new photon is emitted. More entropy is generated and more information from the incoming photon is lost. This results in the emission characteristic becoming increasingly isotropic. Without this angular randomization, light is emitted more frequently into unfavorable directions with higher escape cone losses [47]. Consequently, more thermalization would mean lower escape cone losses. However, this explanation has to be confirmed by wavelength dependent measurements of the angular characteristics of the emitted light.
Another issue is the total height of the escape cone losses. In our results, the losses peak at around 28% in the region with relevant absorption. This could be considered well in agreement with the theoretical prediction of 26%. However, the lower values are below the theoretical value. One explanation could be in the experimental setup: for practical reasons, the openings in the integrating sphere during reflection and transmission measurements are slightly smaller than the samples. Therefore, part of the light being lost into the escape cone is not detected in these measurements.
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Consequently, the escape cone losses might be underestimated. This could also explain the slight overestimation of the spectral collection efficiency visible in Fig. 4.30. However, the quantification of this effect is not straightforward. A first estimation is that the fraction of the losses that could not be measured is, in any case, smaller than the fraction of the covered area. The reason for this assumption is that the escape cone losses predominantly occur close to the excitation and in the covered areas outside the openings, there is no excitation.
4.3.3 Measuring the angular distribution of the guided light The escape cone losses depend on the angle under which emitted light impinges onto the internal surface. Furthermore, photonic structures show a pronounced angular characteristic. Therefore, to be able to understand the effect of the photonic structure on light guiding in the collector, it is interesting to investigate the angular distribution of the light that is trapped in the collector and subsequently guided to the edges. As we will see, the complex angular characteristic is also a benchmark whether the different models describing fluorescent concentrators are able to explain the lightguiding well.
4.3.3.1 Setup To measure the angular characteristic of the guided light, I realized a setup that was first described by Zastrow in [47]. Fig. 4.34 presents a sketch of the experimental setup. An index-matched half cylinder is optically coupled to the edge of the concentrator such that at this edge no total internal reflection occurs. If the cylinder is large in comparison to the thickness of the concentrator, the light impinges on the outer surface of the cylinder perpendicularly. The light leaves the cylinder without significant refraction and the intensity is measured at every angle T. The half cylinder is made from PMMA and is 2 cm thick. The surroundings of the half cylinder are covered with blinds, so only light leaving the concentrator directly into the half cylinder is detected. The blind thickness is 0.5 cm, so the last 0.5 cm of the collector remains unilluminated.
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Fig. 4.34: Experimental setup to measure the angular distribution of the light that is coupled out at the edges of the fluorescent concentrator. A PMMA half cylinder is optically coupled to one edge to avoid internal reflection and refraction.
4.3.3.2 Results I measured the angular distribution on a 5 cm x 5 cm sample from the material BA241. The thickness was 3.2 mm. The measurement was repeated three times and the average calculated. The standard deviation is shown as error bars. The result is shown in Fig. 4.35.
Fig. 4.35: Measured angular distribution of the light which is coupled out at the edges of a 5 x 5 x 0.3 cm3 fluorescent concentrator made from BA241.
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4.3.3.3 Discussion As shown in Fig. 4.35, the intensity drops significantly at angles T § 50° and 130°, which correspond to the critical angle of total internal reflection. Between T § 50° and 130° the light is guided to the edges by total internal reflections. The few photons detected beyond these angles, in expression with T < 50° or T > 130° must have been emitted close to the edge of the concentrator and therefore could reach the cylinder without a reflection at the top or the back surface of the fluorescent concentrator. All this is well in accordance with the simple picture of isotropically emitting dyes and total internal reflection.
However, the angular distribution shows an unexpected anisotropic dip around T = 90°. This dip is also visible in measurements of [47] but was neglected as a measurement artifact at that time. My co-authors and I investigated this interesting feature in [44].
Fig. 4.36: The path of different rays in the fluorescent concentrator. Ray a) is detected with an angle Tslightly less than 90°. Directly before this ray leaves the collector it traverses through the bottom area of the concentrator. At the bottom, only a minor amount of light is emitted, because of the absorption/emission profile in the concentrator. In contrast, ray b) passes through the top section last. That is, many photons are detected with an angle slightly larger than 90°. Rays with angles significantly different from 90°, such as ray c), pass several times through the collector. Therefore no large differences between angles significantly smaller and greater than 90° occur.
76 4.3 Optical characterization of fluorescent concentrator materials
Ray tracing simulations with a model developed by Liv Prönneke [44] and by the independent model presented in this work in chapter 4.4 showed both that the assumed angular emission characteristic changes the angular distribution, but that an anisotropic characteristic prevails independent from the angular emission characteristic. Therefore, an explanation must be found in more fundamental properties of the collector. Here, help comes from the thermodynamic model presented in 4.2.2. As mentioned before, because of the absorption of the incoming light in the concentrator, the intensity of the incoming light drops with increasing distance from the front surface. Thus, the chemical potential also decreases and less light is emitted further away from the front surface. Now one has to consider that light detected at different angles experiences different light paths. The different paths are illustrated in Fig. 4.36.
Light detected with an angle slightly greater than 90° originates partly from the area close to edge and close to the front surface, an area were a high flux of light is emitted. In contrast, the light which is detected with angles slightly smaller than 90° stems either from regions where less light is emitted (close to the bottom of the concentrator) or has to travel longer distances in the concentrator, which means higher re-absorption losses. Light that is detected with angles significantly different from 90° has on average traveled several times through the collector. It originates both from the top and the bottom regions. Therefore, no big differences are obvious between angles significantly smaller and larger than 90°. However, angles above 90° remain slightly more frequent. In conclusion, it is the spatial distribution of the absorption of the incident light and the resulting re-emission profile that is responsible for the anisotropy in the angular distribution.
4.3.4 Short summary of the optical characterization Optical methods offer powerful tools to characterize fluorescent collectors. With photoluminescence measurements I could show the strong effects of re-absorption and a dependence of the luminescence spectrum on the wavelength of the excitation light.
I presented a novel method to determine the spectral collection efficiency of fluorescent concentrator systems. Only three optical measurements with a photo- spectrometer and an integrating sphere are necessary to determine the ability of the concentrator to guide light to its edges. A comparison with results from external quantum efficiency measurements on a system with fluorescent concentrator and attached solar cells showed good agreement. From the measurements, additional relevant data, such as the absorption of the dyes in use and the fraction of light lost into the escape cone, could be derived. Especially in the escape cone measurements, an interesting wavelength dependency occurred.
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Measurements of the angular distribution of the guided light showed interesting features. These can be explained by the absorption profile within the fluorescent collector and are rather independent from the emission profile of the dye. Unfortunately, it is therefore difficult to derive the emission’s angular characteristics from these measurements.
To explain the different measurement results, I offered several models and hypothesizes. To test these different models, a Monte-Carlo based simulation will be presented in the next chapter.
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4.4 Simulating fluorescent concentrators
For a full understanding of fluorescent concentrators, it is helpful to be able to test the different hypotheses of how a fluorescent concentrator works and which effects are important. Therefore, a simulation model based on Monte Carlo methods was developed in the context of this work. The development of this model was a joint project of the University of Ulm and the Fraunhofer Institute for Solar Energy Systems. I developed the physical model of the relevant processes in the fluorescent collector and generated the input data from different measurements; Marion Bendig from the University of Ulm implemented that model with efficient algorithms within the frame of her master’s Thesis [87]. In her work, many details on the simulation and the Monte Carlo method can be found.
Several works have investigated fluorescent concentrators using Monte Carlo methods and ray tracing. One of the first works is the dissertation of Heidler [88]. Heidler modeled absorption of the dye, isotropic emission, total internal reflection, and re- absorption. The model was even capable of simulating a diffuse back reflector and stack configurations. Simulated collection efficiencies exceeded experimental data by 15% on average due to the idealized conditions of the model. However, good agreement between the simulated and measured edge emission spectrum was achieved. Recently, new attempts for simulating fluorescent concentrators have been made [30, 35, 89-92]. Kennedy et al. [90, 91] use a simple model describing absorption of the dye, emission, total internal reflection, and re-absorption to calculate the relative Jsc of solar cells coupled to one edge of the collector and to predict the emitted spectrum leaving at the bottom of the collector. The Jsc values were overestimated by about 10%, but again the emitted spectra agreed well with predictions. Burgers [92] used a quite similar model. He determined relevant parameters, like the dye concentration or the quantum efficiency by fitting the model to measured data. He also included mirrors at the collector edges. With his model, he achieved good agreement between EQE measurements and the simulation-based predictions. In [30, 35] a highly idealized model was presented, that for the first time included a photonic structure. This idealized model is currently being further developed by Liv Prönneke to describe more realistic systems; first results have been published in [44].
In all the previous works, only minor testing of the simulation results against spectrally resolved experimental data, such as reflection and emission measurements, was performed. The angular distribution of the light was neglected as well. Therefore in this work, the simulated data shall be tested against a range of experimental data to
79 4 Fluorescent Concentrators verify the different assumptions on the working principle of fluorescent collectors. The model uses efficient algorithms, which allows for the calculation of complex systems with high accuracy. First results derived with this model were published in [86], where all coauthors who contributed to the model are listed. In this work, I present results that were achieved with a slightly refined model and more accurate input data.
First, I will present the Monte Carlo method shortly and will give an overview of the model. In the following, I will document the input data and how the data was derived. Then I will compare results from a simple method and with experimental data. Subsequently, I will show which modifications of the simple model increase agreement with experimental data.
4.4.1 Monte Carlo simulation The Monte Carlo method uses random numbers for the numerical solution of mathematical problems. Early works on this method are from Metropolis and S. Ulam [93]. At this point, I will only give a very short introduction. Comprehensive presentations can be found in [94, 95]. The term Monte Carlo describes a large set of different methods used in many different applications. Many methods follow a pattern that could be described with three steps [96]:
1. Generate inputs randomly using a certain specified probability distribution.
2. Perform a deterministic computation using the inputs.
3. Aggregate the results of the individual computations into the final result.
A classical example is to determine the area of a circle, inscribed into a square, by shooting randomly onto the square and then counting the holes in the circle. By comparing to the total number of shots, the area fraction of the circle can be estimated, and as the area of the square is known, the area of the circle can be calculated (and the value of the number S). The pattern of the three steps is present in this example: the random shooting corresponds to the generating of random input. The determination whether the hole is in or outside the circle corresponds to the deterministic computing and the division by the total number of shots and multiplying with the area of the square corresponds to the computation of the final result.
The underlying reason, why this method works can be found in the central limit theorem. The central limit theorem states, in simple words, that the sum of large number of random variables is asymptotically normally distributed. Let X be the quantity to be calculated and m a random variable with the expectation value E(m)=X.
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Additionally, m1, m2, m3,…mN are N independent variables, which have the same N distribution as m. According to the central limit theorem m is asymptotically ¦i 1 i normally distributed and, which is important, the expectation value is
N NXmE . (4.33) ¦i 1 i
The expected deviation of the sum of the random variables from NX decreases with a /1 N law with increasing number of variables N. Therefore the value of X can be estimated by simulating N realizations of m and calculating the mean average.
In our example, for the bullet holes in the circle, the expectation value is similar to the area fraction of the circle (without that this fraction would be known before the experiment). Shooting holes corresponds to simulating the random variables, e.g. in the first round of ten shots five are in and five are out, in the second round eight are in and two are out etc. Following the central limit theorem, the mean average of all rounds will be close to the area fraction of the circle. With more rounds, the precision increases, but for doubled accuracy the number of rounds needs to be quadrupled.
For the simulation of fluorescent collectors, the simulated quantities do not follow normal distributions. For instance the penetration depth of the incident radiation follows the exponential Lambert-Beers relation. That is, it is more likely that an incident photon is absorbed close to the surface than close to the back. To sample these random variables with the help of a uniformly distributed random variable y, the inversion method was applied. If m is the random variable with the cumulative distribution function P(x), which gives the probability that mx, than m can be sampled by m=P-1(y). In this relation, P-1(y) is the inverse function of P(x). Obviously, certain requirements for monotony have to be fulfilled for P(x).
4.4.2 The used model
4.4.2.1 Considered processes In the standard configuration, the model considers wavelength dependent reflection, refraction, total internal reflection, absorption in the PMMA matrix and absorption in the dye. After absorption in the dye the probability of the emission is determined by the dye’s quantum efficiency and the emission wavelength is determined by the photoluminescence spectrum of the dye. Fig. 4.37 shows the process diagram of the simulation.
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Fig. 4.37: Process diagram of the simulation model
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The model calculates the reflection of the light at all boundaries with the help of the Fresnel equations:
2 § sin DD · ¨ outin ¸ , Rs ¨ ¸ (4.34) © sin DD outin ¹
2 § tan DD · ¨ outin ¸ . Rp ¨ ¸ (4.35) © tan DD outin ¹
The light is assumed to be unpolarized, so the average value
RR ps R (4.36) 2 was used.
The incident and outgoing angle, Din and Dout, were determined by Snell’s law of refraction
sin Din n2 . (4.37) sin Dout n1
In this relation n1 is the refractive index of the medium from which the light is incident, and n2 the refractive index of the medium the light enters. For the surrounding a refractive index of 1 was assumed. The refractive index of the fluorescent collectors was calculated using the Cauchy equation [97] c O cn 2 . (4.38) 1 O2
2 In this equation, the material constants for PMMA are c1=1.49 and c2=0.004 µm .
Total internal reflection occurs for angles Din bigger than the critical angle Dc, with
n2 . sin Dc (4.39) n1
The presented relationships were transformed into forms that allowed fast computation prior to implementation, e.g. trigonometric functions are very time consuming in calculations, while scalar products can be processed fast. Therefore mathematical
83 4 Fluorescent Concentrators relationships were used to replace trigonometric functions by terms using scalar products.
If an incident ray is still in the collector after the previous events, its mean free path is calculated. The relation that determines the free path length 'w can be derived from the Lambert-Beer characteristic with the help of the inversion method. The relation is 1ln y 'w (4.40) total OD
[87]. In this relation, y is a random variable sampled with a uniform distribution in the interval [0,1). The Dtotal is the sum of the absorption coefficient of the dye Ddye and the absorption coefficient of the PMMA matrix DPMMA. If the ray is absorbed before it hits a boundary of the concentrator, the probability that the ray is absorbed by the dye is
Ddye/Dtotal and the probability that the ray is absorbed by the PMMA DPMMA/Dtotal. If the ray is absorbed by the dye, the probability that an emission occurs is given by the quantum efficiency QE. The wavelength of the emission is sampled according to the photoluminescence spectrum. In the standard model the direction of the emission is distributed isotropically. After any emission, reflection or refraction event, after which the ray is still in the collector, the calculation process is repeated. During the calculations, many different data of the rays are collected and aggregated to give meaningful output values.
4.4.2.2 Input data For a wavelength dependent simulation, the absorption spectrum of the dyes and the PMMA matrix, as well as the photoluminescence spectrum of the dyes must be known. These data were taken from the optical characterization presented in chapter 4.3. To test the simulation, the material properties of BA241 were chosen to be investigated, as for this material the most extensive experimental data was available.
In section 4.3.2.8, the fraction of the incident light that is absorbed by the dye
Absdye Oinc was calculated. Absdye Oinc represents the number of photons absorbed by the dye divided by the number of photons incident on the collector slab. However, only the photons that enter the collector can be absorbed. Therefore, to determine the absorption coefficient D Oinc the reflection of the front surface Rfront Oinc must be taken into account, as only the fraction of (1-Rfront) enters the slab. It is
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1 § Abs O · OD ¨1ln incdye ¸ , inc ¨ ¸ (4.41) d © 1 R Oincfront ¹ with d being the thickness of the fluorescent collector.
It must be said that this relation is only an approximation. In spectral regions with low absorption light might pass the collector and might be reflected at the back surface. In consequence, this light would get a second chance to be absorbed and the inserted thickness of the collector would be inappropriate. However, only around 4% of the transmitted light is reflected back into the collector and the effect is only important in regions of low absorption, so this can be considered a minor uncertainty which is in the magnitude of the uncertainties for Absdye Oinc .
The front reflection Rfront Oinc was determined from the reflection measurements of the reference sample. In the spectral regions above 350 nm, where the absorption of the reference is low, Rfront Oinc was assumed to be half the reference reflection. In the region where reference shows relevant absorption (<350nm) the average value of the region 400-350nm was used.
The obtained spectrum of the absorption coefficient for the BA241 material is shown in Fig. 4.38. This absorption coefficient is the effective absorption coefficient of the dye dispersed with the given concentration in the collector. Changes of the dye’s concentration can therefore be modeled by changing this absorption coefficient.
The same calculation was performed to determine the absorption coefficient of the
PMMA. In this case, the absorption data used was AbsPMMA Oinc 1-T Oinc -R Oinc of the reference sample.
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Fig. 4.38: Absorption coefficient D Oinc of the dye in the BA241 material and of the PMMA matrix determined from the reference sample.
Fig. 4.39: Photoluminescence spectrum used as input for the simulation of the BA241 material.
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The input spectrum for the photoluminescence was taken from the measurements at the back of the 1 mm thick BA241 sample under excitation at Oinc= 490 nm presented in Fig. 4.19. This spectrum was chosen because it should show the lowest influence of re- absorption and should therefore be closest to the real emission of the dye. On the other hand, a strong background signal was present in this measurement that increased with the wavelength. To exclude the background, it was determined from the photoluminescence measurements at the edges, which showed less background, that there should be no photoluminescence signal below Oemit= 512 nm and beyond
Oemit= 724 nm. The background signal was estimated with a linear interpolation between these two points and subtracted from the measurement data. The obtained spectrum is presented in Fig. 4.39.
4.4.3 Results of simple model The described model was used to simulate the results of the performed reflection and transmission measurements, as well as the outcome of the measurements of the angular distribution of the light leaving the collector at the edges. For the simulation of the reflection and the transmission measurements, the area of openings of the integrating sphere was taken into account. The openings are slightly smaller than the 2 x 2 cm2 of the samples used for the reflection and the transmission measurements. The simulated samples were 2 x 2 cm2 as well, and had a thickness of 3.2 mm. In the simulation of the reflection measurement, it was considered additionally that the light impinges with an angle of 4° onto the sample during the measurement. Fig. 4.40 shows the results for the simulation of the reflection measurements, while Fig. 4.41 shows the simulation of the transmission measurement. 100 million rays were shot in each simulation, which takes around 20 minutes on a typical personal computer. As the quantum efficiency of the used dye is not known exactly, it was treated as a free parameter and the results of this parameter variation are shown.
Independent of the quantum efficiency, in the absorption region of the dye the simulated reflection is significantly lower than the measured one. This means that the simulation underestimates the amount of light lost into the escape cone at the front surface. In contrast, in the simulation of the transmission measurement, the simulated values are higher than the measured values in the absorption region. Here, the escape cone is overestimated. Outside the absorption region, the agreement is good.
The difference between measurement and simulation is smaller for higher quantum efficiencies, but is still significant even for a quantum efficiency of 100%. Possible reasons for the observed differences and how the model can be improved will be discussed in the following section.
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Fig. 4.40: Comparison of measured and simulated reflection for different quantum efficiency values of the dye. Independently of the quantum efficiency, the simulated values are lower than the measured values in the absorption region of the dye. With higher quantum efficiency this difference decreases.
Fig. 4.41: Comparison of measured and simulated transmission for a quantum efficiency value of the dye of 99%. The simulated values are higher than the measured values in the absorption region of the dye. The simulation overestimated the escape cone losses through the back surface.
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The angular distribution of the light leaving the fluorescent collector was simulated for a sample size of 5 x 5 cm2 and 3.2 mm thickness. These are the geometric dimensions of the sample used in the experimental determination of the angular distribution. The simulations for the angular distribution were performed with 108 rays shot as well. In the experimental setup 0.5 cm thick blinds fix the fluorescent collector and shield the PMMA half cylinder and the detector from the incident light (see Fig. 4.34). These blinds were considered in the simulation as well. It turned out that the properties of these blinds are among the strongest identified parameters that determine the angular distribution. Fig. 4.42 shows the result of simulations for different blind absorption values in comparison to the measured distribution. A blind absorption of 50% means that 50% of the light that would have been totally internally reflected, is now absorbed when the ray hits the surface neighboring the blind. It is reasonable to expect some blind absorption, as the blind is produced from black anodized aluminum and is in close contact with the collector surface. However, no extra optical coupling between these two elements exists.
The variation of the quantum efficiency was found to have no significant effect on the angular distribution. The quantum efficiency of the dye was 99% for the simulation results presented.
Fig. 4.42: The angular distribution of the light leaving the collector at the edges in comparison to the measured distribution. The simulation was performed with different absorption values of the blinds that are present in the experimental setup. The presented distributions are normalized such that the area under the curves is the same.
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Fig. 4.42 shows the angular distributions normalized, such that the area under the curves is the same for all distributions. Obviously, the effect of the blind absorption is large. With strong blind absorption, only rays that run more parallel to the back and front surface reach the edge. Rays that run more perpendicular hit the surface close to the edges and are absorbed by the blinds. In consequence, the resulting angular distribution is very narrow. For reduced blind absorption, the distribution widens. Independently of the blind absorption, no good agreement between measurement and simulation is achieved. However, the asymmetry of the distribution is reproduced to a certain extent. For instance, there is a maximum at angles slightly larger than 90° which is the case for the measured distribution as well. However, with reduced blind absorption, side peaks occur in the simulated data at angles of 60° and 120° that are not present in the measurement. Furthermore, the angular distribution tends to be too narrow independently from the blind absorption.
4.4.4 Improvements of model
4.4.4.1 Reconstruction of photoluminescence spectrum One result of the photoluminescence measurements presented in section 4.3.1 was that re-absorption and re-emission critically determine the shape of the detected photoluminescence spectrum. Therefore it is reasonable to assume that re-absorption shaped even the spectrum measured at the back of the 1 mm thick sample, which served as input for the simulation. The simulation is capable of determining the spectrum leaving the back of the collector and of comparing it to the input spectrum. A simplified error back propagation approach was used to reconstruct the “true” photoluminescence spectrum from the measurement results. The general idea of this approach is that an assumption for the “true” spectrum is taken as input for the simulation. With this input the resulting spectrum is calculated and compared to the measured one. The difference of both spectra is calculated and a certain fraction of this difference is added to the input spectrum. Subsequently the simulation is repeated. Given that the solution converges, this circle can be repeated until the difference between both spectra is as small as desired. More details on this reconstruction can be found in [87].
This reconstruction was performed for sample dimensions of 2 x 2 x 0.1 cm3 and an assumed quantum efficiency of 99%. The measured input spectrum served both as first assumption for the true spectrum and as the reference result that should be met. Fig. 4.43 shows the measured spectrum and the reconstruction from this input.
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Fig. 4.43: Measured and reconstructed photoluminescence spectrum, normalized such that the peaks at Oemit=570 nm have the same height. In the reconstructed spectrum the peak at around Oemit=540 nm is much more pronounced. This is a reasonable result as this peak is damped by re- absorption and therefore detected only attenuated in the measured spectrum.
The reconstructed spectrum shows a much more pronounced peak at Oemit= 540 nm than the measured spectrum. Naturally, the reconstructed spectrum is not necessarily identical to the real emission spectrum. There might be different spectra that show the same result. However, this is a reasonable outcome for the reconstruction, because the
Oemit= 540 nm peak is damped by re-absorption as it was found in the measurements presented in section 4.3.1. Fig. 4.44 shows a comparison of the simulation results obtained by using the measured spectrum as input for the simulation with the results obtained with the reconstructed spectrum as input.
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Fig. 4.44: Comparison between the simulation results for the reflection, obtained by using the measured spectrum as input for the simulation, with the results obtained with the reconstructed spectrum as input. The results from the reconstructed spectrum show better agreement with the measured results.
The results from the reconstructed spectrum show better agreement with the measured values than the results obtained with the measured input. The reason is that the reconstructed spectrum results into more re-absorption. Consequently, more re- emission into the escape cone takes place and the escape cone losses, which have been underestimated by the simulation so far, are increased.
In Fig. 4.45 the comparison for simulated transmission data is shown. Using the reconstructed photoluminescence spectrum as input does not affect the simulated transmission data much. For the transmission, the escape losses increase a little bit as well, which means that the agreement between measurement and simulation slightly deteriorates. The impact on the angular distribution was checked as well, but no significant effect was found.
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Fig. 4.45: Comparison between the simulation results for the transmission, obtained by using the measured spectrum as input for the simulation, with the results obtained with the reconstructed spectrum as input. The effect of the changed spectrum is minor. However, the agreement is slightly worse with the reconstructed spectrum
From the positive results for the simulated reflection data, it can be concluded that reconstructing the initial photoluminescence spectrum helps to increase the agreement between simulation and measured results. This supports the finding that re-absorption plays a critical role for the properties of the fluorescent collector and must be considered while simulating fluorescent collectors.
4.4.4.2 Wavelength dependent photoluminescence spectrum The photoluminescence measurements in section 4.3.1.2 suggested that the photoluminescence spectrum depends on the excitation wavelength, at least for the investigated dye BA241. Such an excitation dependency would result into varying re- absorption, and is therefore likely to influence the light guiding properties of the fluorescent collector. Hence, it is interesting to investigate the effect of an excitation dependent photoluminescence with the help of the simulation tool.
Unfortunately, only for two different excitation wavelengths was photoluminescence data available (see Fig. 4.21). The excitation wavelengths were Oinc= 440 nm and
Oínc= 490 nm. The available spectra were both prepared in the same way for the use as simulation input data, as described in section 4.4.2.2. They are presented in Fig. 4.46.
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However, using the spectrum obtained under Oinc= 440 nm excitation resulted in no significant differences in the simulated values. The reason might be that higher re- absorption due to the more pronounced peak at around Oemit= 540 nm is compensated by the also more pronounced peak at around Oemit= 685 nm that results into lower re- absorption.
Fig. 4.46: The two measured photoluminescence spectra that were measured with Oinc=440 and Oinc=490 nm excitation respectively, in the form they were prepared to serve as input data for the simulation. Additionally, a hypothetical input spectrum is shown that consists of one single peak centered on Oemit=540 nm. All spectra are normalized such that the peaks at Oemit=540 nm have the same height.
In section 4.3.1.2 it was shown that under excitation with Oinc= 440 nm the peak at
Oemit= 570 nm was present in the measurement of the 3.2 mm thick sample, while more or less only a trunk is visible in the measurement of the 1 mm thick sample. This could be interpreted such that this peak is only the result of re-absorption of photons with wavelength larger than Oemit= 440 nm and subsequent re-emission. Therefore, I investigated this hypothesis with the help of the simulation tool as well. In Fig. 4.46 a hypothetical photoluminescence spectrum is shown that consists of only one peak centered on Oemit= 540 nm. Fig. 4.47 presents the reflection simulated with the spectrum measured under excitation with Oinc= 490 nm, the spectrum simulated with the spectrum consisting of only one peak at Oemit= 540 nm and of a simulation with a
94 4.4 Simulating fluorescent concentrators spectrum obtained from an interpolation of both spectra. In the interpolated spectrum, for wavelengths below Oinc= 440 nm, the spectrum with only one peak was used. For excitation wavelengths above Oinc= 490 nm, the spectrum obtained under Oinc= 490 nm excitation was applied. In between, a linear interpolation between the two spectra was used.
The spectrum simulated with the hypothetical spectrum increased the escape cone losses considerably. However, the interpolation of the two spectra only affected the shorter wavelengths. Overall, the agreement with the measured spectrum could not be increased significantly. In conclusion, the observed dependence of the photoluminescence spectrum on the excitation wavelength seems not to influence the properties of the fluorescent collector significantly.
Fig. 4.47: Reflection spectra simulated with different assumptions for the photoluminescence spectrum. The first spectrum was simulated with the photoluminescence spectrum measured under excitation with Oinc= 490 nm radiation (as were the simulation results presented so far), the second spectrum was simulated by using a hypothetical spectrum consisting of only one single peak centered on Oemit= 540 nm. The third spectrum was simulated with an interpolation of both spectra.
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4.4.4.3 Scattering The facts that the escape cone losses through the front surface are underestimated, while they are overestimated for the back surface, and the fact that the simulated angular distribution is too narrow raises the question whether scattering could be an explanation for these differences. Most light is absorbed and emitted close to the front. If the emitted light running in the direction of the back surface was back scattered, more light would leave the collector at the front surface and consequently less light would leave the collector through the back surface. Additionally, scattering could widen the angular distribution. In [47], the scattering coefficients for the used PMMA is determined. Extruded PMMA has a scattering coefficient of around 1-4.10-2 cm-2, while cast PMMA has a scattering coefficient of 2.10-3 cm-2. The used materials were cast, so the lower value should be used in the simulation. Scattering was implemented into the model as an additional “absorption coefficient” that limits the free path length. Then, with a certain probability, the “absorption event” was decided to be scattering instead of absorption by the dye or by the matrix material. When the event was determined to be scattering, the new direction of the light was sampled using an isotropic angular distribution. Fig. 4.48 shows the comparison of the measured reflection with the simulation of the reflection for different scattering coefficients. Fig. 4.49 shows the results for the angular distribution.
Fig. 4.48: Comparison of the measured reflection with the simulation of the reflection for different scattering coefficients. Only unrealistic high scattering coefficients have a significant impact on the reflection.
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Fig. 4.49: Comparison of the measured angular distribution of the light leaving the collector at the edges with the simulation of the angular distribution for different scattering coefficients. Again, only high scattering coefficients have a significant impact on the angular distribution. However, the expected widening of the distribution is not observed. Only the side peaks are eliminated.
For both reflection values and angular distribution, unrealistic high scattering coefficients are necessary to show a significant impact on the simulated results. In the simulation of the reflection, the scattering increases the loss through the front surface as expected. However, the scattering increases the values for all wavelengths. Therefore the good agreement of the simulation with the measurement outside the absorption range of the dye is destroyed. For the angular distribution, the expected widening of the angular distribution is not achieved. A possible explanation is that the light with angles considerably different from 90° travels a long way through the collector on average. With high scattering, especially this light is therefore lost with high probability. In consequence, scattering seems not to play an important role in the materials of high optical quality used in this work.
Nonetheless, scattering at the interface between collector and the PMMA half cylinder could be a source of the widened angular distribution. The material used for optical coupling is not of the same high optical quality as the PMMA. Furthermore, small air bubbles might have been included into the coupling layer. However, the incorporation of these effects into the simulation was beyond the scope of this work.
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4.4.4.4 Angular distribution of emitted light Up to now, the emission of light by the dye was considered to be isotropic. However, depending on the rigidity of the matrix material and the processes within the dye molecule, certain directions might be preferred for emission as it was discussed in section 4.1.5.1. It is very interesting to see how such an anisotropic emission determines the simulated properties. Zastrow [47] derived the following expression for the likelihood P(T) of a certain emission angle Tby theoretical considerations:
P(T)=1 +Jcos(T)2 . (4.42)
In this expression, Jis the anisotropy coefficient that depends on which situation shall be described. An anisotropy coefficient of 1/3 for example, describes the situation for absorption and emission dipoles aligned in parallel. The emission angle T is measured relative to the electric field vector of the incident radiation. Fig. 4.50 shows the results for the reflection simulated with an anisotropy coefficient of 0.33, while Fig. 4.51 shows the results for the angular distribution. All simulations were performed with the reconstructed photoluminescence spectrum.
Fig. 4.50: Reflection, simulated with isotropic and anisotropic emission in comparison to the measured reflection. With an anisotropic emission the escape cone losses are increased.
98 4.4 Simulating fluorescent concentrators
Fig. 4.51: Angular distribution of the light leaving the collector at the edges, simulated with isotropic and anisotropic emission in comparison to the measured distribution. With an anisotropic emission, the distribution is reasonable reproduced at angles around 90°. However, strong side peaks are present in the simulated data that cannot be found in the measured data.
The anisotropic emission increases the escape cone losses, because light is preferentially emitted into the direction of the top and the bottom surface. With anisotropic emission, the reflection spectrum can be simulated with reasonable agreement. For the peak at around Oinc= 528 nm, the escape cone losses are still slightly underestimated in the very peak region. A possible explanation is that the determined absorption coefficient is underestimated in this region. In this spectral region, practically all light was absorbed by the dye. With the given measurement accuracy, an absorption even stronger than with the calculated absorption coefficient would not have been resolved. A possible solution is to determine the absorption coefficient again on thinner samples.
However, for shorter wavelengths the escape losses are slightly overestimated with anisotropic emission. With the chosen anisotropy coefficient, the light is emitted preferably into the direction of the front and back surface. This corresponds to very little reorientation of the dye molecules, be it by rotation of the molecule or by reconfiguration of the molecule itself. It is therefore reasonable to assume that this strong correlation between absorption and emission state is present predominantly when little thermalization occurs. Therefore one solution could be that for smaller
99 4 Fluorescent Concentrators excitation wavelengths, which correspond to more thermalization, a more isotropic emission prevails, while for longer excitation wavelengths a more anisotropic emission with high escape cone losses is present. This could explain the observed reflection spectrum in the light of the simulation results. Unfortunately, to simulate a wavelength dependent emission anisotropy was beyond the scope of this work.
The agreement of the simulated angular distribution with the measured distribution is increased with an anisotropic emission. Especially at angles around 90° the measured distribution is reproduced in a reasonable manner. However, strong side peaks are present in the simulated data that cannot be found in the measured data. In this context, it makes sense to reconsider the possibility of scattering in the layer that optically couples the collector to the PMMA half cylinder in the experiment. This scattering would affect predominantly the light at angles further away from 90°, because this light would travel a longer distance through the coupling layer. As a consequence, the side peaks could be smoothed out.
Another interesting parameter to investigate would be the surface roughness. The present model assumes perfect surfaces. Little surface roughness could influence the angular distribution; while high surface roughness would severely degrade the light guiding properties. However, these investigations were beyond the scope of this thesis.
4.4.5 Conclusions from simulation With the help of the simulation, different parameters could be investigated on their effect on the properties of the fluorescent collectors. The shape of the photoluminescence spectrum and the angular distribution of the emitted light proved to be very important. In contrast, scattering and the dependence on the excitation wavelength of the photoluminescence spectrum were found to be of minor importance. The model should be further developed to include a wavelength dependent emission anisotropy. With such an amendment the simulation should be capable to precisely reproduce the optical properties of fluorescent collectors. Such a simulation could be used to simulate complete fluorescent concentrator systems for the optimization of key parameters of fluorescent concentrator systems without the need to make an experiment for every step.
100 4.5 Fluorescent concentrator systems
4.5 Fluorescent concentrator systems
In this chapter, I present investigations on complete systems of fluorescent collectors and solar cells. I start with a short discussion of which solar cells are best suited for the application in conjunction with fluorescent concentrators. I show how the efficiency of fluorescent concentrator systems increases when different fluorescent concentrator materials and different solar cell materials are combined in one system. Subsequently, I demonstrate that selectively reflective photonic structures increase the efficiency of fluorescent concentrator systems and investigate their effect in detail, especially how the efficiency varies with system size. In the end, I present concepts for the future development of fluorescent concentrator systems.
4.5.1 Solar cells for fluorescent concentrator systems The fluorescent concentrator materials investigated in this work are active in the visible range of the solar spectrum. In this range, GaInP and GaAs solar cells have a high spectral response (see Fig. 4.52). The spectral response (SR) of GaInP solar cells matches the photoluminescence of dyes active at shorter wavelengths, such as BA241. GaAs solar cells are the better choice to completely use the emitted spectrum of the dyes active at longer wavelengths, such as BA856.
Fig. 4.52: The spectral response of a GaInP and of a GaAs solar cell in comparison to the edge fluorescence of different fluorescent collector materials used in this work. The fluorescence and the spectral response match very well. For the materials active at shorter wavelengths (BA241), GaInP solar cells are best suited, for the materials active at longer wavelengths (BA856), GaAs is the better choice.
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The spectral response only indicates how much current a solar cell generates at a certain wavelength depending on the incident power. For the system efficiency, the voltage of the solar cell is also important. GaInP solar cells have a band-gap of 1.85 eV, which corresponds to a wavelength of 670 nm. The drop in the spectral response that indicates the band-gap can be seen nicely in Fig. 4.52. The typical open circuit voltage (VOC) of a GaInP solar cell is in the region above 1300 mV. This compares to a VOC of typical silicon solar cells of about 600-700 mV. That is, assuming the same fill factor, nearly twice the energy can be utilized if a photon is converted by a GaInP solar cell instead of by a silicon cell. The band-gap of GaAs is at
1.43 eV and the typical VOC is above 1000 mV.
For the application on the edges of fluorescent collectors, the geometric dimensions of the solar cells had to correspond to the elongated form of the concentrator’s edges. At the beginning of this work, I chose the dimensions of the solar cells such that the solar cells were slightly larger than the edge area. Like this, it should be ensured that all emitted light is collected. These solar cells had an active area with heights of 3 mm and 6 mm and a width of 21 mm. To the end of the work, solar cells were designed for larger systems. This time the dimensions were chosen to be slightly smaller than the edges to avoid problems in the assembly of the systems. The active area was 49 mm x 5 mm. The solar cells were produced from the III-V solar cell group at Fraunhofer ISE.
The design of the contact grid of the solar cell must take into account the height of the expected current density during application. Therefore, concentrator solar cells are usually equipped with relatively many fingers. However, the achieved concentration ratios of fluorescent concentrators are relatively low and only part of the solar spectrum is used. In consequence, no special grid design is necessary. I calculated the optimum finger spacing and width with the simulation tool GridSim version4.2 [98]. Because the optimization showed a very broad peak and the specific irradiance on the solar cell was not determined beforehand, a uniform finger spacing of 500 µm was chosen. The finger width was 8 µm.
The solar cells were equipped with a single layer antireflection coating of 65 nm
Ta2O5, which is optimized for the emission range of the dyes between 550 and 650 nm [99].
The solar cells were bonded to a copper base to give mechanical stability. Solar cells and fluorescent collectors must be optically coupled so that the light from the collector enters the solar cells with the lowest possible losses. The optical coupling was realized
102 4.5 Fluorescent concentrator systems either with an acrylic color extended or with silicone. The acrylic color extender provides a mechanically more stable connection, while the optical quality of the silicone is superior.
4.5.2 Systems with different materials The presented organic fluorescent dyes achieve very high quantum efficiencies, but their absorption range is narrow in comparison to the solar spectrum. On the other hand, different dyes with different absorption ranges are available that cover at least the complete visible spectral range. Therefore, it is a rather obvious idea to combine different dyes to use a larger fraction of the solar spectrum. Already in the first research campaign in the 1980s, Wittwer et al. [51] achieved a conversion efficiency of 4% with a system that combined two 3 mm thick plates with different dyes in one stack with GaAs solar cells attached to the edges. The system was 40 cm x 40 cm in size and therefore quite large, so the achieved efficiency can be considered a very good result. The geometric concentration ratio, that is the ratio of the illuminated collector area to the solar cell area, was 16.7. The system produced around 3 times more energy than that the solar cells would have produced if they had been placed directly in the sun.
In section 4.3.2, I presented a method to determine the light guiding efficiency of different collector materials with a set of optical measurements. With this method, I selected promising materials, from which I realized systems of fluorescent collectors with attached solar cells. First, systems with only one material were realized and subsequently a stack with two materials from the most promising combination. The fluorescent collectors in these experiments had geometric dimensions of 2 cm x 2 cm and were 3 mm thick.
GaInP solar cells, as described in the previous section, were attached to the edges of the collectors. In these experiments, the used solar cells with 3 mm height all had efficiencies of 14.4±0.1%, under an AM1.5g spectrum. For the stack with two collector plates on top of each other, I used solar cells with 6 mm height. They all had efficiencies of 15.4±0.1%. The given accuracy reflects the efficiency distribution of the cells and not the absolute uncertainty. The purpose of the experiment was to find the most promising material combination. Therefore, it was important that the used solar cells had similar efficiencies so that the observed differences are a result of the material properties and not of the different solar cell efficiencies. At this point, the absolute height of the efficiency was of minor importance.
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The intensity of the used sun simulator was calibrated with a reference solar cell to 1000 W/m2. No further mismatch correction had been applied. Under all systems, a white bottom reflector made from BaSO4-coated aluminum was placed.
Fig. 4.53 displays the efficiencies of several realized systems. Only to one edge of each fluorescent concentrator solar cells were attached and the other edges were left open. The surroundings of the systems were covered with a black mask, so no light could enter the fluorescent concentrators from the side. As the purpose of this experiment was to compare different materials, the system had not to be optimized for the highest efficiency, e.g. with mirrors at the edges or by attaching solar cells to all four edges. The material denoted BA241 showed the highest efficiency of 2.5% in reference to the 4 cm2 area of the concentrator. The combination with a second material denoted BA856 increased the efficiency to 3%.
Fig. 4.53: Materials identified as promising by the optical measurements were used to realize systems of fluorescent concentrators and solar cells. The material denoted BA241 showed the highest efficiency of 2.5% in reference to 4 cm2 area of the concentrator. The combination with a second material increased the efficiency to 3%. From this stack a system with four solar cells, one at each edge, was built. This system had an efficiency of 6.7%.
From this stack a system with four solar cells, one at each edge, was built. The single solar cells had heights of 6 mm, so every solar cell received the light from both collectors. The four solar cells were interconnected in parallel. This system had an efficiency of 6.7%. A similar system with only one concentrator made from BA241 with four parallel interconnected GaInP solar cells had an efficiency of 5.1%.
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Fig. 4.54: A photograph of the described stack system before the remaining three solar cells were attached.
Fig. 4.55: The External Quantum Efficiencies of a single GaInP solar cell measured under direct illumination, a system with only one fluorescent concentrator (BA241) and of a stack system with two materials. Both systems featured four parallel interconnected GaInP solar cells attached to the edges. The combination of the two materials significantly extends the used spectral range.
It is important to mention that with 4 cm2 these systems are comparatively small. Therefore the concentration ratio is very small: 1.7 for the single fluorescent concentrator system and 0.8 for the stack system. So in fact, the stack system is a de- concentrator. Fig. 4.54 shows a photograph of the stack system before the four solar cells were attached. Fig. 4.55 presents the external quantum efficiency (EQE) of one used GaInP solar cell, of the system with only one fluorescent concentrator and of the stack system. The EQE shows how combining two materials extends the used spectral
105 4 Fluorescent Concentrators range. An additional side effect is also visible in Fig. 4.54. In the spectral range below 350 nm, the EQE of the fluorescent concentrator systems exceed that of the GaInP solar cell. The reason is that light absorbed in this range by the fluorescent dye is emitted at longer wavelengths where the EQE of the GaInP is higher.
Although this system achieved already a very high efficiency, it does not use the full potential of the material, because only GaInP solar cells were used. As we have seen in Fig. 4.52, GaInP does not absorb all photons emitted from the BA856 material. Therefore, I realized a system with GaInP and GaAs solar cells and the BA241 and BA856 materials. The efficiency of the used GaInP solar cells was 16.8±0.1%, and the efficiency of the GaAs solar cells 24.1±0.2%. To absorb all photons, the thickness of the fluorescent collectors was increased to 5 mm. No 5 mm thick sample was available from BA856, so a 3 mm and a 2 mm thick sample were optically coupled with silicone to form one 5 mm thick slab. Both collector plates were 5 x 5 cm2 in size. Two GaInP solar cells were optically coupled with silicone to adjoining edges of the BA241 slab, and likewise two GaAs solar cells to the BA856 slab (Fig. 4.56). In front of the remaining two edges of each collector plate, white reflectors made from Polytetra- fluoroethylene (PTFE) were placed. In this configuration, light that is reflected without change in direction reaches a solar cell after a maximum of two reflections. If the solar cells were attached to opposing edges, it would be possible that light beams bounce back and forth between the solar cell free edges without ever reaching a solar cell. Therefore, a higher efficiency is expected from the chosen geometry.
Fig. 4.56: Sketch of the system setup. On the left the top view is shown. Two GaInP solar cells were optically coupled with silicone to adjoining edges of the BA241 slab, and likewise two GaAs solar cells to the BA856 slab. In front of the remaining two edges of each collector plate and under the whole system, white reflectors made from Polytetrafluoroethylene (PTFE) were placed. They can be seen in the cross section on the right.
106 4.5 Fluorescent concentrator systems
The geometric concentration ratio is 5x for a single system with two attached solar cells. In the stack with two collector plates, the aperture area is still 25 cm2 but the number of solar cells has doubled, so for the stack the geometric concentration is 2.5x.
The system was assembled step by step. The solar cells were attached one by one to the collector plates. In the final system, the two GaInP solar cells were interconnected in parallel, and the two GaAs solar cells were separately connected in parallel. At each point, the IV-characteristic and the efficiency were measured in different configurations: the Ba241/GaInP and BA856/GaAs system separate from each other, the Ba241/GaInP on top of the BA856/GaAs system, and the Ba241/GaInP underneath the BA856/GaAs system. Under all configurations, a white reflector was placed. The efficiency for all systems was calculated in respect to the energy that is incident on the 5 cm x 5 cm collector area, as well as the short circuit current density was determined in respect to this area. Table 4.1 summarizes the important results, for the systems with already two attached and interconnected solar cells.
Measured independently, the single system with the BA856 collector plate and the attached GaAs solar cells has a higher efficiency than the system with the BA241 collector plate and the GaInP solar cells. This can be understood by considering the results of the spectral collection efficiency measurements again (see Fig. 4.25). The BA856 absorbs over a wider spectral range. More photons are collected and hence the short circuit current density is significantly higher. The higher current over- compensates for the lower voltage in comparison to the BA241/GaInP system. However, because of this wide absorption, when the BA856/GaAs is placed on top of the BA241/GaInP system in a stack, nearly no photons that can be used arrive at the lower BA241/GaInP system. Therefore, while the efficiency of the Ba856/GaAs hardly changes in the stack, the efficiency of the BA241/GaInP drops to around 1%. The mathematical sum of these two independently measured efficiencies is therefore 6.6%. It is better to place the BA241/GaInP system on top. In this way, all photons that can be potentially used by this system are absorbed in the BA241 collector and their energy is converted into electric energy at a higher voltage. The BA856/GaAs uses the remaining photons and ensures reasonable spectrum utilization. Nevertheless, the efficiency of the BA241/GaInP system on top of the BA856/GaAs system is lower than when it is measured independently. Without the BA856/GaAs, photons that pass the BA241 collector are reflected at the white bottom and have a second chance to be absorbed in the BA241 collector. In a stack, these photons are absorbed by the BA856. The mathematical sum of the two independently measured efficiencies reaches a very good value of 7.3%. In the most efficient system configuration, the EQE was measured for the two sub-systems (Fig. 4.57).
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Table 4.1: Overview of the achieved efficiencies in different system configurations using different fluorescent collector materials and GaInP and GaAs solar cells. The value with * is corrected for the spectral mismatch between AM1.5g spectrum and the spectrum of the sun simulator.
2 System VOC / mV JSC / (mA/cm ) FF K
BA241 1366 3.8 87% 4.6% 2 GaInP solar cell attached BA856, 1028 6.9 81% 5.8% 2 GaAs solar cell attached
GaAs solar cells in configuration BA856 on 1023 6.7 81% 5.6% top of BA241 GaInP solar cells in configuration BA856 on 1320 0.9 87% 1.0% top of BA241
Combined efficiency 6.6%
GaInP solar cells in configuration BA241 on 1355 3.2 87% 3.8% top of BA856 GaAs solar cells in configuration BA241 on 1008 4.3 82% 3.5% top of BA856
Combined efficiency 7.3%
Combined efficiency with 6.9%* mismatch corrected
The EQE measurement was performed with a filter-wheel monochromator that allowed illuminating the full fluorescent concentrator area. Therefore, the measurement yields the area-average of the EQE. It can be seen nicely that the two systems together cover a wide spectral range. In the EQE of the bottom GaAs/Ba856 system the effect of the absorption in the top system is visible as well. The bottom system shows also some response outside the absorption region (above 700 nm). This is an effect of the bottom reflector, which redirects transmitted light directly to the GaAs solar cells. The effects of the bottom reflector will be discussed in detail in section 4.5.4.
108 4.5 Fluorescent concentrator systems
Fig. 4.57: External quantum efficiency measurements of the two subsystems. The system made from BA241 with two attached GaInP solar cells was placed on top of the system made from BA856 with two attached GaAs solar cells. It can be seen nicely that the two systems together cover a wide spectral range. In the EQE of the bottom system one can clearly see the effect of the absorption in the top system.
The irradiance of the used sun simulator was calibrated with a reference solar cell to be equivalent to 1000 W/m2 under the AM1.5g spectral distribution. However, the spectral response of the reference solar cell and the very special response of the two fluorescent concentrator systems do not match. With the EQE data the mismatch between the spectral response of the used reference cell and of the sub-systems could be calculated and a correction factor be determined that takes into account the differences in the spectral distribution between the spectrum of the sun simulator and the AM1.5g spectrum based on the IEC60904-3 Ed.2 (2008) norm spectrum for AM1.5g non concentrating conditions. It turns out, that with that mismatch correction the efficiency is only 6.9%, which is still a very good value but slightly less than the world record efficiency of 7.1% [40]. Because of the very special spectral characteristics of the systems, the mismatch correction has a high uncertainty and is very sensitive to the used spectrum. A mismatch correction calculated with an only slightly different, older norm spectrum yielded an efficiency of around 7.0%.
The geometric concentration ratio of the system is 2.5x. For a commercial application the system size still has to be increased considerably. In larger systems, the number of
109 4 Fluorescent Concentrators attached solar cells is bigger so that by adequate cell interconnections the current or the voltages of the GaInP and GaAs sub-system can be matched and an integration into one module is possible without any problems. Current matching could also be achieved by producing the GaInP and GaAs solar cells in different sizes.
4.5.3 Systems with silicon bottom cells Until now, materials are missing that are active in the infrared and show high absorption and high quantum efficiency, which is partly due to principal problems associated with organic dyes [47]. The development of new materials, such as luminescent nanocrystals, could overcome this limitation. Some types of nanocrystals have shown absorption and luminescence in the infrared, but quantum efficiencies are still relatively low, e.g. [100]. Another option is to combine the current standard silicon module configuration with fluorescent concentrator systems. This concept is the topic of this section.
Common dyes for fluorescent concentrators do not absorb but transmit radiation in the near infrared. That is why they cannot use this spectral region. On the other hand, the transmitted light can be used to illuminate another solar cell, e.g. a silicon solar cell. Silicon solar cells are especially well suited for this purpose, because their spectral response is highest in the near infrared (Fig. 4.59). This enables a system design where silicon solar cells at the bottom of the fluorescent concentrator convert the infrared radiation (Fig. 4.58). Such a configuration allows for efficient utilization of both visible and infrared radiation. As discussed in the previous section, nearly twice the energy can be utilized if a photon is converted by a GaInP solar cell instead of by a silicon cell.
Fig. 4.58: The combination of a fluorescent concentrator with solar cells attached to the edges and of a common module with silicon solar cells at the bottom allows for efficient utilization of both visible and infrared radiation.
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Fig. 4.59: Transmission of typical fluorescent concentrator materials and the spectral response of a silicon solar cell. The spectral region that is transmitted by the fluorescent concentrators coincides very well with the spectral region in which the spectral response of the silicon solar cell is the highest.
The placement of the GaInP solar cells at the edges of the fluorescent concentrator and of the silicon solar cells underneath offers a high degree of freedom for cell inter- connection. In consequence, a good current- and voltage matching should be possible.
In a first tentative realization, I prepared a fluorescent concentrator system with four GaInP solar cells and a 2 cm x 2 cm fluorescent concentrator. The fluorescent concentrator contained the dye BA241 and was 3 mm thick. I performed this experiment at an early stage of my PhD. At that time no GaInP solar cells with fitting dimensions were available. I used 2 cm x s2 cm GaInP solar cells instead. The solar cells were coupled to the edges of the fluorescent concentrator and the remaining area was covered with black material. The four GaInP solar cells were connected in parallel.
Without the fluorescent concentrator on top, the silicon solar cell had an efficiency of 16.7%. This efficiency was measured under a sun simulator. The intensity was calibrated using a reference solar cell made from silicon. The calibration considered the mismatch between the sun simulator spectrum and the AM1.5g spectrum and the spectral response of a typical high-efficiency silicon solar cell. The same calibration was used for measuring the silicon solar cell, the fluorescent concentrator system and a combination of both. The uncertainty for relative comparisons is in the range of 1-2%
111 4 Fluorescent Concentrators relative. The absolute uncertainty is significantly higher, because of uncertainties in the spectral mismatch correction and the use of a typical value instead of a value based on external quantum efficiency measurements. Anyway, it is the relative comparison we are interested in at the moment.
When the fluorescent concentrator system is placed on top of the silicon solar cell, light that would have been used by the silicon solar cell without any fluorescent concentrators is now redirected towards the GaInP solar cells at the edges of the collector. In consequence, the efficiency measured for the silicon solar cell alone drops to 14.0% with the fluorescent concentrator system on top. The fluorescent concentrator system on top had an efficiency of 3.7% in reference to the 4 cm2 area of the fluorescent concentrator. This efficiency is lower than the efficiencies reported in section 4.5.2, because here no white reflector is placed under the fluorescent concentrator system. The silicon solar cell, in contrast, hardly reflects any light because most is absorbed. Adding the two efficiencies, the total system efficiency is 17.7%, which is significantly higher than the efficiency of the silicon solar cell alone (Fig. 4.60).
Fig. 4.60: Comparison between a silicon solar cell and a system consisting of the same silicon solar cell under a fluorescent concentrator and a parallel interconnection of four GaInP solar cells at the edges of the fluorescent collector. The efficiency is significantly increased by the addition of the fluorescent concentrator system.
112 4.5 Fluorescent concentrator systems
The positive effect of the fluorescent concentrator system can be seen also in the comparison of the spectral efficiencies of the different systems (Fig. 4.61). The spectral efficiency is the fraction of the incoming energy that is utilized at a specific wavelength. The efficiency is calculated by multiplying the spectral response, which gives the current per irradiating power at a specific wavelength, with the voltage at the maximum power point. The spectral efficiency of the silicon solar cell is decreased in the absorption range of the dye (around 400 – 500 nm). However, in this region the fluorescent concentrator system is active. The sum of both efficiencies is significantly higher than the efficiency of the silicon solar cell alone.
Fig. 4.61: Spectral efficiencies of the silicon solar cell under the fluorescent concentrator system, of the parallel interconnection of four GaInP solar cells attached to the edges of the fluorescent concentrator and the sum of both. It can be seen clearly how the fluorescent concentrator system increases efficiency in the region of 400 to 500 nm.
When the solar cells with fitting dimensions were available a more developed system was realized. Again a fluorescent concentrator made from BA241 with 3 mm thickness and an area of 4 cm2 was used. This time four GaInP solar cells with 21 mm x 3 mm active cell area were used. They were optically coupled with an acrylic color extender to the edges of the fluorescent concentrator.
A high-efficiency silicon solar cell with an area of 2 cm x 2 cm was placed under the fluorescent concentrator. The silicon solar cell featured a random pyramids front texture, a 105 nm SiO2 antireflection coating and surface passivation layer. The back contacts were realized as aluminum point contacts.
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To enable the contacting of the front, the fluorescent concentrator system was placed on a 1 mm thick frame made from white PTFE, which was placed around the silicon solar cell. The efficiency of the silicon solar cell alone was 19.0±0.1%. The calibration was done in the same way as described above. The noted uncertainty is the standard deviation from repeated measurements. Under the fluorescent concentrator the efficiency dropped to 14.5±0.1%. The parallel interconnection of the four GaInP solar cells attached to the fluorescent concentrator had an efficiency of 4.3±0.1% in reference to the 4 cm2 area of the fluorescent concentrator when it was placed on top of the silicon solar cell. With 18.8±0.1% the efficiency of this system is about the same as the efficiency of the silicon solar cell alone of 19.0±0.1% (Fig. 4.62). That is, no improvement could be achieved with this setup, even though the efficiency of the fluorescent concentrator system itself did improve.
Fig. 4.62: Efficiency of a 2 cm x 2 cm silicon solar cell and of the same solar cell under a fluorescent concentrator plate of 2 cm x 2 cm and 3mm thickness. Four GaInP solar cells were optically coupled to the edges of the fluorescent concentrator. Without the concentrator the silicon solar cell had an efficiency of 19.0±0.1%. Under the fluorescent concentrator the efficiency dropped to 14.5±0.1%. The parallel interconnection of the four GaInP solar cells placed on top of the silicon solar cell had an efficiency of 4.3±0.1% in reference to the 4 cm2 area of the fluorescent concentrator. No improvement in efficiency was achieved by the addition of the fluorescent concentrator system.
114 4.5 Fluorescent concentrator systems
Although no increase in efficiency was achieved, the fluorescent concentrator might be useful nonetheless. The fluorescent collector acts as covering of the solar cell and could replace the front glass in later modules. Realizing the front glazing with such a fluorescent concentrator system would therefore compensate for the module losses of the photovoltaic system. Nevertheless, system efficiency has to increase significantly to make such systems commercially attractive. A photonic structure as discussed in the next section is one option to increase efficiency. Furthermore, an antireflection coating of the silicon solar cell optimized for the spectrum transmitted by the fluorescent concentrator would increase the performance of the silicon solar cell. Additionally, this antireflection coating could be adapted to reflect more of the light usable by the fluorescent concentrator system. In consequence, also the output of the solar cells at the edges of the collector would rise.
4.5.4 The effect of photonic structures In section 4.1, I showed that the escape cone of internal total reflection is one of the major loss mechanisms of fluorescent concentrators. These losses can be significantly reduced with spectrally selectively reflective filters. Such filters can be realized with photonic structures (section 4.2). In this section I will investigate the effect of such structures on the efficiency of fluorescent concentrator systems.
A possible realization of such a photonic structure is a so-called Rugate filter. It features a continuously varying refractive index profile, which results in the suppression of side lobes that would cause unwanted reflection and loss of usable radiation. In this study, I used commercially available filters (5x5cm2) optimized for the BA241 material. Thy were produced from mso-Jena [83] by Ion-Assisted Deposition (IAD). The filters had an antireflection coating adapted to the absorption range of the dye. The reflection of the filter, the absorption and the photoluminescence of the BA241 fluorescent concentrator are shown in Fig. 4.63. The filter transmits the light in the absorption range of the dye and it reflects the emitted light and therefore has exactly the desired properties.
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Fig. 4.63: Reflection spectrum of the used photonic structure and the absorption and photoluminescence of the fluorescent concentrator the filter was designed for. The reflection of the structure very nicely fits the emission peak of the dye in the concentrator.
To investigate how the filter increases the light guiding efficiency of the concentrators I attached a 21 x 3 mm2 GaInP solar cell on one rim of a 3 mm thick fluorescent concentrator with a size of 2 x 6 cm2 (the cell was attached to the 2 cm rim). A white
BaSO4 bottom reflector was placed under the system and the EQE of the system was measured, with and without the filter on top. During the EQE measurement, the system was illuminated with a 3 mm wide spot in 1 cm distance to the solar cell. Fig. 4.64 shows the comparison of the two measurements and additionally the reflection of the filter. Obviously the filter reduces the efficiency in the region where it is reflective, which is the case for the wanted reflection above 550 nm and also for the unwanted reflection below 380 nm. On the other hand, the filter increases efficiency significantly over a broad spectral range, because it traps the emitted light and guides the light to the sides.
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Fig. 4.64: External Quantum Efficiency (EQE) measurement of a system with a GaInP solar cell attached to a fluorescent collector of 3 mm thickness made from BA241 under which a BaSO4 bottom reflector was placed with and without a photonic structure on top of the collector. Additionally the reflection of the photonic structure is shown. The efficiency is increased significantly over a broad spectral range, because more emitted light is trapped and guided to the sides.
I also realized a system with a 5 mm thick, 5 x 10 cm2 fluorescent concentrator to which I optically coupled one GaInP solar cell with silicone. The solar cell had an active area of 5 x 49 mm2. Hence the relation between illuminated fluorescent concentrator area and solar cell area constitutes a geometric concentration ratio of 20x. The solar cell had an efficiency of 16.7% under AM1.5g illumination. White PTFE served as bottom reflector and also as reflector at the edges that were not covered by solar cells. Without the filter this system had an efficiency of 2.6±0.1% (uncertainty is again for relative comparison) in reference to the 50 cm2 area of the system. The filter increased the efficiency to 3.1±0.1%, which constitutes an efficiency increase of around 20% relative. With the achieved efficiency of 3.1% and the concentration ratio of 20, the realized fluorescent concentrator produces about 3.7 times more energy than the GaInP solar cell had produced on its own. This system is further analyzed in the following section 4.5.5, where size dependent effects are investigated.
The efficiency increase of 20% is already a great success since it shows that photonic structures reduce the escape cone losses significantly. However, the used filter is a multilayer system and therefore costly to produce. In section 4.2.3, I introduced the opal, which is a three-dimensional photonic structure. The opal has the advantage that
117 4 Fluorescent Concentrators it can be produced in a self-organizing, potentially low-cost process. Such opals were realized by Lorenz Steidl from university of Mainz by the self-organization of monodisperse PMMA beads (Fig. 4.65).
Fig. 4.65: SEM image of an opaline film produced from PMMA beads at the University of Mainz. This is a special three-dimensional photonic crystal that can be produced by the self-organization of monodisperse PMMA beads. This film was produced on a sacrifice layer so it could be transferred to a fluorescent concentrator later on.
Producing opaline films directly on the PMMA of the fluorescent collector is difficult, since the PMMA surface is hydrophobic. However, the surface can be made hydrophilic by an oxygen plasma treatment. An alternative approach is producing the opaline film on a sacrifice layer and transferring the film to the fluorescent concentrator.
To investigate the effect of the opal on the collection efficiency of the fluorescent concentrator, an opaline film with properties adapted to the BA241 material was produced on a glass substrate. The diameter of the PMMA beads was 256 nm and around 50 layers of beads were deposited on the glass. The reflection of the opal on the glass is shown in Fig. 4.66 in comparison to the absorption and fluorescence of the dye.
118 4.5 Fluorescent concentrator systems
Fig. 4.66: The reflection of an opaline film made of 256 nm PMMA beads in comparison to the absorption and emission of the fluorescent concentrator. Up to now, the reflection peak of the photonic structure at the emission wavelengths of the dye is not high enough to over compensate the losses due to the reflection of the photonic structure in the absorption range of the dye.
The sample was placed on top of a 2 cm x 2 cm sample of BA241 with one GaInP solar cell attached to one edge. Under the bottom and around the free edges white PTFE reflectors were placed. The efficiency was determined with and without the opal on top. Without the photonic structure the efficiency was 3.3%, but dropped with the opal on top to 3.0%. The reasons for this drop are that for one there is more than 10% unwanted reflection in the absorption range of the dye, which causes severe losses. This unwanted reflection is mostly caused by stacking faults that cause scattering. Second, the reflection peak in the emission region of the dye is not perfectly aligned to the emission spectrum. Moreover, the reflection only peaks at around 70%. Therefore not all the light emitted into the escape cone is reflected back into the concentrator
The reflection can be increased with depositing opaline films with more layers of PMMA beads and by reducing the stacking faults. A reduction of stacking fault would result in a reduction of the unwanted reflection as well. However, increasing the number of layers makes a stacking fault-free assembly of the beads less likely. In consequence, progress in the preparation of the film is necessary, to make it technologically viable to deposit opaline photonic structures on large area fluorescent concentrators.
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4.5.5 The influence of system size on collection efficiency Many losses and especially the escape cone losses depend on the average path the emitted light has to travel until it reaches a solar cell at the edge of the collector plate. Therefore, it is very interesting to investigate the effect of the size of the fluorescent concentrator on the collection efficiency, especially in conjunction with photonic structures. To investigate the size dependency, I used the system described in the 2 previous section with the 2 x 6 cm fluorescent concentrator. A white BaSO4 reflector was placed beneath the concentrator. The illuminated area was then reduced stepwise with the help of black blinds, placed on the fluorescent concentrator (Fig. 4.67) and an IV-measurement was performed for each area size.
Fig. 4.67: Sketch of the measurement setup for the investigation of the size effects. The illuminated area was reduced in 1 cm steps with the help of black blinds, placed on the fluorescent concentrator. The area was reduced starting from the side opposite the solar cell.
Fig. 4.68 displays the open circuit voltage VOC and the short circuit current ISC. The error bars indicate the standard deviation in repeated measurements. When the illu- minated area is increased, more light is collected. Therefore, the total short circuit current increases, and as a consequence the open circuit voltage as well. However, the short circuit current density JSC, calculated by dividing the short circuit current by the particular illuminated area, decreases with increasing area (see Fig. 4.69). The probability of a photon to reach the solar cell at the edge is much lower, if it stems from an absorption/emission process further away from the solar cell. The reason is that parasitic absorption, re-absorption and emission events and the associated escape cone losses are becoming more likely with an increasing path length of the photon.
120 4.5 Fluorescent concentrator systems
Fig. 4.68: Open circuit voltage VOC and short circuit current ISC of the fluorescent concentrator system depending on the illuminated area. With increasing illuminated area, more light is collected and reaches the solar cell at the edge, so the total short circuit current ISC increases. As a consequence, the voltage increases as well.
Fig. 4.69: The short circuit current density JSC depending on the illuminated area. With increasing area, the short circuit current density drops. The reason is that the probability to reach the solar cell at the edge decreases for the photons, which stem from absorption/emission processes further away from the solar cell.
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Fig. 4.70 shows the dependence of the overall system efficiency on the illuminated area. Additionally, the experiment was repeated with a black material and with the photonic structure from mso-Jena under the fluorescent concentrator and with and without the photonic structure on top. The efficiency drops in all cases with increasing area, because the relative effect of the voltage increase is smaller than the relative decrease of the current density. This can be understood as the voltage only increases logarithmically with the current, while the losses should follow some kind of exponential dependence on the average path length, which increases roughly linearly with the area in our configuration. However, the effect of the decreasing efficiency is slightly exaggerated. In an optimized fluorescent concentrator system, one would choose more quadratic geometric dimensions and would place solar cells on all edges of the concentrator. This would reduce the average path length of the light and therefore decrease the path length associated losses.
Fig. 4.70: System efficiency in dependence of the illuminated area. Efficiencies were measured with different bottom reflectors placed under the system and with and without a photonic structure on top. For all systems, efficiency decreases with increasing illuminated area. The error bars indicate the standard deviation in repeated measurements. For these small sizes, a white bottom reflector yields the highest efficiencies.
The differences between the different bottom and top configurations are very enlightening. For all sizes, the efficiencies are the lowest for the case where there is a black bottom material. With a black bottom, all light that passes the fluorescent
122 4.5 Fluorescent concentrator systems concentrator or leaves it in the bottom direction after emission is absorbed and lost. In contrast the photonic structure reflects in the emission range of the dye. If it is placed under the concentrator it increases the efficiency, because it reflects emitted light back into the concentrator. It is important to note that all the light entering the concentrator from the outside is refracted in a way that it would leave the concentrator already after one pass to the opposite surface. So to stay in the concentrator or to become useful it has to be reabsorbed, scattered or absorbed by the solar cell.
Adding the photonic structure on top of the concentrator does not increase the efficiency for the investigated sizes, but reduces it for the small areas. For larger areas, there are no significant differences between the results with and without a photonic structure on top. This is true both for the case with a photonic structure at the bottom and with the white bottom reflector. To understand this, it is helpful to look in more detail into how the white bottom reflector increases the efficiency.
Fig. 4.71: Comparison between an EQE measurement with a white bottom reflector and with a black bottom for a system with a fluorescent concentrator 2 x 2 cm2, 3 mm thick and four parallel interconnected GaInP solar cells at the edges. The illumination spot was located in the center of the concentrator. One can see that the white bottom reflector increases the efficiency in the absorption region of the dye. Especially in the weaker absorbing region a second chance to be absorbed after a reflection from the bottom increases the light collection.
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Fig. 4.71 shows a comparison between an EQE measurement with a white bottom reflector and with a black bottom. Because the white bottom strongly reflects over a broad spectral range, it gives the light a second chance to be absorbed which lies in the absorption range of the dye, but has passed the fluorescent concentrator without being absorbed. Additionally, light outside the absorption range of the dye but within the usable wavelength range of the solar cell is also reflected and therefore has the chance to reach the solar cell directly or by scattering events.
Fig. 4.72: EQE measurements of the 2 x 6 cm2 fluorescent concentrator system with white bottom reflector in different distances to the solar cell. This measurement helps to understand the effect of the white bottom reflector placed under the fluorescent concentrator. The EQE increases significantly with decreasing distance to the solar cell. It increases also in the wavelength range above 550 nm in which the fluorescent concentrator hardly absorbs. This is a clear hint that light is directly reflected onto the solar cell. For small distances this is a quite significant contribution to the overall light collection.
Fig. 4.72 displays external quantum efficiency measurements of the described 2 x 6 cm2 system with white bottom reflector for a variation of the distance between the illumination spot (3 mm diameter) and the solar cell. With smaller distances efficiency also increases strongly in the spectral region above 550 nm. In this region the dye does not absorb. This finding supports the explanation that light is reflected directly to the solar cell from the bottom reflector. As we can see, this absorption-less
124 4.5 Fluorescent concentrator systems light collection contributes significantly to the overall light collection for small areas. Since the reflection of the photonic structure is designed to be high in the emission region of the dye, which is exactly the spectral range above 600 nm, it prevents the light in that region from entering the system and to be directly led to the solar cell by reflection from the bottom. Under these circumstances, although the photonic structure increases the collection of the emitted light, the overall system performance decreases for small areas in comparison to the white bottom reflector alone.
The effect of the absorption-less light collection is present in the system that combined different materials and spectrally matched solar cells, which has been investigated in section 4.5.2, as well. This system reached an efficiency of 6.9% and it would have been great to increase this efficiency even further by applying a photonic structure. Unfortunately, the application of a specially adapted photonic structure did not increase efficiency, because especially the system with the GaAs solar cells attached profited significantly from the absorption-less light collection. Therefore, until now the integration of all features of the advanced fluorescent concentrator system design into one system has not been successful.
However, the effect of the area close to the solar cell is of less relevance for larger systems. Furthermore, the losses due to re-absorption and emission become more important with increasing size of the fluorescent concentrators. That is, the beneficial effect of the photonic structures should be more pronounced for bigger systems. Accordingly, we have seen in the previous section that the photonic structure increased the efficiency of a larger system with 5 x 10 cm2 area by 20% relative. Fig. 4.73 shows the spatially resolved light collection efficiency as it was measured with a Light Beam Induced Current (LBIC) setup on this system with a photonic structure on top. One can see that the collection efficiency is highest close to the solar cell. The efficiency drops with increasing distance to the solar cell and closer to the solar cell free edges. Close to the edges the probability for emitted light to hit the edge surface with an angle smaller than the critical angle of total internal reflection is higher for simple geometrical reasons. If the light leaves the collector at the edges, not all the light is reflected back because of the imperfect reflection of the white reflectors. Interestingly, the collection efficiency increases as well close to the edge opposite the solar cell. This effect was observed in different systems of varying sizes. Therefore it can not be considered a simple measurement artifact. Very likely, light outside the absorption range of the dye is somehow redirected to the solar cell by the bottom and the edge reflector, or by the actual edge of the collector. However, a precise explanation is yet to be developed.
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Fig. 4.73: Light Beam Induced Current (LBIC) scan of the 10 x 5 cm2 sample described above. A photonic structure was placed on top of the fluorescent concentrator during the measurement. A white reflector made from PTFE was placed at the bottom and the edges without solar cells. The edge with the attached solar cell is located at the right in this picture. Not the full collector area was scanned to avoid contact of the scanning head with the wiring of the system. One can see that the collection efficiency is highest close to the solar cell. The efficiency drops with increasing distance to the solar cell and closer to the edges.
Fig. 4.74: Averaged linescans in x-direction from an LBIC scan with and without photonic structure. Close to the solar cell the efficiency is lower with the photonic structure, because it reduces the effectiveness of the bottom reflector for small distances as discussed extensively above. However, over most of the fluorescent concentrator collection efficiency is significantly higher with a photonic structure, resulting in a relative efficiency increase of 20%.
126 4.5 Fluorescent concentrator systems
Fig. 4.74 compares the averaged linescans in the x-direction of the LBIC scan shown in Fig. 4.73 and of a scan without photonic structure. The average was taken from 1.25 to 2.5 cm in the y-direction. Close to the solar cell the efficiency is lower with the photonic structure. This is the result of the reflection of light that would have reached the solar cell by scattering as discussed extensively above. However, over most of the fluorescent concentrator, collection efficiency is significantly higher with a photonic structure, resulting in the relative efficiency increase of 20%. This is a clear demonstration of how photonic structures can help to increase the collection efficiencies of larger fluorescent concentrator systems.
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4.6 The future of fluorescent concentrators
In the previous section, I demonstrated that the collection efficiency of fluorescent concentrator systems can be increased by two independent measures. One approach is to combine different dyes to enlarge the used spectral range. Like this, a high efficiency of 6.9% could be achieved. The other approach is to increase the collection efficiency by the application of a photonic structure, which acts as a bandstop reflection filter in the emission range of the dye. This resulted into a relative efficiency increase of 20% with a commercially available filter. With the achieved efficiency of 3.1% and the concentration ratio of 20, the realized fluorescent concentrator system produces about 3.7 times more energy than the used GaInP solar cell had produced on its own. The detailed analysis of size effects showed that photonic structures are especially beneficial for larger systems. Nevertheless, to make fluorescent concentrators commercially attractive, system sizes and efficiency have to be increased. So the question is: how can fluorescent concentrator systems be further developed from this point?
One rather obvious task is to combine the two investigated approaches into one system: photonic structures and the combination of different materials. However, this will be a challenging task because the reflection of the photonic structure and the absorption/emission characteristics of the dyes have to be aligned in a way that one component does not obstruct the effect of the other feature.
Additionally, the used spectral range must be extended into the infrared in order to achieve competitive efficiencies. From the quantum efficiency measurement presented in the previous section it is clear that in the active region of the dyes the systems reach already quite high quantum efficiencies of up to 45%. Also high voltages of 1320 mV at the maximum power point were achieved. In consequence the main reason for the low overall efficiency below 10% is that only the visible part of the spectrum is used. If one reached 45% quantum efficiency in the range from 650 nm to 1050 nm as well, one could expect an extra current density of around 12 mA/cm2. If the luminescent material required for this purpose emitted in the region between 1050 and 1125 nm, the emitted light could be used by a silicon solar cell, which reaches a maximum power point voltage of around 580 mV. The extra silicon solar cell fluorescent concentrator system then had an efficiency of nearly 7%, which would result into an overall system efficiency of nearly 14%. At this point, this is a rather hypothetical calculation, but it highlights how promising it is to develop materials which show highly efficient luminescence in the infrared. Luminescent nanocrystals from CdSe, CdT, PbSe or PbS
128 4.6 The future of fluorescent concentrators could be promising candidates. However, the interesting spectral region is unfortunately located in between the active regions of standard sized luminescent nanocrystals from these materials.
Also the photonic structures can be further developed. The photonic structures should be deposited directly onto the fluorescent concentrators. This reduces the number of boundaries and therefore unwanted reflections. With an adequate design, the photonic structures can act as an antireflection coating in the absorption range of the dye and as reflector for the emitted radiation at the same time. In this configuration, reflection and escape cone losses are reduced simultaneously. But also even more radical photonic concepts are possible, as I will discuss in the following section.
4.6.1 The “Nano-Fluko” concept We have seen before that photonic structures reduce the escape cone losses. However, even with a photonic structure, light emitted into the escape cone is more frequently subject to loss events. Because it is emitted into a steep angle in respect to the front surface it has a very long effective path until it reaches a solar cell, and therefore suffers more from path length dependent losses. Hence, it would be very beneficial to suppress emission into these unfavorable directions completely. This could be achieved if the photonic structure were so close to the emission process that it restricts emission to certain directions.
Fig. 4.75: Conceptual sketch of a “Nano-Fluko”. A very thin layer of luminescent material with thickness t in the range of wavelength O of the emitted light is placed between two photonic structures, e.g. Bragg stacks. The photonic structures transmit light in the absorption range of the luminescent material with an energy E1. They are reflective in the emission region (E2) of the luminescent material. Because the layer with the luminescent material is so thin, the photonic structures suppress the emission into unfavorable directions.
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One possible realization would be a very thin layer of luminescent material between two photonic structures, e.g. Rugate filters or Bragg stacks (Fig. 4.75), to form a “Nano-Fluko”. In such a configuration, the emission of the light would be restricted to a plane parallel to the photonic structure. Galli et al. showed that the emission of Er3+ can be strongly enhanced, if it is incorporated in a photonic crystal waveguide and that efficient waveguiding occurs [101, 102]. Therefore there is first experimental evidence that such a system can work, and it is an interesting approach to apply this concept to fluorescent concentrators.
Another realization could be a photonic crystal fiber doped with a luminescent material (Fig. 4.76). However, to design the photonic structure around the fiber with the right spectral selectivity will be a demanding task. On the other hand, such a realization would enable very interesting application opportunities. For instance, the fibers could be woven into a flexible fabric with the properties of a fluorescent concentrator.
Fig. 4.76: Alternative realization of a “Nano-Fluko”. The luminescent material is incorporated into a photonic crystal fiber. If the photonic shell is designed with the right spectral selectivity, the fiber could accept light in the absorption range (E1) of the luminescent material from all directions. Emission with energies (E2) would be restricted to the direction of the fiber.
Probably a more realistic option is to incorporate the luminescent material directly into the photonic structure. This could be done for example with an opaline film made from PMMA beads that incorporate much smaller luminescent nanocrystals (Fig. 4.77). If
130 4.6 The future of fluorescent concentrators the optical band-gap in the emission range of the dye is incomplete, emission into certain directions is allowed and effective light guiding occurs.
Fig. 4.77: Sketch of “Nano-Fluko” realized by incorporation of the luminescent material directly into the photonic structure. This could be done for example with an opaline film made from PMMA beads that incorporate much smaller luminescent nanocrystals. If the optical band-gap in the emission range of the dye is incomplete, emission into certain directions is allowed and effective light guiding occurs.
For all the suggested options for realization, several layers with the same dye will be needed to achieve sufficient absorption. Attaching solar cells to these layers, preferably different types of solar cells to layers with different dyes, is a challenge. In Fig. 4.78 two different options are shown. One option is to produce different types of solar cells on one chip, e.g. with a MOVPE-process from III-V semiconductors. Because the required areas will be very small, this could be viable from a commercial point of view as well. Preferably, contact fingers should be aligned between the light guiding layers such that no reflections losses occur. An alternative option would be to vertically cut through conventional tandem solar cells in a process comparable to that used for sliver cells [103]
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Fig. 4.78: Two options of how a “Nano-Fluko” system complete with solar cells could be realized. To achieve good absorption several layers with luminescent materials must be stacked onto each other. The combination of different materials ensures good utilization of the solar spectrum. On the right, the attachment of solar cells made from different materials on one common substrate is shown. The contact fingers should be aligned with the photonic structures so no shading losses occur. On the left, the option is shown to cut a standard tandem solar cell vertically, similar to the sliver cell process and to attach such vertical cuts to the edges of a “Nano- Fluko”.
Although this concept is pretty advanced and its realization has not yet been undertaken, it might be a very interesting option for the future development of fluorescent concentrators. A patent application has been filed for this concept.
132 5 Upconversion
This chapter deals with upconversion. An upconverter generates one high- energy photon out of at least two low-energy photons. At the beginning, I will highlight by which mechanisms upconversion can occur and will introduce the theoretical concepts describing upconversion. I will discuss which materials are suitable as upconverter and show results of extensive optical
characterization of the investigated erbium doped NaYF4. This includes absorption measurements, time and intensity resolved photoluminescence measurements and calibrated photoluminescence measurements to directly measure upconversion efficiency. Based on the experimental results and the theory a simulation tool that models the upconversion dynamics is developed. Finally, experimental investigations on systems with upconverting material attached to silicon solar cells will be presented. The two diploma students I ministered during my PhD, Philipp Löper and Stefan Fischer, both contributed very significantly to the results presented in this section. More details on many subjects can be found in their diploma theses [104, 105].
5.1 Introduction to upconversion
Silicon solar cells lose about 20% of the energy incident from the sun because photons with energy below the band-gap are transmitted straight through the device. Upconversion of photons with energies below the band-gap is a promising approach to overcome these losses. An upconverter generates one high-energy photon out of at least two low-energy photons. For most materials, this involves an intermediate energy level, which is excited by the absorption of the first photon. From this level, a higher excited state can be reached after the absorption of the second photon. If the electron returns directly to the ground state via radiative recombination, one high-energy photon is emitted. Depending on the involved energy levels, this high-energy photon can create a free charge carrier in the solar cell. The concept of upconversion is visualized in Fig. 5.1.
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Fig. 5.1: Bifacial solar cell with an upconverter on its rear side. Sub-band-gap photons (red arrows) are transmitted through the solar cell but absorbed in the upconverter, which is excited successively. By recombination to the ground state, the upconverter emits a photon with sufficient energy to be absorbed by the solar cell (green arrows).
Such an additional upconverter pushes the theoretical efficiency limit for a silicon solar cell illuminated by non-concentrated light from close to 30% [16] up to 40.2% [10]. A big advantage of upconversion is that the upconverter can be placed at the back of the solar cell, as the sub-band-gap photons are transmitted through the solar cell. In this manner, the upconverter does not affect the operation of the original cell. All improvements are real gains, since they come on top of the original performance of the solar cell. Upconversion can be used in conjunction with classical silicon solar cells. So upconversion addresses the fundamental problem of transmission losses, while still retaining the advantages of silicon photovoltaic devices.
134 5.2 The potential of upconversion and ways to increase upconversion efficiency
5.2 The potential of upconversion and ways to increase upconversion efficiency
In this section, I will investigate which efficiency increase can be expected from an additional upconverting system and I will document what has been achieved so far. As the achieved efficiencies are rather low, I will discuss how the upconversion efficiency can be increased. This will comprise a system concept that combines fluorescent concentrators and upconversion. This concept has been developed during my work on this PhD thesis. A second concept to be presented is the use of plasmon resonances. These two concepts will be revisited in following chapters, where theoretical and experimental studies on these concepts are presented.
5.2.1 The potential of upconversion The theoretical limit for the efficiency of a solar cell with additional upconverter has been calculated by Trupke et al. [10]. For a solar cell with a band-gap like silicon illu- minated by non-concentrated light the limit is 40.2%. For concentrated illumination and an ideal band-gap of 1.86 eV, the limit efficiency is 61.4%. These calculations are based on a description of the upconverter/solar cell system by an equivalent circuit with four solar cells and detailed balance calculations and are highly idealized. A more realistic impression of what can be expected from upconversion can be obtained by considering the extra current in the solar cell that could be generated by the upconverted photons.
The number of photons in the AM1.5g solar spectrum with energies below the band- gap of silicon of 1.12 eV is 1.30x1021m-2s-1, which are 30% of the total incident photons. These photons carry 19.2% of the whole energy of the sun’s radiation. If all of these photons generated one free electron in the solar cell, they would yield an extra current of 20.7 mA/cm2. This and the following numbers depend on the spectrum data used for the calculations. I used data configured by Stefan Winter, which are orientated on the IEC60904-3 Ed.2 (2008) norm spectrum for AM1.5g non concentrating conditions and are used by the PTB for calibration.
At least two photons are needed to create one photon via upconversion that has enough energy to create a free electron-hole pair. The maximum extra current achievable with upconversion is therefore 10.4 mA/cm2 only. To achieve this current, it is necessary that always one low-energy photon is combined with a higher energy photon, such that their combined energy exceeds the band-gap. This could be achieved, if the involved energy levels of the upconverter have different energy gaps between them.
135 5 Upconversion
In this work, I will use erbium-based upconverters, because they have shown the highest upconversion efficiencies at present. The absorption range of trivalent erbium is between 1480 and 1590 nm. If all photons with wavelength between the band edge of silicon and 1590 nm were used, this would result into an extra current of 3.0 mA/cm2. This value considers the fact that at least two photons are necessary to create an upconverted photon with sufficient energy to create a free electron-hole pair in the solar cell. High-efficiency solar cells produced at Fraunhofer ISE from n-type silicon have reached efficiencies above 23% [106] and show typically short circuit current densities of 40 mA/cm2. That is, short circuit current density and therefore efficiency could be increased by nearly 8% relative making a total efficiency of 25% possible if the full potential of the erbium based system is realized.
Unfortunately, without any additional means, the trivalent erbium only uses the photons in its absorption range. The amount of photons in this range is about 2.3x1019/(m2s), which could result into an extra current of 0.2 mA/cm2. So even if the trivalent erbium worked as perfect upconverter in its absorption range, the potential efficiency increase is very low. How this problem of the narrow absorption range can be overcome is discussed in the section 5.2.4 about spectral concentration.
5.2.2 Definition of upconversion efficiency Throughout this work, I define the spectral upconversion quantum efficiency
KUC,spectral(Oin,OUC, I) at a certain luminescence wavelength OUC under the excitation with a wavelength Oinc and an irradiance I as
) , OUCUCp )( UC,spectral OOK incUC I),,( , (5.1) ) , Oincincp )( where )p,UC(OUC) is the flux of the upconverted photons with a wavelength OUC and
)p,inc(Oinc) the incident flux of photons with a wavelength Oinc.
A silicon solar cell can use all the photons with energies above its band-gap. The integration over the luminescence wavelength OUC in the usable wavelength range yields the integrated efficiency of the upconversion KUC(Oinc,I):
incUC , I ³KOK ,spectralUC incUC ,, dI OOO UC . (5.2)
With this definition, the maximum quantum efficiency that can be reached is 50 %, because at least two sub-band-gap photons must be absorbed to generate one upconverted photon. The maximum quantum efficiency for upconversion involving
136 5.2 The potential of upconversion and ways to increase upconversion efficiency
three incoming photons is respectively lower. In this work, I will use KUC,spectral(OUC,I) and KUC(Oinc,Oinc,I) to describe the efficiency of the optical process of upconversion. The quantum efficiency of the complete system of solar cell and attached upconverter, defined as the ratio of the generated and collected free charge carriers Imes/q to the incident photon flux )p,inc(Oinc), will be designated EQEUC(Oinc,I):
EQEUC(Oinc,I)= Imes/(q)p,inc(Oinc)). (5.3)
In this context Imes is the current measured during the EQE measurement.
5.2.3 Upconversion efficiencies achieved so far The highest upconversion efficiencies achieved so far have been reported by Richards and Shalav in [107]. They report an external quantum efficiency EQEUC(Oinc,I) of 3.4% 2 at Oinc=1523nm at a very high irradiance of 2.4 W/cm for a system consisting of a 3+ bifacial silicon solar cell and a NaYF4:Er upconverter. The investigated solar cell device was relatively inefficient for illumination from the rear (Krear = 15%), and had high optical losses in the spectral range to be upconverted. They estimate that about 80% of the light was lost, mainly because of reflection and parasitic absorption. The quantum efficiency of the upconverter itself KUC(Oinc,I) was calculated to be 16.7%.
They claim that by addressing the dominating loss mechanisms total EQEUC(Oinc,I) could be increased to 14%. However, these values are still quite far away from the limit of 50% quantum efficiency.
The experiments so far have been carried out with laser illumination and little is known about the behavior of such systems under sun illumination. The reported efficiencies are peak values at certain special wavelengths. Therefore, lower efficiencies could be expected under sun illumination. On the other hand, there are some aspects that might influence the efficiency positively: Under illumination with a broad spectrum transitions will occur between levels which are not evenly spaced. Upconversion from one very low-energy photon and one relatively higher energy photon could enlarge the spectral region that is upconverted. Levels which are responsible for unwanted losses could be populated, closing the loss paths.
5.2.4 Spectral concentration To achieve a significant efficiency improvement by upconversion, it is necessary to use a broad part of the solar spectrum. In contrast, trivalent erbium utilizes only a narrow range. To overcome this constraint, Strümpel et al. proposed to combine the upconverter with a luminescent material [108]. The luminescent material should absorb photons with wavelengths between the band-gap of the solar cell and the
137 5 Upconversion absorption range of the upconverter and emit in the narrow absorption range of the upconverting material. The upconverter then converts these photons to photons with energies above the band-gap of silicon (Fig. 5.2). Because the photons from a broad spectral range are transformed to photons in a narrow spectral range, I call this concept ‘spectral concentration’. This approach increases the upconversion efficiency significantly by two mechanisms: firstly, more potentially upconvertible photons are absorbed. Secondly, the photon density in the absorption range of the upconverter is increased. As I will show later on, upconversion is a nonlinear process. The relationship between incoming radiation and emission is described by a power law. For the investigated material, the relationship is roughly quadratic. With doubled excitation (in the absorption range of the upconverter), the emission is increased four-fold. In consequence, the efficiency of the upconverter increases with increasing intensity of the incoming radiation and therefore as a result of spectral concentration.
Fig. 5.2: The concept of spectral concentration. Erbium has only a very narrow absorption range (red). The combination with a luminescent material can enlarge the used spectral range. The luminescent material should absorb photons with wavelengths between the band-gap of the solar cell and the absorption range of the upconverter (green) and emit in the narrow absorption range of the upconverter. The upconverter then converts these photons to photons with energies above the band-gap of silicon.
5.2.5 An advanced system design for spectral concentration No system design to realize spectral concentration was proposed in [108] and up to now, it has not been realized successfully. In this work, I investigate PbSe and PbS nanocrystalline quantum dots (NQD) as luminescent materials for spectral concentration. The investigated materials were produced in the group of Prof. Lifshitz at the Technion in Haifa. These NQD show strong absorption in the required spectral range and efficient emission. The properties of the NQD can be influenced by their
138 5.2 The potential of upconversion and ways to increase upconversion efficiency size: the emission can be tuned between 0.5 eV to 1.1 eV [100, 109, 110]. NQD with a core of PbSe and a graded shell of a PbSe and PbS alloy have especially good properties. They offer the potential to tailor the crystallographic and dielectric mismatch between the core and the shell. Those core-shell and core-alloy-shell NQDs show photochemical robustness, a high PL internal quantum efficiency between 50- 80%, and a large cross section of absorption [111, 112].
Unfortunately, these NQD also absorb the radiation emitted from the upconverter. Thus, upconverter and luminescent material have to be separated from each other in order to prevent the upconverted radiation from being absorbed by the NQDs. I therefore developed an advanced upconverter system design as depicted in Fig. 5.3. A patent has been granted for this concept [113]. It was first presented in [114] where the co-workers who contributed to this idea are listed as well.
Fig. 5.3: Setup of an advanced upconverter system. The solar cell absorbs photons with energies above the band-gap (Q1). Photons with less energy are transmitted (Q2, Q3). The upconverter transforms especially low-energy photons, with energies in the absorption range of the upconverter (Q3), into high-energy photons, which can be absorbed by the solar cell (Q1). Photons with energies below the band-gap but above the absorption range of the upconverter (Q2) are absorbed by the nanocrystalline quantum dots (NQD), which emit photons in the absorption range of the upconverter (Q3). The emitted radiation is guided by total internal reflection and/or photonic structures to the upconverter. As the upconverter does not cover the whole area, a geometric concentration is achieved. Radiation which is emitted from the upconverter towards the fluorescent concentrator is back reflected by a spectrally selective photonic structure.
139 5 Upconversion
In this concept, the luminescent NQD are incorporated in a transparent matrix material to form a fluorescent concentrator. The upconverting material is located between this fluorescent concentrator and the bifacial solar cell. If the upconverting material does not cover the complete back of the solar cell, an additional geometric concentration in addition to the spectral concentration is achieved. The fluorescent concentrator collects the infrared radiation from all the area and concentrates it to the smaller upconverter area. This additionally increases the photon flux irradiating the upconverter. As mentioned before, because of the non-linearity of upconversion this additionally increases the efficiency of the upconversion. A big advantage of this combined internal geometric and spectral concentration is that it can be applied in addition to an external concentration with lenses and mirrors, so very high intensities at the location of the upconverter and in the relevant spectral region are possible, and therefore high efficiencies.
Selectively reflective photonic structures at the interface between fluorescent concentrator and upconverter prevent the upconverted light from entering the concentrator again, so the problem of the unwanted absorption can be solved (right inset in Fig. 5.3).
A second type of selective mirror could increase the collection efficiency of the fluorescent concentrator by reflecting the light that is emitted by the NQD (left inset in Fig. 5.3). In contrast to conventional fluorescent concentrators with solar cells at the edges of plates exceeding 100 cm2, in this system the light has only small distances to travel before it hits the upconverter. With the photonic structures avoiding escape cone losses, the quantum efficiency of the fluorescent concentrator system should therefore be close to the efficiency of the quantum dots, if re-absorption can be controlled. Additionally, these photonic structures could serve as an effective back mirror for the radiation, which can be utilized by the solar cell. The latter is very important since the solar cell must have a bifacial layout to be able to use the upconverted radiation. Thus, the photonic structure avoids solar cell performance degradation due to the shift from a normal to a bifacial layout.
5.2.6 Enhancing upconversion efficiency by plasmon resonances Another possibility to increase upconversion efficiency might be to use plasmon resonances in metal nanoparticles. Mertens and Polman report in [115] that the photoluminescence intensity of optically active erbium ions positioned close to anisotropic Ag nanoparticles is significantly enhanced if the nanoparticles support plasmon modes that are resonant with the erbium emission. It is believed that the
140 5.2 The potential of upconversion and ways to increase upconversion efficiency
3+ 4 4 photoluminescence enhancement is due to coupling of the Er I13/2í I15/2 transition dipoles with plasmon modes in the Ag nanoparticles, which increases the emission rate. Therefore one can imagine that such nanoparticles could be used to selectively enhance the upconversion emission as well. Another option would be to enhance the absorption of the photons that should be upconverted. This concept is investigated theoretically later on in this work.
141 5 Upconversion
5.3 Upconversion mechanisms and their theoretical description
In this section, I will introduce the different mechanisms by which upconversion can occur. For the important mechanisms, I present a theoretical description of the underlying processes. The presented theory will be later used to develop a model for the upconversion dynamics using rate equations. For this purpose, one emphasis of the theoretical analysis is to develop a formalism that is based on parameters that are accessible experimentally.
Upconversion can occur by different mechanism and can involve one or more ions of the upconverting material. Fig. 5.4 gives an overview over the different possible processes [116] and their relative efficiencies.
Most upconversion mechanisms involve a first absorption process starting from the ground state (GSA). After the ground state absorption excited state absorption (ESA) can occur. In the excited state absorption, the already excited electron is excited to another higher level. If the electron returns directly to the ground state, a high-energy photon can be emitted.
However, the excitation energy after the ground state absorption can also be transferred to another ion. The ion being first directly excited is called a sensitizer (S). The ion to which the energy is transferred is called an acceptor (A). If the acceptor ion has an intermediate level and the excitation occurs successively, the process is called energy transfer upconversion (ETU). The energy transfer upconversion can also be mixed with ground state absorption in the acceptor and subsequent energy transfer that results in the excitation of the highest level. Alternatively, the acceptor can be excited to the intermediate level by energy transfer and then excited state absorption occurs. The ETU can involve ions from different elements, but it can happen as well between ions of the same kind.
If no ion with three levels is involved but the one high-energy level of the acceptor is excited by simultaneous energy transfer from two sensitizer ions, the process is called cooperative sensitization (CS). The emission of a photon from a virtual high-energy state under the involvement of two levels of intermediate energy is called cooperative luminescence (CL). Without the involvement of a real high-energy or intermediate level, second harmonic generation can occur (SHG), while two photon absorption does not involve an intermediate level and the high-energy state is directly excited by a simultaneous absorption of two photons.
142 5.3 Upconversion mechanisms and their theoretical description
Fig. 5.4: Overview over different upconversion mechanisms and their relative efficiencies following Auzel [116]. Vertical arrows describe radiative processes, i.e. the absorption or emission of a photon, which are associated with the excitation or decay of an electronic energy state. The bent arrows describe non-radiative energy transfer processes.
Most of the described mechanisms have low relative efficiencies. The most efficient and therefore important upconversion mechanisms are energy transfer upconversion and ground state/excited state absorption. Therefore, I will restrict the following discussions to these important processes. Only the basic aspects are presented that are necessary to derive the relations that will be used later on in this work.
143 5 Upconversion
5.3.1 Absorption and emission
5.3.1.1 Einstein coefficients The absorption and emission of photons can be conveniently described with the so- called Einstein coefficients [117]. For simplification, I will restrict the discussion at this point to a system with only two energy levels. The absorption of a photon with an energy E12 =мȦ12 causes an electron to jump from a lower level E1 to a higher level E2, if the energy differences E2-E1 = мȦ12. The probability per unit time for one atom which interacts with the spectral energy density u(Z) that an absorption event takes place is B12 u(Z). B12 is the so-called Einstein coefficient for the absorption. The dimension of the spectral energy density is energy per unit volume per frequency bandwidth. Accordingly, the Einstein coefficient for the absorption B12 gives the probability for this transition per unit time, per unit spectral energy density.
The inverse process of the absorption is stimulated emission. Stimulated emission is the process by which an electron is induced to jump from the higher energy level to the lower level by the influence of the spectral energy density u(Z). The probability per unit time for one atom that stimulated emission occurs is B21 u(Z). B21 is the Einstein coefficient for the stimulated emission that gives the probability for this transition again per unit time, per unit spectral energy density.
When an electron decays to the lower energy level while emitting a photon without any external influence, the process is called spontaneous emission. The Einstein coefficient A21 gives the probability per unit time that an electron in state 2 will return spontaneously to state 1 emitting a photon with the energy мȦ12. For the frequency of the different events not only the probability for one atom is important, but also the number of atoms being in the respective state. With N1 being the number of atoms in state 1, and N2 the number of excited atoms, the change of these numbers can be described with the following rate equations:
dN1 Z Z )()( ANuBNuBN (5.4) dt 12121 12212 212
dN2 Z Z )()( ANuBNuBN . (5.5) dt 12121 12212 212
As we will see now, the Einstein coefficients of the different processes are not independent of each other. To obtain relationships between the Einstein coefficients, I
144 5.3 Upconversion mechanisms and their theoretical description will consider the source of the energy density to be thermal radiation and the two level system shall be in thermal equilibrium with this radiation.
In equilibrium, absorption and emission will occur with the same frequency.
Therefore, the rates of change will be zero: dN1/dt = dN2/dt = 0. Under this assumption equation (5.4) can be rewritten to
N2 uB Z1212 )( . (5.6) N1 Z1221 )( AuB 21
Because the system is in thermal equilibrium with its surrounding, the occupation of the two levels is also described by the Boltzmann statistic N § !Z · 2 12 . exp¨ ¸ (5.7) N1 © BTk ¹
By comparing the equations (5.6) and (5.7) an expression for the spectral energy density can be found A u Z 21 . 12 § !Z · ¨ 12 ¸ (5.8) BB 1221 exp¨ ¸ B21 © BTk ¹
On the other hand, the spectral energy density must obey the Planck’s law for thermal radiation
3 !Z 1 . u Z 32 S c § !Z · (5.9) exp¨ ¸ 1 © BTk ¹
By comparing equations (5.8) and (5.9) important relations between the Einstein coefficients can be found:
BB 2112 (5.10)
!Z 3 A 12 B . (5.11) 21 S c32 21
In the case of degenerated states, the degree of degeneracy of the two levels g1 and g2 must be considered and equation (5.10) transforms to
145 5 Upconversion
g1 . B12 B21 (5.12) g2
With these relations it is possible to obtain an expression for the probability that one electron is excited into the higher level by the absorption of a photon W12 and the probability that the electron returns to the ground state by either spontaneous emission or stimulated emission of a photon W21.
32 S gc 1 W12 3 Z )( Au 2112 (5.13) !Z12 g2
§ S c 32 · W ¨1 Z )( ¸ Au (5.14) 21 ¨ 3 21 ¸ 21 © !Z 21 ¹
These equations depend on the energy differences of the transition мȦ12 and the spectral energy density. Both are easily accessible by experiments. The involved constants are well known, leaving only the levels of degeneracy and the Einstein coefficient A21 undetermined. By means of quantum electro dynamics, the Einstein coefficient for the spontaneous emission of a photon because of the transition of an electron from one sub-state 2m2 of the energy level 2 to any sub-state 1m1 of the energy level 1 can be calculated to be
3 3 2 2 nZ12 * nZ12 )1( A 21 mpm { P , (5.15) 21 ! 3 ¦ 1 2 ! 3 12 3 HS 0c m1 3 HS 0c with zmz being a state characterized by the quantum numbers z and mz. The summation 6m1 includes all sub-states of the energy level 1 [118]. The permittivity of vacuum is designated H0. For processes taking place in matter, the dielectric constant )1( of the medium must be considered additionally. The symbol P12 denotes the matrix * element of the dipole operator p that is defined as * * ¦ qp ri . (5.16) i
146 5.3 Upconversion mechanisms and their theoretical description * In this equation q is the elementary charge and ri the position vector of one electron with index i of the valence electrons of the ion, and the summation is performed over all these electrons.
Up to now, the theory is only valid for energy levels with one distinct infinitely sharply defined energy. In reality, the energy levels have a certain width. This can be considered by a line form factor g(Z). The form factor is normalized to unity
³ dg ZZ 1, (5.17) and the probability for the spontaneous emission is
A21(Z) = A21 g(Z). (5.18)
This discussion considered only two energy levels. However, it can be generalized for transitions between more than two energy levels. In such a multilevel system, higher energy states can be populated by subsequent absorption of several photons. If emission takes place from those higher energy levels to the groundstate upconversion occurs. However, excitation of even higher energy levels is a loss mechanism in the context of upconversion. The energy of the additionally absorbed photons results into higher energy photons, but this extra energy is then lost due to thermalization in the solar cell.
5.3.1.2 The link between Einstein coefficients and absorption spectra To model the absorption and emission processes and consequently upconversion, it would be convenient to know the Einstein coefficients of the different transitions. Fortunately the coefficients, and consequently all the transition probabilities given in equations (5.13) and (5.14), can be linked to the experimentally accessible absorption coefficientD(Z). To establish this link, I will introduce a dimensionless quantity called oscillator strength f that is commonly used in the field. It is defined as
2moZ12 2 f P , (5.19) 3!q2 12 with m0 being the mass of the electron. With this expression the Einstein coefficient for the spontaneous emission can be rewritten to be
* 2 1 2Z 2q2 ª§ E · º A 12 «¨ *loc ¸ » fn . (5.20) 21 4SH cm 3 «¨ E ¸ » 0 0 ¬© ¹ ¼
147 5 Upconversion
* * I have introduced the additional term EE )/( 2 in this equation. It takes into account * loc that the local field E at the optically active ion might be considerably different than * loc the average field E in the media. This is especially true for crystals with high sym- metry. For such crystals in the case of absorption, this correction factor is * E n2 2 *loc [119]. (5.21) E 3
The higher the oscillator strengths of a transition the more likely is this transitions to occur. This will result as well in strong absorption. This relation between oscillator strength and absorption coefficient D(Z) is described in a formalized way by the so- called Smakula relation [119]:
* 2 1 2 cm H ª§ E · º f 00 «¨ *loc ¸ » 1 dNn ZZD (5.22) S q2 «¨ E ¸ » ³ ¬© ¹ ¼
In this relation N is the concentration of optically active ions in number per unit volume. The integration must be performed over the spectral range that is associated with the transition of which the oscillator strengths shall be determined. In practice this will be most likely one absorption peak over which the integration must be performed.
5.3.2 Migration of excitation energy The excitation energy can migrate from one excited ion to other ions. This can happen by radiative processes or radiationless by energy transfer.
5.3.2.1 Radiative energy migration A photon emitted by an excited ion can be absorbed by a second ion. The probability for such an energy migration Wmig is given by
1 )1( 2 )1( 2 constW . PP dgg ZZZ (5.23) mig 4S D2 em abs ³ em abs
In this equation gem(Z) and gabs(Z) are the line factors of the emission and absorption 2 )1( )1( 2 transition, Pem and Pabs the dipole matrix elements of the involved transitions and D the distance of the involved ions. The radiative energy migration depends on 1/D2. This allows the migration of excitation energy over rather large distances in comparison to other migration mechanisms.
148 5.3 Upconversion mechanisms and their theoretical description
5.3.2.2 Energy transfer The excitation energy of one ion can be transferred non-radiatively to other ions as well. A theoretical description of this energy transfer was developed in 1948 by Förster [120], which was further developed by Dexter [121] and Soules [122].
As mentioned before, the ion being first directly excited is called a sensitizer (S). The ion to which the energy is transferred is called an acceptor (A). If the excitation of an excited ion is transferred to another excited ion by energy transfer, higher energy levels are populated and energy transfer upconversion (ETU) occurs. However, the excitation energy of higher energy levels can excite lower levels as well. This is the inverse process to ETU and a loss mechanism in the context of upconversion and is called cross-relaxation.
Fig. 5.5: Different ways of how energy transfer can act. On the left, the excitation of an excited ion (S) is transferred to another excited ion by energy transfer, higher energy levels are populated and energy transfer upconversion (ETU) occurs. However, the excitation energy of higher energy levels can as well excite lower levels (right). This is the inverse process to ETU and a loss mechanism in the context of upconversion. This process is called cross-relaxation.
The energy transfer can be caused by electrostatic, magnetic or exchange interaction.
The probability for energy transfer WET from the sensitizer (S) to the acceptor (A) is
2S 2 W )()(2112 dggASHAS ZZZ . (5.24) ET ! int ³ S A
Hint represents the Hamiltonian for the interaction between the ions (S) and (A). The two particle state AS 1,2 describes the starting condition in which ion (S) is in the excited state 2 and ion (A) is in the lower state 1, AS 2,1 describes the final state after energy transfer takes place. gS(Z) and gA(Z) are the line form factors of the two involved transitions. The energy transfer probability is proportional to the overlap of
149 5 Upconversion the two line form factors. This implicitly contains the condition that the two involved transitions must be in resonance.
Fig. 5.6: Energy transfer between the sensitizer ion (S) and the acceptor ion (A). The probability for energy transfer depends on the distance D of the two involved ions, the nature of interaction (electro-static, magnetic or exchange) which is embodied in the exchange Hamiltonian Hint, and the overlap of the line form factors g(Z). The dependency on the overlap implicitly contains the condition that the two involved transitions must be in resonance.
Electrostatic coupling is the most frequent interaction that causes energy transfer. The
Hamiltonian HES that describes the electrostatic coupling of two ions is 1 q2 H ES ¦ * ** . (5.25) 4SH0 n , ji rrD ,, jSiA * * * In this expression D is the distance between the two ions. r ,iA and r , jS are the positions of the electrons relative to the position of the ions. The summation is performed for all valence electrons of (S) and (A). Under the reasonable assumption * * * that D is bigger than r ,iA and r , jS averaged over all azimuth and polar angles the matrix element of HES can be calculated to be approximately [118]
2 2 § · f § · 1 ¨ 1 ¸ ES ASHAS 2112 ¨ ¸ * ¨ 4SH n ¸ ¦ ¨ D 1 kk 21 ¸ © 0 ¹ kk 21 0, © ¹ (5.26) 2 2 kk 21 )!22( k1 )( k2 )( u S PP A 1 kk 2 )!12 ()!12( with
150 5.3 Upconversion mechanisms and their theoretical description
k1 k )( 2 k )( * 2 P 1 P 1 SrS 2)(1 (5.27) S ¦ q1 S kq 11
2 k1 )( and P A accordingly. The indices of the summation k1 and k2 are the order of the multipole transitions in the respective ions.
If these equation are evaluated for the most relevant dipole-dipole interaction, the probability for energy transfer by dipole-dipole interaction WET,dd is
2 § 11 · 4S 22 W ¨ ¸ dd dd )()( dgg ZZZPP . (5.28) ,ddET 6 ¨ ¸ S A ³ S A D © 4SH0 n ¹ 3!
The energy transfer by dipole-dipole interaction is strongly dependent on the distance D of the involved ions. Therefore, the distance over which excitation energy is dissipated by energy transfer is much smaller than with the aforementioned radiative processes.
Under the assumption of a homogenous distribution of the upconverter ions, the distance can as well be described by the concentration of upconverter ions N:
2 § 1 · 4S 22 NW 2 ¨ ¸ dd dd )()( dgg ZZZPP . (5.29) ,ddET ¨ ¸ 3! S A ³ S A © 4SH 0 n ¹ Consequently, the question whether energy transfer occurs is highly dependent on the concentration of the upconverter ions.
5.3.3 Multi-phonon relaxation In the previous sections, I have described that some losses in respect to upconversion arise already from the fundamental processes like absorption, emission, and energy transfer that are involved in the different upconversion mechanisms: by excitation of unnecessary high-energy levels or by cross-relaxation. There is another important loss mechanism that depopulates higher states of excitation: multi-phonon relaxation.
151 5 Upconversion
Fig. 5.7: Visualization of multi-phonon relaxation. During multi-phonon relaxation the excitation energy is dissipated as heat by the emission of phonons. The more phonons are needed to bridge the energy gap between the involved states, the less likely is this kind of relaxation.
During multi-phonon relaxation, the excitation energy is dissipated as heat by the emission of phonons and the electron returns from a higher level i to a lower energy level f. The bigger the energy gap between the two involved levels ǻEif, the more phonons are needed to bridge this gap. The probability for multi-phonon relaxation between the two levels WMPZ,if was found empirically to follow approximately the relation
N ' Eif ,ifMPZ MPZ )0( eWW . (5.30)
WMPZ,if (0) and N are material constants that depend on the material that surrounds the optically active ions [123]. In general, low phonon energies of the host crystal reduce the losses due to multi-phonon relaxation, because in that case many phonons are needed to bridge the energy gaps.
5.3.4 Intensity dependence of upconversion After the absorption of a first photon and the excitation of a higher energy level, upconversion requires that a second photon is absorbed by either the same ion or an ion nearby such that interaction is possible, in a time span short enough such that no relaxation occurs in between. In consequence, upconversion is strongly dependent on the intensity of the incident photon field.
To investigate the intensity dependence of upconversion, I will now consider a simplistic model of a three level upconverter with three evenly spaced energy levels
152 5.3 Upconversion mechanisms and their theoretical description
|0>, |1>, and |2>, with an energy gap мȦ12 between each of the neighboring levels. The model describes a number of ions that are widely dispersed. In this situation, energy transfer is not important and absorption and emission events do not change the energy density significantly. No loss mechanisms are considered.
Under these conditions, the number of ions in state |1> in equilibrium with the energy density u(Ȧ12) can be calculated by evaluating equation (5.4) with dN1/dt = 0 and applying the relation of the Einstein coefficients (5.11) and (5.12):
u Z12 )( g1 . N1 N0 !Z 3 g (5.31) u Z )( 12 0 12 S c32
3 2 3 For u(Ȧ12)<< мȦ12 /(S c ), a case which is also called ‘low injection’, this can be approximated by S 32 gc 1 . N1 | 3 Z Nu 012 (5.32) !Z12 g0
3 2 3 For u(Ȧ12)>> мȦ12 /(S c ), also called ‘high injection’ the approximation is
g1 N1 | N0 . (5.33) g0
We see that for low injection the number of ions in state |1> is proportional to the energy density and the number of ions in state |0>. It can be derived in the same way that the number of ions in state |2> is proportional to the number of ions in state |1>. Hence,
2 v 1 uNN Z 12 (5.34) 2 v uNN Z1202 , i.e. there is a quadratic relationship between the spectral energy density and the occupation of the second energy state and therefore as well between the spectral energy density and the upconversion luminescence from this second level. This relationship can be generalized by iteration for the occupation of a higher level |k> that is populated by the subsequent absorption of k photons:
k k v uNN Z120 . (5.35)
153 5 Upconversion
So we can state that for low injection the relationship between spectral energy density and the upconversion emission is described by a power law. The exponent reflects the number of photons that are necessary to populate the level from which the upconversion emission occurs.
This is still true if energy transfer is the dominant upconversion mechanism. The number Nk of ions in state |k> that is excited by energy transfer from the state |l> to the state |m> is proportional to the product of the number of ions in the respective states:
v NNN mlk . (5.36)
These states have to be populated by the absorption of photons. These photons must have sufficient combined energy to excite the level |k>, therefore under the conditions that only photons with energy мȦ12 are involved it is l m k k v 12 12 uuuN ZZZ 12 . (5.37)
Fig. 5.8: The relative occupation of the first excited level in dependence on the irradiating spectral energy density. In the case of low injection, the occupation depends linearly on the spectral energy density. For high injection the occupation saturates, since stimulated emission is more likely 3 2 3 to occur. For a spectral energy density >мȦ12 /(S c ) more ions are in an excited state than in the ground state (N1/N0 > 0.5) and inversion of the occupation occurs. The occupation of higher excited levels can be obtained by applying the plotted relation iteratively.
154 5.3 Upconversion mechanisms and their theoretical description
The case is different for high injection. As we can see in equation (5.33), the occupation of the excited levels is independent from the spectral energy density and is saturated at a certain value. The reason for this saturation is that an increase in spectral energy density might increase the absorption events that populate the higher levels, on the other hand stimulated emission is increased as well, so there is no net increase in the occupation. The relationship between energy density and occupation is also visualized in Fig. 5.8, which shows a plot of relation (5.31), with the degeneracy levels set to 1.
155 5 Upconversion
5.4 Suitable materials for upconversion
Gibart et al. introduced the concept of upconversion in the context of photovoltaics [124]. They attached a vitroceramic doped with Yb3+ and Er3+ to a substrate-free GaAs solar cell. They achieved an efficiency of 2.5% for input excitation of 1 W with a laser emitting at 1.39 eV. In this material system, the Yb3+ acts as a sensitizer that absorbs photons and transfers the excitation energy to the Er3+ that subsequently emits a high- energy photon. However, the excitation energy of 1.39 eV lies above the band-gap of silicon, hence the used material system is not applicable to silicon solar cells. The same is true for organic materials investigated by Baluschev that showed upconversion in the visible range of the spectrum [125].
Fig. 5.9: Energy levels of trivalent erbium with the wavelength of the emitted photons for transitions back to the ground state. Higher energy levels can be populated by subsequent absorption of several photons or by energy 4 4 transfer. For upconversion for silicon solar cells, the levels I9/2 and I11/2 are especially interesting, because the energy of two sub-band-gap photons is enough to populate these levels and the emissions from these levels are above the band-gap of silicon.
156 5.4 Suitable materials for upconversion
Very suitable as an upconverter for silicon solar cells are Er3+ based materials, like 3+ ENaYF4:Er [126]. Trivalent erbium exhibits 4f energy levels that are conveniently spaced for upconversion for silicon solar cells. That is, there are two quite evenly spaced energy levels which can be excited with sub-band-gap photons leading to the emission of one photon with an energy above the band-gap from a direct transition from the higher excited level to the ground state (see Fig. 5.9). The electronic configuration of erbium and the nature of the energy levels will be discussed in the following section 5.4.1.
The ENaYF4 host crystal shows low maximum phonon energies, so multi-phonon relaxation is not very frequent. The materials used in this work were produced by the group led by Prof. Karl Krämer in the department for chemistry and biochemistry at the University of Bern in Switzerland.
5.4.1 Theoretical aspects of the energy spectrum of trivalent erbium
5.4.1.1 The lanthanoids Erbium is an element that is part of the lanthanoid series. This series constitutes together with scandium and yttrium the group of rare earths. The name ‘rare earth’ is somewhat misleading, as these elements are neither rare in abundance nor can they be considered to be ‘earths’ in the sense of an exact chemical definition. Except lutetium, all lanthanoids feature an incompletely filled 4f electron shell. Their outer electron configuration is 5s25p65d14f16s2 for cerium with an atomic number of 58 to 5s25p65d14f146s2 for ytterbium with an atomic number of 70. Erbium with an atomic number of 68 has the configuration 5s25p65d14f126s2. In this notation the first number is the principal quantum number defining the electron shell, the letter denotes the orbital quantum number or angular momentum li of the individual electrons in that shell in the s, p, d, f notation, and the superscript is the number of electrons in the state defined by the previous two quantum numbers.
Lanthanoid atoms tend to lose three electrons, usually 5d1 and 6s2, forming trivalent ions. These trivalent ions then feature an xenon-core electronic configuration, which features only completely filled orbitals including the 4d, 5s and 5p orbitals, with the addition of the 4f electrons. The 4f sub-shell lies inside the ion, shielded by the 5s2 and 5p6 closed sub-shells. These 4f valence electrons are the ones to be involved in optical transitions. Because of their special properties, lanthanoids are widely used in optical application, such as in lasers or in optical amplifiers.
157 5 Upconversion
5.4.1.2 The Russell-Saunders notation to identify energy levels To understand the transitions between the different energy levels, it is necessary to have a closer look at the nature of these levels. The Hamiltonian of the valence electrons of a free lanthanoid ion Hfree Ion is
Hfree Ion = H0 + Hee + HSO. (5.38)
H0 describes the Coulomb interaction between the nucleus and the inner electrons with the valence electrons, Hee is the energy of the Coulomb interaction between the outer electrons, and HSO is the Hamiltonian of the spin-orbit interaction [118].
The Coulomb interaction Hee between the outer electrons subjects the outer electrons to a non-central force. As a result, the individual orbital angular momentum li is not conserved any more and it is not a good quantum number to describe the state of the ion. Instead, the total orbital angular momentum of all outer electrons L and the total spin angular momentum S can be used (see Fig. 5.10).
However, we have to consider the spin-orbit coupling as well. For light atoms, this can be done with good approximation in the following way: It is Hee >> HSO, so the Coulomb interaction is more important than the spin-orbit coupling. One can consider the Coulomb interaction first, as presented in the previous paragraph, and therefore describe the state with L and S, and afterwards one takes the spin-orbit coupling into account by perturbation theory. Because of the spin-orbit coupling, the two combined angular momentums couple. L and S add together and form a total angular momentum J. This is known as the LS-coupling, which is named Russell-Saunders coupling as well. The state of the ion is then well described with an additional quantum number for J (see Fig. 5.10).
In heavier atoms the situation is different. Here the spin-orbit interactions are larger,
Hee << HSO. Therefore, each orbital angular momentum of a single electron li couples with the individual spin angular momentum si. Together they form the individual total angular momentum ji. These individual total angular momentums then add up to form the total angular momentum. This kind of coupling is known as the jj-coupling.
For lanthanoids, the spin-orbit interaction is approximately as large as the Coulomb interaction between the outer electrons. In consequence, neither the Russell-Saunders nor the jj-coupling are good approximations. Nevertheless, the Russell-Saunders is used in the field to identify the different energy levels. An energy level is assigned the 2S+1 identification LJ. However, the electron configuration of such a state is, in reality, 2S+1 not a pure LJ state that could be derived from the Russel-Saunders approximation,
158 5.4 Suitable materials for upconversion but a superposition of different states that have the same total angular momentum J. 4 3+ For instance, the state denoted S3/2 of a free Er ion can be described as
4 4 2 2 4 S3/2 = 0.8 x S’3/2 - 0.4 x P’3/2 - 0.3 x D’3/2 + 0.2 x F’3/2 +…[127]. (5.39)
4 The ’ indicates the pure states. In consequence, the orbital angular momentum of S3/2 is not completely zero. Nevertheless, I will use this common notation throughout this work.
Fig. 5.10: Illustration of how the energy levels split under the influence of the different effects. At the top, the quantum numbers that describe the energy states are given. With only the influence from the central potential of the nucleus and the inner electrons, it is sufficient to identify the state with the principal quantum that identifies the shell (4 in this case), the individual angular momentum (f in this case) and the number of electrons n that are in this state. Because of the Coulomb interaction between the outer electrons, the total orbital angular momentum of all outer electrons L and their total spin S become relevant. Because of the spin-orbit coupling also the total angular momentum J=L+S is important. The influence of the field of the surrounding crystal causes further splitting of the energy levels.
5.4.1.3 The influence of the crystal field Additional to the internal effects in the ion, the electric field of the crystal that surrounds the ion influences the energy levels as well. Because of the distinct symmetry of the crystal not all directions are equivalent any more. Therefore the z- component of the angular momentum, described by the magnetic quantum number mj, becomes important and the degeneracy in mj is removed. When Hcf is the Hamiltonian that describes the influence of the crystal field, the Hamiltonian HIon of the ion in the crystal is
HIon = H0 + Hee + HSO + Hcf. (5.40)
159 5 Upconversion
In Er3+ the influence of the crystal field is only weak. The 4f electrons lie inside the 5s2 and 5p6 sub-shell. These outer shells partly screen the 4f electrons from the ions of the surrounding crystal. Hence the influence of the crystal field can be calculated with perturbation theory to the energy states of the free ion [118]. Although the in-fluence of the crystal is small, it is very important. Only because of the crystal field optical transitions within the 4f shell are possible, as we will see in the following section.
5.4.1.4 The Judd-Ofelt theory In section 5.3.1.1 the probability for an optical transition between* two electronic state was linked to the matrix elements of the dipole operator p , see e.g. equation (5.15). The dipole operator is of odd parity, while the parity of an electron state is determined by the orbital angular momentum li of the electron. The problem is that the matrix element of an odd operator between two states of the same parity is zero. Therefore, li must change by ±1 during the transitions. This selection rule can as well be understood by considering that a photon has a spin of one. If a photon is emitted or absorbed, consequently the angular momentum has to change by this value [128].
In our case, we are interested in transitions between two 4f states. The individual orbital angular momentum, determined by the quantum number f, is similar for both states. This would mean that no optical transitions were possible. However, one can observe these transitions. The answer can be found in the influence of the crystal field: The perturbation due to the crystal field mixes the 4f states of the free ions with 5d, 5g, 4d or 6s states, which have opposed parity. This makes optical transitions between the 4f states possible. One says, the crystal field induces optical transitions. The probability for such transitions is described by the theory of Judd [129] and Ofelt )1( [130]. Following this theory, the matrix element of the dipole operator P 'JJ is
2 2 )1( 2 t . P 'JJ ¦ : t JaUJaq '' (5.41) t 6,4,2
In this equation, the two involved states are identified by the total angular momentum J and J’ and a, respectively a’, which represent the remaining quantum numbers. U(t) is a tensor operator of rank t. Reduced matrix elements of this tensor operator can be found in literature for different host crystals. ȍt are the Judd-Ofelt intensity parameters. They characterize the strength of the crystal field. These parameters can be determined by measuring the absorption strength of a number of transitions. Once they are known, they can be used to calculate the transition strength of electric dipole transitions between any two levels of the system.
160 5.5 Optical material characterization
5.5 Optical material characterization
In this chapter, I will investigate the different materials needed for an advanced upconverter system with spectral concentration. In expression, I will investigate 3+ NaYF4 : Er and luminescent nanocrystalline quantum dots (NQD), thereby 3+ concentrating on the upconverting material NaYF4 : Er .
At the beginning, I will present how the absorption coefficient is determined, from which the Einstein coefficients of the different transitions can be calculated by using the Judd-Ofelt theory.
Subsequently, different photoluminescence measurements will be shown. Time- resolved photoluminescence measurements will provide insight into the upconversion dynamics. From a comparison of different erbium doping concentrations, energy transfer upconversion will be identified to be the dominant upconversion process. Intensity dependent measurements of the upconversion luminescence will highlight the strong intensity dependence of the upconversion that depends on the number of photons involved in the upconversion. Finally, calibrated upconversion photoluminescence measurements will yield upconversion efficiencies and document the potential of upconversion.
Moreover, the optical properties of some NQDs will be investigated.
5.5.1 Absorption measurements During the absorption of photons, electrons are excited from the ground state to higher energy levels as depicted in Fig. 5.11. The material of which the absorption properties 3+ were investigated in this work, was NaYF4 : Er doped with 20% erbium. An erbium concentration of 20% means that on 20% of the sites of the yttrium, now erbium ions 3+ are located. This is also written NaYF4: 20% Er .
3+ The NaYF4: 20% Er is a microcrystalline powder, with a quite inhomogeneous size distribution. To achieve a more homogeneous distribution, the powder was grinded in a mortar. It is difficult to directly measure the absorption of a powder. Therefore the absorption properties were determined from measurements of the diffuse reflection spectrum applying the Kubelka-Munk theory. For these experiments the powder was filled into a powder cell. In a powder cell, the powder is compressed against a glass window of high transparency. The thickness of the powder layer was 4-5 mm. At such thicknesses, nearly no light is transmitted through the powder. The reflection spectrum 3+ of the NaYF4: 20% Er in the powder cell was measured using a spectrophotometer as described in section 4.3.2. The results are presented in Fig. 5.12.
161 5 Upconversion
Fig. 5.11: Illustration of the absorption processes in the erbium. During the absorption of photons, electrons are excited from the ground state to the higher energy levels.
3+ Fig. 5.12: The reflection spectrum of the NaYF4: 20% Er in a powder cell as measured with a spectrophotometer. The minima in the reflection can be 4 identified with absorption due to transitions from the ground state I15/2 to higher energy levels. The respective higher energy level is depicted in the graph.
162 5.5 Optical material characterization
In the reflection spectrum distinct minima are visible. They can be identified with 4 absorption events due to transitions of electrons from the ground state I15/2 to higher energy levels. From this reflection data, the absorption coefficient can be determined with the help of the Kubelka-Munk theory.
5.5.2 The Kubelka-Munk theory The determination of the absorption coefficient is difficult for powdery substances. Light is scattered by the small particles of the powder. Therefore, the effective path length of the light in the material is considerably higher than the thickness of the layer and cannot be determined easily. Nevertheless, with the theory of Kubelka and Munk [131, 132] the absorption coefficient can be determined from reflection measurements.
The Kubelka-Munk theory describes fine powders, in which the size of the powder particles is of the same order of magnitude as the wavelength of the considered light. Scanning electron microscope pictures showed that for the grinded powder the particle size is in the range 1-2 µm, which is as well the wavelength range of the light that shall be investigated. So from this perspective, the theory can be applied. The luminescence of the material could interfere with the measurements. On the other hand, the measurements are carried out with very little incident intensity, so nearly no luminescence will occur.
The Kubelka-Munk theory is based on balance equations that describe the change of the irradiance I while traversing an infinitesimal thin layer of material with the thickness dz with an absorption coefficient D(O) and a scattering coefficient s(O). The differential equations
zdI OOD O)()())()(( zdIszdIs . (5.42) dz
zdI zdIs OOD ))()(()( zdIs (5.43) dz describe the change of the irradiance I+ of the photon flux in z-direction, and the change of the irradiance I- of the photon flux in the opposite direction. By solving these coupled differential equations with the boundary conditions that
I+() = I-() = 0 and I+(0)=I0, the reflection R(O) of an infinite thick layer can be obtained: D O s O)(2)( E R O)( (5.44) f s )(2)( EOOD
163 5 Upconversion with s OODODE ))(2)()(( .
Since through the thick powder layer no light is transmitted, the boundary conditions can be considered to be fulfilled and R describes reasonable well the reflection of the powder in the powder cell.
However, in equation (5.44) the absorption coefficient is still linked with both the reflection and the scattering coefficient. In order to determine the absorption coefficient, one has to perform a second measurement on a very thin sample. The sample should be thin enough that some light is transmitted and the reflection R is different from R. From solving equations (5.42) and (5.43) with the boundary conditions I+(0)=I0, and I-(d) = 0 with d being the thickness of the layer, the following equations can be obtained (I have omitted the wavelength dependencies for better readability):
§ 1 · 2 R § RRR )1( · s f ln¨ f f ¸ , ¨ ¸ 2 ¨ ¸ (5.45) © 2 d ¹ 1 Rf © f RR ¹
§ 1 · 1 Rf § f RRR f )1( · D ¨ ¸ ln¨ ¸ . (5.46) © 2d ¹ 1 Rf © f RR ¹
Both R and R are accessible experimentally, so the absorption and scattering coefficients can be obtained from these two reflection measurements.
5.5.3 Absorption coefficient and Einstein coefficients To measure the reflection of thin layers, three samples were prepared. The powder was compressed between two glass slides. The thickness d of the powder layers was determined to be 245 µm for one sample, and 224 µm for the two other samples. However, the thickness varied by about 5% for each sample. The reflection of the samples and of a reference was measured with a spectrophotometer. The reference measurement allowed taking into account the reflection of the glass slides. The average reflection due to the powder was calculated. Subsequently, the absorption coefficient could be determined with equation (5.46) and the results of the measurement with the powder cell. The result is shown in Fig. 5.13.
164 5.5 Optical material characterization
3+ Fig. 5.13: Absorption coefficient of NaYF4: 20% Er as determined with several spectrophotometer measurements on thick and thin samples and the Kubelka-Munk theory. Absorption peaks due to transitions from the ground 4 state I15/2 to higher energy levels are nicely visible in the spectrum.
Especially the variation of the thickness causes significant uncertainty for this result. Additionally there are uncertainties from the different spectrophotometer measurements. The uncertainty calculated with Gaussian error propagation is about 10%.
In section 5.3.1.2, I discussed the link between the Einstein coefficients, oscillator strength and matrix elements of the dipole operator. Combining equations (5.19), (5.21), and (5.22) yields
2 27cH0! P dZZD (5.47) 12 2 2 ³ 12SZ 2 Nnn for the matrix element of the dipole operator between two states |1> and |2>. In this relation N is the concentration of optically active ions in number per unit volume and n the refractive index of the material. The integration must be performed over the peak in the absorption spectrum that is linked to the transition between the two states.
Combining this equation with the Judd-Ofelt theory and equation (5.41) yields a relationship between the absorption coefficient and the Judd-Ofelt parameters:
165 5 Upconversion
27cH ! 2 0 ZZD qd 2 : t JaUJa . 2 2 ³ ¦ jjt ii (5.48) ijSZ 2 Nnn t 6,4,2
With this equation the Judd-Ofelt parameters could be determined. The integration in the left part of equation (5.48) was performed for the absorption peaks formed by the six most relevant transitions. The resulting six equations can be expressed as linear equation system of the form * * QUA . (5.49) * The six entries of the vector* A are formed by the left side of equation (5.48) for each integration. The vector Q has three entries that are the Judd-Ofelt parameters we are looking for. The entries of the matrix U with three columns and six rows are given by the reduced matrix elements of the tensor operator U(t) times q2. The values of the reduced matrix elements of the tensor operator U(t) were taken from Carnall, who determined the values for erbium in LaF3 from absorption measurements. Those values are a good estimation as they do not depend strongly on the host crystal in contrast to the Judd-Ofelt parameters [133]. With six equations and three unknown variables this system has no solution. However, a best approximate solution with the lowest error could be calculated via
1 § T · T ** ¨ ¸ QAUUU , (5.50) © ¹
T with U being the transposed matrix of U [134]. The obtained result corresponds to a least square fit with the three Judd-Ofelt parameters as free variables. The Judd-Ofelt -25 2 -24 2 -24 2 parameters were determined to be ȍ2= 2.3·10 m , ȍ4= 1.2·10 m , ȍ6= 1.4·10 m . Considering that a quite complex combination of theories that all involved certain approximations was necessary to calculate these parameters, these results must be considered more as an approximation than as exact parameters.
Nevertheless, it is interesting to use the parameters to calculate the Einstein coefficients for the different possible transitions. Combining equations (5.15) with (5.41) yields an expression
166 5.5 Optical material characterization
3 2 2 Z qn t 12 (5.51) A21 3 ¦ :t 22 JaUJa 11 3 !HS 0c t 6,4,2 that directly links the Judd-Ofelt parameters with the Einstein coefficient of the spontaneous emission. The calculated Einstein coefficients are summarized in Table 5.1.
Because of the involved uncertainties, also the calculated Einstein coefficients are only very rough values. However, even these rough values show certain interesting features. For instance, later in this work, we will see that there is a very strong emission from 4 4 the I11/2 level to the ground state, which is stronger than the emission from the I9/2 level. This relation can as well be found between the Einstein coefficients.
Table 5.1: Einstein coefficients for the spontaneous emission, calculated from the experimentally determined Judd-Ofelt parameters. The unit of the coefficients is 1/s. The columns indicate the level from which the emission occurs, and the rows the final state after the emission.
-1 4 4 4 4 4 2 [s ] I13/2 I11/2 I9/2 F9/2 S3/2 H11/2
4 I15/2 87 105 14 573 1011 434
4 I13/2 4.8 1,5 112 268 124
4 I11/2 0.09 24 88 45
4 I9/2 4.6 33 19
4 F9/2 3.3 2.9
4 S3/2 0.04
5.5.4 Time-resolved photoluminescence A tool to gain further insight in the nature of the upconversion processes and their dynamics are time-resolved photoluminescence measurements. After an excitation pulse, the optically active centers relax via several mechanisms such as radiative recombination, excitation migration, energy transfer and multi-phonon emission. The
167 5 Upconversion time-resolved evaluation of the luminescence provides information about the rates of 3+ the involved mechanisms. Furthermore, the measurements on NaYF4:Er samples doped with different doping concentrations of 10%, 20% and 30% erbium allows conclusion to be drawn, on which are the dominant mechanism leading to population and de-population of energy levels.
5.5.4.1 Lifetime of excited states
For most decay mechanisms, the rate dNi/dt is proportional to the occupation Ni of the level i.
That is dN i U N (5.52) dt ii with Ui being the rate coefficient. The result is an exponential decay
i NtN i 0, exp Uit . (5.53)
The lifetime Wi of a state i can be defined as the inverse of the rate coefficient
1 . W i : (5.54) Ui
The rate coefficient for the spontaneous emission is the Einstein coefficient for the spontaneous emission A (see section 5.3.1.1). Therefore the lifetime for the radiative recombination is Wrad= 1/A.
The multi-phonon relaxation results as well into an exponential decay, as
dNi NW , (5.55) dt , iiMPZ with WMPZ being the probability of the multi-phonon relaxation depopulating level i (see section 5.3.3).
In the case that several mechanisms depopulate one energy level, the rate coefficients of the individual processes add up and the total lifetime can be found by 1111 ¦ ... . (5.56) i m ,im ,irad WWWW ,iMPZ
168 5.5 Optical material characterization
5.5.4.2 Lifetime and energy transfer The decay behavior gets more complicated, when energy transfer is involved. The rate depends on the product of the population of both levels involved and the likelihood of interaction between donor and acceptor and between different donor ions. Different cases have been investigated [135, 136]. A pattern that is found often is that the decay is not exponential on a short time scale and asymptotically exponential for longer periods.
5.5.4.3 Measurement of time-resolved photoluminescence For the measurement of the time-resolved luminescence, the decay of the luminescence from various levels was recorded after excitation of the trivalent erbium to the F3/2 level using a dye laser tuned to 440.7 nm (see Fig. 5.14). The employed dye laser was a Spectra Physics LPD 3002 with a coumarin 47 dye that was pumped by a Spectra Physics LPX100 XeCl excimer laser at 308 nm. Under this excitation, erbium- doped NaYF4 shows strong emissions in the visible and the infrared spectral range. Two photomultiplier tubes served to record the luminescence spectra. For the spectral range from 400 nm to 850 nm, a water-cooled Hammamatsu R928 Photomultiplier was used, while a nitrogen cooled Hamamatsu R5509-72 was used to record the 850 nm to 1600 nm spectral range. The detectors were read out by a multi-channel analyzer with 4000 channels and a time resolution of 't0.2 Ps. Data were acquired and averaged over 1000 sweeps. A detailed description of the experimental procedure and the results can be found in [104].
Prior to acquiring time-resolved data, a luminescence emission spectrum was recorded that showed several peaks at different wavelength that could be assigned to the different transitions as indicated in Fig. 5.14. Time-resolved spectra of the maximum of the luminescence emission were recorded with a bandwidth of up to 2 nm for the 4 4 4 4 4 4 five transitions from the states S3/2, F9/2, I9/2, I11/2 and I13/2 to the ground state I15/2.
The spectra were recorded for NaYF4 samples doped with 10%, 20% and 30% erbium.
169 5 Upconversion
Fig. 5.14: The time-resolved photoluminescence measurements were performed under pulsed laser excitation at 440.7 nm. Prior to the time-resolved measurements a photoluminescence spectrum was recorded. This spectrum showed several peaks at different wavelengths to which the different transitions could be assigned, as indicated in this energy level diagram. Besides the transitions to the ground state, transitions between excited states were observed as well (dashed lines). Time-resolved measurements were then performed for the different transitions to the ground state (solid lines).
5.5.4.4 Results of time-resolved photoluminescence measurements Fig. 5.15 and Fig. 5.16 show the recorded time-resolved photoluminescence spectra of the 20% erbium doped sample. For the observed time span (0.2Ps to 40ms after the 4 pump pulse) the S3/2 level exhibits a build-up phase at times shorter than the maximum experimental time resolution of 0.2 Ps to be followed by a single 4 exponential decay. The level F9/2 shows a short initial non-exponential decay followed 4 by a long single-exponential decay. The populations of the I9/2 shows as well a hardly resolvable build-up phase and a decay that already shows a lot of noise and probably 4 4 background signal at lower intensities. The populations of the I11/2 and I13/2 levels
170 5.5 Optical material characterization show rather long build-up phases, which are followed by decays with long time constants. The long decays of these two levels are shown separately in Fig. 5.16 that covers a longer time span.
Fig. 5.15: Time-resolved photoluminescence of the transitions from the indicated excited levels to the ground state measured on the 20% erbium doped sample.
Fig. 5.16: Time-resolved photoluminescence of the transitions with the especially long life times, measured on the 20% erbium doped sample.
171 5 Upconversion
The decay’s time constants were obtained by fitting the single-exponential function F·exp(-t/W) to the data in their single-exponential regimes. t is the time variable, Fa parameter and W the decay time constant. The decay of the states considered take place by several mechanisms and the states were not pumped directly but rather populated by the decay of higher lying levels. Therefore, the parameter W does not represent the intrinsic lifetime of the considered level. Furthermore, some decays were not perfectly single-exponential. As a consequence the obtained time constant depends slightly on the data range to which the function was fitted. Nevertheless, the time constantW is useful for comparison and to give upper/lower limits for the time constants of the 4 4 involved processes. For the levels I11/2 and I13/2 with significant build-up times a time constant for the build-up Wup was determined as well by fitting the single-exp growth function F (1-exp(-t/Wup)).
Time-resolved spectra were also determined for the samples with 10% and 30% erbium doping. The results are presented in Fig. 5.17 and Fig. 5.18. The determined time constants both for build-up and decay depend strongly on the erbium concentration level. The determined time constants are summarized in Table 5.2.
Table 5.2: Overview of the different time constants for the different transitions at different doping levels.
Energy level 10% Er 20% Er 30% Er
4 S3/2 31 µs 14 µs 7 µs
4 F9/2 612 µs 956 µs 672 µs
4 I9/2 40 µs 17 µs 23 µs
4 I11/2 8 ms 13 ms 7.5 ms
Wup 52 µs 19 µs 15 µs
4 I13/2 18 ms 22.6 ms 13 ms
Wup 19 µs 11 µs 5 µs
172 5.5 Optical material characterization
Fig. 5.17: Time-resolved photoluminescence of the transitions from the indicated excited levels to the ground state measured on the 10% erbium doped sample.
Fig. 5.18: Time-resolved photoluminescence of the transitions from the indicated excited levels to the ground state measured on the 30% erbium doped sample.
173 5 Upconversion
It is interesting to see that the two probably most important energy levels in the context of the upconversion for silicon solar cells have very long time constants. In the case of 4 the I13/2 this is beneficial. If an excited ion stays in that state for a long time, this means that there is enough time for the ion to receive the energy necessary for upconversion, either by the absorption of another photon or by energy transfer. 4 However, the long time constant of the I11/2 is somewhat critical. Here a short lifetime, induced by optical transitions to the ground state would be desirable, because otherwise unwanted processes such as multi-phonon relaxation have more time to take place, which reduces the quantum efficiency.
5.5.4.5 The importance of energy transfer mechanisms In the determined time constants, several aspects support the conclusion that energy transfer plays an important role in the photoluminescence dynamics. Especially the 4 decay of the S3/2 is accelerated with increasing erbium content. Furthermore, the 4 4 4 4 build-ups of the I9/2, I11/2 and I13/2 levels are much faster than the decay of the F9/2 level above them. Therefore, it is unlikely that the lower levels are populated by 4 transitions from the F9/2 level, but likely that excitation migration through radiative or 4 non-radiative energy transfers involving the S3/2 levels is important. From the energy of the excited state levels and the spectral overlap of the transitions between them, the following energy processes appear to be likely:
4 4 4 4 4 x Cross-relaxation Ň S3/2, I15/2ͽļŇ I9/2, I13/2ͽ populating the states I9/2 and 4 I13/2
4 x Another cross-relaxation of the state S3/2 leads to the population of the state 4 4 4 4 4 I11/2: Ň S3/2, I15/2ͽļŇ I11/2, I11/2ͽ
4 The fact that the population of the I13/2 state reaches its maximum prior to the 4 energetically higher state I11/2 indicates that the energy transfer 4 4 4 4 4 4 4 4 Ň S3/2, I15/2ͽļŇ I9/2, I13/2ͽ is stronger than Ň S3/2, I15/2ͽļŇ I11/2, I11/2ͽ. Furthermore, 4 4 4 4 the process Ň I9/2, I15/2ͽļŇ I13/2, I13/2ͽ has to be considered, as this process is mainly responsible for the experimentally observed upconversion processes. To confirm these hypotheses and to gain more insight into the dynamics it would be necessary to directly excite the individual levels, so the real lifetimes of the levels could be determined.
In section 5.3.2.2, it was shown in equation (5.29) that the probability of the energy transfer by dipole-dipole interaction is proportional to the square of the optically active ion concentration, which is the square of the erbium concentration in our case. Under
174 5.5 Optical material characterization
4 the assumption that this is the dominant mechanism depopulating the S3/2 level, the determined decay rates of this level should show a linear dependence on the squared doping concentration. Fig. 5.19 shows a plot of the decay rates determined from the presented measurements in dependence on the squared doping concentration. A clear linear dependence is visible. This strongly supports the conclusion that energy transfer by dipole-dipole interaction plays a very important role in explaining the luminescence dynamics of Er doped NaYF. In the figure, data is shown that was derived from measurements performed by Suyver [137]. He investigated luminescence of Er doped NaYF at different temperatures and doping levels of 2%, 10% and 20%. Suyver 4 measured the luminescence by direct excitation of the S3/2 level. He observed quenching of the luminescence at higher doping levels, but did not investigate the concentration dependence and the link to energy transfer in detail. Transferred to the same form, Suyver’s data supports the linear relationship between squared concentration and decay rate, and therefore the importance of energy transfer. However, his decay rates are on a lower level. This could be explained by the difference in the experimental setup, especially in the controlled temperature and the direct excitation. However, the determined slope of the linear relationship, which is a measure for the strength of the interaction, can be considered to be in agreement with the results of this work within the experimental uncertainties.
4 Fig. 5.19: Dependence of the decay rates of the S3/2 level on the erbium concentration. Obviously, the decay rate depends linearly on the squared erbium concentration. This is a strong hint that the decay is mainly due to energy transfer by dipole-dipole interaction.
175 5 Upconversion
5.5.5 Intensity dependent upconversion photoluminescence Two or more low energy photons are necessary to populate higher energy levels, which eventually results in the emission of a high-energy photon that can be used by the solar cell. Because of this involvement of two or more photons the intensity of upconversion luminescence depends non-linearly on the irradiance of the excitation (see section 5.3.4).
To investigate this relationship, the intensity dependence of the upconversion luminescence of microcrystallineE-NaYF4was investigated experimentally for an erbium doping concentration of 20% in reference to the yttrium content. The sample was excited by a collimated laser beam with 0.76 mm full width of half maximum. The excitation intensities were varied from around 200 Wm-2 to around 2x105 Wm-2. The luminescence was recorded by a Polytec x-dap spectrometer with a silicon CCD detector. The instruments were calibrated with a reference halogen lamp. The upconverting material is only available in powder form. Therefore, the powder was mixed into a binding agent with refractive index of n#1.48 and attached to PMMA carriers. Details of the experiment can be found in [104].
Fig. 5.20: To investigate the relation between the irradiance of the excitation and the intensity of the upconversion luminescence, microcrystalline 3+ NaYF4: 20% Er . Under excitation with 1523 nm laser irradiation the samples showed upconversion luminescence with peaks at 545 nm, 670 nm, 800 nm and 980 nm. These peaks could be identified with the radiative 3+ 4 4 4 4 4 decays of the Er states S3/2, F9/2, I9/2, I11/2 to the ground state I15/2.
176 5.5 Optical material characterization
Under excitation with 1523 nm laser irradiation (Fig. 5.20) the samples showed upconversion luminescence with peaks at 545 nm, 670 nm, 800 nm and 980 nm (See Fig. 5.21). These peaks could be identified with the radiative decays of the Er3+ states 4 4 4 4 4 S3/2, F9/2, I9/2, I11/2 to the ground state I15/2 (see also Fig. 5.20).
For each of the four peaks centered at 545 nm, 670 nm, 800 nm and 980 nm the luminescence spectrum was integrated and plotted as a function of the excitation irradiance (Fig. 5.22).
3+ Fig. 5.21: Luminescence spectra of microcrystallineE-NaYF4: 20% Er at various irradiances of the excitation. The peaks are numbered according to the transitions in Fig. 5.20. The intensity dependence was measured for the four peaks displayed above, corresponding to the spontaneous emission 4 4 4 4 from the erbium states S3/2, F9/2, I9/2, I11/2.
Following equations (5.35) and (5.37) in section 5.3.4 the integrated luminescence is expected to obey a power law
m PL F II exc , (5.57) with IPL being the emittance of the upconversion sample under excitation with the irradiance Iexc, F is a proportionality factor and m the characteristic exponent that defines the power law characteristic. It is common practice [137, 138] to perform a double logarithmic transformation on the data and estimate the parameters of equation (5.57) by a least-squares fit of a function f(x)=log(F)+mx to the data set
(yi,xi)=(log(Iexc),log(IPL)). This method is advantageous because it is very illustrative and weights high and low absolute data values more or less equally over a large range.
177 5 Upconversion
On the other hand, a least-squares fit assumes Gaussian errors. However, assuming
Gaussian experimental errors of (Iexc, IPL) leads to log-normally distributed errors of the logarithmically transformed data. In addition, the case is further complicated as the regime of the nonlinearity (and thus the parameters F and m) changes with the excitation irradiance.
Fig. 5.22: The integrated intensities of the individual peaks of the luminescence spectrum depending on the excitation irradiance. The data sets were fitted to determine the exponent m of the power law that describes the dependence of the upconversion luminescence intensity from the irradiance of the excitation.
Despite the uncertainties, some general trends can be observed in the determined exponents.
x First, the individual exponents tend to decrease with higher irradiances. This is well in agreement with the theoretical calculations presented in section 5.3.4. The reason for this was that with increasing population of the higher levels stimulated emissions become more likely as well.
x Second, the exponents for the transitions from levels that are populated by the absorption of at least three photons are higher than those of the transitions from levels that can be populated by two photons. This is especially true for the exponents at lower irradiances. These findings are in agreement with the theoretical expectation that for low excitation irradiances for a three photon process the characteristic exponent m should be m=3, and for a two photon process m=2 (section 5.3.4). The fact that the experimental values stay below
178 5.5 Optical material characterization
the theoretical predictions can be partly attributed to the existence of higher energy levels that were neglected in the theoretical calculations.
5.5.6 Calibrated photoluminescence measurements For the application in photovoltaics, the efficiency of the upconversion is especially important. Up to now, optical upconversion efficiencies were mostly measured only indirectly by solar cells. Optical measurements usually remained on a qualitative level and no optical upconversion efficiency was measured directly. Therefore, in this work calibrated photoluminescence measurements have been performed to directly determine the potential of upconversion of sub-band-gap photons.
5.5.6.1 Measurement setup and calibration 3+ For these measurements, the powdery upconverter NaYF4 : 20 % Er was filled in a powder cell with an optical window at the front. The upconverter was illuminated through the optical window with an IR-Laser ECL-210 from Santec. The incident wavelength of the laser Oinc can be tuned from 1430 nm to 1630 nm and the power of the laser diode can be varied up to approximately 8 mW, depending on the operation conditions. Since upconversion is a non-linear process, it is very important to know the irradiance on the sample. To determine the irradiance, the photon flux of the excitation
)p,inc(Oinc) was measured at different laser powers with a germanium solar cell, of which the external quantum efficiency (EQE) was known, and a calibrated lock-in amplifier. Additionally, the area of the laser beam was determined to be 3.2 r 0.1 mm2. With these data and the geometrical properties of the experiment, the irradiance I of the laser on the sample could be calculated.
The luminescence spectra of the upconverter were measured with a grating monochromator H25 from Jobin Yvon and a silicon photodiode detector from OEC and a lock-in-amplifier 7265 from signal recovery. The detector is thermo-electrically cooled to -20°C to minimize thermal noise. The chopper was placed between sample and monochromator and operated with a frequency of 15 Hz. Because of the long lifetimes of the involved states in the range of ms, the chopper could not be placed in the excitation beam [139]. The monochromator is optimized for infrared radiation and features a gold grating. Because of the absorption properties of the gold, only luminescence with wavelengths above approximately 600 nm could be observed.
To determine the calibrated efficiency of the upconversion on an absolute scale, the efficiency of the used detection unit must be known. To achieve this goal, the relative spectrum of a tungsten halogen lamp was determined at ISE Callab. This lamp was placed in the excitation light path of the setup. The total number of photons at the
179 5 Upconversion sample position was determined subsequently with the aforementioned germanium solar cell. Afterwards, a white reflector made from BaSO4 coated, roughened aluminum was placed at the sample position. Goniometry measurements on this reflector confirmed that the reflected light had an angular characteristic very close to that of a perfect Lambertian reflector. Combining these results, the reflected photon flux per wavelength and solid angle from the light source in the direction of the detection system is known. By comparing with the output of the detection unit, the detection efficiency could be determined.
While the angular characteristic of the reflected light was Lambertian, it is reasonable to expect the emission characteristic of the upconverter to be isotropic. Therefore, the different angular characteristics were taken into account by calculating a correction coefficient, which transforms the calibration for a diffuse emitter to that for an isotropic one.
The fact that the NaYF4 : 20% Er3+ is a powder results in a certain uncertainty of the upconversion efficiency as determined in the measurements. Because of the scattering of the powder, some emitted photons are lost in the sample. In consequence, in this work an upper and a lower limit of the upconversion efficiency is stated. The lower limit assumes that no photons are lost. One can interpret this lower limit as the effective efficiency of the “powder-cell upconverter” device. The upper limit assumes that light is emitted into the whole sphere (4S), but only half of the photons is detected, namely that half that is emitted directly towards the detector. Therefore, the upper limit is two times the lower limit. The real upconversion efficiency of the NaYF4 : 20% Er3+ material should lie between these two values. Apart from this uncertainty, the main uncertainties stem from the inaccuracy of the calibration of the PL setup and the external quantum efficiency of the reference solar cell. Overall an error of 8 % is estimated for the uncertainty of the optical measurements. Details on the experimental setup and the calibration can be found in [105].
5.5.6.2 Dependence of the luminescence spectrum from the excitation wavelength To measure the excitation spectrum, the excitation wavelength was varied from 1430 nm to 1630 nm in 2 nm steps and the photoluminescence spectrum of the 3+ NaYF4 : 20 % Er was recorded. Fig. 5.23 shows the calibrated measurement of the upconversion spectrum for the upper limit at a constant irradiance of 880 Wm-2. The data are presented as optical spectral upconversion quantum efficiency
KUC,spectral(Oin,OUC, I), as defined in section 5.2.2 in equation (5.1). That is, the detected photon flux of the luminescence is divided by the total incident photon flux.
180 5.5 Optical material characterization
3+ Fig. 5.23: Optical upconversion efficiency of the NaYF4 : 20 Er in a logarithmic scale calculated from calibrated PL measurements. While keeping the irradiance constant, the excitation wavelength was varied from 1430 nm to 1630 nm in 2 nm steps and the PL spectrum was measured. Emission peaks occur at 660 nm, 810 nm and a dominating one at 980 nm.
4 4 4 Three peaks from the transition of the states F9/2, I9/2 and I11/2 to the ground state 4 I15/2 are visible in the spectrum. The corresponding luminescence peaks are centered around the wavelengths of 660 nm, 810 nm and 980 nm respectively.
By integrating over the luminescence wavelength OUC , the integrated optical efficiency of the upconverter KUC(Oinc,I) at a certain excitation wavelength Oinc was calculated (see equation (5.2) in section 5.2.2). As silicon solar cells use photons up to a wavelength of approximately 1150 nm, this integrated optical efficiency including these three peaks is a reasonable estimation of how efficiently sub-band-gap photons can be upconverted into photons that can be used by a silicon solar cell.
In Fig. 5.24, the lower and the upper limit of the integrated optical efficiency in dependence of the excitation wavelength are plotted. The upconversion efficiency peaks at a wavelength of 1523 nm, reaching 6.1 % for the upper and 3.0 % for the lower limit. In the range from 1492 nm to 1547 nm the efficiency of the upconversion in the upper limit is higher than 3 %.
181 5 Upconversion
Fig. 5.24: By integrating over the luminescence wavelength in Fig. 5.23, the integrated optical upconversion efficiency is calculated. Photons with a wavelength of 1523 nm are efficiently upconverted. The shape of the excitation spectrum is formed by the sub energy levels of the Er3+ caused by the influence of the crystal field of the host crystal.
5.5.6.3 Dependence of the upconversion luminescence on the excitation power To measure the dependence of the upconversion luminescence on the excitation power 3+ with the calibrated setup as well, the NaYF4 : 20 % Er was excited at its most efficient wavelength of 1523 nm with different laser powers. The laser power was varied from 0.1 mW to the maximum stable output power of 7.9 mW. This corresponds to an irradiance of 17 Wm-2 to 1370 Wm-2. Fig. 5.25 shows the spectrally resolved optical efficiency of the upconverter KUC,spectral(Oinc,OUC,I) for each laser power. For all luminescence peaks, the efficiency increases with increasing excitation power. The peak at 980 nm shows the highest luminescence efficiency and is detectable right from the beginning. The other peaks are only detectable over a certain 3+ 4 4 threshold of excitation. The radiative transition from the Er states I9/2 to I15/2 at 810 nm is detectable from approximately 100 Wm-2 onwards, while the emission from 4 -2 the state F9/2 at 660 nm is detectable for an irradiance of over 250 Wm .
182 5.5 Optical material characterization
3+ Fig. 5.25: Optical upconversion efficiency of the NaYF4 : 20 Er in a logarithmic scale calculated from calibrated PL measurements. While keeping the excitation wavelength constant at 1523 nm, the laser power and therefore the irradiance was varied from 17 Wm-2 to 1370 Wm-2 and the PL spectrum was measured. The emission peak at 980 nm shows a fast response, while the others are only detectable over certain excitation thresholds.
The dependence of the integrated upconversion efficiency on the irradiance of the excitation is shown in Fig. 5.26. Again, it can be seen how the upconversion efficiency increases with the irradiance. It is also visible that there is some saturation for high irradiances, as was already investigated in more detail in the previous section 5.5.5. In this section, it is of interest, which absolute height upconversion efficiency can reach. In the presented setup an integrated optical efficiency of 8.6 % at the upper limit and 4.3 % at the lower limit for an irradiance of 1370 Wm-2 was achieved.
To confirm the measured values, calibrated measurements were performed at a different setup, which is located at the University of Oldenburg. The measurements were undertaken with the same laser, which was shipped to Oldenburg for this purpose. Because of different setup geometries, higher excitation irradiances could be achieved. An upper limit efficiency of 10.2 % at an irradiance of 1880 Wm-2 was achieved. This was slightly higher than that what would have been expected from an extrapolation of the results from the described setup. Nevertheless, the values are in reasonable agreement. Because of the special definition, a quantum efficiency of above 10% means that more than 20% of the incident photons were participating in the upconversion process. Such high optical efficiencies underline the potential of the 3+ upconverter NaYF4 : 20 % Er to increase silicon solar cell efficiency.
183 5 Upconversion
Fig. 5.26: Due to the non-linearity of the upconversion the integrated optical upconversion efficiency rises with the irradiance. At high irradiance the increase slowly saturates.
Auzel [116] established an efficiency notation KUC,norm(Oinc,I), which explicitly connects the irradiance I with the upconversion efficiency: K O I),( OK I),( incUC . (5.58) , incnormUC I For an ideal two photon upconversion process in a three level system, the upconversion efficiency would depend linearly on the excitation irradiance at low irradiances. With this definition, the normalized upconversion efficiency
KUC,norm(Oinc,I) would therefore be constant.
In the presented experiments, the normalized upconversion efficiency reaches a value of 0.62 cm2W-1 at the upper limit and respectively 0.31 cm2W-1 for the lower limit. The best-known value from literature is 0.07 cm2W-1 [107]. This value was not measured directly, but calculated from electrical measurements on solar cell systems with attached upconverter by considering estimated losses. The fact that considerably higher values were achieved in this work can partly be attributed to the fact that the presented measurements were performed at comparatively low irradiances. In contrast, the measurements of Richards in [107] were performed at 24000 Wm-2. As we have seen in Fig. 5.26, the slope of the efficiency curve decreases. In consequence, the normalized upconversion efficiency KUC,norm(Oinc,I) will be lower at higher excitation irradiances. Nevertheless, the high values are very promising and show the high quality of the material used.
184 5.5 Optical material characterization
5.5.7 Optical properties of luminescent nanocrystalline quantum dots (NQD) In section 5.2.4 I presented the concept of spectral concentration and introduced a novel concept for its realization in section 5.2.5. For this purpose, luminescent materials are necessary that absorb infrared radiation and emit in the absorption range of the upconverter with high quantum efficiency. Luminescent colloidal core-shell PbSe/PbS nanocrystalline quantum dots (NQD) promise to meet these needs. In the core-shell configuration, the PbSe core is surrounded by a PbS coating for electrical passivation and a better oxidation resistance. Because of the quantum confinement effect, changing the size of the core and the shell can be used for tuning the luminescence wavelength [109]. For small NQDs (less than approximately 10 nm outer diameter), the energy levels and therefore the luminescence properties are mainly dominated by the outer diameter [140]. High quality core-shell NQD already achieve a quantum efficiency of over 80 % [111, 112]. The synthesis of these NQD was described by Sashchiuk [141] and Kigel [100].
In this work, several variations of such core-shell PbSe/PbS nanocrystalline quantum dots were investigated in regards to their applicability in a spectral concentration system. The NQD were produced in the group of Prof. Lifshitz at the Technion in Haifa, Israel.
Fig. 5.27 shows the photo luminescence and absorption spectra of the two most promising investigated samples. The NQD were embedded in PMMA with a weight concentration of 2-2.5%. The investigated NQD were applied to upconverter solar cell systems as well, which will be presented later on in this work. However, because of the low quantum efficiencies no positive effects were observed. Therefore, the related work was postponed until more efficient embedded NQDs are available.
Table 5.3 summarizes the different properties of the samples. The listed size of the dots was determined using transmission electron microscope (TEM) measurements of similar dots.
The absorption of the samples was determined from transmission and reflection measurements with a spectrophotometer with an attached integrating sphere as already described in this work. The photoluminescence was recorded with the setup that was used for the calibrated measurements. In contrast to the previous measurements, a 810 nm laser excitation with power of approximately 50 mW was used. These measurements were not calibrated on an absolute scale.
185 5 Upconversion
As it was difficult to excite a measurable signal, the quantum efficiency of the samples is very low. It is known that the quantum efficiency of the NQD drops from 60 % in hexane down to 8 % when they are embedded in PMMA [112]. Hence before a successful application, the issue of implementation of the NQD must be solved successfully.
Nevertheless, first results could be obtained in respect to the spectral properties of the NQD. As can be seen in Fig. 5.27, the slightly larger NQD with a diameter of 5 nm (sample A2) had an emission that fit better to the absorption range of the upconverter than those of the slightly smaller NQD with a diameter of 4.5 nm (sample A1). However, even for the better NQD of sample A2, the match between the photoluminescence and the absorption range of erbium from 1492 nm to 1547 nm can still be improved. First, the emission peak of the photo luminescence should be shifted to longer wavelengths. This would mean synthesizing slightly larger NQD. Second, it would be desirable to have a narrower emission so that all the emitted light can be absorbed. Finally, the overlap between the NQD absorption and emission is quite large, which could lead to unwanted re-absorption losses. Therefore it would be desirable to increase the Stokes shift. One possible solution could be the synthesis of core-shell NQD that show an internal Type-II band structure.
Fig. 5.27: Absorption and photoluminescence spectra of two different types of NQD embedded in PMMA. The absorption and photoluminescence peak of the sample with slightly smaller NQD with a total diameter of 4.5 nm (sample A1) are shifted towards smaller wavelengths in comparison to the peaks of sample A2 with NQD with a diameter of 5 nm. This is a clear effect of the
186 5.5 Optical material characterization
quantum confinement. The absorption peaks at 1680 nm visible in the spectra of both samples stems from absorption of the PMMA matrix.
The investigated NQD were applied to upconverter solar cell systems as well, which will be presented later on in this work. However, because of the low quantum efficiencies no positive effects were observed. Therefore, the related work was postponed until more efficient embedded NQDs are available.
Table 5.3: Overview of the different properties of the investigated samples
Sample A1 A2
Total diameter 4.5 nm 5 nm
Core diameter 3.5 nm 3.6 nm
Thickness of sample 0.55 mm 0.55 mm
Concentration in polymer 2.0-2.5% 2.0-2.5%
First absorption peak 1340 nm 1410 nm
Photo luminescence peak 1434 nm 1496 nm
187 5 Upconversion
5.6 Simulating upconversion
3+ The luminescence and upconversion properties of NaYF4 : 20 % Er are determined by a complex set of different processes: stimulated processes like absorption and stimulated emission, spontaneous processes like spontaneous emission, energy transfer processes and loss mechanisms such as multi-phonon relaxation. To learn more about the interplay of all these different processes and to find possible leverages for optimization, a simulation model based on the theory presented in chapter 5.3 was developed. Until now, extensive experimental and theoretical studies on the properties of different rare-earth doped phosphors have mostly been carried out with regard to the use of these materials in lasers. The same applies for the development of simulation models, e.g. [142]. In contrast, little modeling of the dynamics with regard to the application of upconverters in photovoltaics has been performed. In [143] a rate equation model of photon conversion processes is presented. The model I am going to present in this work is based on rate equations as well, but it is more comprehensive. It describes a system with six energy levels (see Fig. 5.28) which correspond to the* energy levels of erbium. The occupation of these levels is described by a vector N . The single elements of the vector give the relative occupation of the specific level, i.e. * the fraction of ions of a large ion ensemble that is excited to this state. The rate N , by which the occupation changes, depends on the occupation of the states and the interaction between the levels and between different ions. The model considers ground state absorption, excited state absorption, spontaneous emission, stimulated emission, energy transfer and multi-phonon relaxation. Further details and results can be found as well in the master theses of P. Löper [104] and S. Fischer [105].
188 5.6 Simulating upconversion
Fig. 5.28: The model considers six energy levels that correspond to the energy levels of erbium. For easy identification within in the model the levels have been numbered as indicated in the figure. The model assumes that the transitions from level 1 to 2, 2 to 4 and 4 to 6 are directly excited by monochromatic excitation with 1523 nm radiation.
5.6.1 The rate equation model * * In the model, the occupation N and its rate of change N are described by the following differential equation: * * * > @ DNETUNMPZIESEESAGSAN ),( . (5.59)
For most involved processes the rate of change* is the product of the probability W for the relevant transition and the occupation N . The probabilities for the different transitions are described by several matrixes. The matrix GSA describes the ground state absorption, ESA the excited state absorption, SE the spontaneous emission, IE the stimulated emissions and MPZ the multi-phonon* relaxation. Additionally, the vector ETU, which is a function of the occupation N and the distance of the ions D, describes the change in occupation due to energy transfer. The different matrixes are explained with more detail in the following sections.
189 5 Upconversion
5.6.1.1 Ground state and excited state absorption Ground state and excited state absorption are stimulated processes. In section 5.3.1 it was shown that it is possible to describe as well the absorption processes with the
Einstein coefficient Aij for the spontaneous emission. Equation (5.13) gave the probability for an absorption event depending on the spectral energy density u(Z) with which the ion interacts. In the presented experiments, the upconverter was excited by incident radiation that had a certain irradiance. Therefore, the model shall also work with spectral irradiance IQ(Z) instead of with the spectral energy density. These two quantities can be easily converted into each other via n u I ZZ )()( , (5.60) c Q with c being the speed of light in vacuum and n the refractive index.
The model assumes monochromatic excitation with the angular frequency Z, which corresponds to a wavelength of 1523 nm. The model assumes that the transitions from level 1 to 2, 2 to 4, and 4 to 6 are directly excited by this excitation. Therefore the probability of ground state and excited state absorption can be described by the following combined matrix
§ g1 · ¨ A21 00000 ¸ ¨ g2 ¸ ¨ g1 g2 ¸ ¨ A21 A42 0000 ¸ g2 g4 S 22 nc ¨ ¸ ESAGSA I ¨ 000000 ¸ 3 Q g g !Z21 ¨ 2 4 ¸ (5.61) 0 A42 0 A64 00 ¨ g4 g6 ¸ ¨ 000000 ¸ ¨ ¸ g4 ¨ 000 A64 00 ¸ © g6 ¹ .
The Einstein coefficients used were taken from Table 5.1 in section 5.5.3 with the experimentally determined Einstein coefficients.
190 5.6 Simulating upconversion
5.6.1.2 Spontaneous emission The probability of spontaneous emission is given directly by the Einstein coefficients. The model only considers the transitions from which emission was observed in the photoluminescence measurements. The matrix SE is therefore: §0 AAA A A · ¨ 21 31 41 51 61 ¸ ¨0 A21 00 A52 A62 ¸ ¨ ¸ 00 A31 00 0 SE ¨ ¸ . (5.62) ¨ 000 A41 0 0 ¸ ¨ ¸ ¨ 0000 AA 5251 0 ¸ ¨ ¸ © 00000 AA 6261 ¹
5.6.1.3 Stimulated emission Stimulated emission is the inverse process of absorption. From equation (5.14) it can be simply derived that the probability for the stimulated emission can be described via § A 00000 · ¨ 21 ¸ ¨ 21 AA 42 0000 ¸ 22 ¨ 000000 ¸ S nc ¨ ¸ IE 3 IQ . (5.63) !Z21 ¨ 42 0000 AA 64 ¸ ¨ ¸ ¨ 000000 ¸ ¨ ¸ © 00000 A64 ¹
5.6.1.4 Multi-phonon relaxation In section 5.3.3 it was already discussed how the probability for multi-phonon relaxation depends on the energy difference between the involved levels. Accordingly, the matrix describing the probability for phonon relaxation between the different neighboring levels is
§0 e !ZN 21 )( 0 0 0 0 · ¨ ¸ ¨0 e !ZN 21 )( e !ZN 32 )( 0 0 0 ¸
¨ !ZN 32 !ZN 43 )()( ¸ ¨ 00 e e 0 0 ¸ WMPZ MPZ )0( (5.64) ¨ 00 0 e !ZN 43 e !ZN 54 )()( 0 ¸ ¨ !ZN )( !ZN )( ¸ ¨ 00 0 0 e 54 e 65 ¸ ¨ !ZN 65 )( ¸ © 00 0 0 0 e ¹
191 5 Upconversion
The quantities WMPZ(0) and N are material constants of the crystal. They have not yet been determined for the investigated erbium doped NaYF4. Therefore they were treated as free parameter of the model during simulation.
5.6.1.5 Energy transfer Energy transfer is the dominant upconversion mechanism [116]. The energy is transferred from one excited sensitizer ion to the acceptor ion. Following equation (5.28), the overlap of the two involved line form factors determines how likely the energy transfer is. This means that the two transitions involved must be in resonance. Fig. 5.29 indicates which transitions are in sufficient resonance and are therefore considered in the model. The transitions can occur as well in the opposite direction. This is the so-called cross-relaxation that empties higher excited levels and can therefore be considered a loss mechanism in the context of upconversion. Cross- relaxation between the indicated transitions is considered as well in the model.
Fig. 5.29: For energy transfer to take place, the two involved transitions must be in resonance to each other. Four different energy transfer transitions that show sufficient resonance are included in the model. These transitions are shown as colored arrows in the figure. Two arrows of the same color indicate that these two transitions are in resonance. The transition can occur as well in the opposite direction. This is the already mentioned cross-relaxation that empties higher excited levels.
192 5.6 Simulating upconversion
The vector ETU that describes the energy transfer upconversion and the cross- relaxation is composed of four single vectors that each describe one specific transition: * ETETETETDNETU 4321),( , (5.65)
In section 5.3.2.2, the probability for energy transfer due to dipole-dipole interaction was derived. By combining equation (5.28) for the probability with the equations (5.19) and (5.20), which establish a link between the dipole matrix elements and the Einstein coefficients for spontaneous emission, the following expression can be derived
6 ET 3! Sc 9 1 W cc )()( dggAA ZZZ . (5.66) dd 6 2 4 6 SSAA ³ AJJJJ S 4 ZT nn 2 D
In this expression, ZT is the angular frequency of the transition and D the average distance between the ions. The term 9/(n(n2+2)4) stems from the consideration of the change of the local electric field due to the crystal. J’A und JA are the quantum numbers of the total angular momentum for the start and end state of the acceptor ion, while J’S und Js are the respective quantum numbers for the sensitizer ion. The line factors of the transitions are given by gA(Z) and gS(Z).
The rate, by which the occupation changes, is the product of the presented probability times the occupation of both starting levels involved. Additionally, the inverse processes must be considered as well. In the following equations, KET1-KET4 represent the different overlap integrals of the line form factors. For a better traceability, the
Einstein coefficients were written in the form Axy and Ayx to indicate into which direction the transitions occur. However, independent of the order of the indices
Axy=Ayx. In consequence, the vectors describing the different transitions are
§ 2 NNAANAA · ¨ 22421 414212 ¸ 2 ¨ 2 22421 2 NNAANAA 414212 ¸ 6 ¨ ¸ 3! Sc 9 1 ¨ 0 ¸ ET1 K ET1 6 2 4 6 ¨ 2 ¸ (5.67) 4 Z21 nn 2 D 22421 NNAANAA 414212 ¨ ¸ ¨ 0 ¸ ¨ ¸ © 0 ¹
.
193 5 Upconversion
§ 0 · ¨ 2 ¸ ¨ 44642 NNAANAA 626424 ¸ 3! Sc6 9 1 ¨ 0 ¸ ET 2 K ¨ ¸ 6 2 4 6 ET 2 2 4 Z42 nn 2 D ¨ 2 44642 2 NNAANAA 626424 ¸ (5.68) ¨ ¸ ¨ 0 ¸ ¨ 2 ¸ © 44642 NNAANAA 626424 ¹
§ NNAANNAA · ¨ 616412424621 ¸ ¨ NNAANNAA 616412424621 ¸ 3! Sc6 9 1 ¨ 0 ¸ ET3 K ¨ ¸ (5.69) 6 2 4 6 ET 3 NNAANNAA 4 Z21 nn 2 D ¨ 616412424621 ¸ ¨ ¸ ¨ 0 ¸ ¨ ¸ © NNAANNAA 616412424621 ¹
§ 2 NNAANAA · ¨ 33631 616313 ¸ ¨ 0 ¸ 6 ¨ 2 ¸ 3! Sc 9 1 2 33631 2 NNAANAA 616313 ET 4 K ¨ ¸ (5.70) 6 2 4 6 ET 4 ¨ ¸ 4 Z63 nn 2 D 0 ¨ ¸ ¨ 0 ¸ ¨ 2 ¸ © 33631 NNAANAA 616313 ¹
5.6.2 Input parameters Inserting all described matrixes in equation (5.59) results in a set of differential equations. This set was solved with the software program MatLab©. The dynamics of the occupation and photo luminescence are modeled. After a certain time, the resulting values reach equilibrium. In the following, these equilibrium values will be presented. Where possible, the model’s parameters were determined experimentally, i.e. the different Einstein coefficients were determined from the determination of the absorption coefficient (see section 5.5.3) and the angular frequencies of the different transitions were determined from the photoluminescence measurements (see section 5.5.5). For the energy transfer, the distance between the ions is important. It was calculated that the density of the Er3+ ions in the NaYF:20% is 2.1027 m-3 and therefore the distance to the closest neighboring ion 7.9.10-10 m.
194 5.6 Simulating upconversion
Several coefficients could not be determined theoretically or experimentally in the scope of this work and were therefore treated as free parameters of the model. This affects especially the parameters governing multi-phonon relaxation and energy transfer. These parameters were adjusted such that the relative heights of the different photoluminescence peaks were reproduced. The adjustment was performed for the data set of relative peak heights at an irradiance of 2000 Wm-2 as they are presented in Fig. 5.20. The influence of the parameters and the adjustments will be discussed in the following.
Quite independently of the chosen parameters, the model tends to overestimate the occupation of the higher levels 4 to 6. A possible explanation is that the stimulated processes are overestimated. The reason is that for the stimulated processes the model assumes exact the same energy distance between levels 2 to 4 and 4 to 6 as between level 1 and 2. In reality, these transitions do not have exactly the same energy. Therefore, the transitions between the upper levels will not be stimulated as effectively 4 with the incident 1523 nm radiation than the transition between the ground state I15/2 4 and the first excited state I13/2. To allow for these differences, the stimulated processes between the higher levels were damped by a factor of 106. In expression, the Einstein coefficients A42 and A64 in the matrix ESA for the excited state absorption and in the IE matrix for the stimulated emission were divided by 106. This does not mean that the determined Einstein coefficients are wrong by this factor, but that the model is too simple at this point, because it does not involve energy levels with a certain energy width.
Additionally, the Einstein coefficients for all transitions involving the highest two levels were adjusted manually. Without this adjustment, it was not possible to reach the experimentally observed relative peak heights. In section 5.5.3 the Einstein coefficients had been determined from reflection measurements (see Fig. 5.12). For the higher energy transitions a high background signal is present in the reflection measurements. Although the estimated background was subtracted, some background signal may have remained to distort the results for the Einstein coefficients involving the higher energy levels. Good results were achieved, when the experimentally determined values for the Einstein coefficients for the highest two levels were divided by a factor of 5.9. Table 5.4 displays the Einstein coefficients used in the simulation.
195 5 Upconversion
Table 5.4: Einstein coefficients for the spontaneous emission used in the simulation model. The columns indicate the level from which the emission occurs and the rows the final state after the emission. Values that are not bold are different from the experimentally determined values given in section 5.5.3. Those values were obtained by dividing the experimentally determined values by a factor of 5.9. The values indicated with an * were divided by a factor of 106 before they were used in the matrixes for excited state absorption and for stimulated emission to account for the energy mismatch of the corresponding transitions in respect to the 1523 nm excitation (here the values are shown without the damping factor applied).
-1 4 4 4 4 4 [s ] I13/2 I11/2 I9/2 F9/2 S3/2
4 I15/2 87 105 14 97 171
4 I13/2 4.8 1.5* 19 45
4 I11/2 0.09 4.1 15
4 I9/2 0.8 5.6*
4 F9/2 0.56
The multi-phonon relaxation is described by an exponential relation in the form
,ifMPZ WW MPZ exp)0( !ZN if . (5.71)
8 -1 20 -1 Reasonable results were achieved with an WMPZ(0) of 10 s and a N of 10 J . However, better relative heights between the neighboring levels were achieved when individual matrix entries were chosen for two transitions. Multi-phonon relaxation 4 4 from level S3/2 to level F9/2 was amplified by a factor of 18 in relation to the values 4 4 calculated with equation (5.71), while the transitions from level S3/2 to level F9/2 were damped by multiplying by a factor of 0.38. A possible explanation as to why these alterations are necessary, might be that the equation (5.71) is a very simple empirical model that does not describe the full complexity of the multi-phonon interaction.
Table 5.5 displays the values for the KETi that describe the strength of the different energy transfer processes. The order of magnitude of the presented values was taken from [118], for the exact values care has been taken to reflect the different energy match between the involved transitions, i.e. the better the match the higher the factor.
196 5.6 Simulating upconversion
Table 5.5: Different KETi values used in the simulation that describe the strength of the different energy transfer processes. The order of magnitude of the presented values was taken from [118]. The individual values reflect the different energy match between the involved transitions, i.e. the better the match the higher the factor.
-1 Overlap integral [J ]KET1 KET2 KET3 KET4
)()( dgg ZZZ 2.2.1022 3.3.1022 2.4.1022 1.6.1022 ³ A S
5.6.3 Simulation results The simulation was performed for different excitation intensities. Fig. 5.30 shows the luminescence from transitions from the different excited levels to the ground state in dependence on the excitation intensities. Several features are visible that agree nicely with the experimental results and the theoretical expectations on a qualitative level. For all transitions the luminescence increases with increasing irradiance. Thereby, the 4 4 luminescence from the two levels S3/2 and F9/2 that are populated dominantly by three photon processes increases with a steeper slope than the luminescence from the levels that are populated by two photon processes. This is in perfect agreement with the theoretical expectation and with the experimental observation as well. Another interesting feature of the experiment is reproduced: for an irradiance of around 2 4 4 900 W/m , the two curves for the luminescence from level I9/2 and level F9/2 intersect. This intersection appears as well in the experimental data presented in Fig. 5.22. However, here the differences to the experiments become visible as well. In the experimental data, the intersection occurs at an irradiance two orders of magnitude higher. Possible explanations for these differences might be that the irradiance in the model is the irradiance directly at the upconverter ion. Effects of reflection from the powder, absorption by other ions that reduce the effective irradiance on ions further into the material etc. are not taken into account. Furthermore, the laser beam profile is not homogeneous and therefore certain areas are illuminated with considerably lower intensity. In consequence, the experimental values must be considered an average over the luminescence at many different irradiance levels that are lower than the given maximum irradiance on the surface of the sample. So in conclusion, the agreement with the experiment can be considered to be fairly good.
197 5 Upconversion
Fig. 5.30: Photoluminescence from the different excited levels to the ground state as simulated with the presented model. The results agree very well with theoretical expectations and experimental observations. This includes the steeper slope for luminescence from levels populated by three photon processes and the intersection of curves from different levels that was observed experimentally as well.
The presented results were obtained by adjusting numerous free parameters. Therefore, the quality of the model and the question to which extent it describes all relevant processes accurately must remain somewhat unanswered, as flaws of the model might have been obscured by the possibility to make the results fit by adjusting free parameters.
At this point more experimental input would be desirable that could be used both as input parameters or to test the model against. For example time-resolved photoluminescence measurements of every level under direct excitation of this level would yield another direct way to determine the Einstein coefficients for spontaneous emission.
Nevertheless, the model is still very useful to investigate the influence of single parameters and therefore to enhance the understanding of the upconversion dynamics, as we will see in the following section.
198 5.6 Simulating upconversion
5.6.3.1 The influence of multi-phonon relaxation On the one hand, multi-phonon relaxation is an important loss mechanism by which excitation energy is dissipated as heat. On the other hand, multi-phonon relaxation critically determines the relative occupation of neighboring levels that have a small energy gap between them. Fig. 5.31 shows the relative occupation of the higher excited states in dependence on the strength of the multi-phonon relaxation represented by
WMPZ(0).
Fig. 5.31: Relative occupation of the higher excited states in dependence on the strength of the multi-phonon relaxation represented by WMPZ(0). For most states the occupation decreases with higher multi-phonon relaxation because more electrons return to the lower states by multi-phonon 4 relaxations. The level I9/2 is populated exclusively by multi-phonon relaxation from higher levels. Its population shows a maximum for medium strength of the relaxation.
As multi-phonon relaxation is a loss mechanism, it is not surprising to see that for the most levels occupation decreases with increasing strength of the relaxation. 4 Interestingly, the occupation of level I11/2 shows a pronounced maximum at medium strength of the multi-phonon relaxation. This level is populated exclusively by multi- phonon relaxation from higher levels. Therefore, the occupation of this level benefits from higher multi-phonon relaxation at first.
Fig. 5.32 shows, how the multi-phonon relaxation influences the intensity dependence 4 of the luminescence of the I9/2 level.
199 5 Upconversion
4 Fig. 5.32: Normalized luminescence from level I9/2 to the ground state in dependence on the multi-phonon relaxation. The luminescence of the individual levels was normalized to their value at 200 Wm-2 to compare the different intensity dependencies. With higher multi-phonon relaxation, the relative increase of the luminescence with increasing irradiance is more pronounced than for lower multi-phonon relaxation.
Interestingly, the relative increase of the luminescence with increasing irradiance is more pronounced for higher multi-phonon relaxation than for lower multi-phonon relaxation. Fig. 5.32 shows the dependency for the most important luminescence from 4 level I9/2 to the ground state, but the qualitatively same behavior was observed as well for the other transitions. In section 5.3.4, the intensity dependence of the luminescence was investigated with a simple theoretical model. In that simple model, the saturation of the increase in luminescence with increasing irradiance was the result of stronger stimulated emission. The stimulated emission depends on the overall occupation of the higher levels. With multi-phonon relaxation the overall occupation is lower. Therefore, the saturation effect kicks in at higher irradiances. In consequence, the normalized relative occupation should grow roughly the same as with lower multi-phonon relaxation for low irradiances and then should show less signs of saturation for higher irradiances. That is exactly what can be seen in the simulated curves in Fig. 5.32.
200 5.6 Simulating upconversion
5.6.3.2 Simulating the effect of plasmon resonance It was already discussed in section 5.2.6 that external concentration by lenses or mirrors could be complemented by an internal, local intensity increase due to plasmon resonance in metal nanoparticles in order to achieve higher efficiencies. The potential of this concept will be assessed with the help of the simulation tool in this section.
The concept is to achieve an enhancement of photon absorption by designing the nanoparticles in such a way that the plasmons show resonance at the energy of the low 4 4 energy photons, which should be absorbed. That is, the transitions I15/2 to I13/2 and 4 4 I13/2 to I9/2 are amplified.
Fig. 5.33 shows a simulation result of how a gold nanoparticle with a 40 nm radius changes the distribution of the squared absolute value of the electric field normalized to the squared absolute value of the incident electric field in its near field under illumination with 1523 nm irradiation. This simulation was performed by Florian Hallermann at RWTH Aachen. The direction of incidence is from the bottom of the graph in positive y-direction and the polarization is in the xy-plane. The metal nanoparticle does not increase the electric field everywhere, but there are areas with higher and areas with lower electric field. Ten different levels of amplification and attenuation respectively were defined and the relative frequency Fi of each level in the volume around the gold nanoparticle was determined. In Fig. 5.34 the resulting frequency distribution of the irradiance in the volume around the metal nanoparticles is shown for the assumption of a 2000 Wm-2 irradiance on the particle. Results are shown for particle radii of 20, 40 and 60 nm. The frequency distributions show a peak around the initial irradiance of 2000 Wm-2 and a longer tail reaching to higher irradiances. Fig. 5.34 shows the upconversion luminescence in dependence of the irradiance as well. The upconversion luminescence is the sum over all luminescence curves that represent emission of photons that can be used by a silicon solar cell, which were presented in
Fig. 5.30. For each level of irradiance Ii the upconversion luminescence PLUC,i(Ii) was determined. Therefore the effective upconversion luminescence could be determined via
UC ¦ , IPLFPL iiUCi . (5.72) i
201 5 Upconversion
Fig. 5.33: The distribution of the squared absolute value of the electric field normalized to the squared absolute value of the incident electric field around a gold nanoparticle with a radius of 40 nm under illumination with 1523 nm radiation. The direction of incidence is from the bottom of the graph in positive y-direction and the polarization is in the xy-plane. In certain areas the electric field is increased, while in different areas the electric field decreases due to the metal nanoparticle. This simulation was performed by Florian Hallermann at RWTH Aachen.
Fig. 5.34: Relative frequency distribution of the irradiance in the volume around the gold nanoparticles for an irradiance of 2000 Wm-2 at 1523 nm for particle radii of 20, 40 and 60 nm. The frequency distributions show a peak around the initial irradiance of 2000 Wm-2 and a longer tail reaching to higher irradiances. The figure shows the upconversion luminescence dependent on the irradiance as well. The upconversion luminescence is the sum over all luminescence curves, presented in Fig. 5.30, that represent emission of photons that can be used by a silicon solar cell.
202 5.6 Simulating upconversion
For all particle sizes, the upconversion luminescence is increased. The relative increase is 7% for the 20 nm particle, 11% for the 40 nm particle and 16% for the 60 nm particle. These are promising values that underline the potential to increase upconversion efficiency by the application of metal nanoparticles. It will be interesting to investigate even bigger particle sizes in future.
On the other hand, the effect of the nanoparticles on the emission must still be investigated. This effect could by itself increase efficiency. The direct enhancement of the emission of the upconverted photons could be achieved by designing the nanoparticles so they support plasmons that are in resonance with the high-energy 4 4 transitions from the I11/2 or I9/2 levels of the trivalent levels back to the ground level. However it must be clarified whether the particles that increase absorption have negative effects on the emission and vice versa. To investigate the effect of the metal nanoparticles on the emission, it must be known how the plasmons couple with the emission transitions and how this affects the corresponding Einstein coefficients. With the altered coefficients, the model should be able to demonstrate the effect of the particles on the emission. However, these analyses were beyond the scope of this work.
203 5 Upconversion
5.7 Upconversion systems
3+ In the optical measurements, the upconverter NaYF4 : 20 % Er showed a high upconversion efficiency of up to 10.2%. In this section, it is investigated as to how this high efficiency can be transferred to a solar cell system. At first, spectrally resolved measurements of the external quantum efficiency will be presented and compared to the results of the optical measurements. Prior to this work, comparable investigations have been performed by Shalav and Richards [107] and by Strümpel [144]. However, these investigations relied only on the excitation with coherent laser illumination. While the dominant upconversion mechanisms in erbium do not need coherence, this is disadvantageous for two reasons: First, other upconversion mechanisms, which occur under coherent illumination, might influence the experiments. Second, the illumination with a single wavelength does not reflect the situation of the later application, where the material will be illuminated with the broad spectrum of the sun. With a broad spectrum, e.g. photons of different energies might be combined to one high-energy photon. The only experiments performed without laser illumination [125] were restricted to the visible range of the spectrum on organic materials, and are therefore of minor significance for application on silicon solar cells. Therefore, at the end of this chapter additional first measurements of solar cell upconverter systems under concentrated sunlight illumination will be presented.
5.7.1 Used solar cells and experimental setup A bifacial back junction rear side contacted silicon solar cell served as the basis for an upconversion photovoltaic device. The solar cell is designed as a concentrator solar cell and is therefore very well suited to be operated under high irradiances that are beneficial for the upconversion efficiency. The active area of the solar cell is 4.5 x 4.5 mm2. Details on the solar cells’ processing and characterization can be found in [145]. This solar cell has both n- and p-contacts on the rear. Under AM1.5G illumination on the grid-free planar side, the solar cell exhibits around 19 % efficiency. Without an upconversion layer, no spectral response could be measured at wavelengths between 1400 nm and 1600 nm.
The solar cell was operated upside down, i.e. it was illuminated from its rear. In this configuration, various upconverters could be attached to the former front side and the contacting of the solar cell was not hindered by the application of the upconverter. To avoid total internal reflection of light in the infrared that should reach the upconverting material, the grid-free side of the solar cell was not textured. On the other hand, having
204 5.7 Upconversion systems all contact fingers on the front causes serious shading losses. The geometric coverage of the grid fingers amounts to roughly 60 % of the active cell area. This cell design is therefore not suited to reach the highest efficiencies, but it is a convenient test device for the experiments.
Fig. 5.35 shows the schematic setup for the external quantum efficiency (EQE) measurements. During the measurements, the solar cell was placed on a measurement chuck. The measurement chuck has an opening for the upconverter and other optical materials. The chuck is coated with gold to achieve a high reflection in the infrared.
Fig. 5.35: Schematic graph of the experiment for EQE measurements of a solar cell with upconversion in the IR spectral region. The upconverter is attached to the planar grid-free side of a bifacial silicon solar cell.
The same tunable IR-laser as for the optical characterization was used to illuminate the solar cell upconverter systems. Due to different geometrical properties of the experimental setup, higher irradiances for the excitation compared to the optical measurement were possible. The external quantum efficiency of the solar cell upconverter systems was measured in the range of 1430 nm to 1630 nm with an irradiance of 1090 Wm-2. The excitation beam was chopped with low 9 Hz because of the long lifetime of the excitation of the energy levels from the trivalent erbium (see section 5.5.4). Additionally, a continuous bias illumination of 0.04 suns was applied.
205 5 Upconversion
The short-circuit current of the solar cell due to upconverted photons ISC,UC(Oinc,I) under excitation with a wavelength Oinc and an irradiance I was measured using a lock- in amplifier 7265 from signal recovery. The external quantum efficiency was obtained as the ratio of the short-circuit current of the upconversion system and the short-circuit current ISC,ref(Oinc,I) of a germanium reference cell illuminated under the same conditions. The external quantum efficiency of the germanium cell EQEref(Oinc) is known from different measurements with standard solar cell characterization equipment. So the EQE of the upconversion solar cell system EQEUC(Oinc,I) can be calculated by
, OincUCSC II ),( EQE OincUC EQEI Oincref )(),( . (5.73) , OincrefSC II ),(
The uncertainty of the EQEref(Oinc) in the IR spectral region from the calibration of the setup is lower than 3 %, but it is still the dominating error. The statistical errors of both short-circuit currents calculated from 25 measurement points at the same Oinc and I are typically much lower.
5.7.2 Applying the upconverter to the solar cell 3+ Since NaYF4 : 20 % Er is a microcrystalline powder, some kind of binding agent is needed to apply the upconverter to the solar cell. Two different binding agents were tested in this work: the silicone gel Sylgard 184 and zapon varnish.
The silicone acts as a transparent matrix material, in which particles of the upconverter material are dispersed. Samples with different weight concentrations of the upconverter in the silicone and two different thicknesses (approximately 1.5 mm and 3.0 mm) were produced. Silicone is well suited for low weight concentration of the upconverter in the mixture. At high upconverter concentrations, processing of the silicone/upconverter mixture is difficult and the optical quality poor. Additionally, silicon shows quite strong absorption in the spectral region around 1500 nm to 1600 nm, which is disadvantageous as this is the absorption range of the 3+ NaYF4 : 20 % Er .
In contrast, zapon varnish is more like glue that connects and stabilizes the particles of the powder and is therefore applicable for very high upconverter concentrations. The upconverter powder was mixed with zapon varnish. Subsequently, the samples were dried at room temperature. The obtained samples vary in their geometrical properties
206 5.7 Upconversion systems like thickness and shape, but not much in the concentration of the upconverter in the mixture, which is close to 100 %.
The various solidified powder upconverter/binding agent mixtures were optically connected with a refractive index matching liquid to the silicon solar cell, and the
EQEUC(Oinc,I) was measured.
5.7.3 External quantum efficiency with different upconverter samples
The EQEUC(Oinc,I) was measured for various upconverter samples. Fig. 5.36 shows the
EQEUC(Oinc,I) for the best samples with silicone and zapon varnish. The best silicone sample was 3.0 mm thick and had a weight concentration of 25 % of the upconverter in the silicone. The best sample made from zapon varnish was roughly 0.9 mm thick and had an upconverter concentration of almost 100 %. Both systems were measured with an irradiance of 1090 Wm-2.
The EQEUC(Oinc,I) of the best silicone sample peaks only at 0.11 %. This low efficiency can be partly attributed to the overall low upconverter concentration in this sample. Furthermore, the unwanted absorption of the silicone in the absorption region of the erbium further reduces efficiency.
The zapon varnish sample shows much higher efficiencies. The EQEUC(Oinc,I) peaks at 0.34 % at a an incident wavelength of 1522 nm. Just as for the optical efficiency, a normalized quantum efficiency EQEUC,norm(Oinc,I) can be calculated by dividing the efficiency by the irradiance. This makes values obtained at different irradiances more -2 2 -1 comparable. With an irradiance of 1090 Wm the EQEUC,norm(Oinc,I) is 0.03 cm W and therefore 2.2 times higher than best value known so far that was measured by Richards [107].
A strong oscillation is visible in the EQEUC(Oinc,I) signal. The oscillation is caused by oscillations in the transmission of the silicon solar cell as plotted in Fig. 5.37. These oscillations are very likely the result of interference effects within the cell. The transmission in the spectral region of 1430 nm to 1630 nm varies between 25 % and 45 % with a period length of approximately 2.5 nm. Due to this variation in the transmission, the EQEUC(Oinc,I) varies by two effects: first, more or less photons impinge on the upconverter and therefore less photons can be converted. Second, since upconversion is a non-linear process, the efficiency is increasing with increasing photon flux and decreasing when the photon flux is lower.
207 5 Upconversion
Fig. 5.36: EQE measurement of a silicon solar cell with two different upconverter samples optically coupled to its back: one sample with the upconverter immersed in silicone with a relatively low concentration of the upconverter in the silicone, and one sample with the upconverter glued together with zapon varnish with a relatively high concentration of the upconverter in the mixture. The sample with the high upconverter concentration shows a much higher efficiency. This is attributed to the higher upconverter concentration and also to some unwanted absorption in the silicone. The strong oscillations in the EQEUC are caused by the oscillating transmission of the silicon solar cell (see Fig. 5.37)
Fig. 5.37: Transmission of the silicon solar cell in the IR spectral region. Very likely interference effects within the cell cause the strong oscillations.
208 5.7 Upconversion systems
5.7.3.1 Comparison to optical measurements
Fig. 5.38 shows the EQEUC(Oinc,I) divided by the transmission Tcell(Oinc) of the solar cell. However, this division only eliminates the first effect, but the effect caused by the non-linear upconversion efficiency remains. Hence, the effect of the solar cell’s transmission can not be fully eliminated. Nevertheless, a similarity of the
EQEUC(Oinc,I) divided by the transmission of the solar cell to the optically determined
KUC(Oinc,I) from Fig. 5.24 becomes visible.
Fig. 5.38: The EQEUC(Oinc,I) divided by the transmission of the silicon solar cell Tcell in comparison to the integrated optical efficiency presented already in Fig. 5.24. By dividing the electrical measurement by the solar cells transmission the strong oscillations in the signal can be partly eliminated. In this way, the substructure formed by the sub energy levels of the Er3+ is visible in both measurements that are well in agreement.
The quantum efficiency at 1522 nm is 0.7 % for the EQEUC(Oinc,I)/Tcell(Oinc). This is the quantum efficiency for the photons that actually reached the upconverter. This quantum efficiency reflects the efficiencies of the several involved processes: the quantum efficiency of the upconversion, the efficiency by which upconverted photons reach the solar cell, and the utilization of the upconverted photons by the solar cell. The dominant peak of the upconversion emission is at 980 nm. The external quantum efficiency of the solar cell EQEcell(O) at 980 nm is roughly 50 %. Therefore, the optical upconversion efficiency is estimated to be 1.4 %.
At around 1522 nm the silicon solar cell transmits roughly 40 % of the light. Therefore the actual irradiance impinging on the upconverter is 440 Wm-2. The optical
209 5 Upconversion
upconversion efficiency KUC(Oinc,I) at this irradiance is 1.9 % at the lower limit (see section 5.5.6). That means that the results from the electrical measurement are a little bit lower than that what would be expected from the optical measurements. This could be the result of additional optical losses. For instance, the upconverted light will impinge from all angles onto the silicon surface, resulting in reflection losses especially for shallow angles of incidence. Furthermore, there is scattering and parasitic absorption within the upconverter and in the zapon varnish. Moreover, there will be electrical losses due the inhomogeneous illumination of the solar cell. Taking these losses into account, one can state that the optical and the electrical measurements are very well in agreement.
5.7.3.2 Intensity dependence of EQE
Fig. 5.39 shows the EQEUC(Oinc,I) and the EQEUC,norm(Oinc,I) for different irradiances at a wavelength of 1522 nm of the incident photons. While the EQEUC(Oinc,I) increases with increasing irradiance, the EQEUC,norm(Oinc,I) slightly decreases. This means that the EQEUC(Oinc,I) grows a little bit less than linearly with the irradiance, which would have been the expectation for a perfect two photon process and a three level system. Already in the optical measurements the characteristic exponents had been lower than the theoretical expectations (Fig. 5.22) and saturation effects had occurred for higher irradiances. Therefore this result is well in agreement with the optical measurements.
Fig. 5.39: The EQEUC(Oinc,I) of the solar cell/upconverter device increases with higher irradiances. The EQEUC,norm(Oinc,I) defined as the ratio of EQEUC and irradiance, however, is slightly decreasing. This means that the EQEUC(Oinc,I) grows a little bit less than linearly with the irradiance.
210 5.7 Upconversion systems
5.7.3.3 Time-resolved solar cell response Besides the spectrally resolved features, it is interesting as well, whether the time- resolved features of the optical measurement could also be found in the response of the solar cell upconverter system. The upconversion solar cell response under excitation with 1522 nm was measured as a function of time using a Tektronix TDS3034 digital oscilloscope. Fig. 5.40 shows the time-resolved response. It exhibits a very slow decay. A single-exponential fit holds a decay time constant of 17.9 ms. Because the response of a silicon solar cell is magnitudes faster, this time constant has to be attributed to the luminescence decay of the upconversion layer. The time constant of 17.9 ms is slightly 4 larger than the 13 ms as reported in section 3 for the state I11/2, which is responsible for the dominant 980 nm luminescence.
4 Bearing in mind that the I11/2 decay was observed optically after pulsed excitation into 4 the F3/2 level whereas the solar cell response decay followed a continuous wave 4 4 4 excitation of the transition I15/2 Æ I13/2 Æ I9/2 and supposedly a multi-phonon 4 4 relaxation I9/2 Æ I11/2, the agreement is reasonable.
Fig. 5.40: The solar cell short-circuit current shows a build-up and decay pattern as 3+ observed for E-NaYF4: 20% Er . The decay time constant of 17.9 ms was obtained by a single-exponential fit.
5.7.4 Upconversion solar cell system under concentrated sunlight The spectrally resolved measurements presented in the previous section are well suited to investigate the spectral behavior of the upconverter. However, the later application will be under continuous illumination with a broad spectrum. Therefore, the best
211 5 Upconversion upconverter/solar cell device based on the zapon bound upconverter was measured under concentrated white light to determine the short circuit current ISC.
5.7.4.1 Experimental setup and method Fig. 5.41 shows a schematic of the experimental setup. Several lenses concentrate the light of a sun simulator onto the solar cell. To increase the relative impact of the upconversion layer, a polished silicon wafer with a thickness of 160 µm blocks most of the light that can be used directly by the silicon solar cell, but transmits the far IR photons suitable for upconversion. However, a part of the light that can be used directly by the silicon solar cell is still transmitted. This light has the function of a bias illumination that ensures that the solar cell is operated under sufficient illumination conditions to be able to make efficient use of the upconverted photons. In this configuration, the benefit of the upconversion due to a raised short-circuit current ISC is much more easily detectable than under full AM1.5 sun illumination.
Fig. 5.41: Schematic of the setup to measure the IV-characteristic of solar cells under concentrated white light. With lenses, the light of a Xe-lamp is concentrated on the solar cell. A polished silicon wafer serves as a long pass filter (see Fig. 5.42). The measurement chuck can be cooled and its position fixed with a vacuum exhaust.
212 5.7 Upconversion systems
The optical properties of the used silicon wafer are plotted in Fig. 5.42. Below a wavelength of 1180 nm, the transmission decreases from roughly 53 % to 0 % at wavelengths shorter than 930 nm. Therefore, some photons usable by a silicon solar cell are transmitted and induce a small offset current.
The solar cells were mounted on the same measurement chuck as described in the previous chapter for the measurements of the external quantum efficiency. The chuck was cooled to keep the solar cell temperature near standard conditions. However, as the upconverter was mounted underneath the solar cell, the full solar cell did not have direct thermal contact with the cooled chuck. Therefore, an unavoidable inhomogeneous temperature profile might have been present in the solar cell during the measurements.
Fig. 5.42: Optical properties of the polished silicon wafer used as long pass filter. Above 1200 nm it shows no significant absorption. In this spectral region, the reflection is around 47 %. This means 53 % of the photons suitable for upconversion are transmitted. Between 930 nm and 1150 nm some photons are transmitted that can produce free carriers in a silicon solar cell.
The concentration of the light was measured with a calibrated back contact Si solar cell designed for concentrated light, similar to the cells used in the silicon solar cell upconverter device. With the ISC of the reference cell under concentration and the ISC under one sun the concentration of the impinging light can be calculated. With two different settings of the lenses, two different concentration levels were reached. These concentration levels were 147±2 and 242±6 suns. In the calculation of these results, the mismatch between the AM1.5 norm spectrum and the spectrum of the Xe-lamp
213 5 Upconversion modified by the transmission of the lenses has been taken into account. The light spot is not fully homogeneous. Therefore the concentration level varies slightly with the exact position of the solar cell. To make sure that observed differences are due to real effects and not due to different positions of the device, every measurement was repeated 5-6 times and for each repetition the solar cell was removed and mounted again to cover the fluctuation due to different positions in the determined uncertainty as well. The given uncertainty is the uncertainty of the average value of the repeated measurements. The additional silicon wafer transmits roughly 53.5 % in the spectral area below the band-gap of silicon. Therefore, one can state that the effective concentration level of the light impinging on the silicon solar cell/upconverter system corresponds to a concentration of 79±1 and 129±3 below the band-gap of silicon. However, these concentration levels can only be used as a rough orientation, as the spectral region below the band-gap of the silicon was not considered in the determination of the concentration level with silicon solar cells. Therefore, for efficiency calculations, exact photon fluxes in the relevant spectral regions will be used later on. These photon fluxes could be calculated from the measurement of a relative spectrum of the Xe lamp and the presented determination of the concentration levels with the silicon solar cells.
3+ NaYF4 : 20 Er is a good diffuse reflector as well. Therefore, photons with energies slightly above the band-gap of silicon could be reflected by the upconverting powder and absorbed by the silicon solar cell. In this case, the application of the upconverter would increase solar cell efficiency without any significant upconversion taking place.
Therefore, the ISC was measured from the silicon solar cell with a diffuse reflector without upconverting properties optically coupled to the back of the solar cell. For this purpose, polytetrafluorethylene (PTFE, also known as Teflon) was used, which is a very good reflector and often used as reflection standard. A comparison of the 3+ reflectivity of PTFE and a thick, approximately 0.9 mm, layer of the NaYF4 : 20 Er solidified with zapon varnish dried on an optical glass is plotted in Fig. 5.43.
214 5.7 Upconversion systems
3+ Fig. 5.43: Comparison of the reflectance of the NaYF4 : 20 % Er solidified with zapon varnish on an optical glass and the reflectance of PTFE. The upconverter sample shows some absorption peaks at wavelengths of the transitions between the energy levels and reflects overall roughly 10 % less than PTFE.
It is obvious that the reflection of the PTFE is higher than that of the upconverter sample. Therefore, a short-circuit current measured with upconverter that exceeds the current measured with PTFE back reflector should be a clear sign of a positive effect of upconversion that proves that efficiency can be increased by the application of an upconverter in comparison to a simple back reflector design.
To extract the extra current due to the upconverter ISC,UC the average of the short- circuit current measurements with PTFE reflector ISC,PTFE is subtracted from the average of the measurements with upconverter attached to the silicon solar cell ISC,Zap :
, , III ,PTFESCZapSCUCSC . (5.74)
5.7.4.2 Results Table 5.6 shows the different measured and calculated short-circuit current values. Fig.
5.44 visualizes the results. For ISC,PTFE and ISC,Zap the uncertainties of the average values as determined from the repeated measurements are listed as uncertainties. The uncertainty of ISC,UC was calculated with Gaussian error propagation from these values. The relative error of ISC,UC is quite high, as ISC,UC itself is quite small but the result of the subtraction of two relatively big values. In Fig. 5.44 the uncertainties of the concentration are shown as well. This uncertainty reflects the uncertainty of the average value determined from the repeated measurements of the concentration level.
215 5 Upconversion
Fig. 5.44: Extra short-circuit current due to the upconverter ISC,UC and the spectrally integrated external quantum efficiency of the silicon solar cell upconverter device EQEUC,device()p,cell) at two different concentration levels. This is the first time a significant effect of an upconverter on the short-circuit current of a silicon solar cell was measured under white light illumination. Both extra current and EQEUC,device()p,cell) show a trend of increasing with higher concentration. This fact supports the conclusion that the observed effect is due to upconverted photons as this is the kind of non-linear behavior which is expected from upconverting material.
Despite all uncertainties, a significant increase of the short-circuit current due to the upconverter was observed. For instance, at 129x concentration the short circuit current with white PTFE reflector was 3.26 r 0.07 mA. This current was increased by 0.69 r 0.08 mA to 3.95 r 0.04 due to the addition of the upconverting layer. To my best knowledge, this is the first time that such an increase in short-circuit current due to upconversion has been measured on a silicon solar cell under white light.
From the short-circuit current measurements a spectrally integrated external quantum efficiency of the solar cell/upconverter device EQEUC,device()p,cell) can be calculated via
I ,UCSC . EQE ,deviceUC ) ,cellp )( (5.75) q ) ,cellp
In this equation q is the elementary chargeand)p,cell is the photon flux impinging on the solar cell in the absorption range of the upconverter. For calculating this photon flux, the transmission of the additional silicon wafer, the area of solar cell of 4.5 x 4.5 mm2, the concentration level and the changes in the spectrum due to the addition of lenses were taken into account. This flux critically depends on which
216 5.7 Upconversion systems spectral range is chosen to be the absorption range of the upconverter. Therefore the calculations were performed for three different absorption ranges: a narrow range from 1480-1630 nm, in which the upconverter shows significant response (see Fig. 5.24), a medium range from 1460-1600 nm, which includes as well the spectral ranges in which the upconverter shows very little response, and a very wide range from 1430- 1630 nm. The corresponding photon fluxes and the resulting efficiencies are listed in
Table 5.6. The EQEUC,device()p,cell) for the medium absorption range is plotted as well in Fig. 5.44. The theoretical expectation is that the integrated quantum efficiency increases with increasing irradiance because of the non-linearity of the upconversion. Unfortunately, experimental uncertainty is quite high for the higher concentration measurement, mainly due to a smaller illumination spot with higher inhomogeneity with a resulting higher sensitivity to the solar cell position. Nevertheless, a clear trend that both the extra current and the EQEUC,device()p,cell) increase with increasing irradiance is visible. This agreement with the theoretical expectation supports the conclusion that the observed effect is due to upconversion. For further evidence measurements should be performed with a larger set of concentration levels.
It is an interesting question, how the upconversion efficiencies under white light illumination compare to those measured with monochromatic laser excitation. For this purpose, it has to be considered that only roughly 40 % of the photons impinging on the solar cell are transmitted through the cell (see Fig. 5.37). The photon flux impinging on the upconverter )p,abs,UC is estimated to be , ) ,, UCabsp ) , Tcellcellp (5.76)
This result can only be an estimate, because the upconverter is optically coupled to the solar cell, while the transmission measurements were performed with the silicon solar cell in air. In consequence the reflection from the grid-free surface is present in the transmission data, but will be less pronounced in the data of the system measurements. Nevertheless, the estimate should be reasonable because most of the overall reflection is due to the unchanged reflection of the grid, which covers nearly 60% of the front surface, while the grid-free surface was equipped with an antireflection coating and therefore has low reflection. Additionally, it has to be taken into account that the EQE of the solar cell EQEref(Oinc) is only 50% at 980 nm, where the dominating peak of the upconversion emission occurs. In consequence, the optical measurement equivalent efficiency of the upconversion KUC,converter()p,abs,UC) can be estimated to be:
I ,UCSC , KUC,converter ) ,, UCabsp )( (5.77) q ,, UCabsp ) EQEref nm)980(
217 5 Upconversion
Table 5.6: Summary of the results of the measurements under concentrated white light
Concentration onto the solar cell 79r1 129r3 upconverter device [suns]
ISC,PTFE [mA] 1.67 r 0.02 3.26 r 0.08
ISC,Zap [mA] 1.99 r 0.02 3.95 r 0.04
ISC,UC [mA] 0.33 r 0.03 0.69 r 0.08
-1 Photon flux )p,cell [s ]
With UC absorption range
1430-1630 nm (3.62 r 0.04)1017 (5.78 r 0.13)1017
1460-1600 nm (2.53 r 0.03)1017 (4.04 r 0.09)1017
1480-1580 nm (1.80 r 0.02)1017 (2.88 r 0.06)1017
EQEUC,device()p,cell) [%]
With UC absorption range
1430-1630 nm 0.57 r 0.05 0.77 r 0.09
1460-1600 nm 0.81 r 0.07 1.07 r 0.13
1480-1580 nm 1.14 r 0.09 1.49 r 0.19
KUC,converter()p,abs,UC [%]
With UC absorption range
1430-1630 nm 2.8 r 0.2 3.7 r 0.5
1460-1600 nm 4.1 r 0.3 5.3 r 0.7
1480-1580 nm 5.7 r 0.5 7.5 r 0.9
KUC,converter(Oinc,)p,abs,UC) from optical 2.6-5.3 3.7-7.4 measurements [%]
218 5.7 Upconversion systems
At a concentration of 129 suns, an optical measurement equivalent upconversion efficiency KUC,converter()p,abs,UC) of 5.3 r0.7 % is reached under the assumption of a medium absorption range of the upconverter. To achieve the same photon flux impinging on the upconverter under laser illumination at 1523 nm as it was impinging in the absorption range of the upconverter during the concentrated white light measurement, a laser irradiance of 1047 Wm-2 is necessary. As can be seen in Fig. 5.26, at this irradiance the lower limit is 3.7 % and the upper limit 7.4 % in the optical measurements. The optical measurement equivalent upconversion efficiency
KUC,converter()p,abs,UC) lies perfectly between these limits. This is true as well for the lower concentration level. This result is more special than it appears on first sight. For one, based on the spectral measurements in the absorption range of the upconverter there are wavelengths with associated upconversion efficiency considerably below the peak values. Furthermore, the solar cell only utilizes photons that actually reach the solar cell. This corresponds to the conditions for the lower limit, while the upper limit was based on the assumption that more photons are emitted than detected because of optical losses in the upconverter powder. These two facts would make efficiencies under white light illumination considerably below the lower limit reasonable. In contrast, upconversion efficiencies under white light illumination appear to be at the same height or even higher than under monochromatic excitation.
This result can be partly attributed to the uncertainty of determining the photon flux that actually reaches the upconverter. On the other hand, efficiencies are so high that there must be effects that positively influence the efficiency under white light. One possible positive effect is that the energy gaps between the energy levels involved in the upconversion process are not centered on exactly the same energy. Therefore, illumination with slightly different photon energies may enhance the probability of an upconversion process. Additionally, during the experiments with the white light the upconverter is illuminated on a larger area and not with a small spot like with the laser. With only a small area illuminated, a considerable part of the excitation energy could migrate to non-illuminated areas by radiative and non-radiative processes. As excitation intensity in these regions is low, the dissipated energy hardly contributes to upconversion and therefore this dissipation constitutes a loss mechanism. These losses should be reduced under larger area white light illumination.
Due to the special definition of upconversion quantum efficiency, the achieved quantum efficiency of around 5% means that 10% of the photons incident in the absorption range of the upconverter were used. This quite positive finding supports the hope that upconverters can successfully enhance silicon solar cell efficiencies.
219 5 Upconversion
5.8 Conclusions and outlook on the application of upconverting materials to silicon solar cells
In this work several promising results were obtained that constitute significant progress in the field of upconversion research. This includes progress in the theoretical modeling, the investigation of the time dynamics of erbium doped NaYF4, calibrated optical measurements that showed up to 10% upconversion efficiency and measurements of complete systems of silicon solar cells and upconverter. Record efficiencies were achieved and for the first time a positive effect of an upconverting layer on the short-circuit current of a silicon solar cell could be demonstrated under white light illumination.
Nevertheless, significant challenges remain to be solved until upconversion can be applied successfully to increase silicon solar cell efficiencies. Fig. 5.45 shows the EQE of a silicon concentrator solar cell as used in this work measured with standard solar cell characterization equipment, and the additional response in the spectral range around 1500 nm due to the additional upconversion layer as it was presented in Fig. 5.36 in section 5.7.3. Two facts are obvious from this figure: first, the utilization of the spectrum is still incomplete and the achieved efficiency due to the upconverter is too low to have a significant positive effect on the overall solar cell performance. Furthermore, these efficiencies were achieved under high concentration conditions.
Fig. 5.45: EQE of a silicon concentrator solar cell as used in this work measured with standard solar cell characterization equipment and the additional response in the spectral range around 1500 nm due to the additional upconversion layer as it was presented in Fig. 5.36 in section 5.7.3.
220 5.8 Conclusions and outlook on the application of upconverting materials to silicon solar cells
On the other hand, with spectral concentration a concept was presented, and for the first time a design for its realization introduced, that could positively solve these issues. In combination with a luminescent material, the spectrum could be utilized more completely and additional internal concentration could be achieved.
The promising upconversion efficiency of 5%, representing 10% photon utilization, was achieved under white light illumination at a concentration level of 129 suns. This concentration level was calculated from reference measurements with a silicon solar cell and served to calibrate the overall irradiance. If the photon flux in the absorption range of the upconverter from 1460-1600 nm is considered, the effective concentration is about 5.7 times higher because of the differences in the Xe-lamp spectrum modified by the transmission of the lenses in comparison to the AM1.5 norm spectrum. Therefore the effective concentration level for the upconverter is about 735 suns.
On the other hand, in the spectral range between the band-gap of silicon and 1460 nm, there are around 13 times more photons than in the absorption range of the upconverter. Therefore spectral concentration could yield an internal concentration factor of around 10, assuming a quantum efficiency of 80% of the luminescent nanocrystalline quantum dots (NQD). Additionally, the NQD could be incorporated into a fluorescent concentrator as discussed in section 5.2.5. This could yield an additional concentration of at least a factor of 10. Therefore, an overall internal concentration of a factor of 100 should be possible. In consequence, high enough concentration levels for high upconversion efficiencies should be achievable with low external concentration factors of around 10, and in any case with higher concentrating systems. However, considerable progress in the field of luminescent NQD and especially in their incorporation into transparent matrix materials is necessary to make this concept possible.
Moreover, the investigated solar cell/upconverter system structures can be further developed in addition to the concept of spectral concentration to achieve efficiencies well beyond the level of today. One issue is the optimization of the upconverter material itself. For instance it will be interesting to investigate whether replacing Y by
La, Gd, or Lu in the NaYF4 host lattice can increase upconversion efficiencies because the maximum phonon energy and thus the unwanted non-radiative decay is reduced. Until now, an unexplored possibility is the use of neodymium instead of erbium. Neodymium features energy levels suitable for upconversion for an excitation at around 1650 nm [146]. This would be advantageous because lower energy photons could be used and a larger number of photons could contribute to spectral concentration. Additionally, neodymium features larger absorption cross sections. On
221 5 Upconversion the other hand, energy levels in between the levels involved in the upconversion could induce losses.
Finally, the solar cell itself has to be optimized to make the best use of the upconverted light. A first step is to have aligned contacts on both surfaces of the solar cell, to reduce the shading losses in comparison with the solar cell used in this study. Another important issue is the optical coupling of the solar cell and the upconverter to achieve high transmission of light in both directions. Accordingly, specially adapted antireflection coatings have to be developed. To convert the light emitted from the upconversion system efficiently, the solar cell must possess a bifacial layout with high rear side efficiency. Under illumination from the back, most electron-hole pairs are generated close to the back surface of the crystalline silicon solar cell. To achieve high rear side efficiency, a high diffusion length of the generated free carriers is necessary so they can reach the p/n-junction close to the front. In consequence, n-type silicon would be a good choice, as n-type silicon shows significantly higher diffusion lengths than the common p-type silicon [147]. A possible design is shown in Fig. 5.46.
Fig. 5.46: Design for a solar cell optimized for the application of an upconverter. The main features are: n-type material to achieve a high rear side efficiency, adapted anti-reflection coatings for high transmission, both for the upconvertible light and the upconverted light, and an aligned contact grid design on back and front surface to avoid shading losses.
The first application of upconversion will be in concentrator modules using crystalline silicon solar cells. A first reason for this assumption has been discussed extensively in this work: the solar cells and hence the upconverter system is illuminated with higher intensities in concentrator modules. Because of the non-linear characteristic of the
222 5.8 Conclusions and outlook on the application of upconverting materials to silicon solar cells upconverter this results into higher upconversion efficiencies and the positive effect of the upconverter is more pronounced. But there are additional reasons: the specific costs per area can be higher than in large-area modules. Furthermore, processing of the solar cells and assembly of the concentrator modules have more elements of a pick-and- place-technology. This resembles modern lighting technology, which involves as well luminescent material and structures that are related to the proposed upconversion system. Today’s concentrator technology is dominated by expensive multi-junction solar cells based on III-V semiconductors. Applying the upconverting systems will help to narrow the efficiency gap between silicon solar cells and the multi-junction cells, while maintaining the cost advantage of silicon solar cells.
As there will be internal concentration onto the upconverter, the upconverter will not cover the whole area and therefore only little amounts of upconverter material are necessary, hence material costs will be reasonably low. Therefore the cost efficiency is critical determined by how much extra processing costs occur. These could be kept low, if the addition of the upconverter system is incorporated into the cell production and the module assembly. For instance, photonic structures made from silicon alloy could simultaneously provide surface passivation on the solar cell and therefore no extra processing step would be required, or the matrix material with the embedded luminescent materials could provide the mechanical interconnection of the cell to the module and would therefore replace the glue in current modules. In consequence, it is likely that the achievable efficiency increase will be high enough to justify the additional costs for an upconversion system.
The application of upconversion is not limited to crystalline silicon solar cells. Because it only requires adding an optically active layer system to solar cells without in- fluencing the electrical properties, upconversion can be applied to nearly all existing or emerging solar cell technologies. If high enough internal concentration were reached, thin-film photovoltaics could be an attractive surrounding for the application of up- conversion. Micro-crystalline silicon solar cells, for instance, show low current densities due to incomplete absorption of light at longer wavelengths. On the one hand, this is a challenge for the use of the upconverter radiation. On the other hand, a larger amount of unused photons is available for upconverting in a broader spectral range. This will provide for a higher flux of unconvertible photons, which is advantageous because of the non-linear behavior of the upconversion efficiency. Furthermore, the relative increase in current due to the upconverter could be higher. In consequence, up- conversion has the potential to lower costs for different kinds of photovoltaic technologies and therefore will potentially find widespread application throughout photovoltaics.
223
6 Summary
Most solar cells today are made from silicon. However, silicon solar cells do not use the full solar spectrum. They do not absorb photons with energies below the band-gap of silicon, and they convert the energy of photons which exceeds the band-gap into heat instead of electricity. Several concepts are discussed to overcome the resulting fundamental efficiency limits. One especially promising concept is photon management. Photon management means the splitting or modifying of the solar spectrum before the photons are absorbed in the solar cells in such a way that the energy of the solar spectrum is used more efficiently. Photon management has the advantage that the solar cells themselves remain fairly unchanged and well-established solar cell technologies can be used. Therefore, photon management has a high potential for realization.
In this thesis, I explored concepts to increase the efficiency of photovoltaic systems with the means of photon management. I concentrated on two related concepts using luminescent materials that feature many advantages: first, fluorescent concentrators with photonic structures, and second, upconversion of sub-band-gap photons. For both concepts, this work comprises theoretical models and simulation tools that highlight the important mechanisms and processes, help the general understanding of the concepts and allow one to draw new conclusions on general working principles. The experimental work ranged from basic material investigations, for which new methods were developed and new experimental setups realized, to the fabrication and characterization of complete photovoltaic systems, for which record efficiencies were achieved. Finally, based on the findings of this work, new system designs were developed in both fields that constitute real conceptual progress, documented in granted patents and pending patent applications.
6.1 Fluorescent concentrators
Fluorescent concentrators are a well-known concept to concentrate both diffuse and direct light without tracking. A fluorescent concentrator consists of a slab of a transparent matrix material doped with a luminescent material. The luminescent material absorbs incoming radiation and subsequently emits radiation with a longer wavelength. Most of the emitted radiation is trapped by total internal reflection and guided to solar cells mounted at the edges of the fluorescent concentrator. A stack of different fluorescent concentrators with different luminescent materials can use a wide
225 6 Summary spectral range. Such a configuration can be used to split the solar spectrum, because the different fluorescent concentrators each collect different fractions of the spectrum. In combination with spectrally adapted solar cells, each fraction can be converted by solar cells that are the most efficient in that spectral range.
In this work, I presented entropic considerations that show that the maximum achievable concentration depends on the Stokes shift between absorbed and emitted radiation. Because of the energy dependence, the imposed fundamental limit could become critical for fluorescent concentrators operating in the infrared. Therefore during the development of NIR emitting materials for fluorescent concentrators, care must be taken to achieve large enough Stokes shifts.
I presented a thermodynamic model of fluorescent collectors, in which the chemical potential of the excited dye molecules is an important parameter. The chemical potential determines the emission of radiation through the generalized Planck’s law. The chemical potential and consequently the emission of light are not constant throughout the cross-section of the collector, because of the absorption profile in the collector. This was found to be the main source for the asymmetric angular distribution of the light leaving the edges of the collector, which has been determined experimentally in this work.
I developed a new method to determine the spectral collection efficiency of fluorescent collectors. Only three optical measurements with a photospectrometer and an integrating sphere are necessary to determine the ability of the concentrator to guide light to its edges. This method constitutes a fast and easy way to scan reasonably similar samples to find the one, which is best suited for application in fluorescent concentrator systems. For fully quantitative results on an absolute scale, for samples with large Stokes shifts and/or very different properties, additional corrections must be applied. For the investigated samples, the spectral collection efficiency reached values above 60% in the absorption region of the used dye. A comparison with results from external quantum efficiency measurements on a system with fluorescent collector and attached solar cells showed good agreement. The information necessary for the correction can also be used to derive additional relevant data, such as the absorption of the dyes in use and the fraction of light lost into the escape cone.
Photoluminescence measurements showed that the photoluminescence spectrum of the dyes in the concentrators depends on the excitation wavelengths. However, due to re-absorption of emitted light no differences are present in the spectrum of the light that leaves the concentrators at the edges.
226 6.1 Fluorescent concentrators
A simulation tool for the light-guiding properties of the fluorescent collector was developed, which is based on Monte-Carlo methods. This tool allows testing different hypotheses that could explain the results of the optical characterization. The shape of the photoluminescence spectrum emitted by the dye and the angular distribution of this emitted light proved to be very important for the properties of the collector. In contrast, scattering and the dependence on the excitation wavelength of the photoluminescence spectrum were found to be of minor importance. The model should be further developed to include wavelength dependent emission anisotropy. With such an amendment the simulation could be used for the optimization of key parameters of fluorescent concentrator systems.
For the realization of fluorescent concentrator systems, specially adapted solar cells made from GaInP and GaAs were produced. These materials were chosen because their band-gap and therefore the resulting solar cell characteristics fitted nicely to the emission of the used luminescent materials. The solar cells have special geometries and adapted antireflection coatings. With these solar cells and different fluorescent collector materials, several different systems were realized. I demonstrated that the collection efficiency of fluorescent concentrator systems can be increased by two independent measures. First, the combination of different dyes enlarges the used spectral range. In this way, a high efficiency of 6.9% was achieved. Second, photonic structures that act as a bandstop reflection filter in the emission range of the dye reduce the escape cone losses and therefore increase the collection efficiency of the overall system. The system efficiency could be increased by 20% with a commercially available filter. With the achieved efficiency of 3.1% and the concentration ratio of 20, the realized fluorescent concentrator system produces about 3.7 times more power than the used GaInP solar cell had produced on its own. The detailed analysis of size effects showed that photonic structures are especially beneficial for larger systems.
With the achieved efficiencies, it is obvious that fluorescent concentrators are no high- efficiency approach. Hence, in practical applications the achieved concentration ratio and the resulting cost reduction potential will be important. To make fluorescent concentrators commercially attractive, system sizes and efficiency have to be increased. One important issue is to extend the used spectral range into the infrared. One concept that might help to increase concentration levels and light guiding efficiency is the novel “Nano-Fluko” concept presented in this work.
227 6 Summary
6.2 Upconversion
Photon upconversion of sub-band-gap light is a promising approach to overcome the fundamental problem of sub-band-gap losses while still retaining the advantages of silicon photovoltaic devices. An upconverter generates one high-energy photon out of at least two low-energy photons. Several mechanisms cause upconversion, of which excited state absorption (ESA) and energy transfer upconversion (ETU) are the most frequent ones. The involved processes can be theoretically described with the help of Einstein coefficients. The derived model allows theoretically predicting the intensity dependence of the upconversion luminescence. At low excitation irradiance, the upconversion luminescence from one level obeys a power law with a characteristic exponent k, which reflects the number of photons necessary to populate this level. For higher irradiance the increase in luminescence saturates because stimulated emission processes and population of higher levels become more important.
The Einstein coefficients can be determined from absorption coefficient data, with the help of the Judd-Ofelt theory. In this work, erbium doped microcrystallineE-NaYF4 was investigated as an upconverter material. This material was only available as microcrystalline powder, which makes absorption measurements difficult. Therefore, the Kubelka-Munk theory was applied to derive the absorption coefficient of the material from reflection measurements on samples of various thicknesses. With the combination of these theories, the Einstein coefficients could be estimated that served as input for further theoretical modeling.
Based on the obtained Einstein coefficients and the according theory, a simulation tool that models the upconversion dynamics was developed. The model includes ground state and excited state absorption, energy transfer and multi-phonon relaxation. The model is capable of reproducing qualitatively experimental results such as the dependence of the upconversion luminescence on the irradiance. The model can be used to study the effect of different parameters, such as the multi-phonon relaxation, on the upconversion dynamics. It was found that multi-phonon relaxation critically determines the relative occupation of the different levels and also affects the dependence on the irradiance. The effect of plasmon resonance in metal nanoparticles on the upconversion was investigated using the model. The intensity distribution around a gold nanoparticle of 60 nm radius was found to increase upconversion luminescence by 16% in comparison to the case without the particle.
Time-resolved photoluminescence measurements yielded first insights into the time dynamics of the involved processes. Long time constants were found for the excitation
228 6.2 Upconversion decay of two energy levels that are most important for the upconversion for silicon solar cells. The time constants depend on the erbium upconverter concentration. From this dependence it could be concluded that energy transfer plays a very important role in the luminescence dynamics, and therefore most likely for upconversion as well. Intensity dependent photoluminescence measurements showed an increase of photoluminescence intensity with increasing irradiance following a power law as predicted from theory.
With calibrated photoluminescence measurements it was possible to directly determine the upconversion efficiency. Spectrally resolved measurements showed an active and efficient spectral range from 1480-1580 nm. Integrated upconversion efficiency increased with increasing irradiances to 10.2 % at the upper limit at an irradiance of 1880 Wm-2 at a wavelength of 1523 nm. Because at least two low-energy photons are necessary to generate one high-energy photon, this means that more than 20% of the incident photons contributed to the generation of upconverted photons. Normalized to the excitation irradiance, this is the highest upconversion efficiency achieved so far.
3+ The E-NaYF4:20% Er was applied to bifacial silicon concentrator solar cells in different binding agents. External quantum efficiency measurements of the complete system showed very good agreement with the optical measurements. The efficiency of the complete system peaks at 0.34% in the upconversion regime at an incident wavelength of 1522 nm and an irradiance of 1090 Wm-2. Normalized to the intensity, this is again the highest measured value. These experiments were carried out under monochromatic laser excitation. However, solar cells are used in sunlight. Therefore, measurements under concentrated white light were performed as well. For the first time in the context of upconversion for silicon solar cells, a positive effect of an upconverting layer on the current could be measured under white light. Very interestingly, the achieved efficiencies for a broader spectral range are at the same level as the peak values under monochromatic excitation. This means that there must be mechanisms that influence upconversion efficiency positively under white light excitation. The better excitation of all involved transitions with slightly different energies and a larger illuminated area could be possible explanations.
The positive results under white light illumination promise that upconversion can be applied to enhance silicon solar cell efficiencies. On the other hand, prior to an industrial application, the used spectral range and the achieved efficiencies must be increased considerably. The presented concept of spectral concentration might help to achieve this goal: a luminescent material absorbs in a wide spectral range and emits in
229 6 Summary the absorption range of the upconverter. This increases efficiency by two mechanisms: first, more photons are used, and second the photon flux in the absorption range of the upconverter is increased, increasing the upconversion efficiency. For the realization of this concept, I developed a system design that combines spectral concentration with geometric concentration by a fluorescent concentrator. Therefore the high concentration levels needed for sufficient upconverter efficiencies can be achieved internally without high external concentration. The application of spectrally selective, reflective photonic structures, avoids re-absorption losses and the solar cell is equipped with a good back-reflector. For the realization of this concept, progress in the implementation of luminescent nanocrystalline quantum dots is necessary. Further fields for optimization are the silicon solar cells, which should be adapted to make better use of the upconverter light, and the upconverter itself, where new materials might boost efficiency.
In conclusion, new insights were gained and significant progress was achieved in the two investigated fields, fluorescent concentrators and upconversion. This progress opens a positive perspective for the application of photon management. Nevertheless, considerable efforts are still necessary until these concepts can fulfill their promise to reduce solar electricity costs and to help the widespread dissemination of photovoltaics.
230 7 Deutsche Zusammenfassung
Die meisten Solarzellen werden heutzutage aus kristallinem Silizium hergestellt. Diese Solarzellen nutzen die im Sonnenspektrum enthaltene Energie aber nur unvollständig aus. Photonen mit einer Energie unterhalb der Bandlücke werden nicht absorbiert. Bei Photonen mit Energien oberhalb der Bandlücke geht der Teil der Energie, der die Bandlücke übersteigt, als Wärme verloren. Es gibt mehrere Konzepte, wie diese prinzipiellen Verluste reduziert werden können. Besonders vielversprechend ist dabei der Ansatz des Photonen-Managements. Photonen-Management zielt darauf, den Wirkungsgrad von Solarzellensystemen zu erhöhen, indem das Sonnenspektrum aufgeteilt oder verändert wird, bevor das Sonnenlicht von Solarzellen absorbiert wird. Der Vorteil dieses Ansatzes ist es, dass die eigentlichen Solarzellen im Wesentlichen unverändert verwendet werden können und deshalb auf etablierte Solarzellentechnologien zurückgegriffen werden kann. Im Vergleich zu anderen Ansätzen hat das Photonen-Management deshalb ein hohes Realisierungspotenzial.
In dieser Arbeit habe ich zwei verwandte Konzepte des Photonen-Managements untersucht: Fluoreszenzkonzentratoren mit photonischen Strukturen und die Hochkonversion von Photonen mit Energien unterhalb der Bandlücke von Silizium. Diese Konzepte verbindet, dass lumineszente Materialien zum Einsatz kommen. Für beide Konzepte wurden theoretische Modelle aufgestellt sowie Simulationsprogramme entwickelt. Mit diesen Modellen konnten die wesentlichen Wirkmechanismen untersucht und das Verständnis vertieft werden. Die experimentellen Arbeiten reichten von der Untersuchung wesentlicher Materialeigenschaften bis zur Realisierung und Charakterisierung kompletter Solarzellensysteme. Für die experimentellen Untersuchungen wurden zum Teil neue Methoden entwickelt und neue Versuchsaufbauten realisiert. Aufbauend auf den Ergebnissen dieser Arbeiten wurden in beiden Gebieten konzeptionell weiterführende Ansätze für neue Systemarchitekturen entwickelt. Diese wurden zum Teil bereits patentiert bzw. sind Gegenstand laufender Patentanmeldungen.
7.1 Fluoreszenzkonzentratoren
Fluoreszenzkonzentratoren sind ein bekanntes Konzept, um diffuses und direktes Sonnenlicht zu konzentrieren, ohne dass dazu das Photovoltaiksystem der Sonne nachgeführt werden muss. Fluoreszenzkonzentratoren bestehen aus einem transparenten Material, in welches ein lumineszentes Material eingebracht wurde. Das
231 7 Deutsche Zusammenfassung lumineszente Material absorbiert einfallende Strahlung und emittiert anschließend Strahlung mit einer etwas größeren Wellenlänge. Der Großteil der emittierten Strahlung wird durch Totalreflexion im Konzentrator gefangen und zu Solarzellen an den Seitenflächen geleitet. In einem Stapel mit unterschiedlichen Fluoreszenzkonzen- tratoren kann das Sonnenspektrum aufgeteilt werden und jeder Teil des Spektrums kann zu Solarzellen geleitet werden, die für diesen Bereich besonders effizient sind.
In dieser Arbeit habe ich entropische Überlegungen präsentiert, die zeigen, dass die maximal erreichbare Konzentration eines Fluoreszenzkonzentrators von der Stokes- Verschiebung zwischen einfallender und emittierter Strahlung abhängt. Die sich daraus ergebene prinzipielle Grenze kann für Konzentratoren, die im nahen Infrarot aktiv sind, zu einem begrenzenden Faktor werden. Deshalb ist es wichtig, bei der Entwicklung der dafür notwendigen Materialien auf eine möglichst große Stokes- Verschiebung zu achten.
Fluoreszenzkonzentratoren lassen sich mit Hilfe eines thermodynamischen Modells beschreiben, in dem das chemische Potenzial der angeregten Farbstoffmoleküle ein wesentlicher Faktor ist. Dieses bestimmt über das verallgemeinerte Planck’sche Strahlungsgesetz die Emission von Strahlung. Das chemische Potenzial ist über den Querschnitt durch den Konzentrator nicht konstant. Dadurch wird nahe der Oberfläche mehr Licht emittiert. Mit Hilfe dieses Modells konnte die Winkelverteilung des Lichtes, das den Fluoreszenzkonzentrator an den Kanten verlässt, erklärt werden. Diese war im Rahmen dieser Arbeit experimentell bestimmt worden und hatte eine unerwartete Asymmetrie gezeigt.
Im Rahmen dieser Arbeit entwickelte ich eine neue Methode, um die Seitenleit- effizienz, also die Fähigkeit der Fluoreszenzkonzentratoren Licht zu ihren Seitenflächen zu leiten, spektral aufgelöst zu bestimmen. Dafür sind lediglich drei Messungen mit einem Photospektrometer und einer Ullbricht-Kugel notwendig. Mit dieser Methode können ähnliche Materialien sehr einfach bezüglich ihrer Eignung für einen Einsatz in Fluoreszenzkonzentratoren miteinander verglichen werden. Für eine vollständig quantitative Bestimmung der Seitenleiteffizienz, für Proben mit einer sehr großen Stokes-Verschiebung und zum Vergleich von Proben mit sehr unterschiedlichen Eigenschaften müssen die Ergebnisse noch einer Korrektur unterzogen werden. Die für die Korrektur notwendigen Daten können außerdem benutzt werden, um noch weitere Eigenschaften der Konzentratoren zu bestimmen. Dazu zählen die Absorption der verwendeten Farbstoffe und der Anteil des Lichtes, der durch den Verlustkegel der Totalreflexion verloren geht. Die untersuchten Materialien erreichten Seitenleiteffizienzen von bis zu 60%. Die Ergebnisse der neuen
232 7.1 Fluoreszenzkonzentratoren
Methode zeigten eine gute Übereinstimmung mit Messungen der externen Quanteneffizienz an Systemen aus Fluoreszenzkonzentratoren und Solarzellen.
Photolumineszenzmessungen zeigten, dass das Photolumineszenzspektrum von der Anregungswellenlänge abhängt. Durch den Einfluss von Reabsorption ist allerdings bei dem Licht, das den Kollektor an den Seiten verlässt, kein Einfluss der Anregungswellenlänge mehr festzustellen.
Um die unterschiedlichen Hypothesen zu überprüfen, die zur Erklärung der Ergebnisse der optischen Charakterisierung dienten, wurde eine Simulation der Lichleit- eigenschaften der Fluoreszenzkonzentratoren entwickelt. Es zeigte sich, dass die Form des Photolumineszenzspektrums und die Winkelcharakteristik der Emission die Lichtleiteigenschaften erheblich beeinflussen. Im Gegensatz dazu spielten Streuung und die Wellenlängenabhängigkeit der Photolumineszenz nur eine untergeordnete Rolle. Wahrscheinlich lässt sich die Übereinstimmung mit den Messergebnissen noch weiter verbessern, indem eine Wellenlängenabhängigkeit der Winkelcharakteristik der Abstrahlung berücksichtigt wird. Damit sollte das Modell sehr gut für die Optimierung von Fluoreszenzkonzentratorsystemen einsetzbar sein.
Zur Realisierung von Systemen aus Solarzellen und Fluoreszenzkonzentratoren wurden Solarzellen aus GaInP und GaAs hergestellt. Die Bandlücken dieser Materialien ermöglichen eine besonders effiziente Ausnutzung der von den Fluores- zenzkonzentratoren geführten Strahlung, welche im sichtbaren Spektralbereich liegt. Die Solarzellen besaßen spezielle geometrische Abmessungen und angepasste Anti- reflexionsschichten. Aus diesen Solarzellen wurde mit unterschiedlichen Fluoreszenz- konzentratormaterialien eine Vielzahl von Systemen realisiert. Dabei ließ sich der Wirkungsgrad der Systeme mit zwei unabhängigen Ansätzen signifikant steigern: Die Kombination unterschiedlicher Materialien vergrößerte den ausgenutzten Spektralbereich, so dass ein Wirkungsgrad von 6.9% erreicht wurde. Zum anderen reduzieren photonische Strukturen mit spektral selektiv reflektierenden Eigenschaften die Strahlungsverluste durch den Verlustkegel der Totalreflexion. Dadurch ließ sich der Systemwirkungsgrad um 20% steigern. Mit dem für das untersuchte System erzielten Wirkungsgrad von 3.1% und der hohen 20fachen Konzentration lieferte dieses System aus Fluoreszenzkonzentrator und Solarzelle das 3.7fache der Leistung, welche die verwendete GaInP Solarzelle alleine geliefert hätte. Eine detailliert Untersuchung größenabhängiger Effekte zeigte, dass photonische Strukturen insbesondere für größere Systeme sinnvoll sind.
Mit den erzielten Wirkungsgraden sind Fluoreszenzkonzentratoren kein Hocheffizienz- Ansatz. Für praktische Anwendungen sind daher die erreichbare Konzentration und
233 7 Deutsche Zusammenfassung das sich daraus ergebende Kostensenkungspotenzial interessant. Um Fluoreszenzkonzentratoren kommerziell interessant zu machen, müssen deshalb die Systemgrößen und der Wirkungsgrad weiter gesteigert werden. Außerdem muss der genutzte Spektralbereich ins Infrarote ausgedehnt werden. Ein Ansatz der evt. helfen könnte, die Konzentration und die Wirkungsgrade zu steigern, ist das “Nano-Fluko“- konzept, das ich in dieser Arbeit präsentiert habe.
7.2 Hochkonversion
Die Hochkonversion von Photonen mit Energien unterhalb der Bandlücke von Silizium ist ein vielversprechender Weg auch die Energie dieser Photonen nutzbar zu machen und gleichzeitig die Vorteile von Siliziumsolarzellen zu erhalten. Hoch- konverter erzeugen ein hochenergetisches Photon aus mindestens zwei Photonen mit niedrigerer Energie. Die wichtigsten Hochkonversionsmechanismen sind die Absorption eines Photons durch ein Atom, das sich bereits in einem angeregten Zustand befindet und die Energietransfer-Hochkonversion. Die an der Hochkonversion beteiligten Prozesse lassen sich mit Hilfe der Einsteinkoeffizienten beschreiben. Ein daraus abgeleitetes theoretisches Modell erlaubte eine qualitative Vorhersage der Intensitätsabhängigkeit der Hochkonversion. Bei niedrigen Anregungsintensitäten hängt die Intensität der Hochkonversionslumineszenz über ein Potenzgesetz von der Anregungsintensität ab. Der Exponent wird dabei durch die Anzahl der für den Hochkonversionsprozess notwendigen Photonen bestimmt. Bei höheren Anregungs- intensitäten flacht sich der Verlauf ab, insbesondere weil angeregte Niveaus verstärkt durch stimulierte Emission entvölkert werden.
Mit Hilfe der Judd-Ofelt Theorie lassen sich die Einsteinkoeffizienten aus dem Absorptionskoeffizienten eines Materials berechnen. In dieser Arbeit wurde Erbium dotiertes, mikrokristallines E-NaYF4 als Hochkonverter untersucht. Dieses Material ist nur als mikrokristallines Pulver verfügbar. Deshalb wurde die Kubelka-Munk Theorie angewendet, um aus Reflexionsmessungen den Absorptionskoeffizienten zu bestimmen. Durch die Kombination dieser Theorien konnten die Einsteinkoeffizienten abgeschätzt werden. Diese dienten dann im Weiteren als Eingangsparameter für die Simulation der Hochkonversionsdynamik.
Mit Hilfe der experimentell bestimmten Einsteinkoeffizienten und der vorgestellten Theorie wurde ein auf Ratengleichungen basierendes Simulationsmodell der Hoch- konversionsdynamik entwickelt. Das Modell berücksichtigt Absorption im Grund- zustand und in den angeregten Zuständen, Energietransfer und Multi-Phononen-Über- gänge. Das Model ist in der Lage, die experimentell gefundene Abhängigkeit der
234 7.2 Hochkonversion
Hochkonversionslumineszenz von der Anregungsintensität qualitativ zu reproduzieren. Außerdem kann das Modell eingesetzt werden, um die Wirkung der unterschiedlichen Einflussgrößen genauer zu untersuchen. So bestimmt die Stärke der Multi-Phononen-Übergänge sehr stark die relative Besetzung der einzelnen Energieniveaus, sowie den Verlauf der Hochkonversionslumineszenz in Abhängigkeit von der Anregungsintensität. Das Modell konnte dazu eingesetzt werden, die Wirkung von Plasmonenresonanz in Metall-Nanopartikeln zu untersuchen auf die Hochkonversion zu untersuchen. Ein Gold–Nanopartikel mit 60 nm Radius erhöhte die Hochkonversionslumineszenz um 16% im Vergleich zum Fall ohne Partikel.
Mit Hilfe von zeitaufgelösten Photolumineszenzmessungen konnten erste experimentelle Einblicke in die zeitliche Dynamik der Photolumineszenz einzelner Übergänge gewonnen werden. Aus der Abhängigkeit der charakteristischen Zeit- konstanten von der Konzentration des Erbium Hochkonverters konnte geschlossen werden, dass Energietransfer maßgeblich die Dynamik der Lumineszenz bestimmt. Intensitätsabhängige Messungen der Hochkonversionslumineszenz zeigten einen Anstieg der Intensität der Hochonversionslumineszenz bei höheren Anregungs- intensitäten. Dieser Anstieg folgte einem Potenzgesetz, wie auch von der Theorie erwartet worden war.
Mit kalibrierten Photolumineszenzmessungen war es möglich, die Effizienz der Hochkonversion direkt zu messen. Spektral aufgelöste Messungen zeigten einen aktiven Spektralbereich von 1480-1580 nm. Die integrierte Hochkonversionseffizienz steigt mit der Anregungsintensität an. Bei einer Anregung mit 1880 Wm-2 bei einer Wellenlänge von 1523 nm wurde eine Hochkonversionseffizienz von 10.2% erreicht. Weil mindestens zwei niederenergetische Photonen notwendig sind, um ein hoch- energetisches Photon zu erzeugen, bedeutet dieser Wert, dass mehr als 20% der einfallenden Photonen genutzt wurden. Normiert auf die Bestrahlungsdichte der Anregung ist dies die höchste jemals gemessene Hochkonversionseffizienz.
3+ Das E-NaYF4 :20% Er wurde mit Hilfe unterschiedlicher Bindemittel auf bifaciale Silizium Solarzellen aufgebracht. Die Solarzellen sind für den Einsatz in Konzentratorsystemen optimiert. Messungen der externen Quanteneffizienz (EQE) zeigten sehr gute Übereinstimmung mit den spektral aufgelösten optischen Messungen. Die EQE des Systems erreichte einen Spitzenwert von 0.34% bei einer Wellenlänge von 1522 nm und einer Bestrahlungsstärke von 1090 Wm-2. Normiert auf die Bestrahlungsstärke ist auch dies der höchste jemals gemessene Wert. Diese Experimente wurden unter Anregung mit monochromatischer Laserstrahlung durchgeführt. Solarzellen werden aber normalerweise mit dem kontinuierlichen
235 7 Deutsche Zusammenfassung
Sonnenspektrum bestrahlt. Deshalb wurden auch Experimente unter Anregung mit weißem Licht durchgeführt. Zum ersten Mal im Kontext von Hochkonversion für Siliziumsolarzellen konnte dabei ein positiver Effekt des Hochkonverters auf den Kurzschlussstrom der Solarzelle gezeigt werden. Interessanterweise waren die gemessenen Hochkonversionseffizienzen für eine Anregung mit einem breiten Spektrum auf der Höhe der besten Werte unter monochromatischer Anregung. Eine bessere Anregung aller beteiligten Übergänge, deren Energien sich teilweise leicht unterscheiden, sowie die größere bestrahlte Fläche könnten hierfür Erklärungen sein.
Die positiven Resultate insbesondere unter Anregung mit weißem Licht lassen eine Anwendung von Hochkonvertern zur Effizienzsteigerung von Siliziumsolarzellen realistisch erscheinen. Allerdings ist bis jetzt der ausgenutzte Spektralbereich zu klein und die erzielten Wirkungsgrade noch zu niedrig. Hier könnte der Ansatz der spektralen Konzentration Abhilfe schaffen. Dabei absorbiert ein lumineszentes Material Photonen aus einem breiten Spektralbereich und emittiert Photonen im Absorptionsbereich des Hochkonverters. Dies erhöht die Hochkonversionseffizienz über zwei Mechanismen: Erstens werden mehr Photonen ausgenutzt, und zweitens erhöht sich die Photonenflussdichte im Absorptionsbereich des Hochkonverters. Aufgrund der nichtlinearen Intensitätsabhängigkeit steigt dadurch die Hoch- konversionseffizienz. Im Rahmen dieser Arbeit habe ich ein Konzept vorgestellt, wie ein solches System realisiert werden kann. In diesem Konzept werden spektrale Konzentration und geometrische Konzentration mit Hilfe eines Fluoreszenz- konzentrators miteinander kombiniert. Dadurch lassen sich die für hohe Hoch- konversionswirkungsgrade notwendigen hohen Intensitäten ohne aufwendige externe Konzentration mit Linsen oder Spiegeln erreichen. Zusätzlich verhindern spektral selektiv reflektierende Strukturen Reabsorptionsverluste, und die Solarzelle erhält trotz bifacialen Designs einen guten Rückseitenreflektor. Für die Realisierung des Konzeptes ist aber noch wesentlicher Fortschritt in der Entwicklung lumineszenter Nanokristalle und deren Einbettung notwendig. Das Gesamtsystem lässt sich außerdem noch durch die Optimierung der Solarzellen verbessern. Eventuell lassen sich auch Fortschritte durch die Verwendung neuer Hochkonvertermaterialien erzielen.
Zusammenfassend wurden in den beiden untersuchten Gebieten, Fluoreszenz- konzentratoren und Hochkonversion, neue wichtige Erkenntnisse gewonnen und konzeptioneller Fortschritt erzielt. Dieser Fortschritt eröffnet Perspektiven für eine erfolgreiche Anwendung der Konzepte. Allerdings ist noch umfangreiche Forschung notwendig, bis diese ihr Versprechen erfüllen können, zu einer weiteren Verbreitung der Photovoltaik beizutragen.
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248 9 Appendix
9.1 Abbreviations
Variable Meaning
Al Aluminum
AM Air mass
EQE External quantum efficiency
e Electron
ESA Excited state absorption
ETU Energy transfer upconversion
Fluko Fluorescent collector or fluorescent concentrator system
FWHM Full width half maximum
GaAs Gallium Arsenide
GaInP Gallium Indium Phosphide
GSA Ground state absorption
h Hole
IR Infrared
NQD Nanocrystalline quantum dot
PL Photoluminescence
PTFE Polytetrafluoroethylene
PMMA Polymethylmethacrylate
Si Silicon
SR Spectral response
sr Steradiant
UV Ultraviolet
249 9 Appendix
9.2 Glossary
Variable Unit Meaning
a m Lattice constant
A m2 or cm2 Area
2 2 Ainc m or cm Area that receives radiation
2 2 Aemit m or cm Area that emits radiation
Einstein coefficient of spontaneous -1 Aij s emission between the two energy levels i and j
Fraction of incident radition that is Abs dye absorbed by the dye
Fraction of incident radiation that is Abs mes absorbed (and not emitted again)
Fraction of incident radition that is Abs matrix absorbed by the matrix
DD Q D O m-1 or cm-1 Absorption coefficient
Absorption coefficient in the absorption D m-1 or cm-1 abs region of the fluorescent collector
-1 -1 Ddye m or cm Absorption coefficient of the dye
Absorption coefficient in the emission D m-1 or cm-1 emit region of the fluorescent collector
-1 -1 DPMMA m or cm Absorption coefficient of the PMMA
D ° Angle
Din ° Angle of incident ray in refraction event
Dout ° Angle of outgoing ray in refraction event
250 9.2 Glossary
Variable Unit Meaning
Radiant intensity, defined as radiant energy per unit time, per unit surface area (on % W/(m2 sr) which radiation incidents), per unit solid angle
2 %inc W/(m sr) Incident intensity
2 %int W/(m sr) Intensity inside a medium
Number of emitted/incident photons per 2 Bp,Q 1/(s m sr Hz) time, per area, per unit solid angle, and per frequency interval
3 2 B12 m /(Js ) Einstein coefficient for the absorption
Fraction of incident radition that is detected C mes in centermount measurements
F Free parameter used in different settings d m or cm Thickness, Thickness of the layer i
D m Distance
E J or eV Energy
EC J or eV Lowest energy in the conduction band
EF J or eV Fermi level
Fermi energy of the electrons in the E J or eV FC conduction band
Fermi energy of the holes in the valence E J or eV FV band
Ei J or eV Energy state i
Eg J or eV Band-gap energy
EQE External quantum efficiency
251 9 Appendix
Variable Unit Meaning
External quantum efficiency of system of
EQEsystem(Oinc) fluorescent collector with attached solar cells
External quantum efficiency of system of
EQEsystem,optical(Oinc) fluorescent collector with attached solar cells calculated from optical measurements
External quantum efficiency of a system of EQE (O ,I) UC inc solar cell and upconverter
External quantum efficiency of a system of -1 2 EQEUC,norm(Oinc,I) W m solar cell and upconverter normalized to the irradiance of the excitation
Spectrally integrated external quantum
EQEUC,device()p,cell) efficiency of the solar cell/ upconverter device
E(m) Expectation value of the random variable m
H Étendue
Hinc Étendue of incident beam
Hemit Étendue of emitted beam
f Oscillator strength
Flux of photons (i.e. photons per unit time) Fp,Q, inc per unit area, per unit bandwidth, and per Fp,Q, emit 4S solid angle of the incident/emitted field.
Fi Relative frequency of the irradiance level i
FF Fill factor
) W Radiant flux
)p 1/s Photon flux
Flux of upconverted photons with a )p,UC(OUC) 1/s wavelength ,OUC
252 9.2 Glossary
Variable Unit Meaning
Incident flux of photons with a wavelength )p,inc(Oinc) 1/s Oinc.
Photon flux impinging on the solar cell in ) 1/s p cell the absorption range of the upconverter
Photon flux impinging on the upconverter
)p,abs,UC 1/s cell in the absorption range of the upconverter gi Degeneracy factor of energy level i g(Z) Line form factor
Line form factor of the transition in the g (Z), g (Z) A S acceptor ion, respectively the sensitizer ion
Line form factor of the emission, g (Z), g (Z) em abs respectively the sensitizer transition
Generation rate of electron-hole pairs, per g 1/(s cm2) eh area
J Anisotropy coeeficient
Hamiltonian that describes the coulombic
H0 J interaction between the nucleus and the inner electrons with the valence electrons
Hamiltonian that describes the influence of the electric field of the crystal Hcf J
Hamiltonian that describes the coulombic H J ee repulsion between the electrons
Hamiltonian that describes electrostatic H J ES coupling of two ions
Hamiltonian that describes an ion in a H J Ion crystal
253 9 Appendix
Variable Unit Meaning
HIon, free J Hamiltonian that describes a free ion
Hamiltonian that describes interaction of H J int two ions
Hamiltonian that describes the spin-orbit H J SO interaction
K Efficiency
Kabs Absorption efficiency of the luminescent material due to its absorption spectrum with respect to the transmitted solar spectrum
Kcell Efficiency of the solar cell under illumination of the edge emission of the fluorescent collector
Kcoup Efficiency of the optical coupling of solar cell and fluorescent collector
Kmat “Matrix efficiency”, (1-Kmat) is the loss caused by scattering or absorption in the matrix.
Kreabs Efficiency of light guiding limited by self-
absorption of luminescent material, (1-reabs) is the energy loss due to re-absorption
Relative efficiency of upconversion K rel processes
KS(O) Spectral collection efficiency
Kstok “Stokes efficiency”, (1-Kstok) is the energy loss due to the Stokes shift
Ktrans,front Transmission of the front surface in respect to the solar spectrum
Ksystem System efficiency
254 9.2 Glossary
Variable Unit Meaning
Ktrap Fraction of the emitted light that is trapped by total internal reflection
Ktref Efficiency of light guiding by total internal reflection
Spectral upconversion quantum efficiency
at a certain luminescence wavelength OUC KUC,spectral(Oin,OUC,I) under the excitation with a wavelength Oinc and an irradiance I
KUC(Oinc,I) Integrated upconversion efficiency
Integrated upconversion efficiency -1 2 KUC,norm(Oinc,I) W m normalized to the irradiance of the excitation
Ke J or eV Electro-chemical potential of electrons
Kh J or eV Electro-chemical potential of holes
Irradiance, defined as radiant energy per , W m-2 unit time, per unit surface area on which radiation incidents
-2 Icell W m Irradiance on the solar cell
Irradiance of excitation radiation in I W m-2 exc photoluminescence measurements
-2 Ii W m Irradiance of irradiance level i
Emittance of sample in photoluminescence I W m-2 PL measurements
-2 IUC W m Irradiance on the upconverter
Spectral irradiance, defined as radiant energy per unit time, per unit surface area I (Z) W m-2 Hz-1 Q on which radiation incidents, per unit frequency bandwidth
255 9 Appendix
Variable Unit Meaning
Irradiance in z-direction and in the opposite I , I , W m-2 + - direction
, A Current
Imes A Measured current
ISC A Short-circuit current
Short-circuit current measured with a PTFE
ISC,PTFE A reflector attached to the back of the solar cell
Short-circuit current of the reference solar I A SC,ref cell
Part of the short circuit current which is I A SC,UC due the upconverted photon
Short-circuit current measured with the
ISC,Zap A upconverter attached to the back of the solar cell
Particle flux per area, of electrons, holes, j , j , j 1/(s cm2) e h eh and electron-hole pairs
J mA/cm2 Current density
2 Jsc mA/cm Short circuit current density
Total angular momentum of a single j kg·m2s-1 i electron
Total angular momentum of a system of J kg·m2s-1 electrons
Summation index giving the multipol order k i k of the transition in the ion i.
Orbital angular momentum of a single l i electron
256 9.2 Glossary
Variable Unit Meaning
Orbital angular momentum of a system of L electrons
O m or nm Wavelength of light
Oemit m or nm Wavelength of emitted light
Oinc m or nm Wavelength of incident light
O0 m or nm Design wavelength for photonic structure
Characteristic exponent that defines the m power law characteristic
2 me, mh m /Vs Mobility of electrons, holes
Emittance, defined as radiant energy per M W m-2 unit time, per unit surface area from which radiation is emitted
P J Chemical potential
Chemical potentials of the electrons, holes,
Pe, Ph, Peh J and the sum of chemical potential of electrons and holes
Dipole matrix elements of a transition )1()1()1( ,, PPP emabsij C m between the levels i and j, respectively for the absorption and emission transition n, n(O),n(Q) Refractive index
Charge carrier concentration of electrons, n , n 1/m3 e h holes
1 1/m3 Concentration of optically active ions
1L Number of ions being in a certain state i
257 9 Appendix
Variable Unit Meaning
Vector that describes the occupation of energy levels. The single elements of the * vector give the relative occupation of the N specific level, i.e. the fraction of ions of a large ion ensemble that is excited to this state.
Q Hz Frequency
QincQemit Hz Frequency of an incident/emitted photon
2 pext W/m Extracted power density
PLUC a.u. Intensity of upconversion luminescence
Q J Radiant energy
QE Quantum efficiency of the luminescent material
Angle, in most contexts the polar angle in ș ° polar coordinates
șc ° Critical angle of total internal reflection
Half of the opening angle of the cone, from ș ° inc which radiation is received
Half of the opening angle of the cone, in ș ° emit which radiation is emitted
Recombination rate of electron-hole pairs, r . 1/(s cm2) eh per area
R Reflection coefficient
Fraction of incident photons that is detected R mes during the reflection measurement
R Reflection coefficient of infinite thick layer
-1 Ui s Rate coefficient
258 9.2 Glossary
Variable Unit Meaning s O m-1 or cm-1 Scattering coefficient
Spin angular momentum of a single s Js i electron
Spin angular momentum of a system of S Js electrons
Si Singlet state of a molecule with number i
V J K-1 Entropy per photon t s Time
7 K Temperature
7S K Temperature of the sun
7 K Ambient temperature
7A K Absorber temperature
T Transmission
Tcell Transmission of the solar cell
Fraction o f incident photons that is T mes detected in the transmission measurement
WWup s Decay / Build-up time constant u(Z) J/(m3 Hz) Spectral energy density
U(t) Tensor operator of rank t
Number of the vibrational state of the v i electron state with number i
V V Voltage
VOC V or mV Open circuit voltage
Voltage than can be measured externally at V V or mV cell the solar cell
259 9 Appendix
Variable Unit Meaning
Probability that an electron is excited into
W12 1/s the higher level by the absorption of a photon
Probability that an electron returns from an excited state to the ground state by either W 1/s 21 spontaneous emission or stimulated emission of a photon
Probability for excitation energy migration W 1/s mig by emission and absorption of a photon.
WET 1/s Probability for energy transfer
Ȧ 1/s Angular frequency
: Solid angle
Solid angle from in which radiation is : emit emitted
Solid angle from which radiation is : inc received
ȍt Judd-Ofelt intensity parameters.
260 9.3 Physical Constants
9.3 Physical Constants
Variable Value Unit Meaning
c 299 792 458 m / s Speed of light in vacuum
-12 H0 8.854 187 817…u10 F / m Permittivity of vacuum
h 6.626076u10-34 J s Planck constant -34 м=h/2S 1.054572u10
-23 kB 1.380 6504u10 J / K Boltzmann constant
-31 m0 9.109 382 15u10 kg Electron rest mass
q 1.602 176 462(63)u10-19 C Elementary charge
261
10 Author’s Publications
10.1 Refereed journal papers
J. C. Goldschmidt, M. Peters, M. Hermle, and Stefan W. Glunz, Characterizing the light guiding of fluorescent concentrators, Journal of Applied Physics 2009, 105, p. 114911-1 – 114911-9.
J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S.W. Glunz, und G. Willeke, Increasing the efficiency of fluorescent concentrator systems, Solar Energy Materials & Solar Cells, 2009, 93, p. 176-182.
M. Peters, J. C. Goldschmidt, P. Löper, B. Bläsi, und A. Gombert, The effect of photonic structures on the light guiding efficiency of fluorescent concentrators, Journal of Applied Physics, 2009, 105, p. 014909-1 - 014909-10.
M. Peters, J. C. Goldschmidt, T. Kirchartz, B. Bläsi, The photonic light trap – Improved light trapping in solar cells by angularly selective filters, Solar Energy Materials & Solar Cells, 2009, 93, p. 1721-1727
J. C. Goldschmidt, M. Peters, L. Prönneke, L. Steidl, R. Zentel, B. Bläsi, A. Gombert, S. Glunz, G. Willeke and U. Rau, Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies, Physica Status Solidi A, 2008, 205(12), p. 2811-2821.
B. Ahrens, P. Löper, J. C. Goldschmidt, S. Glunz, B. Henke, P. Miclea and S. Schweizer, Neodymium-doped fluorochlorozirconate glasses as an upconversion model system for high efficiency solar cells, Physica Status Solidi A, 2008, 205(12), p. 2822-2830.
A. Goetzberger, J. C. Goldschmidt, M. Peters and P. Löper, Light trapping, a new approach to spectrum splitting, Solar Energy Materials & Solar Cells, 2008, 92, p. 1570-1578.
Submitted
M. Peters, J. C. Goldschmidt and B. Bläsi, Comparison of the principle efficiency limits for concentration and angular confinement in photovoltaic converters, submitted to Progress in Photovoltaics, 24.8.2009.
263 10 Author’s Publications
B. Groß, G. Peharz, G. Siefer, M. Peters, T. Gandy, J. C. Goldschmidt, J. Benick, S. W. Glunz, A. W. Bett, and F. Dimroth, Four-junction spectral beam splitting photovoltaic receiver with high optical efficiency, submitted to Progress in Photovoltaics, 15.10.2009.
In preparation
S. Fischer, J. C. Goldschmidt1, P. Löper, M. Hermle, S. Glunz, K. Krämer, D. Biner Detailed experimental analysis of upconversion to enhance solar cell efficiencies, to be submitted in January 2010.
10.2 Conference papers
J. C. Goldschmidt, S. Fischer, P. Löper, M. Peters, L. Steidl, M. Hermle, S. W. Glunz, Photon management with luminescent materials, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria.
Löper, P., M. Künle, A. Hartel, J. C. Goldschmidt, M. Peters, S. Janz, M. Hermle, S. W. Glunz, M. Zacharias, Silicon quantum dot superstructures for all-silicon tandem solar cells, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria.
M. Peters, J.C. Goldschmidt, B. Bläsi, Photonic Structures and Solar Cells, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria.
J. C. Goldschmidt, P. Löper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Krämer, D. Biner, Advanced upconverter systems with spectral and geometric concentration for high upconversion efficienciesm, in Proceedings IUMRS International Conference on Electronic Materials, 2008, Sydney, Australia, p. 307-311 Digital Object Identifier 10.1109/COMMAD.2008.4802153.
J. C. Goldschmidt, M. Peters, F. Dimroth, S. W. Glunz and G. P. Willeke, Efficiency enhancement of fluorescent concentrators with photonic structures and material combinations, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 193-197.
P. Löper, J. C. Goldschmidt, M. Peters, D. Biner, K. Krämer, O. Schultz, S. W. Glunz, J. Luther, Upconversion for silicon solar cells: Material and system characterization, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 173-180.
264 10.2 Conference papers
M. Peters, J. C. Goldschmidt, P. Loeper, B. Bläsi and G. Willeke. Lighttrapping with angular selective filters, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 353-357.
S. Fischer, J. C. Goldschmidt, P. Löper, S. Janz, M. Peters, S. W. Glunz, A. Kigel, E. Lifshitz, K. Krämer, Material characterization for advanced upconverter systems, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 620-623.
C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau. Directional selectivity and light-trapping in solar cells, in Photonics for Solar Energy Systems II, Strasbourg, France, SPIE, 2008, p. 70020A-11.
M. Peters, J. C. Goldschmidt, P. Löper, L. Prönneke, B. Bläsi, and A. Gombert, Design of photonic structures for the enhancement of the light guiding efficiency of fluorescent concentrators, in Photonics for Solar Energy Systems II, Strasbourg, France, SPIE, 2008, p. 70020V-11.
M. Bendig, J. Hanika, H. Dammertz, J. C. Goldschmidt, M. Peters and M. Weber. Simulation of fluorescent concentrators, in IEEE/EG Symposium on Interactive Ray Tracing, 2008, Los Angeles, California, USA, p. 93-98.
J. C. Goldschmidt, P. Löper, M. Peters, A. Gombert, S. W. Glunz, G. Willeke Progress in photon management for full spectrum utilization with luminescent materials, in Proceedings of 20th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2008), 2008, Bad Gastein, Salzburg, Austria.
M. Peters, J. C. Goldschmidt, P. Löper, C. Ulbrich, T. Kirchartz, S. Fahr, B. Bläsi, S. W.Glunz, A. Gombert. Photonic structures for the application on solar cells, in Proceedings of 20th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2008), 2008, Bad Gastein, Salzburg, Austria.
M. Peters, J. C. Goldschmidt, P. Löper, B. Blaesi and A. Gombert, Photonic crystals for the efficiency enhancement of solar cells, in EOS Topical Meeting on Diffractive Optics, 2007, Barcelona, Spain.
J. C. Goldschmidt, M. Peters, P. Löper, O. Schultz, F. Dimroth, S. W. Glunz, A. Gombert, G. Willeke, Advanced fluorescent concentrator system design, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference, 2007, Milan, Italy, p. 608-612.
265 10 Author’s Publications
P. Löper, J. C. Goldschmidt, M. Peters. D. Biner, K. Krämer, O. Schultz, S.W. Glunz, J. Luther, Efficient upconversion systems for silicon solar cells, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference, 2007, Milan, Italy, p. 589-594.
M. Peters, J. C. Goldschmidt, P. Löper, A. Gombert and G. Willeke, Application of photonic structures on fluorescent concentrators, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference, 2007, Milan, Italy, p. 177-181.
J. C. Goldschmidt, M. Peters, P. Löper, S. W. Glunz, A. Gombert, G. Willeke, Photon management for full spectrum utilization with fluorescent materials, in Proceedings of 19th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2007), 2007, Bad Hofgastein, Salzburg, Austria.
J. C. Goldschmidt, S. W. Glunz, A. Gombert and G. Willeke, Advanced fluorescent concentrators, in Proceedings of the 21st European Photovoltaic Solar Energy Conference, 2006, Dresden, Germany, p. 107-110.
J. C. Goldschmidt, S. W. Glunz, A. Gombert, G. Willeke, Advanced Fluorescent Concentrators, in Proceedings of 18th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2006), 2006, Rauris, Salzburg, Austria.
J. C. Goldschmidt, O. Schultz and S. W. Glunz, Predicting multi-crystalline silicon solar cell parameters from carrier density images, in Proceedings of the 20th European Photovoltaic Solar Energy Conference, 2005, Barcelona, Spain, p. 663-666.
O. Schultz, S. W. Glunz, J. C. Goldschmidt, H. Lautenschlager, A. Leimenstoll, E. Schneiderlöchner, G. P. Willeke, Thermal oxidation processes for high-efficiency multicrystalline silicon solar cells, in Proceedings of the 19th European Photovoltaic Solar Energy Conference, 2004, Paris, France, WIP-Munich, ETA-Florence, p. 604- 607.
J. C. Goldschmidt, K. Roth, N. Chuangsuwanich, A. B. Sproul, B. Vogl and A. G. Aberle. Electrical and optical properties of polycrystalline silicon seed layers made on glass by solid-phase crystallization, in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, 2003, Osaka, Japan, p. 1206-1209.
K. Roth, J. C. Goldschmidt, T. Puzzer, N. Chuangsuwanich, B. Vogl and A. G. Aberle, Structural properties of polycrystalline silicon seed layers mad on glass by solid-phase crystallisation, in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, 2003, Osaka, Japan, p. 1202-1205.
266 10.3 Oral presentations
10.3 Oral presentations
J. C. Goldschmidt, S. Fischer, P. Löper, M. Peters, L. Steidl, M. Hermle, S. W. Glunz, Photon management with luminescent materials, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria
J. C. Goldschmidt, M. Peters, F. Dimroth, S. W. Glunz and G. P. Willeke, Efficiency enhancement of fluorescent concentrators with photonic structures and material combinations, 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain.
J. C. Goldschmidt, P. Löper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Krämer, D. Biner, Advanced Upconverter Systems with Spectral and Geometric Concentration for high Upconversion Efficiencies, IUMRS International Conference on Electronic Materials, 2008, Sydney, Australia.
J. C. Goldschmidt, „Neuartige Solarzellenkonzepte“ oder „Wie man Photonen managt?“, 83. Stipendiatenseminar der Deutschen Bundesstiftung Umwelt, Deutsche Bundesstiftung Umwelt, Roggenburg, Germany, 9.–13.06.2008
J. C. Goldschmidt, P. Löper, M. Peters, A. Gombert, S. W. Glunz, G. Willeke, Progress in photon management for full spectrum utilization with luminescent materials, 20th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2008). 2008, Bad Gastein, Salzburg, Austria
J. C. Goldschmidt, Novel solar cell concepts – How to manage photons, Ornstein Colloquium, Utrecht University, The Netherlands, 15.11.2007
J. C. Goldschmidt, Neuartige Solarzellenkonzepte, 79. Stipendiatenseminar der Deutschen Bundesstiftung Umwelt, Deutsche Bundesstiftung Umwelt, Benediktbeuren, Germany, 5.–9.11.2007
J. C. Goldschmidt, M. Peters, P. Löper, S. W. Glunz, A. Gombert, G. Willeke, Photon management for full spectrum utilization with fluorescent materials, 19th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2007), 2007, Bad Hofgastein, Salzburg, Austria.
J. C. Goldschmidt, S. W. Glunz, A. Gombert and G. Willeke, Advanced fluorescent concentrators, 21st European Photovoltaic Solar Energy Conference, 2006, Dresden, Germany.
267 10 Author’s Publications
J. C. Goldschmidt, Neuartige Solarzellenkonzepte, 68. Stipendiatenseminar der Deutschen Bundesstiftung Umwelt, Deutsche Bundesstiftung Umwelt, Papenburg, Germany, 11.-16.6.2006
J. C. Goldschmidt, S. W. Glunz, A. Gombert, G. Willeke, Advanced Fluorescent Concentrators, 18th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2006), 2006, Rauris, Salzburg, Austria.
J. C. Goldschmidt, Solarzellen: Alte Rekorde und neue Konzept, Graduiertenkolleg – Nichtlineare Optik und Ultrakurzzeitphysik, Technische Universität Kaiserslautern, Germany, 11.1.2006
J. C. Goldschmidt, O. Schultz and S. W. Glunz, Predicting multi-crystalline silicon solar cell parameters from carrier density images, 20th European Photovoltaic Solar Energy Conference, 2005, Barcelona, Spain.
10.4 Patents
J. C. Goldschmidt, P. Löper and M. Peters, Solarelement mit gesteigerter Effizienz und Verfahren zur Effizienzsteigerung, Deutsches Patent, 10 2007 045 546.3, granted
A. Goetzberger, J. C. Goldschmidt, M. Peters and P. Löper, Photovoltaik-Vorrichtung und deren Verwendung, pending
J. C. Goldschmidt, M. Peters, M. Hermle, P. Löper, B. Bläsi, Lumineszenzkollektor mit mindestens einer photonischen Struktur mit mindestens einem lumineszenten Material sowie diesen enthaltendes Solarzellenmodul, pending
M. Peters, J. C. Goldschmidt, B. Bläsi, Kombination aus Konzentrator und winkelselektiven Filter für hocheffiziente Photovoltaik-Systeme, pending
M. Peters, B. Bläsi, J. C. Goldschmidt, Hubert Hauser, Martin Hermle, Pauline Voisin Strukturierungskonzept für effizientes Lighttrapping in Siliziumsolarzellen, pending
M. Hermle, B. Bläsi, M. Peters, H. Hauser, J.C. Goldschmidt, Solarzelle und Verfahren zu deren Herstellung, pending
268 10.5 Other publications
10.5 Other publications
J. C. Goldschmidt, M. Peters, F. Dimroth and S. W. Glunz, Zurück in die Zukunft - mit neuen Konzepten erlebt eine alte Konzentratortechnologie ihre Renaissance. Erneuerbare Energien, 2008. Nov 2008: p. 48-52.
F. Creutzig and J. C. Goldschmidt (Editors), Energie, Macht, Vernunft - der umfassende Blick auf die Energiewende. Taschenbuch ed. 2008, Aachen: Shaker Media. p. 352. ISSBN 3868580700
J. C. Goldschmidt, Einfluss von inhomogenen Materialeigenschaften auf die Effizienz multikristalliner Silizium-Solarzellen, Diplomarbeit, Fakultät für Mathematik und Physik, 2005, Universität Freiburg: Freiburg. p. 92.
J. C. Goldschmidt, Seeding Layers on Textured Glass Substrates for Crystalline Silicon Thin-Film Solar Cells, Bachelor Thesis, Key Centre for Photovoltaic Engineering, Bachelor for Photovoltaic Engineering, University of New South Wales, November 2002, p. 54
M. Peters, A. Bielawny, B. Bläsi, R. Carius, S.W. Glunz, J.C. Goldschmidt, H. Hauser, M. Hermle, T. Kirchartz, P. Löper, J. Üpping, R. Wehrspohn, G. Willeke Photonic Concepts for Solar Cells, in Physics of Nanostructured Solar Cells, V. Badescu, Editor, Nova Science, to be published in 2010
269
11 Curriculum vitae
Jan Christoph Goldschmidt
born 3rd of July 1979 in Schlüchtern
Education
1985-1998 Primary school, Gymnasium, Abitur (1,0)
10/1999-02/2005 Albert-Ludwigs-Universität Freiburg
Major subject: Physics/Diploma
Minor subjects: Micro-systems Engineering, and Seminconductor Physics and Technology
02/2002-11/2002 University of New South Wales in Sydney (UNSW), Australia
Research project on silicon thin-film solar cells
03/2004-02/2005 Diploma thesis at Fraunhofer Institute for Solar Energy Systems (ISE) on high-efficiency multi-crystalline silicon solar cells
02/2005 Diploma (very good)
08/2005-09/2009 PhD thesis at Fraunhofer ISE/ University of Konstanz
Scholarships
Studienstiftung des deutschen Volkes
Deutscher akademischer Austauschdienst (DAAD)
Heinrich Böll Stiftung
Deutsche Bundesstiftung Umwelt (DBU)
Work experience
08/1998-08/1999 Community service at Diakoniekrankenhaus Freiburg
06/2001-01/2002 Research assistant at Fraunhofer ISE
04/2003-02/2004 Research assistant at Fraunhofer ISE
04/2005-06/2005 Internship at McKinsey&Company Inc.
271
12 Acknowledgements
I would like to thank Prof. Dr. Gerhard Willeke for the supervision and advancement of this PhD thesis.
I thank Prof. Dr. Thomas Dekorsy for being the second assessor of this thesis.
I am very thankful to Dr. Stefan W. Glunz for the great opportunity to work in his group and later his department, for his inspiring enthusiasm, his motivation, and his support.
I thank Dr. Martin Hermle and Dr. Oliver Schultz-Wittmann, who became my group leaders, for their feedback, support, and encouragement.
It was a great honor and privilege to work together with Prof. Dr. Adolf Goetzberger. I am thankful for the chance to learn from his experience. His creativity is tremendously inspiring, and his humor made the collaboration very enjoyable.
My master students Philipp Löper and Stefan Fischer contributed significantly to this thesis. Furthermore, it was a great pleasure to work together with them.
My colleague Marius Peters joined me in the quest to enhance solar cell efficiencies by photon management. This has been a great collaboration, which resulted in many interesting discussions, a huge amount of new ideas, and great fun as well.
Many students supported this work during their internships or their time as student research assistant, by performing measurements, by cycling to the hardware store to buy equipment, by proof reading this thesis etc. I am thankful for the support of Michael Rauer, Anna Walter, Katarzyna Bialecka, Janina Löffler, Rena Gradmann, Tim Rist, Wesley Dopkins, and Marcel Pinyana.
I am thankful to all my colleagues with whom I shared an office, for the friendly atmosphere and the great fun we had together. I would like to especially mention Elisabeth Schäffer and Thomas Roth, with whom I shared an office for the longest period. Additional to discussion on all kind of subjects, I profited a great deal from their knowledge and support in many areas. I would also like to mention my old friend Tobias Kalden, who showed that music and solar energy perfectly match, and with whom I had many ice cream breaks during his part time job at ISE.
Many more colleagues at Fraunhofer ISE contributed to this work. I am especially thankful to Armin Bösch, Henning Helmers, and the team of the III-V solar cell group,
273 12 Acknowledgements who provided me with the III-V solar cells used in this work; to Benedikt Bläsi and Andreas Gombert, from whom I learned a lot about optics, to Prof. Wittwer, Armin Zastrow and Franz Brucker, who shared their knowledge from the early Fluko-research period with me; to Jochen Hohl-Ebinger and Holger Seifert, who contributed to various calibration efforts; and to the team of the mechanical workshop, who did a great job in producing all the special components for the measurement setups.
I am grateful for all the collaborations with many colleagues from outside the Fraunhofer ISE, with whom I had very fruitful discussions and who supported this work by various means. I would like to mention Bernd Ahrens, Prof. Dr. Gottfried Bauer, Marion Bendig, Daniel Biner, PD Dr. Rudolf Brüggemann, Dr. Andreas Büchtemann, Florian Hallermann, Prof. Dr. Karl Krämer, Ariel Kigel, Prof. Dr. Efrat Lifshitz, Prof. Dr. Andries Meijerink, Liv Prönneke, Lorenz Steidl, and all the other colleagues of the “Nano”-projects.
I gratefully acknowledge the scholarship support from the Deutsche Bundesstiftung Umwelt, and the ideational support from the Heinrich-Böll Stiftung and the German National Academic Foundation.
I thank my friends for the distraction from my work, for enduring me being late at the mensa and for their support.
I am very thankful to all my family for supporting me through my studies and this PhD work and especially my parents, whose gracious support and encouragement through all these years made all this possible.
Finally, I would like to thank my wonderful wife Berit Lange. Not only had she the calm hand that I lacked, when soldering contacts to solar cells, but she gave me great support of all kinds through all this work.
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