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TOPICAL REVIEW Engineered nanomaterials for solar energy conversion

Vladan Mlinar

School of Engineering, Brown University, Providence, RI 02912, USA

E-mail: vladan [email protected]

Received 7 November 2012, in final form 7 December 2012 Published 8 January 2013 Online at stacks.iop.org/Nano/24/042001 Abstract Understanding how to engineer nanomaterials for targeted solar-cell applications is the key to improving their efficiency and could lead to breakthroughs in their design. Proposed mechanisms for the conversion of solar energy to electricity are those exploiting the particle nature of light in conventional photovoltaic cells, and those using the collective electromagnetic nature, where light is captured by antennas and rectified. In both cases, engineered nanomaterials form the crucial components. Examples include arrays of semiconductor nanostructures as an intermediate band (so called intermediate band solar cells), semiconductor nanocrystals for multiple exciton generation, or, in antenna–rectifier cells, nanomaterials for effective optical frequency rectification. Here, we discuss the state of the art in p–n junction, intermediate band, multiple exciton generation, and antenna–rectifier solar cells. We provide a summary of how engineered nanomaterials have been used in these systems and a discussion of the open questions. (Some figures may appear in colour only in the online journal)

1. Introduction thin-film technologies. Examples include amorphous Si, thin- film Si, CuInSe2, CdTe, and dye-sensitized photochemical The proposed mechanisms for the conversion of solar energy cells. Current, third generation, PV should lead to an to electricity include those exploiting the particle nature increase in efficiency. Proposed improved solar cells include of light in conventional photovoltaic cells, where absorbed e.g., high efficiency multi-gap tandem cells, multiple exciton photons generate electron–hole pairs, and those using the generation solar cells, intermediate band solar cells (IBSCs), collective electromagnetic nature of the light, where sunlight hot carrier converters, /thermophotonics, is captured by antennas and rectified. In recent years, there etc. Furthermore, it has been proposed that sunlight could be has been immense progress in solar-cell technologies and a captured by (nano)antennas and rectified using a diode by dramatic decrease in their cost. For example, the efficiency exploiting the wave nature of the light [3–5,2]. of solid-state photovoltaic (PV) cells started with values Engineered nanomaterials are the key building blocks of ∼5% [1], but now there are routinely achievable values of the current generation solar cells. For example, the idea of >20% in Si-based systems and >30% in GaAs-based behind the IBSCs is to introduce one or more energy levels systems [2]. within the bandgap so that they absorb photons in parallel with Perhaps the best way to track the technological progress the normal operation of a single-bandgap cell [6]. The search is by examining the three generations of PV, defined by the for optimal sub-bandgap absorbers has been focused on highly increase of efficiency versus the reduction in cost [2]. First mismatched semiconductor alloys that naturally exhibit an generation PV includes solar cells made of semiconducting intermediate band (IB) [7,8,6], and on nanostructures, in p–n junctions, such as single crystal Si and poly-grain particular arrays of quantum dots that form an IB [9–11,8, Si. Second generation PV reduced cost by introducing the 6].

+11$33.00 10957-4484/13/042001 c 2013 IOP Publishing Ltd Printed in the UK & the USA Nanotechnology 24 (2013) 042001 Topical Review Other examples include the potential usage of semi- 2. p–n junction solar cells conducting nanocrystals in multiple exciton generation solar cells, where excitation of a semiconductor nanocrystal by a The solar spectrum contains photons with energies ranging single, high-energy photon may result in a few electron–hole from about 0.5 eV to 3.5 eV. Conventional solar-cell pairs [2, 12–19], or nanomaterials for the design of optical technology is based on a single p–n junction, benefiting from antennas with a typical dimension of ∼100–1000 nm, one electron–hole pair for each absorbed photon, as shown supporting modes which exhibit extremely short wavelengths in figure1(a). When light quanta are absorbed, electron–hole and strong confinement of the electromagnetic field on the pairs are generated, and if their recombination is prevented nanometer scale [5,2, 20]. they can reach the junction, where they are separated by an A new playground has opened for engineered nanoma- electric field. terials, and at this point it is simply not sufficient to focus Current photovoltaic technologies utilize semiconduc- only on technological improvements. Further technological tors, such as large crystals of , or thin films of breakthroughs depend strongly on an improved fundamental , (CdTe), or copper understanding of electronic, optical, and transport properties indium gallium selenide (CIS). The semiconductor material of nanomaterials and finding an efficient way to transfer has to be able to absorb a large part of the solar spectrum, technology from research laboratories to industry. Recent which is determined by its bandgap, as illustrated by examples advances in computational nanoscience, combined with in figure1(b). For example, amorphous silicon has a higher state-of-the-art experiments, could potentially enable such bandgap (1.7 eV) than (1.1 eV), which breakthroughs. means that it absorbs the visible part of the solar spectrum Quantum mechanical models have become sophisticated more strongly than the infrared portion of the spectrum. enough to handle nanosystems of a few tens or a few The p–n junction solar cells based on crystalline ∼ thousands up to hundreds of thousands of atoms, including silicon now routinely achieve an efficiency of 22% [23, excitations and many-body effects. They are able to handle 2]. The maximum thermodynamic efficiency for single- realistic structural information obtained from the structural bandgap devices, assuming detailed balance, is 31%, the Shockley–Queisser limit [24]. It is obvious from figure1(b) characterization measurements and take into account all the that by layering materials with different bandgaps one can relevant effects, including the strain and piezoelectric effects, improve the efficiency. This is the underlying idea of the and external magnetic and electric fields [21]. Using these multi-layer (‘tandem’) cells, which are highly efficient, but models we can, at least in principle, connect structure and also expensive [2]. physical properties of a nanomaterial. The energy conversion efficiency of solar cells based Furthermore, combining the quantum methods with on thin-film silicon is typically lower than that of bulk machine learning algorithms has opened new pathways for silicon [23]. These limitations have been overcome by the design and engineering of nanomaterials with targeted employing light-trapping schemes. The incoming light is properties [21]. Once a targeted physical property has been obliquely coupled into the silicon and the light traverses the defined, the quantum mechanical models and search/machine film several times, enhancing the absorption in the films [23]. learning algorithms are employed to deduce one or a few The minimum thickness of the material is defined by the best candidate nanomaterials. It was suggested that, for thermodynamical limit on light trapping [25]. However, recent technological applications, the same method could be used findings demonstrate that, in principle, any semiconductor to optimize the nanomaterials with respect to the targeted material can exceed the light-trapping limit when the local physical property, avoiding a long and costly process that density of optical states (LDOS) of its absorbing layer exceeds includes nanomaterials’ fabrication and characterization [21]. the LDOS of the bulk semiconductor material [22]. This could However, before even considering the application of the potentially allow for the design of novel solar cells that can predictive-theory-guided design to solar cells, we need to absorb light from the entire solar spectrum, but are ∼10 nm understand the current fundamental and practical problems thick [22]. with the solar cells. Only then can we discuss how realistic Another way of creating the p–n junctions in semicon- and potentially useful the predictive-theory-guided design ductors is by utilizing the electric field effect, where the could be. concentration of charge carriers in a semiconductor is altered Here, we discuss the state of the art in p–n junction, by the application of an electric field. Very recently, it has IB, multiple exciton generation, and antenna–rectifier been proposed to exploit this effect to induce a p–n junction, solar cells. We provide a summary of how engineered enabling, at least in principle, a high quality p–n junction to be nanomaterials have been used in these systems and a made of basically any arbitrary semiconductor [26]. The idea discussion of the open questions. For example, we address is to carefully design the top electrode so the gate electric field recent findings on how to exceed the thermodynamical limit can sufficiently penetrate the electrode and more uniformly on light trapping [22], or very recently reported multiple modulate the semiconductor carrier concentration and type. exciton generation enhancement of photocurrent in PbSe The method is illustrated on the example of silicon and copper nanocrystal-based solar cells [19]. Understanding how to oxide, where in the case of silicon, the top contact is made of engineer nanomaterials for targeted solar-cell applications a single layer of graphene across the surface [26]. is the key to improving their efficiency and could lead to The major factors limiting the conversion efficiency are breakthroughs in the design. the inability to absorb photons with energy less than the

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Figure 1. (a) Schematic diagram of a conventional single-junction semiconductor (CSC). Absorbed light with photon energies greater than the bandgap produces carriers, electrons and holes. Loss processes are nonabsorption of below-bandgap photons, heat losses, and radiative recombination. (b) Different materials absorb different parts of the solar spectrum depending on their bandgaps.

Figure 2. (a) Band diagram of an intermediate band solar cell (IBSC). Simultaneous with normal operation of the cell, below-bandgap photons get absorbed by the two transitions to and from the intermediate level contributing to the photocurrent. (b) Limiting efficiency for IBSC and conventional SC (CSC) as a function of E1 (intermediate band–valence bandgap). We used data from Laque and Marti [27]. bandgap, thermalization of photon energies exceeding the band (CB), enabling, at least in principle, IBSCs to achieve bandgap, and radiative recombination losses [23,2]; see both high current and high voltage. figure1(a). When a photon is absorbed with energy greater The IB has to be partially occupied to enable absorption than the bandgap of a semiconductor, the resultant carrier from the VB into the empty states of the IB, and from undergoes fast cooling via phonon scattering and emission. occupied states of the IB to the CB. Splitting the Fermi Three approaches have been put forward to address level into three separate quasi-Fermi levels preserves the high this loss of efficiency [2]: (i) increasing the number of output voltage of the cell [6]. Of course, VB to IB and IB energy levels, typically by using a stack of multiple p–n to CB transitions must be optically allowed and strong, and junctions in different semiconductor materials (figure1(b)); the IB needs to be electronically isolated from both the CB in this way higher-energy photons are absorbed in the and the VB, so VB to IB and IB to CB absorption spectra higher-bandgap semiconductors and lower-energy photons do not have spectral overlaps with each other [8, 11, 27]. The in the lower-bandgap semiconductor; (ii) capturing carriers theoretical limiting efficiency of IBSC is 63% [27], derived before thermalization, yielding a higher photovoltage; and at isotropic sunlight illumination and assuming the Sun and (iii) multiple-carrier-pair generation per high-energy photon Earth temperatures to be 6000 K and 300 K, respectively. or single-carrier-pair generation with multiple low-energy Under the same conditions, the maximum efficiency of a photons, leading to the enhancement of the photocurrent. single-gap solar cell was 41%. Variation of the efficiency with the IB–VB gap E1 is shown in figure2(b), where we used data 3. Intermediate band solar cells from Laque and Marti [27]. The quest for finding optimal sub-bandgap absorbers has The main idea behind IBSCs is to introduce one or been focused on (i) alloys that naturally exhibit an IB [7,8,6] more energy levels within the bandgap such that they and (ii) nanostructures, in particular arrays of quantum dots absorb photons in parallel with the normal operation of a (QDs) that form an IB [9–11,8,6]. single-bandgap cell [6,8,2, 27, 28]. A band diagram of an Bulk IBSCs. The electronic band structure of highly IBSC is shown in figure2(a). Sub-bandgap energy photons are mismatched semiconductor alloys can be tuned both absorbed through transitions from the valence band (VB) to experimentally and theoretically to exhibit three electronically the intermediate band (IB) and from the IB to the conduction isolated energy bands [8]. In highly mismatched alloys this

3 Nanotechnology 24 (2013) 042001 Topical Review can be achieved by the substitution of a relatively small deposited material [35, 36]. The shape and average size fraction of host atoms with an element of very different of these QD islands depend mainly on factors such as the electronegativity. Examples include III–V and II–VI alloys, in strain intensity in the layer as related to the misfit of the which group V and VI anions are replaced with the isovalent lattice constants, the temperature at which the growth occurs, N and O, respectively, see e.g., [29, 30]. The electronic and the growth rate. The islands evolve to the state of structure of such alloys is determined by the interaction quasi-equilibrium in which they assume the shape of pyramids between localized states associated with N or O atoms and or lenses formed on a thin wetting layer, that are then capped the extended states of the host semiconductor matrix. As by the barrier material. The main advantages of the SK a result the conduction band splits into two subbands with growth mode are fabrication of defect-free QDs of small sizes, distinctly nonparabolic dispersion relations [29], affecting the homogeneity in sizes and shapes of QDs, formation of ordered optical and electrical properties of these alloys. A narrow arrays of 3D coherent islands, and fairly convenient growth lower band can be formed only if the localized states processes [35, 36]. Indeed, their structural perfectness (no lie well below the conduction band edge. Consequently, impurities, dislocations, and defects), the excellent isolation the absorption spectrum is modified by adding two new from the environment, and the ability to charge the system absorption edges, which can be tuned, at least in principle, with a few electrons or holes (multiexcitons), have made to fall within the solar energy spectrum [30]. Experimental them essential in studying many-particle physics in confined examples include the formation of an IB within the spaces [37, 38]. Unlike colloidal QDs, where nonradiative bandgap of highly mismatched semiconductor alloys such decay channels rapidly destroy multiexcitons and, e.g., cause as Zn1−yMnyOxTe1−x and GaNxAs1−x−yPy [29, 30]. The IB blinking in photoluminescence (commonly interpreted as was detected by spectral photoreflectance measurements, and being caused by the presence of extra charges that enhance its formation was attributed to band anticrossing. In order nonradiative decay rate) [39, 40], in self-assembled QDs to obstruct electron tunneling between the IB and CB, and the multiexcitons ‘survive’ (and decay radiatively). Also, consequently maintain a high open-circuit voltage, blocking the photocorrosion and photostability [41] of colloidal QDs, layers were introduced. This was successfully demonstrated where QDs stability depends on the solution (e.g., it was on an example of GaN0.024As0.976 [28,8]. found that CdS QDs in nonpolar solvent were remarkably From theoretical and computational viewpoints, numer- stable even under UV light irradiation) [41], do not influence ous ab initio calculations have been performed in the quest for self-assembled QDs. optimal IB materials. The most promising of these has been In order to create a mini-band, some measure of V In S , which has strong sub-bandgap absorption and 0.25 1.75 3 homogeneity must exist between the successive an inherent partially filled IB [7]. This is important because it layers. However, the strain may accumulate so that layers of means that the IB is already partially filled without having to coherent quantum dots may no longer be formed, thus limiting rely on impurity doping, which reduces densities and therefore the number of QD layers [42–44]. The strain-induced limit of lowers absorption levels. the number of QD layers can be lifted by employing systems Bulk IBSCs have so far exhibited efficiencies far below with the strain symmetrization within the structure, such as the their potential, and the issue of finding the best candidate (In, Ga)As/Ga(As, P) system [11]. It was found that, whereas materials for this technology is essential if IBSC research is the number of QD layers was indeed increased, the intensity to succeed. Quantum dot IBSCs. An IB can also be formed from of absorption between QD-confined electron states and the the confined states of QDs situated within the bandgap host CB was weak (because of their localized-to-delocalized of a host semiconductor. QDs should be closely spaced character) and the position of the IB within the matrix and with high quality interfaces, which would enable the bandgap did not satisfy suitable energetic locations for the strong wavefunction overlap and the formation of minibands. IB [11]. To achieve strong absorption to and from the IB, a high Furthermore, one of the challenges in the QD IBSC concentration of QDs is required. By engineering the design has been the loss of output voltage at room temperature parameters such as QD geometry (size and shape), inter-dot compared to reference solar cells without an IB [6]. The loss separation, and dot arrangement, one can optimize IB position of voltage at room temperature is caused by the thermal escape and width to achieve the maximum efficiency [31, 32]. of electrons from the IB to the CB (in addition to tunneling of Typically, self-assembled (In, Ga)As QDs embedded in a electrons from the IB to the CB) [6,8]. GaAs matrix have been used as an IB (see, e.g., [6]). Thus, from a fundamental viewpoint, there is a need Other examples include InAs QDs in a GaAs/(Al, Ga)As for better understanding of the nature of the IB (localized matrix [33], or GaSb QDs in GaAs [34]. Interestingly, some of versus extended), and carrier relaxation processes. From these devices have demonstrated features of IBSC operation, a purely technological viewpoint, the quest for improved and achieved efficiencies over 18% [10,6]. fabrication techniques and more suitable materials (strain Self-assembled QDs consist of 104–106 atoms of a symmetrization and strong absorption between the IB and semiconductor such as (In, Ga)As embedded in another CB) has only just begun. As an illustration of the sensitivity semiconductor matrix, e.g., GaAs. They are fabricated by of the problem, careful fabrication of InAs/GaAs IBSCs led the Stranski–Krastanov (SK) growth mode, which uses the to a significant elimination of output-voltage reduction [45], natural lattice mismatch between the substrate and the potentially opening pathways for room temperature IBSCs.

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Figure 3. The single photon generation of multiple excitons (electron–hole pairs). (a) Bulk and (b) nanocrystal.

Figure 4. (a) The ideal profiles for carrier multiplication efficiency η, the number of excitons generated by absorption of a photon, for bulk PbSe (green), nanocrystals NC1 (blue) and NC2 (red). The shaded region represents the AM1.5G solar spectrum [49]. (b) Quantum yield versus photon energy for PbSe [13, 50, 15, 47] and PbS [13, 17, 47] nanocrystals (NCs) and bulk; data from various groups illustrate wide variations of reported MEG QYs. The quantum yield represents the averaged number of excitons per absorbed photon. QY = 200% means all dots have two excitons.

4. Multiple exciton generation solar cells photogenerated carriers may be affected by quantization effects, and lead to more efficient solar cells (figure3(b)). For Multiple exciton generation (MEG), or carrier multiplication, example, hot carrier cooling rates of impact ionization could is the generation of more than one electron–hole pair become competitive with the rate of carrier cooling [2, 13]. (exciton) by absorption of one photon [46–48]. High-energy Numerous experiments have confirmed the existence photons, at least twice the bandgap energy, absorbed in a of MEG in nanocrystals (although not without controversy, bulk semiconductor can generate one or more additional as discussed below) by showing that excitation of a electron–hole pairs close to the bandgap energy through a semiconductor nanocrystal by a single, high-energy photon scattering process, known as impact ionization (the inverse may result in a few electron–hole pairs (figure3(b)) [2, of Auger recombination) (figure3(a)) [2, 47, 48, 46]. The 12–19]. The single photon generation of multiple excitons impact ionization was previously observed in bulk Si, PbS, occurs on a very short time scale following photon absorption, PbSe, Ge, InSb, etc. This effect is inefficient in bulk because where the efficiency increases with the energy of the photon. the rate of impact ionization is much slower than the rate of Figure4(a) shows the ideal profiles for multiple exciton radiative recombination at low electron energies (in visible generation efficiency η [48, 46] in bulk PbSe Eg = 0.27 eV and near IR spectrum) and the need to conserve momentum. In (green), nanocrystal NC1 with Eg = 0.72 eV (1722.2 nm) addition, the impact ionization in bulk is not useful for energy (blue) and nanocrystal NC2 with Eg = 1.3 eV (954 nm) conversion purposes because the required photon energies lie (red). The efficiency η is defined as the number of excitons outside the solar spectrum (3.5 eV); e.g., it requires ∼7 eV generated by absorption of a photon. It was calculated using photons to produce one extra carrier in silicon [19, 46,2]. the detailed balance model under the assumptions that all Thus, it was proposed that MEG can be more efficient photons with energies above the bandgap were absorbed and in semiconducting nanocrystals [12, 15]. Given the unique those with energies less than the bandgap were not, that electronic structure properties of nanocrystals–atomic-like the only loss is the radiative recombination, and that all electronic structure and size-dependent bandgap energies [15, photogenerated carriers are collected [48]. The calculations 38], it was suggested that the relaxation dynamics of also give the maximum efficiency depending on the bandgap,

5 Nanotechnology 24 (2013) 042001 Topical Review max defined as η (Eg) = 4/Eg [48]. In our case this gives, e.g., virtual multiexciton state that is strongly coupled to a real max max η (Eg = 0.72) = 5 and η (Eg = 1.3) = 3. multiexciton state; to incoherent impact ionization, analogous Figure4(b) shows quantum yield (QY) versus photon to bulk impact ionization with appropriate modifications of energy for PbSe [13, 50, 15, 47] and PbS [13, 17, 47] the electronic states [16, 51,2]. In order to distinguish nanocrystals and bulk. The quantum yield represents the between different interpretations, one would need additional averaged number of excitons per absorbed photon. Data from constraints on the set of initial parameters. The set of initial various groups illustrate wide variations of reported MEG parameters includes the coupling strength between excitons QYs [13–19, 50]. This caused controversies, especially at the and multiexcitons, decay rates, and/or density of states. This beginning, because the reported experimental probes of MEG is still an open issue. have relied only on indirect evidence of the existence and Theoretical/computational models should link structure efficiency of MEG (signature of Auger recombination within (typically extracted from structural characterization measure- the exciton population decay traces) [16, 46, 18,2]. ments) and predict or explain experiment. They should also In a typical MEG experiment, ultrafast transient predict any size dependence, explain how MEG is influenced absorption spectroscopy is used to infer the number of by the coupling of the nanocrystal to its environment, electron–hole pairs produced per absorbed photon. Samples and provide understanding of how MEG is influenced by are illuminated with a low-intensity beam of high-energy coupling of nanocrystals. However, structural information photons, and the ensuing dynamics of multiexciton decay about nanocrystal systems is not complete. For example, versus single exciton decay are measured. If a fast component it is difficult to extract information about the surface of with a lifetime similar to multiexciton lifetimes is observed a nanocrystal, so it is not clear whether a charge carrier in addition to exciton decay, it is attributed to multiexcitons. can reside at the nanocrystal surface in deep-trap energy However, MEG artifacts exist and can give ‘false positive’ states or not. One could, e.g., analyze different nonradiative signatures of MEG. For example, the single exciton decay decay channels for an assumed nanocrystal structure and then can acquire a fast component due to opening of nonradiative discuss the plausibility of the constructed scenarios. channels, e.g., electron or hole traps in a nanocrystal From a more pragmatic (but not necessarily recom- surface [46]. Detailed discussion of the measurement of mended) viewpoint, whereas understanding of the underlying MEG versus its artifacts, and the proposed ways to minimize physics is unquestionably important, the primary interest chances of overestimating MEG QY, is given in [46]. should lie in demonstrating that MEG can occur in a working Furthermore, disagreements have arisen over the role solar cell. MEG-induced enhancement of photocurrent in of quantum confinement for MEG. Interpretations range PbSe nanocrystal-based solar cells has been very recently from those showing that the MEG efficiency of the PbSe achieved [19], so the practical challenge is how to improve the nanocrystal is about twice the efficiency observed in MEG-enhanced quantum efficiency and search for different or bulk PbSe [19, 48] to those stating that the advantage new candidate nanomaterials for MEG, e.g., PbSe nanorods, of nanocrystal MEG is merely due to a possibly larger carbon-based nanostructures, etc [19, 21]. Usage of simple photovoltage owing to quantum confinement [46]. Finally, empirical models that heavily rely on experiment can be more there is the issue of the impact the MEG can have on solar useful than employment of detailed many-body atomistic energy conversion, demonstrating that MEG can occur in a methods. Also, although not the most elegant approach, it is working solar cell. not uncommon in materials science to use linear regression Very recently, MEG-induced enhancement of photocur- or neural networks to interpret experimental data when rent in PbSe nanocrystal-based solar cells was demon- physical models do not exist or are difficult to implement; strated [19]. For the best device measured, the external see, e.g., [52]. The underlying equations do not have to be quantum efficiency, defined as the spectrally resolved ratio of physically justified and the parameter set is determined by collected charge carriers to incident photons, peaked at 114 ± fitting the equations to a large set of experimental data [21, 1%. The associated internal quantum efficiency, corrected 52]. for reflection and absorption losses, was 130% [19]. The solar-cell architecture incorporated arrays of QD layers in 5. Antenna–rectifier system for solar energy p–n planar heterojunctions. Special attention was paid to conversion the chemistry of PbSe QD surfaces, including removing long-chain organic ligands (such as oleic acid) while con- Solar energy can be converted to electricity by exploiting the trolling electrical properties, and using four distinct chemical wave nature of light instead of its particle nature: sunlight treatments (1,2-ethanedithiol, which showed reduced MEG, is captured by (nano)antennas and then rectified [3–5,2]. and hydrazine, methylamine, and ethanol, which preserved The fact that this approach had been previously successfully MEG). Furthermore, the beneficial aging effect on the solar applied at longer wavelengths in radio and microwave cell performance was observed under oxygen and water-free frequency bands [53] opened the possibility, at least initially, nitrogen storage conditions [19]. for high efficiency conversion of solar energy. The uses of Theoretical studies regarding the basic mechanisms of rectennas in the microwave region have been investigated over MEG give confusing results. Models offering explanations of the past half century for power transmission and detection. MEG range from those that consider a coherent superposition Applications have included long-distance power beaming, of single and multiple exciton states; to excitations of a signal detection, and wireless control systems [53,4].

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Figure 5. (a) Block diagram of antenna and rectifier system and load; (b) proposed realization of rectenna system using nanowires. Nanowires behave as antennas and the tip of the nanowires and surface create rectifying tunneling junctions. It was suggested that the nanowire’s asymmetrical, nonplanar geometry in conjunction with the flat anode is an essential requirement for increasing the cut-off frequency of the diode (for more details see [5]).

Conventional rectennas consist of two distinct elements [53, 85%, and are based on rather elementary considerations. For 4,5], a dipole antenna plus a separate rectifying diode such as example, the model Sun–space–absorber–solar cell gives the an MIM or Schottky diode, as illustrated in figure5(a). efficiency of ∼85% [4], whereas the model Sun–space–solar In the case of solar energy conversion to electricity, a cell, which included entropy losses, led to the value of rectenna device should collect and rectify electromagnetic ∼93% [62,4]. radiation distributed over a wide range of submicron Unfortunately, it is not clear which one of these methods wavelengths (from the infrared (IR) through the visible applies to the rectenna system. Whereas the simple models, 14 portion of the spectrum, extending the range to 10 Hz which give overly optimistic values of efficiency, do not and higher), which, in contrast to monochromatic microwave include specific features of the antenna–rectifier solar cells, radiation, is also incoherent and unpolarized. Schottky diodes the model based on replacing the antenna by a resistor is as are generally limited to frequencies less than 5 THz [54] and good as the initial assumption that the antenna can be replaced conventional MIM diodes have been used up to frequencies by a resistor at the temperature TR. This assumption is valid of about 100 THz [54–56,5]. So, it is not obvious if an for lower frequencies (up to the near IR) [4, 53], but it is not antenna–rectifier system, as used for monochromatic radio clear to what degree the resistor replacement can be used in and microwave radiation, can be simply applied for solar the optical frequency range. Thus, the question of determining energy conversion, for example, how to design an antenna to the theoretical limiting conversion efficiency of the rectenna collect sunlight, or how to obtain efficient optical frequency solar cell (that includes all the characteristics of the system) is rectification. still open. The conversion efficiency for the rectenna system in the From a (more important) practical viewpoint, the design case of monochromatic radio and microwave radiation is of antennas and rectifiers operating at optical frequencies more than 80% [53]. Estimates for the theoretical limiting represents a significant challenge due to the required size and conversion efficiency of the antenna–rectifier solar cells range frequency of operation (see, e.g., [5, 20]). We are in a situation from 48% [2, 57, 58] to 95% [58], depending on how the in which we need to, on one hand, improve our understanding antenna–rectifier solar cells were modeled. of the behavior of materials used for antennas, e.g. metals, In one model [2,4, 57, 58], electrical noise power in the optical regime, which differs from that at frequencies received through an antenna is replaced by a resistor at a below the IR, and on the other hand improve the ability to temperature TR, whose resistance is equal to the radiation resistance of the antenna. If the antenna can be replaced by fabricate optical antennas with nanometer dimensions. For the resistor at a given temperature, the rectification occurs example, the common requirement for an antenna structure is that its size is comparable to the wavelength of the only if the diode is at a lower temperature TD (TD < TR). collected light. For optical antennas this gives a typical There is no rectification for TR = TD, otherwise the second law of thermodynamics is violated, the so called Brillouin dimension of ∼100–1000 nm. Such (nano)antennas support paradox [59]. Note that the equivalent arguments can be localized plasmon polaritons, which exhibit extremely short found in Feynman analysis of the ratchet as an engine [60], wavelengths and strong confinement of the electromagnetic where it was shown that the engine cannot work if the field on the nanometer scale [20]. In addition to the size vanes and the ratchet are at the same temperature. In both requirements, to produce an effective output signal, the cases the efficiency is less than the Carnot efficiency because antenna must be coupled to a device that can respond in a time of the unavoidable heat exchange between the two thermal t ∼ 1/f , which for optical frequencies corresponds to times of − − reservoirs [61]. It was shown that, if the antenna was replaced 10 15–10 13 s [5]. by a resistor at the temperature TR = 6000 K, the maximum So far, optical antennas have been produced in a variety efficiency was ∼48% [57, 58,2,4]. Obviously, this is a of sizes and shapes [63,5], including, e.g., thin wire or disappointingly low value and casts doubt on the usefulness whisker, dipole, bow-tie, etc. For example, figure5(b) shows of the approach. a thin wire antenna consisting of arrays of vertically aligned Other reported values of the theoretical limiting nanowires, where the tips of the nanowires and surface create conversion efficiency of the rectenna system are higher than rectifying tunneling junctions [5, 64, 55]. For a review and

7 Nanotechnology 24 (2013) 042001 Topical Review recent developments on antenna issues in rectenna solar cells be found to be Mott insulators. Also, such oxides can show see, e.g., [5, 20, 65, 66]. interesting behavior when driven by high frequency fields. In order to get an efficient rectification at optical To summarize, whereas the entire rectenna concept for frequencies, the diode will have to respond fast enough solar energy conversion may be very difficult to realize in to operate at optical frequencies, and have a relatively practice, the problems such as understanding the materials low turn-on voltage. It will also require sufficiently small behavior at optical frequencies, design and fabrication of capacitance to minimize its time constant [5]. antennas with a typical dimension of ∼100–1000 nm, or the Quantum point-contact (QPC) devices, e.g. whisker issue of efficient optical frequency rectification and how to diodes, have been used in measurements of absolute engineer nanomaterials to rectify on such high frequencies, frequencies up to the green portion of the visible represent challenges that need to be addressed. As to the spectrum, demonstrating a response time of the order of solar energy conversion using rectennas, at this point only femtoseconds [5]. a proof-of-concept device will provide convincing evidence One way to realize QPCs is in a break junction by regarding this approach. pulling apart a piece of conductor until broken, or, in a more controlled way, in a two-dimensional electron gas (2DEG), 6. Discussion and summary e.g. in GaAs/AlGaAs heterostructures [67]. Rectification of the terahertz field has been discussed both experimentally Engineered nanomaterials are the key building blocks of and theoretically, in terms of its coupling to the source–drain solar cells, irrespective of the mechanisms for the conversion bias, or in terms of modulating the QPC gate voltage [68]. of solar energy to electricity—those exploiting the particle Theoretically, one can model, e.g., current fluctuations in a nature of light and those using the collective electromagnetic ballistic QPC biased by applied voltage and irradiated by nature, where light is captured by antennas and rectified. external field, where the external field could be considered Understanding how to engineer nanomaterials for targeted to be either coherent (e.g. microwave radiation) or incoherent solar-cell applications is the key to improving their efficiency (e.g. representing the environment at high enough temperature and could lead to breakthroughs in the design. or a heat phonon pulse) [69]. The design of nanomaterial-based solar cells is far QPCs can also be created by positioning the tip of a from being straightforward. Traditional approaches for the scanning tunneling microscope close to the surface of a improvement of the design of solar cells, or the design of solar conductor [70, 71]. The tunneling phenomenon in these QPC cells based on new mechanisms, have relied on the intuition of devices is such that the current passes predominantly through researchers, focusing on trial-and-error search and accidental the sharp protrusion closest to the planar sample surface. The discovery. rectification properties of tunneling junctions at fixed gap Alternatively, predictive-theory-guided design combines width originate from material, geometrical, and/or thermal quantum mechanical methods and search/machine learning asymmetry, and photo-stimulated changes in the electron flux algorithms, such as genetic algorithms, data mining, or distribution [5, 72, 64, 55]. neural networks, to design optimized nanomaterials with Material asymmetry is expected when the electrodes targeted physical properties [21]: we define a targeted physical have different work functions: the barrier shape will be property and then employ the quantum mechanical and asymmetric at zero bias. Thermal asymmetry will occur search/machine learning algorithms to deduce the structure. when there is a temperature difference between the two Of course, this sounds very appealing, especially because the electrodes causing different electron occupations of the states computer-generated nanomaterials could be counterintuitive involved in tunneling. Geometrical asymmetry represents and difficult to discover otherwise, and the actual fabrication asymmetry of the electrodes comprising the tunnel junctions. of a large number of structures and their processing could be Examples include the geometrical asymmetry effect in avoided. The main premise behind this approach is that theory STM [70], or optical rectification caused by the nonlinear is able to correctly link the structure and the property. tunneling conduction between gold electrodes separated by The real test for all those predictive methods would a subnanometer gap [71]. The asymmetrical, nonplanar be to fabricate nanomaterials using information from the geometry of the pointed whisker in conjunction with the flat theoretically predicted structure, and then check how their anode is an essential requirement for increasing the cut-off measured physical properties correspond to the targeted frequency of the diode, but inconsistent with the planar ones. Let us analyze and discuss the solar-cell design from geometry [5]. the viewpoints of traditional versus predictive-theory-guided There have been many innovative proposals on how to design. achieve efficient optical frequency rectification. For example, In the ‘simplest case’ where the underlying physical very recently, Sabou et al [73] theoretically investigated processes are well understood, solar-cell design includes a idealized junctions between oppositely doped Mott insulators, search for optimal constituent nanomaterials and geometries. modeling them as one-dimensional chains of interacting For example, a thermodynamical limit on the light spin-polarized fermions. They predicted efficient rectification trapping within a semiconductor can be overcome by using at very high frequencies. For practical realizations, Sabou subwavelength nanomaterial-based solar absorbers, such et al [73] recommended transition metal oxides, which, as nanowires that have elevated local density of optical although often predicted to be conductors by band theory, can states [22]. Thus, the design reduces to the search for optimal

8 Nanotechnology 24 (2013) 042001 Topical Review materials, ideally those that could absorb light from the entire nanocrystal systems is not complete. For example, it is solar spectrum. difficult to extract information about the surface of a The design is more complicated for IBSCs. The quest nanocrystal, so it is not clear whether a charge carrier for finding optimal sub-bandgap absorbers has been focused can reside at the nanocrystal surface in deep-trap energy on (i) alloys that naturally exhibit an IB [7,8,6] and (ii) states or not. One could, e.g., analyze different nonradiative nanostructures, in particular arrays of quantum dots (QDs), decay channels for an assumed nanocrystal structure and that form an IB [9–11,8,6]. The problem is twofold then discuss the plausibility of the constructed scenarios. here—from a fundamental viewpoint, there is a need for From a more pragmatic viewpoint, whereas understanding better understanding of the nature of the IB (localized versus of the underlying physics is unquestionably important, the extended), and carrier relaxation processes; however, from primary interest lies in demonstrating that MEG can occur a more practical viewpoint, bulk- and QD-based IBSCs in a working solar cell. This has been very recently have been fabricated already, but they have so far exhibited achieved [19], so the practical challenge is how to improve the efficiencies far below their potential. For example, to lift the MEG-enhanced quantum efficiency and search for different strain-induced limit of the number of QD layers in the IB, it or new candidate materials for MEG, e.g., PbSe nanorods, was intuitively clear that it could be achieved by employing carbon-based nanostructures, etc. The recent advances in systems with the strain symmetrization within the structure, computational design could enable such a search for optimal such as the (In, Ga)As/Ga(As, P) system [11]. However, materials and geometries, as discussed in [21]. whereas it was found that the number of QD layers was Application of the rectenna system for energy conversion increased, the intensity of absorption between QD-confined has been present in the literature for quite some time [3–5,2], electron states and the host CB was weak and the position discussing theoretical efficiency [4,2] and proposing various of the IB within the matrix bandgap did not satisfy suitable antenna–rectifier realizations [3–5, 65, 66, 71,2]. At this energetic locations for the IB [11]. A careful implementation point only a proof-of-concept device will provide convincing of the predictive-theory design could have led to different evidence regarding this approach. However, regardless of results, especially given that electronic and optical properties how difficult it may be to realize the whole rectenna of QDs are very well understood and the design rules for a QD concept for solar energy in practice, the problems such as IBSC known [32]. Thus, the issue of finding the best candidate understanding the materials behavior at optical frequencies, materials for the current technology is still open. design and fabrication of antennas with a typical dimension Although intuitively clear, it is important to stress that of ∼100–1000 nm, or the issue of efficient optical frequency the problem is not only to design solar-cell devices based on rectification and how to engineer nanomaterials to rectify at well understood physical principles, but also to control subtle such high frequencies represent challenges that need to be details such as tricks in fabrication which can play a relevant addressed. role. Perhaps this statement is best illustrated by the example of fabrication of InAs/GaAs IBSCs. One of the challenges Acknowledgment in QD IBSC design has been a loss of the output voltage at room temperature compared to reference solar cells without This work was supported by NASA EPSCoR. an IB [6]. The loss of voltage at room temperature is caused by thermal escape of electrons from the IB to the CB (in addition to tunneling of electrons from the IB to the CB). References However, ‘careful fabrication’ led to a significant elimination of output-voltage reduction [45]. [1] Chapin D M, Fuller C S and Pearson G L 1954 A new silicon p–n junction photocell for converting solar radiation into The issues with the design of MEG solar cells are electrical power J. Appl. Phys. 25 676–7 rather complex. From an experimental viewpoint, the issues [2] Conibeer G 2007 Third-generation Mater. 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