Design and Performance Analysis of an Efficient GaAs/AlGaAs Heterojunction Bipolar Transistor

A thesis submitted to the Department of Electrical and Electronic Engineering (EEE) of Bangladesh University of Engineering and Technology (BUET)

In partial fulfillment of the requirement for the degree of MASTER OF SCIENCE IN ELECTRICAL AND ELECTRONIC ENGINEERING by Sakib Hassan (Roll No.: 1014062235 P) DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING (EEE) BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY (BUET)

MAY 2017

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Declaration

It is hereby declared that this thesis or any part of it has not been submitted elsewhere for the award of any degree or diploma.

Signature of the candidate

______

Sakib Hassan

(Roll No.: 1014062235 P)

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Acknowledgements

First, I would like to express my gratitude towards the Almighty Allah for the strength, courage, and perseverance that He has bestowed throughout my academic life. I am thankful to Him for whatever I have achieved thus far in my educational pursuit. Next, I would like to express gratitude towards my thesis supervisor, Dr. Md. Kawsar Alam, Associate Professor of the Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka for the patient guidance, encouragement, and advice that he has provided throughout the time I have been his student. I consider myself extremely lucky to have such a wise, inspiring, and helpful supervisor who not only answered all the questions and queries and but also provided ample computational resources to aid my research endeavor. I will always be grateful to him for introducing me to the world of research and teaching a systematic approach towards research work.

I would also like to express my appreciation to the members of my thesis committee, Dr. Quazi Deen Mohd Khosru, Dr. Md. Ziaur Rahman Khan and Dr. Md. Anwarul Abedin, for their valuable feedback and suggestion on my work.

Completing this thesis work would have been all the more difficult were it not for the continuous help and support I received from fellow researcher in ‘Photonics Lab’ - Zabir Ahmed.

I would like to take this opportunity to thank my parents for their love, guidance, and influence. I also thank my wife for her continuous support and inspiration. Their belief in me has always been the source of strength in the most trying times.

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Abstract

In this work, we propose a highly efficient three-terminal heterojunction bipolar transistor solar cell. We have chosen GaAs/AlGaAs material system in this regard for its excellent optoelectronic properties. Rigorous optical and electrical performance analysis through computer simulation has been carried out to characterize the designed device. Usually, the efficiency of the solar cell depends on material composition, absorption of light, carrier transport, recombination etc. In our proposed structure, we have optimized these parameters to enhance the efficiency to a maximum value of 35.6%. We have determined the optimum layer thickness for the designed cell by varying the layer thickness of different regions of the structure and calculating efficiency through optoelectronic simulation. We have also changed the doping of three regions and found out the doping concentration for which the efficiency is maximized. We further investigated the effect of different loss mechanisms

(recombination) that occur inside the solar cell and find out the dominant loss mechanism.

We have also examined the role of photon recycling effect on the performance of designed solar cell. Finally, we have compared our result with conventional heterojunction solar cell and shown that this novel three-terminal device yields higher efficiency. The analysis and results presented in this thesis would provide a clear guideline for designing HBT based photovoltaic devices.

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Table of Contents

Declaration ……………………………………………………………………………...... iii Acknowledgements …………………………………………………………………………iv Abstract………………………………………………………………………………………v Table of Content…………………………………………………………………………… vi List of Figures……………………………………………………………………………..viii List of Tables……………………………………………………………………………...…x

Chapter 1 Introduction ...... 1

1.1 Solar Cell: History and Background ...... 2

1.1.1 First Generation Solar Cell— Based ...... 5

1.1.2 Second Generation Solar Cells— Solar Cells ...... 5

1.1.3 Third Generation Solar Cells ...... 7

1.2 Multijunction/Tandem Solar Cell...... 11

1.3 Solar Cell Design: Challenges ...... 13

1.4 Heterojunction Bipolar Transistor Solar Cell...... 15

1.5 Objective of the Thesis ...... 16

1.6 Overview of the Thesis ...... 17

Chapter 2 Theory and Modeling ...... 18

2.1 HBT Solar Cell: Basic Key Concepts ...... 18

2.1.1 Operation of PN Junction Solar Cell ...... 18

2.1.2 HBT Solar Cell (HBTSC) ...... 20

2.2 Numerical Modeling ...... 28

2.2.1 Optical Simulation Model ...... 29

2.2.2 Electrical Simulation Model ...... 33

2.3 Benchmarking ...... 36

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Chapter 3 GaAs/AlGaAs HBT Solar Cell: Design and Performance Analysis ...... 38

3.1 Device Design ...... 38

3.1.1 Device Structure...... 38

3.1.2 Choice of Material System...... 39

3.2 Result and Analysis ...... 41

3.2.1 Effect of Varying Layer Thickness ...... 42

3.2.2 Effect of Doping ...... 44

3.2.3 Effect of Recombination ...... 46

3.2.4 Effect of SRH recombination: ...... 48

3.2.5 Effect of photon recycling ...... 49

3.2.6 Optimized Structure ...... 51

3.2.7 Comparison with Conventional Heterojunction Solar Cell Configuration .... 56

3.2.8 Comparison with Other Material Systems ...... 57

Chapter 4 Conclusion and Future Work ...... 59

4.1 Conclusion ...... 59

4.2 Future work ...... 61

References ...... 62

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List of Figures

Fig. 1.1 Various types of solar cell technologies and trends of development...... 3 Fig. 1.2 Reported timeline of solar cell energy conversion efficiencies since 1976 [16]. ... 4 Fig. 1.3 Cost efficiency of different generation of solar cell technologies [50]...... 11 Fig. 1.4 A schematic of an InGaP/GaAs/Ge multijunction/tandem solar cell [51]...... 12 Fig. 1.5: Heterojunction bipolar structure to be used as solar cell proposed by Marti and Luque [63]...... 15 Fig. 2.1 A PN junction and the corresponding energy band diagram...... 19 Fig. 2.2 Energy band diagram of a PN junction solar cell along with absorption of photons, electron-hole pair generation, and transportation of excited carrier [64]...... 20 Fig. 2.3 ZnO/CDS/CIGSe/Mo heterojunction solar cell and corresponding energy band diagram. The different bandgap absorbs different energy photons ultimately giving a broadband absorption of the solar spectrum [66]...... 21 Fig. 2.4 Operation of heterojunction bipolar transistor structure as solar cell. The emitter and the collector are shorted together...... 22 Fig. 2.5 (a) Air mass determination. (b) Sunlight intensity for different air mass [67] . .... 23 Fig. 2.6 The absorption coefficient, α, in a variety of semiconductor materials at 300K as a function of the vacuum wavelength of light [67]...... 24 Fig. 2.7 Different recombination mechanisms inside a photovoltaic device such as (a) Shockley-Read-Hall (SRH) (b) Auger (c) radiative recombination [67]...... 26 Fig. 2.8 The J-V characteristics of a solar cell along with the power-voltage curve...... 27 Fig. 2.9 Simulation work flow of Maxwell’s equation solution...... 30 Fig. 2.10 Yee grid in three-dimensional simulation domains...... 31 Fig. 2.11 Boundary conditions in FDTD simulation...... 33 Fig. 2.12 The current-voltage characteristics and the power-voltage characteristics of the GaAs/AlGaAs heterojunction solar cell reported in Ref. [70]...... 36 Fig. 3.1 3D Schematic of the proposed three terminal HBT solar cell. The emitter region is heavily n-type doped except for the region below the base, which is heavily p-type doped for making the base terminal connection. The contacts are assumed to be made of Aluminum...... 39 viii | P a g e

Fig. 3.2 The J-V and P-V characteristics of the 5 µm GaAs and 0.7 µm AlGaAs HBT 2 solar cell before optimization. The Jsc and Voc are found to be 28.58 mA/cm and 1.01 V...... 41 Fig. 3.3 Ideal optical short-circuit current density calculated in FDTD solver for different thicknesses of GaAs and AlGaAs layers...... 42 Fig. 3.4 Dependence of (a) short-circuit current (b) open-circuit voltage and (c) efficiency on the layer thickness of GaAs and AlGaAs layer...... 43 Fig. 3.5 Effect of (a) base and (b) emitter doping on the efficiency of the solar cell...... 45 Fig. 3.6 Effect of different recombination processes on the J-V characteristics of the HBT solar cell (structure-X). The doping and recombination parameters are used as default values...... 47 Fig. 3.7 Effect of different recombination processes on the P-V characteristics of the HBT solar cell (structure-X)...... 47 Fig. 3.8 Contribution of SRH, Auger, and radiative recombination to the total loss mechanism in HBT solar cell structure-X...... 48

Fig. 3.9 Effect of SRH lifetime on (a) Jsc, (b) Voc, and (c) efficiency of the HBT cell (structure-X). The doping concentration of the emitter and collector regions are assumed to be 1×1019 cm-3 and 1×1018 cm-3 respectively. The base doping is taken in such way to satisfy Eq. 3.1...... 49 Fig. 3.10 Effect of photon recycling on the efficiency of the HBT solar cell. The inclusion of photon recycling effect reduces EHP capture rate and hence increase efficiency...... 50 Fig. 3.11 (a) AM 1.5G solar spectrum (b) Absorption spectrum of the optimized HBT solar cell (blue line) along with the absorption spectrum of unoptimized structure (green dotted line)...... 53 Fig. 3.12 Spatial absorbed optical power of highest efficiency, optimized 0.5 µm AlGaAs and 45 µm GaAs HBT solar cell...... 54 Fig 3.13 Spatial Electric field (magnitude) distribution of highest efficiency, optimized 0.5 µm AlGaAs and 45 µm GaAs HBT solar cell...... 55 Fig. 3.14 The (a) J-V and (b) P-V characteristics of the optimized structure. The input power is taken to be 100 mW/cm2...... 55

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List of Tables

Table 2.1 Comparison of values of Jsc, Voc, and η from our simulation and that reported

in Ref. [70]...... 37 Table 3.1 Basic electrical properties of the material system used in the simulations...... 40

Table 3.2 The effect of doping in different region on Jsc and Voc ...... 46 Table 3.3 Results of optical and electrical simulations...... 52 Table 3.4 Comparison of performance of HBT solar cell and conventionally configured solar cell...... 56

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Chapter 1 Introduction

The world has an insatiable appetite for energy. Electricity system worldwide is expanding, global demand for, and dependence on electricity is increasing with the ever increasing population along with rapid technological development and increased demand for mechanization and comfort. Currently, the world consumes around 10 terawatts (TW) per year, and by 2050, it is projected to be about 30 TW [1]. The International Energy Outlook 2013 (IEO2013) by the United States Energy Information Administration, also projects that global energy consumption will increase by 56% between 2010 and 2040 [2]. Currently, most of this energy is supplied by fossil fuels - oil, gas, etc. According to IEO2013, fossil fuels will continue to supply almost 80% of total energy consumption through 2040. However, these fossil fuels are not infinite. Terra Symbiosis predicts that with the current rate of growth of energy consumption, global oil reserve will be depleted within 50 to 100 years; natural gas reserve will be exhausted in 60 to 70 years and coal reserve will be depleted in around 200 years [3]. Apart from the limited reserve of fossil fuels, the use of fossil fuels raises severe environmental concerns. The burning of fossil fuels produces around 21.3 billion tonnes (21.3 giga tonnes) of carbon dioxide (CO2) per year, however it is calculated that natural processes can only absorb about half of that amount. Therefore, there is a net increase of 10.65 billion tonnes of atmospheric carbon dioxide per year [4]. The associated release of CO2 from these anthropogenic sources has dramatically altered the composition of the atmosphere and may detrimentally impact global temperature (by causing the average surface temperature of earth rise in response), sea levels, and weather patterns [5]. Most of the scientists agree that this will cause adverse effect on human civilization. This calls for rigorous exploration of decarbonized alternative, that is clean and environment friendly energy sources, which we call renewable energy.

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The sun sends us daily staggering amount of energy in the form of heat and radiations that we call . Solar energy is one of the most promising renewable energy sources of the modern era and a limitless source of energy which is available at nearly no cost [6, 7]. For example, earth’s ultimate recoverable resource of oil, estimated at 3 trillion barrels, contains 1.7×1022 joules of energy, which the sun delivers to our planet in 1.5 days [8]. Since 120,000 TW of solar radiation strikes on the surface of the earth, 10% efficient solar conversion systems covering 0.16% of the land would produce 20 TW of power, nearly twice the annual global energy consumption right now [9]. Moreover, the major benefit of solar energy over other conventional power generators is that the sunlight can be directly harvested into solar energy with the use of small and tiny photovoltaic (PV) solar cells [10, 11]. This type of electrical energy production method is cost effective, generates no toxic materials/greenhouse gasses, and follows green approach [7]. Thus, PV will play a significant role in meeting the world future energy demand and the present is considered as the “tipping point” for PV.

1.1 Solar Cell: History and Background

The history of the solar cell goes back to 1839 when the photovoltaic effect was experimentally demonstrated first by French physicist Edmond Becquerel [12]. He discovered the photovoltaic effect while experimenting with an electrolytic cell made up of two metal electrodes placed in an electricity-conducting solution—electricity generation increased when exposed to light. In 1883 Charles Fritts built the first solid- state photovoltaic cell by coating the semiconductor selenium with a thin layer of to form the junctions; the device was only around 1% efficient. Subsequently, in 1946 Russel Ohl invented the cell made of [12, 13]. Physicists at Bell Laboratories - Daryl Chapin, Calvin Fuller, and Gerald Pearson discovered that silicon is more efficient than selenium, creating the first practical solar cell — 6% efficient [14]. This discovery led to solar cells capable of powering electrical equipment. In 1956, Western Electric began selling commercial licenses for its silicon PV technologies; however, the prohibitive costs of silicon solar cells keep them from widespread market saturation. After years of experiments to improve the efficiency and commercialization of , solar energy gained support when the government used it to power equipment - the first solar-powered satellite, Vanguard 1. In 1970, the rise of 2 | P a g e oil price gives impetus for and producing solar cells from low-cost materials. Since then research and progress have been massive. Traditionally, the solar cell technologies are divided into three generation [15]. A tree diagram of the different generation of solar cells along with trends of development is shown in Fig. 1.1. The best- reported efficiency of some of the solar cells of three generations is given in Fig. 1.2.

Fig. 1.1 Various types of solar cell technologies and trends of development.

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Fig. 1.2 Reported timeline of solar cell energy conversion efficiencies since 1976 [16].

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1.1.1 First Generation Solar Cell—Wafer Based

The first generation of solar cells, also known as silicon wafer-based photovoltaic, is the dominant technology for terrestrial applications today, accounting for more than 85% of the solar cell market. Single-crystalline and multi-crystalline wafers, used in commercial production, allow power conversion efficiencies up to 25%, although the fabrication technologies at present limit them to about 15 to 20% [7, 10, 11, 17, 18]. These types of solar cells dominate the market and are mostly those seen on rooftops. The major benefits of this solar cell technology are their good performance and high stability. However, they are rigid (i.e. they cannot be used for the cases where flexibility is necessary) and require a lot of energy in production (since their processability depends on vacuum deposition methods).

1.1.1.1 Single/ Solar Cell: Monocrystalline solar cell, as the name indicates, is manufactured from single crystals of silicon by a process called Czochralski process [18-20]. During the manufacturing process, Si crystals are sliced from the big sized ingots. These large single crystal productions require precise processing as the process of “recrystallizing” the cell is more expensive and multiprocess. The efficiency of monocrystalline single solar cells lies between 17% - 18% [21].

1.1.1.2 Solar Cell (Poly-Si or Mc-Si): Polycrystalline PV modules are generally composed of a number of different crystals and the processing is more economical. Polycrystalline Si solar cells are currently the most popular solar cells and are believed to occupy up to 48% of the solar cell production worldwide during 2008 [22]. Though they are slightly cheaper to fabricate compared to monocrystalline silicon solar panels, yet are less efficient ~12% - 14%.

1.1.2 Second Generation Solar Cells—Thin Film Solar Cells

The second generation of photovoltaic materials is based on the use of the thin-film deposition of semiconductors, such as , ,

5 | P a g e indium gallium diselenide or copper indium sulfide. For example, silicon-wafer cells have light absorbing layers up to 350 µm thick, while thin-film solar cells have very thin light absorbing layers, generally on the order of 1 µm thickness [23]. The efficiencies of thin film solar cells tend to be lower compared to conventional solar cells, around 6% to 10%. However, manufacturing costs are also lower so that a price in terms of $/watt of electrical output can be reduced. Besides, decreased mass allows fitting panels on light materials or flexible materials, even textiles.

1.1.2.1 Amorphous Silicon Thin Film (a-Si) Solar Cell: The “amorphous” word with respect to a solar cell means that the comprising silicon material of the cell lacks a definite arrangement of atoms in the lattice, non-crystalline structure, or not highly structured. Amorphous Si (a-Si) PV modules are the primitive solar cells that are first to be manufactured industrially and can be manufactured at a low processing temperature, thereby permitting the use of various low cost, polymer, and other flexible substrates. These substrates require a smaller amount of energy for processing [23]. Therefore, the a- Si solar cell is comparatively cheaper and widely available. These are fabricated by coating the doped silicon material to the backside of the substrate/glass plate. The main issue of the a-Si solar cell is the poor and almost unstable efficiency. The cell efficiency automatically falls at PV module level. Currently, the efficiencies of commercial PV modules vary in the range of 4% - 8%. They can be easily operated at elevated temperatures, and are suitable for the changing climatic conditions where the sun shines for few hours [24].

1.1.2.2 Cadmium Telluride (CdTe) Thin Film Solar Cell: Among thin-film solar cells, cadmium telluride (CdTe) is one of the leading candidates for the development of cheaper, economically viable photovoltaic (PV) devices, and it is also the first PV technology at a low cost [21, 25, 26]. CdTe has a band gap of ~1.5 eV as well as high optical absorption coefficient and chemical stability. These properties make CdTe most attractive material for designing of thin-film solar cells. It is generally constructed by sandwiching between cadmium sulfide layers to form a p-n junction diode. Its efficiency usually operates in the range 9% - 11% [21, 27]. However, there are various environmental issues with cadmium component of the solar cell. Cadmium is regarded as a heavy metal and potential toxic agent that can accumulate in human bodies, animals, and plants. The disposal of the toxic Cd based materials, as well as their recycling, can be highly expensive and damaging to our environment and society [17, 24]. Therefore, a 6 | P a g e limited supply of cadmium and environmental hazard associated with its use are the main issues with this CdTe technology [26-28].

1.1.2.3 Copper Indium Gallium Di-Selenide (CIGS) Solar Cells: CIGS is a quaternary compound semiconductor comprising of the four elements, namely: copper, indium, gallium and selenium [17]. CIGS is also direct band gap type semiconductors. Compared to the CdTe thin film solar cell, CIGS holds a higher efficiency ~10% - 12%. Due to their significantly high efficiency and economy, CIGS-based solar cell technology forms one of the most likely thin film technologies.

1.1.3 Third Generation Solar Cells

The third generation of photovoltaic cell is a research goal due to a dramatic increase in efficiency that maintains the cost advantage of second-generation materials. The approaches include dye-sensitized nanocrystalline or Gratzel solar cells, organic polymer- based photovoltaic, tandem (or multi-junction) solar cells, hot carrier solar cells, plasmonic and solar cells. Third generation cells are the new promising technologies but are not commercially investigated in detail till now.

1.1.3.1 Nano Crystal Based Solar Cells: Nanocrystal-based solar cells are generally also known as quantum dots (QD) solar cells. These solar cells are composed of a semiconductor, generally from transition metal groups which are in the size of nanocrystal range made of semiconducting materials. QD is just a name of the crystal size ranging typically within a few nanometers in size, for example, materials like porous Si or porous TiO2, which are frequently used in QD. With the advance of nanotechnology, these nanocrystals of semiconducting material are targeted to replace the semiconducting material in bulk state such as Si, CdTe or CIGS. In conventional compound semiconductor solar cells, generally, a photon will excite an electron thereby creating one electron-hole pair [29]. However, when a photon strikes a QD made of the similar semiconductor material, numerous electron-hole pairs can be formed, usually 2 or 3, also 7 has been observed in few cases [7, 30]. This type of solar cell has excellent thermal stability and 50% less expensive than conventional Si cell.

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1.1.3.2 Polymer Solar Cells: Polymer solar cells (PSC) are generally flexible solar cells due to the substrate. A PSC is composed of serially connected thin functional layers coated on a polymer foil or ribbon. It works usually as a combination of the donor (polymer) and an acceptor (fullerene). There are various types of materials for the absorption of sunlight, including organic material like a conjugate/conducting polymer [7, 31]. In 2000, Heeger, MacDiarmid, and Shirakawa fetched the Nobel Prize in Chemistry for discovering a new category of polymer materials known as conducting polymers [32]. The PSC and other organic solar cells operate on the same principle known as the photovoltaic effect, i.e., where the transformation of the energy occurs in the form of electromagnetic radiations into electrical current. Yu et al. mixed poly [2-methoxy-5-(2’- ethylhexyloxy)-p-phenylene vinylene] (PPV), C60 and its other derivatives to develop the first polymer solar cell and obtained a high power conversion efficiency [33]. This process triggered the development of a new age in the polymer materials for capturing the solar power. After significantly optimizing the parameters, researchers achieved efficiency over 3.0% for PPV type PSCs [33, 34]. These unique properties of PSCs opened a new gateway for new applications in the formation of stretchable solar devices including textiles and fabrics [35]. A modern recycling concept known as polarizing organic photovoltaic (ZOPV) was also developed for increasing the function of liquid crystal displays utilizing the same polarizer, a photovoltaic device and proper light conditions/ [35].

1.1.3.3 Dye-Sensitized Solar Cells (DSSC): Recent research has been focused on improving solar efficiency by molecular manipulation, use of nanotechnology for harvesting light energy [36-38]. The first DSSC solar cell was introduced by Michel Gratzel in Swiss federal institute of technology. DSSCs based solar cells generally employ dye molecules between the different electrodes. The DSSC device consists of four components: a semiconductor electrode (n-type TiO2 and p-type NiO), a dye sensitizer, redox mediator, and a counter electrode (carbon or Pt) [39]. The DSSCs, attractive due to the simple conventional processing methods like printing techniques, are highly flexible, transparent and low cost as well [17]. The novelty in the DSSC solar cells arise due to the photosensitization of nano-grained TiO2 coatings coupled with the visible optically active dyes, thus increasing the efficiencies greater than 10% [36-39]. However, there are certain challenges like degradation of dye molecules and hence stability issues [17]. This is due to poor optical absorption of sensitizers which results in poor conversion

8 | P a g e efficiency. The dye molecules generally degrade after exposure to ultraviolet and infrared radiations leading to a decrease in the lifetime and stability of the cells. Moreover, coating with a barrier layer may also make the manufacturing more expensive and lower the efficiency.

1.1.3.4 Quantum well solar cell: Competitive costs and performance can be achieved by using quantum wells and quantum dots in crystalline solar cells. The quantum well solar cell (QWSC) is a novel device with the potential to achieve high efficiency in an alternative approach to tandem or cascade solar cells. Different losses in a standard p–n- junction limit the efficiency to ~30% and ways to avoid these losses to significantly increase the efficiency of QWSCs are analyzed by Green et al. [40] . In the simple QWSC, quantum wells of a lower bandgap material are grown within the space-charge region of p–n or p–i–n-structures. MBE or MOCVD are used to fabricate QWSCs.

1.1.3.5 Carbon nanotube cells: The concept of carbon nanotube (CNT) cell is a revolutionary idea in which a transparent conductor material made of CNT provides an excellent current. CNT is formed by hexagonal lattice carbon. Researchers at University of Wisconsin-Madison believe that these cells can convert 75% of light into electricity.

1.1.3.6 3D solar cells: Three-dimensional solar cells that capture nearly all of the light that strikes them and could boost the efficiency of photovoltaic systems while reducing their size, weight, and mechanical complexity. The new 3D solar cells, created at the Georgia Tech Research Institute, capture photons from sunlight using an array of miniature “tower” structures that resemble high-rise buildings in a city street grid [41, 42]. Solar3D Inc. plans to commercialize such 3D cells, but its technology is currently patent-pending [41].

1.1.3.7 Metamaterial-based Solar Cell: Metamaterials are heterogeneous materials employing the juxtaposition of many microscopic elements, giving rise to properties not seen in ordinary solids. Using these, it may become possible to fashion solar cells that are excellent absorbers over a narrow range of wavelengths. Although high absorption in the microwave regime has been demonstrated, however, not yet in the 300 - 1100 nm wavelength regime [43].

1.1.3.8 Thermophotovoltaic: This is the technology of generating electricity from heat via photons. The heat source can be waste heat from industry, re-radiation from the solar

9 | P a g e cell, heat produced in chemical reaction etc. A basic thermophotovoltaic system consists of a thermal emitter and a photovoltaic diode cell. The temperature of the thermal emitter varies between different systems from about 900 °C to about 20000 °C [44], although in principle TPV devices can extract energy from any emitter with temperature elevated above that of the photovoltaic device. TPV systems usually attempt to match the optical properties of thermal emission (wavelength, polarization, direction) with the most efficient absorption characteristics of the photovoltaic cell, since unconverted thermal emission is a major source of inefficiency. Most groups focus on gallium antimonide (GaSb) cells; germanium (Ge) is also suitable. The efficiency of thermophotovoltaic can reach up to 83% [45].

1.1.3.9 Plasmonic Solar Cell: A plasmonic solar cell is a type of thin film solar cell that converts light into electricity with the assistance of [46]. They are typically less than 2 μm thick and theoretically could be as thin as 100 nm [47]. They can use substrates which are cheaper than silicon, such as glass, or steel. One of the challenges for thin film solar cells is that they do not absorb as much light as thicker solar cells made with materials with the same absorption coefficient. Methods for light trapping are important for thin film solar cells [48]. Plasmonic cells improve absorption by scattering light using metal excited at their surface . Incoming light, at the plasmon resonance frequency, induces electron oscillations at the surface of the nanoparticles. The oscillating electrons can then be captured by a conductive layer producing an electrical current. The voltage produced is dependent on the bandgap of the conductive layer and the potential of the electrolyte in contact with the nanoparticles.

1.1.3.10 : Perovskites are a class of compounds defined by the formula ABX3 where X represents a halogen such as I−, Br−, Cl−, and A and B are cations of different size. Perovskite solar cells are recent discovery among the solar cell research community and possess several advantages over conventional silicon and thin film based solar cells. Solar cell efficiencies of devices using these materials have increased from 3.8% in 2009 to 22.1% in early 2016 (NREL efficiency chart). The perovskite-based solar cells can have efficiency up to 31% [49].

Cost efficiency of the solar cell technology is one of the important considerations for determining commercial feasibility. Figure 1.3 shows the cost efficiency graph of three 10 | P a g e generations of solar cells. We see that the cost of the earlier first generation solar cells was higher and their efficiency was also lower. Extensive research effort reduced the cost while uplifting the efficiency. The second generation solar cells are significantly lower in cost but they also suffer from lower efficiency due to the reduced absorption in a thin film. Nonetheless, the third generation solar cells prove to be very promising in terms of both cost and efficiency. This is due to the invention and development of the new solar suitable material system, new improved device architecture along with enhanced light- trapping techniques.

Fig. 1.3 Cost efficiency of different generation of solar cell technologies [50].

1.2 Multijunction/Tandem Solar Cell

The theoretical efficiency of a single-junction cell is around 31%. Better efficiencies could be obtained with more-efficient use of the solar spectrum. Cells made from multiple material layers can have multiple bandgaps and will, therefore, respond to multiple light wavelengths, capturing and converting some of the energy that would otherwise be lost to relaxation. Combining two or more cells of different bandgaps into a multijunction 11 | P a g e arrangement increases the amount of work done per photon. In other words, a multijunction/tandem cell is a unique form of solar cell consisting of two or more sub cells which together convert more of the sunlight spectrum into electricity and therefore increase the overall cell efficiency. To increase power, the cells should be current matched and joined in series by a tunnel diode. A schematic of an InGaP/GaAs/Ge multijunction/tandem solar cell is shown in Fig. 1.4.

Fig. 1.4 A schematic of an InGaP/GaAs/Ge multijunction/tandem solar cell [51].

Theoretically, an infinite number of junctions in a tandem/multijunction solar cell would have a limiting efficiency of 86.8% under highly concentrated sunlight. The best multi- junction cells have already reached efficiency around 41% with no concentration and 46% under concentrated sunlight [52, 53]. However, the technology is very expensive and these solar cells are therefore used today mainly for space applications, like Mars Rover mission. Commercial examples of tandem cells are widely available at 30% under one- sun illumination [52]. To date, the higher price and higher price-to-performance ratio of the tandem cell have limited their use to special roles, notably in aerospace where their high power-to-weight ratio is desirable.

In terms of space power applications, the Si cell efficiency is low and susceptible to radiation damage. In the late 1980s, GaAs cells were used to fabricate flat-plate arrays due to high efficiencies and lower radiation-induced degradation than Si cells. GaAs

12 | P a g e single-junction solar cells with efficiencies of ~25% were reported for concentrated AM0 sunlight many years ago [54, 55]. Metal organic chemical vapour Deposition (MOCVD), liquid-phase epitaxy, and molecular beam epitaxy (MBE) are usual methods for fabricating III–V solar cells. Enhanced efficiencies may be realized by stacking GaAs either monolithically or mechanically on booster cells of lower bandgap materials such as Si, Ge, CIS, GaSb, or InGaAs. For ultra-high-efficiency cells to be widely applied, it will be necessary to improve conversion efficiency and reduce cost. One approach is the fabrication of GaAs/Si cells. However, in this case, GaAs films contain dislocations. The InGaP/InGaAs/Ge triple-junction concentrator solar cell has demonstrated ~37.0% efficiency [56]. New approaches on novel materials and structures for 50% efficient multijunction cells are presented by Yamaguchi et al. [57].

1.3 Solar Cell Design: Challenges

Although the literature shows promising values of efficiency, however most of these results are confined to the laboratory or in simulation/theoretical work. Practical achievement of the high efficiency commercially feasible solar cell has still a long way to go. Although, extensive research is going on to find new material systems and device architectures, fabrication cost and complexity are an important concern. The tandem solar cell may yield high conversion efficiency, however there are still many issues to be solved. The tandem type is basically constructed as a series of stripes connected in a straight line. The total voltage would be the sum of the voltage of each layer, while the electric current is constant within a circuit. Therefore, if the effectiveness of power generation falls even within just a single layer at any level, it would cause a bottle-neck effect, and decrease the amount of the electric current flow for the entire line. For instance, even if an optimized tandem type is based on the ideal sunlight of AM1.5, the layer aiming the wavelength around the red zone would have a significant power loss, since the red light would be weakened on a cloudy day. As a result, the tandem type only shows its advantages on sunny days, and it is limited to areas which are advantageous in terms of the geographical condition. Although tunneling junctions are used nowadays to solve this current matching issue, however there are also optical and electrical losses

13 | P a g e associated with it along with fabrication complexity [58-60]. Another problem is that impurity diffusion from highly doped tunnel junctions during overgrowth of the top cell increases the resistivity of the tunnel junction.

Recently, Perovskite solar cell has been showing great promise. However, current issues with Perovskite solar cells are their stability and durability. The material degrades over time, when exposed to light and moisture and hence a drop in overall efficiency. Therefore, more research is needed to bring these cells into the marketplace. On the other hand, unfortunately, OPV cells efficiency is significantly lower than that of inorganic- based devices, representing a big point of weakness at the present. This is mainly due to the fact that organic semiconductors have a much higher band gap with respect to inorganic semiconductors. In addition, Organic photovoltaic (OPV) cells are very susceptible to oxygen and water [61].

Nowadays, new material systems, as described above, are being investigated to improve the efficiency of solar cell. A key issue is material purity. Current solar cell designs require high-purity and therefore expensive materials. This is because impurities of low quality material block the flow of electric charge and cause losses. That problem would be diminished if charges had to travel only a short distance, through a thin layer of material. However thin layers would not absorb much sunlight and hence would not give a higher generation of carriers. On the other hand, expensive material, which are of higher quality, suffers from commercial viability. Moreover, some of the materials are not environment-friendly and even toxic which concern the researchers.

Quantum well and quantum dot solar cells are showing good potential. Nevertheless, the fabrication process and the cost are a major hindrance. Similar is the case for plasmonics and nanostructure-based solar cells. Although the simulation of these solar cells shows higher efficiencies, however the perfect growth of different size and shapes of complex nanostructures is not possible. Hence, the efficiency predicted in the simulation is not achieved practically. Moreover, the stability of these nanostructured solar cells is also a great issue. Nanostructured materials have larger surface area; for nanostructured devices, improper passivation of internal surfaces can hinder long-term stability [62]. Moreover, no consensus exists among the research community on how to properly characterize the stability. Low-maintenance, long-lifetime solar simulators are not readily available, and lifetime tests inherently take a long time to perform [62]. In brief, development of low

14 | P a g e cost, commercially viable, highly efficient photovoltaic device is the major challenge now for the research community.

1.4 Heterojunction Bipolar Transistor Solar Cell (HBTSC)

To circumvent the major challenges discussed in the previous section and to devise a scalable, affordable, highly efficient, and fabrication-feasible solar cell, a novel concept of using heterojunction bipolar transistor (HBT) structure as the solar cell has been proposed by Marti and Luque [63] as shown in Fig. 1.5.

Fig. 1.5: Heterojunction bipolar structure to be used as solar cell proposed by Marti and Luque [63].

The proposed three-terminal structure does not require any tunneling junction and is free from current matching problems. They also analytically showed that for a particular combination of material bandgaps, it can yield up to 54% efficiency. They calculated the efficiency limit of the three-terminal HBT solar cell by a contour plot, where the varied both the high bandgap and low bandgap material. They also find out the Ebers-Moll circuit model of the HBTSC. Although the heterojunction solar cell is very common nowadays, however the use of heterojunction bipolar transistor structure as a solar cell was first proposed by Marti and Luque. The device naturally emerges as a three-terminal solar cell and can also be used as a building block of multijunction solar cells with an 15 | P a g e increased number of junctions. The practical importance of this structure is the simplicity of the structure and well-matured growth technology of this kind of devices. As a result, low-cost, high-performance device fabrication will be possible. Although the structure is HBT, in operation, it differs from BJT. In a heterojunction bipolar transistor, the emitter injection efficiency has to be maximized (made equal to one); on the contrary, in HBT solar cell, it has to be made equal to zero. HBT solar cell can be used as the building block of the more complex multijunction solar cell without the requirement of tunneling junction [63].

1.5 Objective of the Thesis

Although Marti and Luque first proposed the HBT solar cell, no specific HBT solar cell design with compatible materials has been proposed yet based on this novel concept. Consequently, no detailed analysis or optimization study on the optical and electrical characteristics of HBT solar cell has been done. Roles of different recombination processes and design parameters (e.g. thickness, doping etc.) have also not been explored. Therefore, the objectives of this work are:

i. To design an efficient GaAs/AlGaAs HBT solar cell for broadband absorption of the solar spectrum and compare its performance with conventional heterojunction based solar cell.

ii. To calculate the optical characteristics (absorption spectrum, optical generation rate, and optical short-circuit current density) and electrical characteristics (short-circuit current, open-circuit voltage, and efficiency) with the variation of different design parameters (layer thickness, doping etc.) and thus obtain an optimized HBT structure.

iii. Study the effect of different recombination processes (Shockley-Read-Hall, Auger, radiative), photon recycling, and other non-ideal effects on the performance of the cell.

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1.6 Overview of the Thesis

Chapter 1 provides general introduction followed by historical background, design challenges, and objective of the work.

Chapter 2 covers the basic key concepts of the solar cell including the heterojunction bipolar transistor solar cell and its operation. Then we describe the numerical techniques utilized in this work. Finally, benchmarking of the simulator is discussed.

In chapter 3, we discuss the detail design consideration of the GaAs/AlGaAs three- terminal heterojunction bipolar transistor solar cell. The results obtained from the simulation are also presented. Based on the results, an optimized structure is proposed along with the comparison of the designed cell with conventional and heterojunction solar cells using other material systems.

Chapter 4 contains the concluding remarks along with suggestions for future work on the topic.

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Chapter 2

Theory and Modeling

In this chapter, some of the basic key concepts related to the heterojunction bipolar transistor solar cell and the numerical modeling will be discussed. At first, the elementary solar cell, which is PN junction solar cell, will be discussed. Then the basics of heterojunction solar cell and heterojunction bipolar transistor solar cell will be presented. Relevant fundamental concepts like recombination, photo-generation, and various performance metrics etc. will also be discussed in brief. Having developed the key concepts, we will then discuss the optical and electrical numerical simulation model. Finally, the benchmarking of the developed model will be discussed.

2.1 HBT Solar Cell: Basic Key Concepts

2.1.1 Operation of PN Junction Solar Cell

A PN junction is a boundary or interface between two types of semiconductor material. PN junctions are formed by joining n-type and p-type semiconductor materials. Since the n-type region has a high electron concentration and the p-type has a high hole concentration, electrons diffuse from the n-type side to the p-type side. Similarly, holes flow by diffusion from the p-type side to the n-type side. This process continues until an electric field (E) forms between the positive ion cores in the n-type material and negative ion cores in the p-type material. This region is called the "depletion region". A "built-in" potential ɸbi, due to, E is formed at the junction. The electrons which are in the p-type regions are called minority carrier electrons and the holes which are in the n-type regions are called minority carrier holes. The electrons and holes that reach into this depletion

18 | P a g e region are drifted in opposite direction, i.e. to their majority carrier regions. A simple PN junction and its energy band diagram are shown in Fig. 2.1. In a simple PN junction solar cell, light enters the cell and create electron-hole pairs in both p-type and n-type regions. These carriers then diffuse and reach into the depletion region. Then they are swept away by the electric field of the depletion region to the majority carrier area respectively and then collected at the terminals.

Fig. 2.1 A PN junction and the corresponding energy band diagram.

For a solar cell to work properly, doping is must to create PN junction. Otherwise, charge separation and collection would not be possible. Different regions of the solar cells are doped with different concentration for different purposes. Doping concentration for silicon semiconductors may range anywhere from 1013 cm-3 to 1019 cm-3.

The band gap of a semiconductor is the minimum energy required to excite an electron that is stuck in its bound state into a free state where it can participate in conduction. The lower energy level of a semiconductor is called the "valence band" (EV) and the energy level at which an electron can be considered free is called the "conduction band" (EC).

The band gap (EG) is the gap in energy between the bound state and the free state, i.e., between the valence band and conduction band. This is an important parameter for a solar cell as the absorption of light depends on it. Different materials have different bandgap. For example, Si has a bandgap of 1.12 eV, Ge has a bandgap of 0.66 eV, and GaAs has a bandgap of 1.42 eV. The photons with energy greater than or equal to that of the bandgap of the material are capable of exciting electrons to the conduction band. However, photon 19 | P a g e with energy less than the bandgap cannot excite the electron. Therefore, the choice of material for solar cell should be such that the cell absorbs maximum energy density portion of the solar spectrum to get maximum output. The photo-excitation and carrier transport process are shown in Fig. 2.2.

Fig. 2.2 Energy band diagram of a PN junction solar cell along with absorption of photons, electron-hole pair generation, and transportation of excited carrier [64].

2.1.2 HBT Solar Cell (HBTSC)

Heterojunction solar cell is a hot topic in photovoltaic research of late as it shows the potential for higher conversion efficiency at industrial production level [65]. A heterojunction is an interface that occurs between two layers of different semiconductors having different bandgaps. As we already know that the absorption of the photon in a solar cell depends on the bandgap of the material, heterojunction based solar cells can absorb more photons than the single/homojunction cells as the bandgap of the materials are different, each capturing photons of different energy and hence different portion of the solar spectrum. As a result, the absorption linewidth of heterojunction solar cells is broadband as well as the generation rate and hence the efficiency is also higher. Figure 2.3 shows a schematic of a heterojunction solar cell along with energy band diagram.

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Fig. 2.3 ZnO/CDS/CIGSe/Mo heterojunction solar cell and corresponding energy band diagram. The different bandgap absorbs different energy photons ultimately giving a broadband absorption of the solar spectrum [66].

Till now, most of the heterojunction based solar cells are of two terminals. That is electrons are collected in one terminal and holes are collected at another terminal. Due to the intrinsic conduction and valence band discontinuity in heterostructure devices, the carrier transport mechanism is hindered. As a result, higher absorption and generation sometimes cannot give higher power output due to the problem in carrier transport and collection. Hence, efficiency is lowered.

Heterojunction bipolar transistor solar cell (HBTSC) is based on three terminals to facilitate the efficient collection of the generated carriers. The cell is divided into three regions- emitter (E), base (B), and collector (C), similar to that of HBT. It can be either NPN or PNP type depending on the mode of operation. Basically, there are two back to back PN junctions. The cell is illuminated through the front emitter region which consists of higher bandgap material. The base and the collector are of lower bandgap material. One of the key advantages of this structure is that the effective diffusion length of the carrier is reduced. The electron generated adjacent to BC junction, for example, can easily diffuse to the proximate BC junction and does not need to diffuse all the way to far EB junction. This ultimately reduces the probability of recombination in the course of

21 | P a g e diffusion and hence provides an advantage to increase the base layer width for complete absorption of the solar spectrum. As the holes are only collected at the base contacts and electrons are collected at both the emitter and collector terminals, the total current in the base is equal to the sum of the currents in collector and emitter. The schematic of heterojunction bipolar transistor structure as solar cell is shown in Fig. 2.4.

JJJbase emitter collector (2.1)

Fig. 2.4 Operation of heterojunction bipolar transistor structure as solar cell. The emitter and the collector are shorted together.

There are some other fundamental concepts that are required to know for developing accurate and reliable simulation model of HBT solar cell. They are discussed in brief below:

2.1.2.1 Solar Spectrum is the power per unit area received from the sun in the form of electromagnetic radiation. Irradiance may be measured in space or at the earth's surface after atmospheric absorption and scattering. It is measured perpendicular to the incoming sunlight. The Air Mass is the path length which light takes through the atmosphere 22 | P a g e normalized to the shortest possible path length (that is, when the sun is directly overhead). The Air Mass quantifies the reduction in the power of light as it passes through the atmosphere and is absorbed by air and dust [67]. In other words, the air mass represents the proportion of atmosphere that the light must pass through before striking the earth relative to its overhead path length, and is equal to Y/X as shown in Fig. 2.5. The air mass is defined as:

1 AM  , (2.2) cos where θ is the angle from the vertical (zenith angle). When the sun is directly overhead, the air mass is 1. The standard spectrum at the earth's surface is called AM 1.5G (the G stands for global and includes both direct and diffuse radiation) [67].

(a) (b)

Fig. 2.5 (a) Air mass determination. (b) Sunlight intensity for different air mass [67] .

2.1.2.2 Photo-absorption and photocarrier-generation The absorption coefficient determines how far into a material light of a particular wavelength can penetrate before it is absorbed. It is a useful parameter which gives the distance into the material at which the light drops to about 36% of its original intensity or alternately has dropped by a factor of 1/e. Different semiconductor materials have

23 | P a g e different absorption coefficients as shown in Fig 2.6. Materials with higher absorption coefficients more readily absorb photons, which excite electrons into the conduction band. Knowing the absorption coefficients of materials aids engineers in determining which material to use in their solar cell designs. The absorption depth can be calculated by the inverse of the absorption coefficient. Higher energy light is of a shorter wavelength and has a shorter absorption depth than lower energy light, which is not as readily absorbed and has a greater absorption depth. Absorption depth affects aspects of solar cell design, such as the thickness of the semiconductor material [67].

Fig. 2.6 The absorption coefficient, α, in a variety of semiconductor materials at 300K as a function of the vacuum wavelength of light [67].

The generation of an electron-hole pair can be calculated at any location within the solar cell, at any wavelength of light, or for the entire standard solar spectrum. Generation is the greatest at the front surface of the material, where the majority of the light is absorbed. Because the light used in PV applications contains many different wavelengths, many different generation rates must be taken into account when designing a solar cell. The higher generation rate gives higher photocurrent and hence higher .

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2.1.2.3 Recombination When a photon excites an electron in the conduction band, it is in a metastable state. Therefore, eventually, it will stabilize back into the valence band, which is just opposite of photo-excitation process. Therefore, when the electron stabilizes back down into the valence band, it also effectively removes a hole. This process is called recombination. Recombination is a process that is diametrically opposed to generation and hence an undesirable loss process. There is basically three major recombination process that occurs in solar cell (as shown in Fig. 2.7) and they are described as follows:

• Trap-Assisted (Shockley-Read-Hall) Recombination: The recombination process in the trap-assisted model assumes that there are unoccupied "trap" states (also referred to deep-level defect states) within the band gap. Typically, these states result from impurities (either intentional or unintentional), and the most active traps have energy levels near the middle of the band gap. Recombination occurs when an electron relaxes (transfers energy to the lattice or emits a photon) to the trap state from the conduction band, and sequentially, a hole from the valence band relaxes to the same trap state. The rate at which a carrier moves into the energy level in the forbidden gap depends on the distance of the introduced energy level from either of the band edges. Therefore, if energy is introduced close to either band edge, recombination is less likely as the electron is likely to be re-emitted to the conduction band edge rather than recombine with a hole which moves into the same energy state from the valence band. For this reason, energy levels near mid-gap are very effective for recombination. • Auger Recombination: Auger Recombination involves three carriers. An electron and a hole recombine, but rather than emitting the energy as heat or as a photon, the energy is given to a third carrier, an electron in the conduction band. This electron then thermalizes back down to the conduction band edge. Auger recombination is most important at high carrier concentrations caused by heavy doping or high-level injection under concentrated sunlight. In silicon-based solar cells (the most popular), Auger recombination limits the lifetime and ultimate efficiency. The more heavily doped the material is, the shorter the Auger recombination lifetime.

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Fig. 2.7 Different recombination mechanisms inside a photovoltaic device such as (a) Shockley-Read-Hall (SRH) (b) Auger (c) radiative recombination [67].

• Radiative Recombination: In a radiative transition, a conduction band electron will relax directly, emitting a photon whose energy approximately equals that of the band gap, and then recombine with a hole in the valence band. The opposite process occurs when a photon is absorbed by an electron in the valence band, promoting it to the conduction band and leaving a hole in its place. Radiative recombination transitions are typically significant only in materials with a narrow bandgap, or a band structure that permits direct transitions in momentum (e.g. GaAs). Radiative recombination is typically negligible in bulk silicon.

2.1.2.4 Performance metrics The performance of a solar cell, including HBTSC, is determined by several parameters like open-circuit voltage (Voc), short-circuit current density (Jsc), current-voltage characteristics (J-V), efficiency (η), fill factor (FF) etc. The J-V characteristic of a solar cell is shown in Fig. 2.8.

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Fig. 2.8 The J-V characteristics of a solar cell along with the power-voltage curve.

The point at which J-V curve intersects the vertical axis is known as the short-circuit condition, and it defines how the cell operates if a wire is connected between its terminals, shorting it out. The current flow here is known as short-circuit current. For an ideal solar cell at most moderate resistive loss mechanisms, the short-circuit current and the light-generated current are identical. Therefore, the short-circuit current is the largest current which may be drawn from the solar cell [68].

The point at which a curve intersects the horizontal axis is known as the open-circuit condition. The open-circuit voltage is the maximum voltage available from a solar cell, and this occurs at zero current. Voc depends on the saturation current of the solar cell and the light-generated current.

For each point on the graph, the voltage and current can be multiplied to calculate power. Maximum power point is the point on the J-V curve of a solar cell corresponding to the maximum output electrical power, Pmax = VMPIMP.

The efficiency, η of a solar cell is defined as the ratio of the output power (electrical) to the input power (optical). Another defining term in the overall behavior of a solar cell is

27 | P a g e the fill factor. This is the ratio that describes how close the J-V curve of a solar cell resembles a perfect rectangle, which represents the ideal solar cell: FF= Pmax / Voc Jsc.

In heterojunction bipolar transistor solar cell simulation, voltage is applied to the base terminal and the emitter and the collector terminals are shorted out to the same potential (ground) as shown in Fig. 2.4. The J-V curve can be found by applying a varying voltage at the base terminal and finding the total current from the device for each applied voltage. Then the performance metrics can be calculated as described above.

2.1.2.5 Fabrication of HBT The fabrication of HBT is a matured technology and inexpensive. It is primarily grown by metal organic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE) techniques. Other techniques are used depending on the material system. IBM and others use UHV CVD for SiGe; other techniques used include MOVPE for III-V systems. There are several simple methods for doping like diffusion, ion implantation etc. In addition to base, emitter and collector layers, highly doped layers are deposited on either side of collector and emitter to facilitate an Ohmic contact, which is placed on the contact layers after exposure by photolithography and etching [69].

2.2 Numerical Modeling

The solar cell is an optoelectronic device. Hence, the modeling of the solar cell requires both optical and electrical simulation. In optical part, the interaction of light with matter is simulated. The optical simulation determines the generation of electron-hole pairs in the semiconductor material by calculating the absorbed optical energy. The electrical simulation takes the optical generation information from optical simulation and simulates the carrier transport by taking into account the distribution of dopants that give rise to the built-in electric fields, the mobility of free carriers, and the physical processes that result in the recombination of charge. These two simulations can determine the performance metrics of the solar cell.

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For optical simulation, several commercial numerical tools/software are available for time domain and frequency domain analysis. However, every such tool comes with certain limitation in regard to custom geometry or simulation conditions. Moreover, material characterizations and the definition of different parameters are some of the key aspects of the customized simulation. Among a number of commercial software, we chose Lumerical FDTD Solutions based on finite difference time domain (FDTD) algorithm for optical simulation. Compared to frequency domain method, an FDTD method provides a number of advantages. In frequency domain analysis, several simulations have to be done in order to get the response of the device in different frequencies. However, in FDTD, one single simulation can do the job as a broadband pulse in injected into the device and it saves a lot of time.

On the other hand, for electrical simulation, we also choose Lumerical DEVICE solution which solves the drift-diffusion and continuity equation self-consistently to find the electrical performance characteristics of the solar cell. In Lumerical DEVICE solver, different kinds of recombination mechanisms can be incorporated to better predict the performance of a solar cell like a real device. This chapter describes the numerical simulation model and the mathematical formulation. Then it concludes by reproducing the work of Wang et al. [70] to verify the integrity of the simulation setup and material model.

2.2.1 Optical Simulation Model

2.2.1.1 Finite Difference Time Domain Model The FDTD simulator is based on the simultaneous time-dependent solution of Maxwell’s third and fourth equations which are given by

D   H (2.3) t DE()()  *  0 r (2.4) H 1    E (2.5) t  0

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The time-dependent Maxwell’s equations are discretized using central difference approximations to space and time partial derivatives. These finite-difference equations are then solved in a leapfrog manner. In other words, the electric field vector components in a volume of space are solved at a given instant in time and then the magnetic field vector components in the same spatial volume are solved at the next instant in time. This process is repeated over and over again. Depending on the type of source used in the simulation domain, these leapfrogging time steps are run a finite number of times. The workflow of solving Maxwell’s equations is shown in Fig. 2.9.

Fig. 2.9 Simulation work flow of Maxwell’s equation solution.

This method of solving Maxwell’s equation was first proposed by Yee, in a seminal paper published in 1966 [71]. Solutions of a set of finite difference equations for time and space dependent equations for loss-less materials was proposed in that paper. The commercial electromagnetic simulator used in our work is also based on Yee’s algorithm. A spatially staggered vector component of the E-field and H-field about rectangular unit cells of a Cartesian computational grid was proposed in this algorithm. It was arranged in a way so that each E-field vector component is located midway between a pair of H-field vector

30 | P a g e components. This grid was later referred to as Yee grid. Figure 2.10 shows the arrangement of Yee grid for three-dimensional simulation regions. Apart from proposing spatially staggered field vectors, Yee also proposed a leapfrog scheme for stepping in time such that electric field and magnetic field are temporally staggered. As a result, electric field updates are computed halfway of each time-step between consecutive H- field updates and vice versa.

Fig. 2.10 Yee grid in three-dimensional simulation domains.

In optical solver, we also calculate some of the important parameters. The absorbed power (Pabs) is calculated by

P0.5 | E |2 imag ( ), (2.6) abs where ω is the angular frequency and  is the constant, E is the electric field. We used (n, k) data to model the dispersive material. The generation rate (G) is calculated by [72]

G  gd, (2.7)

31 | P a g e where g is defined as

P P0.5| E |2 imag ( ) g abs abs . (2.8) 

Here, is the reduced Planck’s constant. This optical generation rate is used as input in the electrical solver.

Assuming that all absorbed photons generate electron-hole pairs, the photo-generation current (A/m) can be obtained by

I qg, (2.9) where q is the electron charge.

2.2.1.2 Boundary Condition Reflection from simulation boundaries is one of the major sources of error in FDTD simulators. At least one or more boundaries of typical electromagnetic simulation need to be infinitely extended. To make the simulation domain wide enough to let the scattered wave decay is not a computationally efficient approach. As a result, absorbing boundaries are incorporated into the simulation space. Various types of absorbing boundary conditions (ABC) may be employed in order to resolve this problem [73, 74]. One of the most effective among all ABCs is the perfectly matched layer developed by Berenger [75]. The basic idea of the perfectly matched layer (PML) technique is to add an additional lossy layer around the simulation region with intrinsic impedance matched with the media at the outermost simulation region which ensures zero reflection from the interfaces and the field is attenuated while propagating through the media. It is ensured that the field intensity attenuates to zero before it hits the simulation boundary. We used PML boundary condition in our simulation.

In FDTD simulations, total response of a periodic structure can be extracted from simulation results of just one unit cell. To achieve that, the periodic boundary condition is applied along the axis of symmetry. Periodic boundary condition can be applied in one or

32 | P a g e more boundaries of the simulation. Bloch boundary condition is similar to periodic boundary condition. The application of this boundary condition is necessary when the structure is periodic but the EM field has a phase shift between each period. Such case arises when the incident light is obliquely incident. In our simulation, we have used periodic boundary conditions. The boundary conditions are shown in Fig. 2.11.

Fig. 2.11 Boundary conditions in FDTD simulation.

2.2.2 Electrical Simulation Model

2.2.2.1 Charge Transport Solver The Charge Transport (CT) solver is a physics-based electrical simulation tool for semiconductor devices, which self-consistently solves the system of equations describing the electrostatic potential (Poisson’s equation) and density of free carriers (the drift- diffusion equations). The drift-diffusion model is an established and robust method that will produce accurate results for a wide range of semiconductor devices under common operating conditions. Lumerical DEVICE solves the following drift-diffusion equations for electrons and holes (carriers):

J q nE  qD  n, n n n (2.10)

J q pE  qD  p, p p p (2.11) 33 | P a g e

kTB Dn()() p  n p , q (2.12)

where Jn(p) is the electron (hole) current density, µn(p) is the mobility of electron (hole),

Dn(p) is the diffusivity of electron (hole), n and p are electron and hole densities, E is the electric field, kB is the Boltzmann constant, and T is the temperature.

To solve the drift-diffusion equations, the electric field must be known. To determine the electric field, the following Poisson's equation is solved:

(), Vq  dc (2.13)

where  dc is the dc dielectric permittivity, V is the electrostatic potential (E= - V),  is the net charge density defined as

   p n C, (2.14) which includes the contribution C from the ionized impurity density. Finally, the auxiliary continuity equations are required to account for charge conservation:

n 1  JRnn  , tq (2.15)

p 1   JRpp  , tq (2.16)

where Rn,p is the net recombination rate (the difference between the recombination rate and generation rate). The physical processes associated with the material are assumed to act equivalently when applied to electrons or holes, and as a result, R = Rn = Rp. The recombination and generation processes are important factors in the material-specific calculation of carrier behavior. Multiple recombinations and generation processes are modeled, which may depend on temperature, impurity (doping) concentration, carrier concentration, electric field, and current density.

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The system of equations solved by DEVICE admits both a steady-state and time-varying result. By enforcing the condition

np 0 tt (2.17) in the continuity equations, the carrier density and electrostatic potential can be solved at steady-state. Steady-state simulations can be used to examine the system’s behavior at a fixed operating point.

2.2.2.2 Boundary Conditions

Two categories of boundary condition are present in DEVICE: those that relate to the electrostatic potential (Poisson’s equation) and those that relate to the carrier densities (the drift-diffusion equations). Poisson’s equation and the drift-diffusion equations are second-order partial differential equations (PDE), and each requires that the solution be explicitly specified for at least one location. This is known as a Dirichlet boundary condition. For the electrostatic potential, the Dirichlet condition takes the form of a boundary (internal or external) with a fixed voltage specified,

V() x V 1 (2.18)

as is typical of an electrical contact. For the carrier densities, the majority carrier concentration is set to its equilibrium value at the interface between a contact and the semiconductor, such that ρ = n-p+C.

At internal boundaries between two domains that are not contacts, the boundary conditions are determined by the physical properties of the interface. In the case of the electrostatic potential, the electric flux density must be continuous across the boundary in the absence of a surface charge. For the electron and hole densities, boundary conditions between the semiconductor and adjacent materials may be specified in terms of a surface recombination current density, which will default to zero (no carrier flux across the

35 | P a g e boundary) for insulators or an infinite recombination velocity (forcing the carrier density to its equilibrium value) for contacts. At the external (open) boundaries of the simulation domain, homogeneous Neumann boundary conditions are applied: the electric field normal to the boundary is set to zero as is the surface recombination current density. Physically, this corresponds to an insulating boundary across which no charge can flow.

2.3 Benchmarking

Benchmarking of the simulator or solver is very important to make sure that the simulation results are reliable and accurate. We benchmarked our solvers by reproducing the work of Wang et al. [70]. The current-voltage characteristics and the power-voltage (P-V) characteristics of the GaAs/AlGaAs heterojunction solar cell of Wang et al. simulated by our solver are shown in Fig. 2.12.

)

2 30 30 )

25 25 2 20 20 15 15

10 J-V (our simulation) 10

P-V (our simulation) Power (mW/cm 5 5 J-V (reported by Wang et al.) Current Density (mA/cm 0 0 0.2 0.4 0.6 0.8 1 Voltage (V)

Fig. 2.12 The current-voltage characteristics and the power-voltage characteristics of the GaAs/AlGaAs heterojunction solar cell reported in Ref. [70].

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Our simulation results match well with their result. The comparisons of the key parameters are also given in Table 2.1.

Table 2.1 Comparison of values of Jsc, Voc, and η from our simulation and that reported in Ref. [70] .

Parameter Our Simulation Ref. [70]

2 Jsc (mA/cm ) 30.48 29.49

Voc (V) 1.063 1.10

η (%) 28.14 28.35

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Chapter 3 GaAs/AlGaAs HBT Solar Cell: Design and Performance Analysis

Here we propose a heterojunction bipolar transistor solar cell based on the structure reported in Ref. [63]. We choose GaAs/Al0.85Ga0.15As material system for the device. The details of design and simulation results are discussed and analyzed in the following sections.

3.1 Device Design

3.1.1 Device Structure

The schematic of the HBT structure configured as a solar cell is shown in Fig. 3.1. The structure is based on the device proposed by Marti and Luque [63]. The considered architecture is a single heterojunction NPN transistor. The emitter region is of wide bandgap material while the base and the collector regions are of low bandgap material. The emitter and collector regions are designed to be heavily n-doped and the base region is to be p-doped which form two PN junctions in the structure. Both the emitter and base contacts are at the front side and the collector contact is at the back side of the structure. The length (x-direction) and height (y-direction) of the base and emitter contacts are assumed to be 1 µm and 0.5 µm respectively. The collector contact is assumed to be span through entire backside with a height of 0.5 µm. Below the base contact, there is a heavily doped p-type region to prevent minority carrier recombination at the surface [76, 77]. An anti-reflection coating (ARC) is used on the top of the emitter layer to reduce the reflection [70].

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Fig. 3.1 3D Schematic of the proposed three terminal HBT solar cell. The emitter region is heavily n-type doped except for the region below the base, which is heavily p-type doped for making the base terminal connection. The contacts are assumed to be made of Aluminum.

3.1.2 Choice of Material System

To increase the power conversion efficiency of the HBT solar cell, the bandgap of the materials should be such that photon absorption maximizes as a whole. We select

Al0.85Ga0.15As/GaAs material system for the proposed HBT solar cell for multiple reasons. The bandgap of AlGaAs is ~2.1 eV (corresponds to a wavelength of ~580 nm) and GaAs is ~1.42 eV (corresponds to a wavelength of ~800 nm). These wavelengths correspond to a high-energy-density portion of the solar spectrum. Thus, GaAs has been used in the base and collector while Al0.85Ga0.15As has been used in the emitter region. Therefore, the combination of the two material systems can absorb broadband higher- energy-density portion of the solar spectrum. Moreover, the electron diffusion length in p- type GaAs (base region) can be as high as 70 µm enabling the use of the much thicker base for broadband absorption [78]. Additionally, GaAs and AlAs have almost the same lattice constant. Therefore, layers would have a very little induced strain, which allows them to be grown almost arbitrarily thick with little defects [79]. GaAs is also known to be resistant to radiation damage giving GaAs solar cells long-term stability [80]. Moreover, the temperature coefficient of GaAs is 0 (zero) which means GaAs/AlGaAs

39 | P a g e

HBT solar cell is suitable for high-temperature operations and thus highly suitable for outdoor/rooftop commercial applications.

The key electrical properties of the chosen material systems used in this work, taken from different kinds of literature [70, 78, 81-84], are given in Table 3.1. However, there are some parameters that are not uniquely reported in the literature. For example, SRH lifetime, radiative recombination coefficient incorporating photon recycling [85-87] etc. For such cases, we varied those parameters within a practical range to find the minimum as well as maximum possible performance limit of the designed device.

Table 3.1 Basic electrical properties of the material system used in the simulations.

Features GaAs Al0.85Ga0.15As

Band Gap (eV) 1.42 2.11

DC permittivity 13.1 12.2

Work function (eV) 4.78 4.71

Electron effective mass (me/mo) .067 0.39

Hole Effective mass (mh/mo) 0.44 0.75

Electron Mobility (cm2/V-s) 8500 410

Hole Mobility (cm2/V-s) 470 127

SRH lifetime (µs) 10-3 - 103 10-3 - 103

Radiative recombination -10 -10 -20 (EHP capture rate (cm3/s)) 1.3×10 - 7×10 1.4×10 Auger recombination -30 -30 (Carrier capture coefficient (cm6/s)) 7×10 7×10

40 | P a g e

3.2 Result and Analysis

As a starting point to our analysis, we have taken a 5 µm thick GaAs and 0.7 µm thick

Al0.85Ga0.15As HBT structure and calculated different performance metrics. We started with reasonable values of different parameters and these values were used as the default ones unless otherwise stated. The emitter, base, and the collector doping concentration were taken to be 1×1018 cm-3, 1×1015 cm-3, and 1×1018 cm-3 respectively. Emitter and collector are diffusion doped and the base is uniformly doped. We assumed the SRH lifetime to be 5 µs, radiative recombination coefficient to be 1.3×10-10 cm3/s, and EHP capture coefficient (Auger recombination) to be 1.3×10-30 cm6/s. The choices of these parameters are based on the typical values used in GaAs-based solar cells [63, 82, 88-90]. From our simulation, we found the efficiency of this preliminary structure to be 25.35% which is similar to that of the single junction GaAs solar cells. The J-V and P-V characteristics of the structure are shown is Fig. 3.2.

30 30 ) 2

25 25 ) 2 20 20

15 15

10 10 Power (mW/cm 5 5 Current density (mA/cm 0 0 0 0.2 0.4 0.6 0.8 1 Voltage (V)

Fig. 3.2 The J-V and P-V characteristics of the 5 µm GaAs and 0.7 µm AlGaAs HBT 2 solar cell before optimization. The Jsc and Voc are found to be 28.58 mA/cm and 1.01 V.

As the efficiency was similar to those single junction solar cells, there was scope for further optimization of this structure for increasing the efficiency. As a result, we

41 | P a g e investigated the effect of different design parameters on the performance and tried to find an optimized structure based on the result of our investigation.

3.2.1 Effect of Varying Layer Thickness

As mentioned previously, the long diffusion length of minority carrier electrons in GaAs and therefore the flexibility in collecting photo-generated electrons at two terminals, instead of one terminal as available in traditional cells, facilitate us to increase GaAs base layer thickness for near complete absorption of the solar spectrum. Therefore, we varied the thickness of the GaAs layer to find an optimum thickness that can maximize the efficiency. In this regard, we have varied the GaAs layer thickness from 5 µm to 70 µm and calculate the optical generation rate and ideal optical short-circuit current density. The ideal optical short-circuit current density with the variation of GaAs and AlGaAs layer thickness is shown in Fig. 3.3.

)

2 46

50 44 45 42 40 40 35 38 30 2 36 70 Optical Optical Current Density (mA/cm 1.5 60 50 1 30 40 34  20 AlGaAs Layer Thickness ( m) 0.5 0 10 GaAs Layer Thickness (m)

Fig. 3.3 Ideal optical short-circuit current density calculated in FDTD solver for different thicknesses of GaAs and AlGaAs layers.

42 | P a g e

We then used the optical generation rate in electrical solver to find the open-circuit voltage, short-circuit current, and efficiency for different base thicknesses. As the mobility, and consequently, diffusivity and diffusion length of the minority carrier hole in n-type AlGaAs is significantly lower than minority carrier electron in p-GaAs and illumination of the device is through the AlGaAs layer, it requires that the thickness of this layer to be significantly shorter than that of the base region. Hence, we show the variation of the thickness of AlGaAs emitter layer from 0.5 µm to 2 µm. Nonetheless, we performed simulation increasing the AlGaAs layer thickness beyond 2 µm and observed that the efficiency actually decreases due to the above-mentioned factors. We kept the highly n-type doped collector layer thickness fixed at 0.5 µm. The results are shown in Fig. 3.4.

)

2 1.06 36 40 1.05 38 34 0.5 um AlGaAs 1.04 0.5 um AlGaAs 0.5 um AlGaAs 0.7 um AlGaAs 0.7 um AlGaAs 0.7 um AlGaAs 36 1.0 um AlGaAs 1.0 um AlGaAs 32 1.0 um AlGaAs 1.5 um AlGaAs 1.03 1.5 um AlGaAs 1.5 um AlGaAs 2.0 um AlGaAs 2.0 um AlGaAs 2.0 um AlGaAs 34 1.02 30 Efficiency (%) Efficiency 32 1.01

Open-circuit Voltage (V) Voltage Open-circuit 28 30 1

Short-circuit Current Density(mA/cm Current Short-circuit 0.99 26 20 40 60 20 40 60 20 40 60 GaAs Layer Thickness (m) GaAs Layer Thickness (m) GaAs Layer Thickness (m)

(a) (b) (c)

Fig. 3.4 Dependence of (a) short-circuit current (b) open-circuit voltage and (c) efficiency on the layer thickness of GaAs and AlGaAs layer.

From Fig. 3.3, we see that ideal optical current density increases as we increase GaAs thickness from 5 µm. However, after a certain thickness, it saturates and even decreases later as the increment of optical generation rate is nearly zero with further increase in active region area. Due to the same reason, the device short-circuits current density and efficiency also show a similar trend as shown in Fig. 3.4 (a) and 3.4(c), where we plot the

Jsc and η of the cell for different GaAs and AlGaAs layer thicknesses. Voc decreases 43 | P a g e slightly with the increase in GaAs layer thickness as shown in Fig 3.4 (b) which can be attributed to the increase of recombination with the increase of layer thickness. From Fig.

3.4, it is also evident that η is dominated by the Jsc in the device as it increases even though the Voc is decreased with the increase of GaAs layer thickness. This is because of the fact that the decrease in Voc is not significant compared to the increase in Jsc with the increase of GaAs (base) layer thickness. The fill factors of the designed structures are found to be invariant with the layer thickness and calculated to be around 87%.

3.2.2 Effect of Doping

Doping is one of the most important design parameters on which Jsc, Voc, and η depend. We varied the doping of emitter, base, and the collector regions and find their effects on electrical characteristics. To study this, we take 0.5 µm AlGaAs and 45 µm GaAs structure which we denote as structure-X. The SRH lifetime also highly depends on doping concentration which can be modeled as [83]

1   , (3.1) SRH BN where N is the doping concentration in cm-3 and B = 2×10-10 cm3/s is for GaAs/AlGaAs material system [83, 84].

First, we varied the p-type base doping from 5×1012 cm-3 to 5×1017 cm-3 of structure-X.

We kept the doping of emitter and collector to be fixed at the default values. The Jsc and

Voc decrease with increasing p-type base doping which is opposite to the conventional n-type base solar cells. This declining behavior is associated with the decrease of SRH lifetime with the increase of doping. Although the efficiency increases at first for increasing the doping concentration, it decreases after reaching a peak value. The drop in efficiency after the peak can also be attributed to the decrease in SRH lifetime for higher doping concentrations. The base doping vs. efficiency is shown in Fig. 3.5 (a).

44 | P a g e

36 36

35 35.5

34 35

33 34.5

32 34 Efficiency (%) Efficiency (%)

31 33.5

33 30 12 14 16 18 16 18 20 10 10 10 10 10 10 10 -3 -3 Base Doping (cm ) Emitter Doping (cm )

(a) (b)

Fig. 3.5 Effect of (a) base and (b) emitter doping on the efficiency of the solar cell.

We also investigated the effect of the emitter and collector doping. However, due to the thin layer thickness of emitter compared to the base, the variation in doping in emitter showed little effect except for very high doping concentration. For example, we varied the n-type emitter doping from 5×1016 cm-3 to 5×1019 cm-3 for structure-X. It is seen that 19 -3 the Jsc, Voc remained almost same up to the doping concentration of 1×10 cm . The efficiency showed a maximum value of ~35.6% for emitter doping of 1×1017 cm-3 as 19 -3 shown in Fig. 3.5 (b). However, for a doping concentration of 5×10 cm and higher, Jsc,

Voc, and efficiency decline sharply due to the decreased SRH lifetime at higher doping concentrations. On the other hand, the thin collector has relatively minor impact on the performance of the HBT solar cell. The effect of doping in different region on Jsc and Voc is shown in Table 3.2.

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Table 3.2 The effect of doping in different region on Jsc and Voc

2 Region Doping Concentration Jsc (mA/cm ) Voc (V)

5 ×1012 39.88 0.993

5×1013 39.88 0.9929 14 5×10 40.07 0.9948 5×1015 40.02 1.009 Base 5×1017 39.04 1.015 5×1016 40.37 1.008

1×1017 40.28 1.008 18 Emitter 1×10 40.02 1.009 5×1019 37.65 1.007

3.2.3 Effect of Recombination

As we described earlier, there are three major recombination processes: Shockley-Read- Hall (SRH), radiative, and Auger. We investigate the effect of these three recombination processes on the current density and efficiency of the cell. To study this, we again take 0.5 µm AlGaAs and 45 µm GaAs structure (structure-X). We have used the default values of doping concentrations in three regions. The results are shown in Fig. 3.6 and Fig. 3.7. 2 From the figures, we see that without any recombination (ideal case), Jsc is 40.7 mA/cm ,

Voc is 1.1 V and the corresponding efficiency is 39.56%.

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)

2 40

30

20 Without any recombination SRH recomination 10 SRH+Radiative recombination SRH+Radiative+Auger recobination Current Density (mA/cm

0 0.2 0.4 0.6 0.8 1 Voltage (V)

Fig. 3.6 Effect of different recombination processes on the J-V characteristics of the HBT solar cell (structure-X). The doping and recombination parameters are used as default values.

Without any recombination 40 SRH recombination

) SRH+Radiative recombination 2 SRH+Radiative+Auger recombination 30

20

Power (mW/cm 10

0 0.2 0.4 0.6 0.8 1 1.2 Voltage (V)

Fig. 3.7 Effect of different recombination processes on the P-V characteristics of the HBT solar cell (structure-X).

Among the three recombination processes, SRH recombination has been found to be 2 2 dominant. Although it insignificantly reduces Jsc to 40.59 mA/cm (from 40.7 mA/cm ), however, the Voc and η is reduced to 1.03 V (from 1.10 V) and 36.6% (from 39.56%)

47 | P a g e

2 respectively. Radiative recombination further reduces Jsc to 40.39 mA/cm , Voc to 1.009 V, and η to 35.72%. Lastly, the Auger recombination has the minimal effect on the performance of the designed cell. It reduces the efficiency to 35.37%. It is observed that the current density does not reduce significantly with the incorporation of different recombinaition like the drop in voltage. This is because we have kept the layer thickness within diffusion limit of the material system. As a result, the annealing of electron-hole pair is not significant to reduce the current. In brief, SRH, radiative and Auger recombination account for 70%, 21.5%, and 8.5% of the losses respectively (also shown in Fig. 3.8). The combined effect of three recombination processes is the 10.6% (relative) reduction of efficiency to 35.37 % compared to 39.56% from the ideal case.

80%

60%

40%

20%

0% SRH Radiative Auger

Fig. 3.8 Contribution of SRH, Auger, and radiative recombination to the total loss mechanism in HBT solar cell structure-X.

3.2.4 Effect of SRH recombination:

As the SRH recombination is the dominant loss mechanism in our HBT structure, we investigate this loss mechanism in detail. Figure 3.9 shows how Jsc, Voc, and η vary with the SRH lifetime. It can be seen that Jsc, Voc, and efficiency increase with the increase of

SRH lifetime, as expected. However, all these metrics saturate after  SRH = 5µs. Thus, we

48 | P a g e opine that radiative recombination becomes more dominant at higher values of SRH than SRH recombination and hence, the efficiency becomes insensitive to SRH lifetime. The efficiency drops sharply and significantly below SRH lifetime of 0.1 µs. The lower efficiency at lower SRH lifetime values highlights the importance of the high-quality defect-free material system for a solar cell. )

2 42 1.05 36

40 34 1 38 32 0.95 36 30 28 34 0.9 26 32 Efficiency (%) 0.85 24

30 Open-circuit Voltage (V) 22

28 0.8 -3 0 4 10-3 100 104 10-3 100 104 10 10 10

Short-circuit Current Density (mA/cm  (s)  (s)  (s) SRH SRH SRH

(a) (b) (c)

Fig. 3.9 Effect of SRH lifetime on (a) Jsc, (b) Voc, and (c) efficiency of the HBT cell (structure-X). The doping concentration of the emitter and collector regions are assumed to be 1×1019 cm-3 and 1×1018 cm-3 respectively. The base doping is taken in such way to satisfy Eq. 3.1.

3.2.5 Effect of photon recycling

One of the advantages of using direct bandgap material like GaAs is that the recombination process is frequently dominated by radiative band-to-band direct recombination [87]. That is, the electron and hole recombine radiatively emitting a photon with an energy equivalent to the bandgap of GaAs, which can be reabsorbed. Although the self-consistent simulation of this process is complicated, one of the simplest ways to incorporate this effect is to scale the radiative recombination coefficient (EHP capture rate) by the Ashbeck coefficient [91]. In absence of unique value of this coefficient in literature, we varied radiative recombination coefficient from 1.3×10-10 cm3/s to 7×10-10

49 | P a g e cm3/s (no photon recycling effect [78]) and calculate the efficiency for structure-X. However, it can be noted that G. W. Hooft reported an average value of radiative recombination coefficient for GaAs to be 1.3×10-10 cm3/s [85]. The result of the simulation for varying radiative recombination coefficient is shown in Fig. 3.10. It can be observed that the efficiency is 32.5% without considering the photon recycling effect. However, the efficiency increases to ~35.37% after including photon recycling (~8% rise).

35

34.5

34

33.5 Efficiency (%) 33

32.5 1 2 3 4 5 6 7 EHP Capture Rate (cm3/s) x 10-10

Fig. 3.10 Effect of photon recycling on the efficiency of the HBT solar cell. The inclusion of photon recycling effect reduces EHP capture rate and hence increase efficiency.

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3.2.6 Optimized Structure

We varied different design parameters separately and studied the effect of these parameters on the performance of the HBT solar cell to find an optimized structure which yields optimum efficiency. First, we optimize the structure in terms of layer thickness. From our investigation, we observed that the increase in AlGaAs layer decreases the efficiency of the cell due to the poor electrical response characteristics of AlGaAs material. As a result, we varied the thickness of AlGaAs layer up to 2 µm. Although, an increase of base layer thickness increases carrier generation due to increased absorption, nevertheless we need to keep in mind the material cost for large volume commercial production and the increase of recombination losses with larger base thickness. Hence, we tried to find the layer thickness which gives highest optical generation rate (i.e. highest optical short-circuit current density). The simulation results (both optical and electrical) are shown in Table 3.3. We observe that optical short-circuit current density increases with the increase of layer thickness, as expected, reaching a maximum value of 47.35 mA/cm2 for 2 µm AlGaAs and 65 µm GaAs layer (structure-M). However, the higher optical short-circuit current density does not lead to higher current at the terminal and higher efficiency due to different losses associated with carrier transport. Therefore, we find out the Jsc, Voc, and η by electrical simulations incorporating different loss mechanisms. From the electrical simulation, we see that the structure yielding highest optical short-circuit current density does not yield the highest efficiency due to losses for increased layer thickness. We find from electrical solver that the structure-M has short- circuited current density of 40.13 mA/cm2 and efficiency 35.16% which is not the highest as evident in Table 3.3. However, we find that for 0.5 µm AlGaAs and 45 µm GaAs, the efficiency is found to be highest 35.37% for the emitter and base doping concentration of 1×1018 cm-3 and 5×1015 cm-3 respectively. Then, we also varied the doping in three different regions, as described in previous section (Section 3.2.2), and calculated the efficiency. We find from the simulation that the efficiency of this structure maximizes to 17 -3 15 -3 35.6% for emitter doping of 1×10 cm and base doping of 5×10 cm . The Jsc of this 2 structure is 40.21 mA/cm and Voc is 1.009 V. We take this to be the optimized structure. Our previous analysis shows that the shorter thickness of collector layer makes the HBT solar cell insensitive to the doping concentration of collector regions.

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Table 3.3 Results of optical and electrical simulations.

AlGaAs GaAs layer Optical SC Jsc Voc Efficiency thickness current density (mA/cm2) layer (V) (%) (mA/cm2) thickness (µm)

(µm)

5 33.76 28.29 1.05 26.02 15 38.61 32.66 1.0311 29.41

30 44.11 37.43 1.018 33.23 0.5 45 46.74 40.02 1.009 35.37 62.5 46.91 40.16 1.002 35.28 5 34.21 28.61 1.053 26.4 15 40.61 34.38 1.032 30.96

30 44.66 38.01 1.019 33.73 0.7 45 46.85 40.21 1.009 35.35 60 47.00 40.31 1.002 35.33 70 46.9 40.09 0.999 35.11 5 34.06 28.28 1.05 26.08 12.5 39.33 33.07 1.03 29.94

20 42.55 36.02 1.0266 32.06 1 35 46.16 39.38 1.015 34.88 50 46.84 40.02 1.006 35.25 57.5 46.91 40.1 1.003 35.23 70 46.89 40.06 0.99 35.06 5 35.34 29.14 1.053 26.9 20 42.42 35.72 1.026 31.8 35 46.14 39.18 1.015 34.7 1.5 52.5 47.06 40.04 1.005 35.24 67.5 47.14 40.11 1.000 35.11 5 36.27 29.71 1.054 27.43 20 42.61 35.78 1.026 31.84 35 46.64 39.47 1.015 34.95

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50 47.26 40.08 1.006 35.31 65 47.35 40.13 1.001 35.16 2

Moreover, among the recombination mechanisms, as described in the previous section, Auger recombination has the minimal effect. Thus, while optimizing the structure, we can ignore their effects. Additionally, SRH lifetime was calculated by the Eq. 3.1. The radiative recombination coefficient for GaAs is taken to be 1.3×10-10 cm3/s which are the average value reported in [85].

The absorption spectrum of this optimized structure along with solar spectrum (AM 1.5G) is shown in Fig. 3.11. From the figure, we see that the device absorbs most of the higher energy portion of the solar spectrum from 400-900 nm. The increased base layer thickness stretches the absorption beyond 900 nm resulting in near complete absorption of the solar spectrum.

Solar Spectrum (AM 1.5G) /nm) 1.5 2

1 a 0.5

0

Power (W/m Power 500 1000 1500 2000 2500 Wavelength (nm)

Absorption Spectra of optimized HBTSC 0.8 Absorption Spectra of initial structure 0.6 b 0.4 0.2

Absorption (a.u.) Absorption 500 1000 1500 2000 2500 Wavelength (nm)

Fig. 3.11 (a) AM 1.5G solar spectrum (b) Absorption spectrum of the optimized HBT solar cell (blue line) along with the absorption spectrum of unoptimized structure (green dotted line).

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The spatial distribution of optical absorbed power and electric field intensity is plotted in Fig. 3.12 and Fig. 3. 13. From this figure, we observe that the optical absorbed power and field distribution are highest on the front face where light enters the devices. They gradually decrease as light is gradually absorbed in the cell producing electron-hole pairs. The J-V characteristics and P-V characteristics of the structure are shown in Fig. 3.14. From J-V characteristics, we see that the base current is equal to the sum of emitter and collector current, which satisfies Eq. 2.1. This is the maximum possible efficiency that can be achieved given the above-mentioned recombination and design parameters.

Fig. 3.12 Spatial absorbed optical power of highest efficiency, optimized 0.5 µm AlGaAs and 45 µm GaAs HBT solar cell.

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Fig 3.13 Spatial Electric field (magnitude) distribution of highest efficiency, optimized 0.5 µm AlGaAs and 45 µm GaAs HBT solar cell.

) 40 2

) 30 2 30 J b J 20 20 c J e 10 10 Power (mW/cm Current Density (mA/cm

0 0 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 Voltage (V) Voltage (V)

(a) (b)

Fig. 3.14 The (a) J-V and (b) P-V characteristics of the optimized structure. The input power is taken to be 100 mW/cm2.

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3.2.7 Comparison with Conventional Heterojunction Solar Cell Configuration

Most of the conventional solar cells, both planar and even heterojunction, are two- terminal devices. However, our structure is of three terminals, although we have shorted out two terminals (emitter and collector). Therefore, we investigate the benefit of having one extra terminal to the performance of the device. To study this, we take 0.5 µm AlGaAs and 62.5 µm GaAs HBT structure. We simulate the same structure with both three terminals and two terminals. We find that the Jsc of the three-terminal structure is 2 40.16 mA/cm , but the Jsc of same structure with conventional two-terminal is 33.7 mA/cm2. The efficiency of the three and conventional two terminal device is 35.28% and 28.41% respectively. The comparison of the simulation results are shown in Table 3.4.

Table 3.4 Comparison of performance of HBT solar cell and conventionally configured solar cell.

2 Structure Jsc (mA/cm ) Voc (V) η (%)

Three-terminal HBTSC 40.16 1.002 33.7

Two-terminal conventional 35.28 0.97 28.41 % heterojunction solar cell

As we described earlier in section 2.1.2, due to the presence of one extra terminal, the effective diffusion length of photo-generated carriers are reduced. Thus, there is less overall recombination of excited carriers resulting in increased current density from the device. Moreover, as the charged carriers collected at the terminals (emitter and collector) are independent of each other, the total current from the terminals add; whereas, in the multijunction solar cell, the total current was limited by the lower current of the sub cells. Therefore, higher current yields higher output power and greater efficiency in HBT solar cell.

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3.2.8 Comparison with Other Material Systems

We have chosen GaAs/AlGaAs material system due to its excellent optoelectronic properties for solar cell application. This is also evident from simulation result as we have calculated a maximum efficiency of 35.6% for our HBT solar cell using this material system. To further justify the choice of our material system, we have compared our results with the heterojunction solar cells of other material systems. As Si still dominates the solar cell industry, at first, we compare our result with Si-based heterojunction solar cell. The integration of III-V compounds with Si has been rigorously investigated for over 20 years. There has been widespread research on Si/GaAs heterostructure solar cell. However, the efficiency reported till date is not very high. This is due to the high lattice mismatch resulting in defects. Although research has been going on to overcome this issue. For example, Andre et al. reported a GaAs/Si solar cell with intermediate SiGe layer having efficiency around 18% [92]. Diaz et al. designed a tandem solar cell of GaAsP/SiGe on Si substrate having an efficiency of 18.9% [93]. Another potential combination, in terms of matured growth technique and availability, is Si/SiGe material system. Hsieh et al. proposed a thin film Si/SiGe solar cell with 16% efficiency. The problem with Ge solar cell is that the lower bandgap of Ge produces lower Voc and the lattice mismatch is of this material system is 4% which is also relatively high [94]. Lueck et al. reported a dual junction GaInP/GaAs solar cell grown on SiGe/Si substrate having an efficiency of 20% and 16.8% for the two cells respectively for AM 1.5G [95]. Ali et al. reported that their design enhance the efficiency of Si solar cell with SiGe layer. They calculated efficiency for different mole fraction of Ge and found the maximum efficiency of ~20% [96].

Apart from Si, GaN-based solar cells are also investigated widely nowadays. InGaN alloys are studied increasingly as a prospective material for solar cells due to their tunable bandgaps covering the major part of the solar spectrum and superior photovoltaic characteristics including high absorption coefficients and high carrier mobility. Moreover, high thermal stability, superior radiation resistance, and excellent chemical tolerance of InGaN alloys allow them to operate under harsh environments, where Si cells may not be good enough. However, they also suffer from the higher density of dislocation serving as non-radiative recombination center, large lattice mismatch etc. Nevertheless, Bai et al. reported an InGaN/GaN MQW solar cell having a maximum efficiency of 1.28% with

57 | P a g e nanohole [97]. With similar material system, Arif et al. reported an efficiency of 1.4% [98].

After comparison with some of the potential heterojunction material system, it can be concluded that our chosen material system yields outstanding efficiency and hence a good choice for HBT solar cells.

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Chapter 4 Conclusion and Future Work

4.1 Conclusion

In conclusion, it can be said that solar photovoltaic technology is one of the most promising renewable energy technologies, which has the potential to shape a clean, reliable, scalable and affordable electricity system for the future. Worldwide extensive research - on developing new solar cell device architecture and finding new material system - is going on to confront the challenge of improving efficiency. As a part of this effort, in this thesis, following contributions were made:

• We proposed a high-efficiency GaAs/AlGaAs NPN heterojunction bipolar transistor solar cell based on novel three-terminal architecture. From the extensive literature review, we identified different problems and challenges of designing and improving the efficiency of a solar cell. Then we come up with our own solution to overcome major challenges and proposed a highly efficient device. Our device shows 5% more efficiency than the conventional two-terminal heterojunction solar cells. • We choose GaAs/AlGaAs material system for our device due to its suitable optical and electrical properties for the high-efficiency solar cell. We have compared the results of our GaAs/AlGaAs HBT solar cell with heterojunction based solar cells of other material systems and showed that out material system has superior performance. • We explored the effect of different design parameters. We varied the thickness of the GaAs and AlGaAs layers to find the optimum thickness for broadband absorption of solar spectrum and thereby harnessing maximum power. We observed that increasing the GaAs layer thickness increases photocurrent, up to a certain point beyond which saturation is reached. Moreover, most importantly, the

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increase of the layer thickness is limited by the carrier transport mechanism. We observed that the high carrier generation does not lead to high output current at the terminal due to transport losses of photo-generated carriers. As a result, both detail optical and electrical simulation was required and hence have been done to find the performance of the designed cell. We also varied some other key parameters like doping. We find that the base doping has pronounced effect on the efficiency of the cell. Due to the small thickness compared to the base, the emitter doping has a less pronounced effect on the efficiency except for the high value of emitter doping at which the efficiency drops significantly. However, the collector doping has minimal effect and thus can be ignored. • We also investigated the effect of photon recycling effect and observed that this also increases the efficiency by 8%. • Based simulation result, we find out an optimized structure that gives a maximum efficiency of 35.6%.

We expect that our investigation and analysis would provide a comprehensive understanding and clear direction for design and optimization of HBT solar cell.

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4.2 Future work

While our proposed HBT solar cell shows impressive efficiency, there are still scopes for further improvement of the efficiency and also for studying different aspects. These are:

➢ The performance of HBTSC with more new material systems can be explored. Some potential material systems would be GaN/AlGaN, InP, InGaP, InGaAsP etc. The use of 2D material and metamaterial could also be an interesting work. ➢ Another obvious extension of this work could be the use of different light trapping nanostructure or grating structure to enhance the light-matter interaction and thus increase efficiency. Nowadays, the use of these kinds of nanophotonic structures is extensively explored which shows promising results. ➢ The use of Plasmonic nanostructure which excites surface plasmon causing light concentration, trapping, and enhanced field distribution can also be explored [99, 100]. This may ultimately enable the designer to reduce the volume of active material layer facilitating low-cost large scale commercial production. ➢ In this work, the ARC layer is not modeled in details. Rigorous optical simulation of ARC layer and study the use of the different material as ARC could be a topic of future study. ➢ The effect of the band to band tunneling and impact ionization can also be investigated.

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