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Semiconductor thermionics for next generation solar cells: photon enhanced or pure thermionic?

Semiconductor thermionics for next generation solar cells: photon enhanced or pure thermionic? ARTICLE https://doi.org/10.1038/s41467-021-24891-2 OPEN Semiconductor thermionics for next generation solar cells: photon enhanced or pure thermionic? 1,2 1,2 Ehsanur Rahman & Alireza Nojeh Semiconductors have been used in solar energy conversion for decades based on the pho- tovoltaic effect. An important challenge of photovoltaics is the undesired heat generated within the device. An alternative approach is thermionics, which uses the thermal excitation of electrons from an emitter to a collector across a vacuum gap. If the emitter is a p-type semiconductor, the photogeneration-induced quasi-Fermi level splitting can reduce the effective barrier for electron emission—a mechanism used by a photon enhanced thermionic emission device. Here, we evaluate the prospects of this alternative solar conversion tech- nology considering different semiconductor materials and thermionic device configurations. We also reveal that whether such a device operates in the photon enhanced or purely thermionic mode, depends on the complex interplay among materials properties, device physics and solar concentration level. 1 2 Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada. Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada. email: ehsanece@ece.ubc.ca NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 1 1234567890():,; ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 olar energy conversion is an important field of research due Results to solar radiation’s renewable nature and abundance as well Operation of a thermionic solar cell. Before delving into the Sas the rising environmental pollution concerns of conven- details of materials and device physics and the associated chal- tional energy sources. At present, photovoltaics is the most widely lenges in a semiconductor thermionic solar cell, it is worth con- used mechanism for generating solar electricity with demon- sidering its basic operation with the help of a simple device strated large scale implementation for both terrestrial and space schematic and its energy band diagram as shown in Fig. 1. A basic applications. However, the efficiency of this technology is cur- thermionic solar cell consists of two electrodes known as the rently limited to around 20% for most practical systems. emitter (or cathode) and collector (or anode) separated by a Although above-Shockley-Queisser performance has been vacuum gap. In the emitter, the photogenerated electrons will demonstrated in multijunction photovoltaics and concentrated undergo thermalization and various recombination processes, photovoltaics (CPV) , these alternatives have not seen widespread thereby broadening the thermal distribution of the electron utilization due to higher complexity and the associated costs. The population. Moreover, due to the photoexcitation of a large primary challenges in photovoltaics can be traced to sub-bandgap number of electrons, their thermal population may also be 2,3 photon loss and above-bandgap thermalization loss . Even for a upshifted, which is the photon enhancement effect. The electrons tandem photovoltaic cell, which can minimize the first loss by in this excited thermal population that have sufficient energy to using multiple materials with different bandgaps, the second loss overcome the vacuum barrier will leave the material. These is inevitable, and the resulting heat is not only unutilized but also emitted electrons will be absorbed by the collector where they will degrades the device performance . thermalize again and do useful work with their remaining energy An interesting alternative to photovoltaics, which can turn this as they return to the emitter via an external circuit (the load challenge into a benefit, is thermionic emission. Although ther- receiving the generated power). mionic energy converters (TECs) using metallic electrodes have However, beyond this simple description, there are many 5–8 been considered for solar conversion since the 1950s ,they intricate and interrelated pieces of materials and device physics eventually gave way to photovoltaics due to many other that ultimately determine the operational mode and performance 9–11 challenges . A more recent development to solar thermionics is merits of a semiconductor thermionic solar cell. To investigate these to utilize the very material used in photovoltaics (i.e., semi- effects, we have chosen silicon (Si) and gallium arsenide (GaAs), conductors). In particular, a photon enhanced thermionic emission which have distinct properties. For example, Si, which is the most 12–14 (PETE) device is an insightful concept that uses a p-type widely used material in photovoltaics, has an indirect bandgap and semiconductor to combine the benefits of photovoltaics and ther- weaker optical absorption. On the other hand, GaAs is a direct- mionics: it takes advantage of the photogeneration-induced quasi- bandgap material with a sharp absorption onset near the Urbach 28,29 Fermi-level splitting to reduce the effective emission barrier for edge . Moreover, GaAs has a bandgap very close to the electrons while still delivering a high output voltage; it also utilizes previously reported theoretical optimal value for PETE devices . the thermalization process to help electrons escape the material. Also, the carrier diffusion lengths in these two materials are quite Thus, the combined effects of light and heat on electron emission, different, thanks to their vastly different recombination 15–17 30 studies of which go back to the works of Fowler and DuBridge , parameters .There arealsosignificant differences between their has found a promising new application in solar energy conversion. effective densities of states and dielectric properties. For both Taking advantage of this synergy between heat and light, PETE materials, we also study how the device configuration might affect devices were estimated to outperform state-of-the-art solar cells, the performance of a thermionic solar cell. with an efficiency of around 40% for a single-stage device and 13,18 higher than 50% with a second thermal cycle . These early estimates were based on simplified models to show the potential of Effect of cathode thickness. First, we discuss how material the concept. To study these devices in more detail, subsequent properties affect the optimal emitter thickness and the mode of works have investigated some of the relevant physics such as operation in a semiconductor thermionic solar cell. In general, 19–21 20,22–24 thermal balance , the space charge effect ,spatial varia- the choice of the optimal thickness is dictated by the maximiza- 25–27 tions of the charge carrier density and near-field radiative tion of the absorption of the solar spectrum and minimization of 20,22 coupling to varying degrees (a detailed list of the different the recombination of excess carriers during their transport to the aspects of the physics treated in some of the previous key papers is emitting surface. These requirements are contradictory in terms provided in Supplementary Table 1). However, a comprehensive of the material’s thickness. Based on our studies of different treatment of all the important materials and device physics has been device configurations (which will be discussed later), we found missing. Owing to the complex interplay of the various pieces of that, under maximum conversion efficiency, Si maximizes the physics involved, studying their individual contributions while absorption of the solar spectrum. In other words, the nonradiative simplifying other aspects does not enable a realistic analysis of these recombination-induced heating effect compensates for the carrier photothermal phenomena and devices based on them. As a result, loss in Si at higher thicknesses (Fig. 2a) and results in a pure fundamental questions still need to be addressed: whether or not a thermionic mode of operation. This finding is in contrast to the semiconductor thermionic device would operate in the PETE mode; previous studies of Si cathodes where an optimal thickness for Si 26 26 and what the trends in device behavior and performance limits are was predicted , possibly due to the simplifications made in ref. if all the crucial physics are taken into account. Such a compre- (see Supplementary Table 1). On the other hand, for GaAs, hensive study is the topic of the present work. recombination loss becomes a limitation at larger thickness Our findings show that the device performance, while highly thereby resulting in a specific desired thickness that maximizes promising, is limited by the various tradeoffs in terms of material efficiency (Fig. 2b) by using the photon enhanced mode. There- properties and device physics. Moreover, we reveal that the PETE fore, considering these aspects of recombination and optical mode is not guaranteed in a semiconductor thermionic solar cell absorption, the trends in device efficiency with the material’s under optimal operation, nor is it necessary for achieving a thickness could vary from one semiconductor to another (Fig. 2). performance comparable to photovoltaics. This work sheds light The different behaviors seen in Fig. 2a, b with respect to doping on the issues and challenges in semiconductor thermionic solar level may be understood based on the fact that the electrode conversion that need to be overcome when considering a com- temperatures, optimal gap size, and optimal operating voltage are plete device-level operation. interdependent in a non-trivial way through energy balance and 2 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE Fig. 1 Operation of a semiconductor thermionic solar cell. a The schematic of a thermionic solar converter’s operation. b A simple band diagram of a semiconductor thermionic solar cell. E and E are the equilibrium Fermi levels in the emitter and collector, respectively, and E is the emitter quasi- F,E F,C F,n Fermi level for electrons in the PETE mode. φ is the maximum motive in the interelectrode space and e is the electron charge. φ and φ are the work m E C functions of the emitter and the collector, respectively. T and T are the temperatures of the emitter and the collector, respectively. E , E , and E are the E C C V g conduction band minimum, the valance band maximum and the bandgap energy, respectively. V is the voltage difference between the two electrodes (and across the load). Fig. 2 Variation of the solar conversion efficiency with emitter thickness. The data are shown at the maximum power point for a Si and b GaAs for different p-type doping levels in the emitter and a solar concentration ratio of 100. obtained self-consistently. At a fixed solar concentration, as the (as will be seen later), the output voltage does not increase in the 17 −3 doping level in the GaAs cathode is increased from 10 cm to same manner at higher doping levels, and hence the trends in output 20 −3 10 cm , the recombination probability increases, leading to higher power and efficiency are dominated by the trend in the current. For 18 −3 cathode temperature. This in turn increases the radiative coupling, the rest of this study, we use a doping level of 10 cm . necessitating a wider interelectrode gap for the optimal operating point. The wider gap results in a higher space charge barrier, reducing the emission current. Therefore, with an increase in the Effect of interelectrode gap width and solar concentration.We doping level, initially the output power decreases. However, the now discuss how the device configuration affects the semi- increased doping level also leads to a higher optimal output voltage, conductor thermionic solar cell’s performance. The space charge and so the output power and efficiency eventually recover at the effect is due to the Coulombic repulsion among the electrons upper limit of the doping level. In the case of silicon, due to the lack transiting the device’s interelectrode space, which results in an of or weak photon enhancement effect at the optimal operating point additional energy barrier (Fig. 1b) for subsequent electron NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 3 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 31,32 emission and transport . Among the methods of mitigating Fermi-level shift at the emitter surface is zero or negative (i.e., this effect, using a micro-gap structure is in principle the simplest n=n ≤ 1). eq and results in a compact device with the fewest number of com- Figure 5a also shows that, while GaAs takes advantage of ponents. However, the micro-gap device performance is con- photon enhancement and provides slightly higher current density strained by the near-field enhancement of interelectrode thermal at elevated concentration levels, Si prefers a pure thermionic radiative coupling. This near-field effect arises due to the coupling mode. This challenges the prevalent assumption that PETE is the of evanescent waves between the electrodes when the gap width is natural mode of operation of semiconductor thermionic devices. comparable to the characteristic wavelength of thermal radiation For example, in contrast to the present result, the simplifications (which is given by Wien’s displacement law and is of the order of a made in ref. led to the prediction of a high photon 33,34 micrometer in practical temperature ranges) . Besides, irre- enhancement factor for Si cathodes. (The present model can spectively of the gap size, there are additional energy loss reproduce the results of ref. by incorporating similar mechanisms such as thermal radiation to the ambient and thermal simplifications, as shown by benchmarking in Supplementary conduction through the leads. The latter contains a tradeoff Fig. 10.) We note that, even for GaAs, which tends to capitalize between the Joule heating effect and thermal conduction, leading on the photon enhancement effect, this mode is not guaranteed: to an optimal value for the lead resistance . In a micro-gap with the change of the collector material (which also changes the device, the relative strength of these various energy exchange strength of interelectrode radiative coupling), even GaAs may channels depends on the gap width and ultimately determines the prefer to operate in the pure thermionic mode (see Supplemen- electrode temperatures. This interplay among different energy tary Fig. 4). exchange channels as a function of the gap width is shown in The non-monotonic, semi-plateau-like behavior of the photon Fig. 3 at the maximum power point (MPP). enhancement effect in GaAs in Fig. 5a may be understood as The corresponding efficiency and electrode temperature trends follows. As the solar concentration is raised, the emitter are shown in Fig. 4. The variations of these quantities’ gap width temperature tends to rise, leading to a higher thermionic emission dependence with solar concentration are shown in the Supple- current and thus a stronger space charge effect. This is countered mentary Figs. 1–3. These strong dependencies of the energy by a reduction in the optimal gap size, which in turn strengthens exchange channels, electrode temperatures and conversion the near-field radiative coupling and thus opposes the rise in efficiency on gap width and solar concentration level demonstrate emitter temperature. Since the carrier densities depend on the importance of a complete account of the complex temperature, a signature of this behavior is also observed in the interdependencies of materials properties and device physics. photon enhancement factor. We now consider how the above tradeoffs translate to relevant For comparison with conventional solar thermionics employing performance metrics at the MPP for a wide range of solar metal electrodes, in Fig. 5b we also show the conversion concentrations (Fig. 5). Figure 5a shows the trend in the device performance using tungsten electrodes and a selective tungsten current and the photon enhancement factor (n/n ). The latter is pyramid solar absorber (this comparison is motivated by the long eq a measure of the amount of optical upshift in the electron Fermi- history of solar thermionics using metallic emitters, which dates level due to illumination, which can be written as back to the 1950s; it is intriguing to know where the relatively new concept of semiconductor thermionics stands in comparison to its E  E ¼ k T lnðn=n Þ; metal counterpart). Interestingly, Fig. 5b shows that even without F;n F;E B E eq leveraging the photon enhancement effect, Si can outperform GaAs for higher concentration levels in terms of overall conversion where n is the steady-state electron density at the emitter surface performance. These findings signify that, although the PETE mode under photoexcitation and n is the equilibrium electron density. eq is in principle desirable, achieving this mode is not trivial in all k is the Boltzmann constant and T is the emitter temperature. B E semiconductor devices, nor is it necessary at all concentration levels. The pure thermionic mode is defined as the case where the We also note that the efficiency predictions for GaAs at higher contribution from the excess electrons (under illumination) to the Fig. 3 The interplay among different energy exchange channels in a semiconductor thermionic device. The data are shown as a function of the interelectrode distance (also referred to as gap width) for a Si and b GaAs at MPP under a solar concentration ratio of 100. The symbols (starting from the top) represent the interelectrode radiative and thermionic exchange, emitter thermal radiation loss to the ambient, net heat conduction through the lead and non-equilibrium radiative recombination loss, respectively. 4 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE Fig. 4 Trends in thermionic solar conversion efficiency and electrode temperatures as a function of the interelectrode gap width. The data are shown for a Si and b GaAs at MPP under a solar concentration ratio of 100. The symbols with subscript E and C represent the emitter and collector temperatures, respectively. Fig. 5 Performance metrics of different gap-optimized thermionic solar converters. a MPP current density and the corresponding photon enhancement factor (n/n ) for different semiconductor materials as a function of solar concentration ratio. n and n represent the conduction band electron density at eq eq the emitter surface under steady-state and equilibrium conditions, respectively. b MPP output power density and solar conversion efficiency for different semiconductor materials as a function of solar concentration ratio. The performance of a tungsten device is also shown for comparison between metal and semiconductor thermionics. concentration levels may not be achievable in practice as that materials considered (Fig. 6b). Regarding the trend versus gap material begins to decompose well below its melting point. width, for Si, the excess carrier contribution is negligible over most To gain further insight into these two materials’ different behaviors of the gap range (a signature of the pure thermionic mode of concerning the photon enhancement effect, in Fig. 6a, b we show the operation), whereas for GaAs, this contribution, while still being trends in steady-state conduction band electron density at the positive, gradually decreases with increasing gap width. We emitting surface together with the contribution from photogeneration attribute these differences to the varying degrees of thermal (under MPP), as a function of both the gap width and the solar generation enhancement and the associated increase in recombina- concentration level. It is worth noting that the dependence of the tion probability as well as the different thickness optimization mode of operationongap widthisnot trivial. As the gap width is criteria for these two materials. The trends with increasing solar increased, the cathode temperature increases (see Fig. 4a, b) due to concentration level can be explained by similar reasoning. The the net result of the interplay among the energy exchange channels. combined effect of the gap width and solar concentration level on This will increase the thermal generation of electron-hole pairs and the photon enhancement factor is shown in Fig. 6c, d). the associated recombination probability, which ultimately determine the steady-state carrier density in the cathode at the emitting surface, Micro-gap and macro-gap device performance comparison. whichinturn informs themodeof operation. Finally, we note that there exist alternative TEC structures that also Interestingly, while the total carrier concertation shows an mitigate the space charge effect: the vapor TEC involves the + 31 upward trend for both materials (for the trend with gap width, this inclusion of positive ions (such as Cs ) , which will neutralize the is due to a stronger thermal generation at elevated temperatures negative charge of the transiting electrons, while the triode TEC with the increase of gap width; for the trend with solar uses a gate electrode between emitter and collector to prevent the concentration, this is due to both higher photon flux and increased 36,37 buildup of a negative charge cloud . These structures, although thermal generation with increasing concentration level), the excess involving their own specific loss mechanisms, do not need small carrier contribution shows completely different trends for the two interelectrode gaps and hence do not incur near-field radiative loss. NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 5 -2 (%) J (A cm ) max MPP T (K) n/n eq MPP (%) -2 MPP P (W cm ) max (%) T (K) max MPP ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 Fig. 6 Trends of conduction band electron density and contributions from photogeneration at the emitter surface with gap width and solar concentration ratio. a Conduction band electron density (equilibrium (n ) and steady-state (n)) and the associated photon enhancement factor (n/n )as eq eq a function of interelectrode gap width. The data are shown at MPP and for a solar concentration ratio of 100. b Steady-state and excess carrier density (δn) in the conduction band for different semiconductor materials as a function of solar concentration ratio at MPP. Photon enhancement factor for c Si and d GaAs as a function of interelectrode gap width and solar concentration ratio. The data are shown at MPP and the dash-dotted line indicates the boundary between the PETE and pure thermionic regimes. Therefore, it is in principle possible for them to enable higher Figure 7 also shows that, under optimal operation and for performance compared to micro-gap devices. Within our model, we different device structures, the realistic thermionic solar cell can gain insight into the upper limit of performance for these efficiencies for the two semiconductors studied (which are also devices by neglecting the loss mechanisms associated with space widely used in photovoltaics) are comparable to those of charge and its mitigation strategy. For the materials studied in this commercial single-junction photovoltaic cells at the higher work, the performance improvement resulting from such macro- concentration levels. To further improve the device performance, gap architectures was found to be marginal (Fig. 7) (this indicates a second thermal cycle can be implemented, which would utilize that, in fact, for these two materials, at the optimal gap size, the the waste heat released from the collector. This second stage can near-field radiative coupling in the micro-gap structure was already be a thermoelectric, thermophotovoltaic or any other type of heat minimal). It is worth noting that these alternatives also involve engine. With such hybrid operation, the conversion efficiency can other challenges. For example, a vapor TEC’s lifetime is limited by be comparable to the multijunction and CPV performance and the availability of the ions, and ion deposition might result in can exceed the Shockley-Queisser limit . This hybrid generation unwanted secondary electron emission sources; in a triode TEC, capability is an additional advantage of thermionic and PETE gate leakage can reduce conversion efficiency and the device also devices due to their high temperature operation. requires additional circuitry to set up the gate voltage and magnetic fields to prevent electrons from striking the gate . Note that the results shown in Fig. 7 are based on a best-case estimate for macro- Discussion gap devices, and even then these devices do not present a significant Based on the above results and analyses, we conclude that while advantage over the micro-gap device for the materials considered. thermionic conversion using semiconducting emitters is a 6 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE Overall, the concept of semiconductor thermionics is still in early stages and much remains to be investigated on the experi- mental front. However, such experimental and design efforts also require a comprehensive understanding of this conversion mechanism and its underlying physics. Therefore, in this work, we revealed the effects of these materials and device physics, providing realistic performance estimates for devices based on widely used semiconductors. Methods Overview of the modeling approach. For the analysis of the semiconductor thermionic solar cell carried out in this work, we took into account the spatial dependence of optical absorption and transport of the photogenerated carriers within the emitter. Charge carrier transport inside the cathode, in general, involves both drift and diffusion. However, in cases where the electric field inside the cathode is negligible, the drift component can be neglected and the carrier balance is dictated by the diffusion mechanism. A discussion on these mechanisms as Fig. 7 Performance comparison between different thermionic device relevant to the present study can be found in Supplementary Note 1. Electron transport in the interelectrode space and the associated space charge effect were configurations. At each solar concentration ratio, the data are shown at incorporated using a phase space formalism. The interelectrode radiative exchange MPP, and the optimal interelectrode gap width was chosen for the micro- was calculated using fluctuational electrodynamics and the electrode temperatures gap devices. For macro-gap devices, the interelectrode gap width is of the were calculated using complete energy balance. An overview of the implementation order of a millimeter. of these physics is discussed below, and the detalied formulation is presented in the Supplementary Information. Cathode. The absorption profile of the solar spectrum and the associated spatial promising path and can address the thermal limitation of pho- variations of the photogenerated electron-hole pairs in the semiconductor emitter tovoltaics, its overall performance is still directly limited by were analyzed using the particle continuity equation that governs the generation, materials and physics-related challenges. Moreover, beyond those recombination and transport of the charge carriers. The various radiative and fundamental issues, additional difficulties need to be overcome nonradiative recombination mechanisms were implemented using theories that are valid under both low and high injection levels. The associated recombination for thermionics to compete with photovoltaics. Here we point out coefficients and lifetimes were taken from the literature. The detailed imple- these issues and possible solutions to both fundamental and mentation of the cathode model is discussed in Supplementary Note 1. For Si practical challenges, in order to provide a broader perspective as (where the solar conversion performance monotonically improves with the well as to motivate further research into semiconductor thickness), the material’s thickness was taken to be 20 µm (this thickness was chosen so that at least 80% of the solar spectrum is absorbed). Also, the resulting thermionics. efficiency almost saturates at this thickness, justifying saving on additional com- First, the high temperature stability of various electrodes, surface putational expenses associated with larger thicknesses. For GaAs, the thickness was coatings and electrical contacts needs to be ensured (in addition, taken at its optimal value (Fig. 2b) for the doping level considered. For emitter contact geometry needs to be optimized for maximum access to electron affinity, we considered a value of 1 eV (obtainable through appropriate −2 −2 surface coating) and the theoretical value of 120 Acm K was used for sunlight; the contact design technologies from existing CPV systems Richardson’s constant for thermionic current calculations. may be of help in this regard). Also, the emission and collection For incident solar radiation, we considered the AM 1.5 direct plus circumsolar probability of the thermally excited electrons need to be increased as spectrum concentrated by different concentration ratios used in this study. The much as possible, and surface treatment may provide a solution. For upper level of the solar concentration ratio used (500x) is based on practically example, the Richardson constant of nitrogen-incorporated diamond achievable values, as shown in both commercial and laboratory-based CPV systems . We have chosen p-type doping in the emitter to maximize the photon films was improved by four orders of magnitude via hydrogen 39 enhancement effect in case this mode occurs during the solar cell’s operation. For plasma treatment . Additionally, surface recombination needs to be the collector, we considered a heavily n-type doped semiconductor made of the minimized(unless thedeviceisoperating in thepurethermionic same material as the emitter. For the analyses shown in Figs. 3–7, we considered a 18 −3 mode). This may be achieved by adding an energy barrier near the p-type doping level of 10 cm in the cathode. The anode work function was taken to be 1 eV. For the study of metal thermionics, we considered tungsten emitting surfacesuchasbycreatingaheterostructure . In addition, electrodes due to the material’s high melting point. As the intrinsic work function trap-assisted recombination can be detrimental to the photon of tungsten is too high to obtain significant thermionic emission at practically enhancement effect. This carrier loss mechanism strongly depends on achievable temperatures, we assumed a barium-activated tungsten cathode and a the growth process of the material and material handling during Cs-activated tungsten anode . The heat transfer coefficient of the anode to the 41 −2 heat sink was taken as 0.1 Wcm , which represents the upper limit of cooling by device fabrication steps , and needs to be minimized. free convection. Manipulating the material dimensionality via micro- and nano-fabrication techniques may result in improved material Space charge and near-field radiative coupling. The space charge effect was properties such as increased optical absorption, higher electron treated by solving the coupled Poisson-Vlasov equations. The related phase space emission probability, reduced thermal conductivity, etc. For analysis of the thermionically emitted electrons in the space charge mode is dis- example, carbon nanotube arrays with long-range alignment cussed in the Supplementary Note 2. The interelectrode thermal radiative coupling (CNT forests), grown using chemical vapor deposition, exhibit was calculated using fluctuational electrodynamics. This ab initio method accounts for the near-field coupling of the evanescent waves as well as the far-field propa- near-perfect optical absorption over a wide spectral range and 43,44 gating waves, and the interference of the thermally generated electromagnetic efficient heating and multiphoton photothermal emission . waves in the device’s interelectrode space. The detailed implementation of this Semiconducting CNTs that may exploit the PETE mechanism can model is discussed in the Supplementary Note 3. be created by controlling the nanotube chirality. However, the CNT work function is typically above 4.5 eV and needs to be Semiconductor material properties. The semiconductor material’s properties 45,46 reduced through coatings with high temperature stability . such as spectral absorptivity, reflectivity and electron and hole mobilities were Vertically aligned III–V nanowire arrays have also shown low taken from various experimentally validated models considering their temperature and doping dependencies. The dielectric permittivities (which are needed for reflectance over the visible spectrum, which can be tuned by optical absorption and thermal radiation calculations) of the materials were taken 47 48 adjusting the nanowire diameter or the growth time . The from various empirical models considering their temperature and doping depen- ultimate challenge is to combine all the desired properties into a dencies. These dielectric models are discussed in the Supplementary Note 4. The single material or heterostructure. density of states and conductivity effective mass for the materials were taken from NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 7 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 the literature. The temperature dependence of the effective density of states was 21. Segev, G., Rosenwaks, Y. & Kribus, A. Efficiency of photon enhanced considered. The temperature-induced bandgap narrowing effect was considered thermionic emission solar converters. Sol. Energy Mater. Sol. Cells 107, using the empirical Varshni relation. The equilibrium Fermi level was calculated 125–130 (2012). using the charge neutrality criterion with experimentally reported energy levels for 22. Liu, X., Xia, H. & Xuan, Y. 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Eng. 157, 113758 (2019). 8 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE 49. Littau, K. A. et al. Microbead-separated thermionic energy converter with Additional information enhanced emission current. Phys. Chem. Chem. Phys. 15, 14442–14446 (2013). Supplementary information The online version contains supplementary material 50. Rahman, E. & Nojeh, A. Interplay between near-field radiative coupling and available at https://doi.org/10.1038/s41467-021-24891-2. space-charge effects in a microgap thermionic energy converter under fixed heat input. Phys. Rev. Appl. 14, 024082 (2020). Correspondence and requests for materials should be addressed to E.R. 51. Rahman, E. & Nojeh, A. Semiconductor thermionics for next generation solar Peer review information Nature Communications thanks Gideon Segev and the other, cells: photon enhanced or pure thermionic? https://doi.org/10.6084/m9. anonymous, reviewer(s) for their contribution to the peer review of this work. figshare.14818590.v1 (2021). Reprints and permission information is available at http://www.nature.com/reprints Acknowledgements Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in We acknowledge financial support from the Natural Sciences and Engineering Research published maps and institutional affiliations. Council of Canada (Grants No. RGPIN-2017-04608 and No. RGPAS-2017-507958). This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program. Ehsanur Rah- Open Access This article is licensed under a Creative Commons man thanks the Natural Sciences and Engineering Research Council of Canada for a Attribution 4.0 International License, which permits use, sharing, Vanier Canada Graduate Scholarship and the University of British Columbia for an adaptation, distribution and reproduction in any medium or format, as long as you give International Doctoral Fellowship and Faculty of Applied Science Graduate Award. appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless Author contributions indicated otherwise in a credit line to the material. If material is not included in the E.R. conceived and designed the project, performed the study, analyzed the data and article’s Creative Commons license and your intended use is not permitted by statutory composed the initial draft. A.N. provided technical guidance, directed the project and regulation or exceeds the permitted use, you will need to obtain permission directly from analyzed the data. E.R. and A.N. wrote the manuscript. the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. Competing interests The authors declare no competing interests. © The Author(s) 2021 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 9 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nature Communications Springer Journals

Semiconductor thermionics for next generation solar cells: photon enhanced or pure thermionic?

Nature Communications , Volume 12 (1) – Jul 30, 2021

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ARTICLE https://doi.org/10.1038/s41467-021-24891-2 OPEN Semiconductor thermionics for next generation solar cells: photon enhanced or pure thermionic? 1,2 1,2 Ehsanur Rahman & Alireza Nojeh Semiconductors have been used in solar energy conversion for decades based on the pho- tovoltaic effect. An important challenge of photovoltaics is the undesired heat generated within the device. An alternative approach is thermionics, which uses the thermal excitation of electrons from an emitter to a collector across a vacuum gap. If the emitter is a p-type semiconductor, the photogeneration-induced quasi-Fermi level splitting can reduce the effective barrier for electron emission—a mechanism used by a photon enhanced thermionic emission device. Here, we evaluate the prospects of this alternative solar conversion tech- nology considering different semiconductor materials and thermionic device configurations. We also reveal that whether such a device operates in the photon enhanced or purely thermionic mode, depends on the complex interplay among materials properties, device physics and solar concentration level. 1 2 Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada. Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada. email: ehsanece@ece.ubc.ca NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 1 1234567890():,; ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 olar energy conversion is an important field of research due Results to solar radiation’s renewable nature and abundance as well Operation of a thermionic solar cell. Before delving into the Sas the rising environmental pollution concerns of conven- details of materials and device physics and the associated chal- tional energy sources. At present, photovoltaics is the most widely lenges in a semiconductor thermionic solar cell, it is worth con- used mechanism for generating solar electricity with demon- sidering its basic operation with the help of a simple device strated large scale implementation for both terrestrial and space schematic and its energy band diagram as shown in Fig. 1. A basic applications. However, the efficiency of this technology is cur- thermionic solar cell consists of two electrodes known as the rently limited to around 20% for most practical systems. emitter (or cathode) and collector (or anode) separated by a Although above-Shockley-Queisser performance has been vacuum gap. In the emitter, the photogenerated electrons will demonstrated in multijunction photovoltaics and concentrated undergo thermalization and various recombination processes, photovoltaics (CPV) , these alternatives have not seen widespread thereby broadening the thermal distribution of the electron utilization due to higher complexity and the associated costs. The population. Moreover, due to the photoexcitation of a large primary challenges in photovoltaics can be traced to sub-bandgap number of electrons, their thermal population may also be 2,3 photon loss and above-bandgap thermalization loss . Even for a upshifted, which is the photon enhancement effect. The electrons tandem photovoltaic cell, which can minimize the first loss by in this excited thermal population that have sufficient energy to using multiple materials with different bandgaps, the second loss overcome the vacuum barrier will leave the material. These is inevitable, and the resulting heat is not only unutilized but also emitted electrons will be absorbed by the collector where they will degrades the device performance . thermalize again and do useful work with their remaining energy An interesting alternative to photovoltaics, which can turn this as they return to the emitter via an external circuit (the load challenge into a benefit, is thermionic emission. Although ther- receiving the generated power). mionic energy converters (TECs) using metallic electrodes have However, beyond this simple description, there are many 5–8 been considered for solar conversion since the 1950s ,they intricate and interrelated pieces of materials and device physics eventually gave way to photovoltaics due to many other that ultimately determine the operational mode and performance 9–11 challenges . A more recent development to solar thermionics is merits of a semiconductor thermionic solar cell. To investigate these to utilize the very material used in photovoltaics (i.e., semi- effects, we have chosen silicon (Si) and gallium arsenide (GaAs), conductors). In particular, a photon enhanced thermionic emission which have distinct properties. For example, Si, which is the most 12–14 (PETE) device is an insightful concept that uses a p-type widely used material in photovoltaics, has an indirect bandgap and semiconductor to combine the benefits of photovoltaics and ther- weaker optical absorption. On the other hand, GaAs is a direct- mionics: it takes advantage of the photogeneration-induced quasi- bandgap material with a sharp absorption onset near the Urbach 28,29 Fermi-level splitting to reduce the effective emission barrier for edge . Moreover, GaAs has a bandgap very close to the electrons while still delivering a high output voltage; it also utilizes previously reported theoretical optimal value for PETE devices . the thermalization process to help electrons escape the material. Also, the carrier diffusion lengths in these two materials are quite Thus, the combined effects of light and heat on electron emission, different, thanks to their vastly different recombination 15–17 30 studies of which go back to the works of Fowler and DuBridge , parameters .There arealsosignificant differences between their has found a promising new application in solar energy conversion. effective densities of states and dielectric properties. For both Taking advantage of this synergy between heat and light, PETE materials, we also study how the device configuration might affect devices were estimated to outperform state-of-the-art solar cells, the performance of a thermionic solar cell. with an efficiency of around 40% for a single-stage device and 13,18 higher than 50% with a second thermal cycle . These early estimates were based on simplified models to show the potential of Effect of cathode thickness. First, we discuss how material the concept. To study these devices in more detail, subsequent properties affect the optimal emitter thickness and the mode of works have investigated some of the relevant physics such as operation in a semiconductor thermionic solar cell. In general, 19–21 20,22–24 thermal balance , the space charge effect ,spatial varia- the choice of the optimal thickness is dictated by the maximiza- 25–27 tions of the charge carrier density and near-field radiative tion of the absorption of the solar spectrum and minimization of 20,22 coupling to varying degrees (a detailed list of the different the recombination of excess carriers during their transport to the aspects of the physics treated in some of the previous key papers is emitting surface. These requirements are contradictory in terms provided in Supplementary Table 1). However, a comprehensive of the material’s thickness. Based on our studies of different treatment of all the important materials and device physics has been device configurations (which will be discussed later), we found missing. Owing to the complex interplay of the various pieces of that, under maximum conversion efficiency, Si maximizes the physics involved, studying their individual contributions while absorption of the solar spectrum. In other words, the nonradiative simplifying other aspects does not enable a realistic analysis of these recombination-induced heating effect compensates for the carrier photothermal phenomena and devices based on them. As a result, loss in Si at higher thicknesses (Fig. 2a) and results in a pure fundamental questions still need to be addressed: whether or not a thermionic mode of operation. This finding is in contrast to the semiconductor thermionic device would operate in the PETE mode; previous studies of Si cathodes where an optimal thickness for Si 26 26 and what the trends in device behavior and performance limits are was predicted , possibly due to the simplifications made in ref. if all the crucial physics are taken into account. Such a compre- (see Supplementary Table 1). On the other hand, for GaAs, hensive study is the topic of the present work. recombination loss becomes a limitation at larger thickness Our findings show that the device performance, while highly thereby resulting in a specific desired thickness that maximizes promising, is limited by the various tradeoffs in terms of material efficiency (Fig. 2b) by using the photon enhanced mode. There- properties and device physics. Moreover, we reveal that the PETE fore, considering these aspects of recombination and optical mode is not guaranteed in a semiconductor thermionic solar cell absorption, the trends in device efficiency with the material’s under optimal operation, nor is it necessary for achieving a thickness could vary from one semiconductor to another (Fig. 2). performance comparable to photovoltaics. This work sheds light The different behaviors seen in Fig. 2a, b with respect to doping on the issues and challenges in semiconductor thermionic solar level may be understood based on the fact that the electrode conversion that need to be overcome when considering a com- temperatures, optimal gap size, and optimal operating voltage are plete device-level operation. interdependent in a non-trivial way through energy balance and 2 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE Fig. 1 Operation of a semiconductor thermionic solar cell. a The schematic of a thermionic solar converter’s operation. b A simple band diagram of a semiconductor thermionic solar cell. E and E are the equilibrium Fermi levels in the emitter and collector, respectively, and E is the emitter quasi- F,E F,C F,n Fermi level for electrons in the PETE mode. φ is the maximum motive in the interelectrode space and e is the electron charge. φ and φ are the work m E C functions of the emitter and the collector, respectively. T and T are the temperatures of the emitter and the collector, respectively. E , E , and E are the E C C V g conduction band minimum, the valance band maximum and the bandgap energy, respectively. V is the voltage difference between the two electrodes (and across the load). Fig. 2 Variation of the solar conversion efficiency with emitter thickness. The data are shown at the maximum power point for a Si and b GaAs for different p-type doping levels in the emitter and a solar concentration ratio of 100. obtained self-consistently. At a fixed solar concentration, as the (as will be seen later), the output voltage does not increase in the 17 −3 doping level in the GaAs cathode is increased from 10 cm to same manner at higher doping levels, and hence the trends in output 20 −3 10 cm , the recombination probability increases, leading to higher power and efficiency are dominated by the trend in the current. For 18 −3 cathode temperature. This in turn increases the radiative coupling, the rest of this study, we use a doping level of 10 cm . necessitating a wider interelectrode gap for the optimal operating point. The wider gap results in a higher space charge barrier, reducing the emission current. Therefore, with an increase in the Effect of interelectrode gap width and solar concentration.We doping level, initially the output power decreases. However, the now discuss how the device configuration affects the semi- increased doping level also leads to a higher optimal output voltage, conductor thermionic solar cell’s performance. The space charge and so the output power and efficiency eventually recover at the effect is due to the Coulombic repulsion among the electrons upper limit of the doping level. In the case of silicon, due to the lack transiting the device’s interelectrode space, which results in an of or weak photon enhancement effect at the optimal operating point additional energy barrier (Fig. 1b) for subsequent electron NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 3 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 31,32 emission and transport . Among the methods of mitigating Fermi-level shift at the emitter surface is zero or negative (i.e., this effect, using a micro-gap structure is in principle the simplest n=n ≤ 1). eq and results in a compact device with the fewest number of com- Figure 5a also shows that, while GaAs takes advantage of ponents. However, the micro-gap device performance is con- photon enhancement and provides slightly higher current density strained by the near-field enhancement of interelectrode thermal at elevated concentration levels, Si prefers a pure thermionic radiative coupling. This near-field effect arises due to the coupling mode. This challenges the prevalent assumption that PETE is the of evanescent waves between the electrodes when the gap width is natural mode of operation of semiconductor thermionic devices. comparable to the characteristic wavelength of thermal radiation For example, in contrast to the present result, the simplifications (which is given by Wien’s displacement law and is of the order of a made in ref. led to the prediction of a high photon 33,34 micrometer in practical temperature ranges) . Besides, irre- enhancement factor for Si cathodes. (The present model can spectively of the gap size, there are additional energy loss reproduce the results of ref. by incorporating similar mechanisms such as thermal radiation to the ambient and thermal simplifications, as shown by benchmarking in Supplementary conduction through the leads. The latter contains a tradeoff Fig. 10.) We note that, even for GaAs, which tends to capitalize between the Joule heating effect and thermal conduction, leading on the photon enhancement effect, this mode is not guaranteed: to an optimal value for the lead resistance . In a micro-gap with the change of the collector material (which also changes the device, the relative strength of these various energy exchange strength of interelectrode radiative coupling), even GaAs may channels depends on the gap width and ultimately determines the prefer to operate in the pure thermionic mode (see Supplemen- electrode temperatures. This interplay among different energy tary Fig. 4). exchange channels as a function of the gap width is shown in The non-monotonic, semi-plateau-like behavior of the photon Fig. 3 at the maximum power point (MPP). enhancement effect in GaAs in Fig. 5a may be understood as The corresponding efficiency and electrode temperature trends follows. As the solar concentration is raised, the emitter are shown in Fig. 4. The variations of these quantities’ gap width temperature tends to rise, leading to a higher thermionic emission dependence with solar concentration are shown in the Supple- current and thus a stronger space charge effect. This is countered mentary Figs. 1–3. These strong dependencies of the energy by a reduction in the optimal gap size, which in turn strengthens exchange channels, electrode temperatures and conversion the near-field radiative coupling and thus opposes the rise in efficiency on gap width and solar concentration level demonstrate emitter temperature. Since the carrier densities depend on the importance of a complete account of the complex temperature, a signature of this behavior is also observed in the interdependencies of materials properties and device physics. photon enhancement factor. We now consider how the above tradeoffs translate to relevant For comparison with conventional solar thermionics employing performance metrics at the MPP for a wide range of solar metal electrodes, in Fig. 5b we also show the conversion concentrations (Fig. 5). Figure 5a shows the trend in the device performance using tungsten electrodes and a selective tungsten current and the photon enhancement factor (n/n ). The latter is pyramid solar absorber (this comparison is motivated by the long eq a measure of the amount of optical upshift in the electron Fermi- history of solar thermionics using metallic emitters, which dates level due to illumination, which can be written as back to the 1950s; it is intriguing to know where the relatively new concept of semiconductor thermionics stands in comparison to its E  E ¼ k T lnðn=n Þ; metal counterpart). Interestingly, Fig. 5b shows that even without F;n F;E B E eq leveraging the photon enhancement effect, Si can outperform GaAs for higher concentration levels in terms of overall conversion where n is the steady-state electron density at the emitter surface performance. These findings signify that, although the PETE mode under photoexcitation and n is the equilibrium electron density. eq is in principle desirable, achieving this mode is not trivial in all k is the Boltzmann constant and T is the emitter temperature. B E semiconductor devices, nor is it necessary at all concentration levels. The pure thermionic mode is defined as the case where the We also note that the efficiency predictions for GaAs at higher contribution from the excess electrons (under illumination) to the Fig. 3 The interplay among different energy exchange channels in a semiconductor thermionic device. The data are shown as a function of the interelectrode distance (also referred to as gap width) for a Si and b GaAs at MPP under a solar concentration ratio of 100. The symbols (starting from the top) represent the interelectrode radiative and thermionic exchange, emitter thermal radiation loss to the ambient, net heat conduction through the lead and non-equilibrium radiative recombination loss, respectively. 4 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE Fig. 4 Trends in thermionic solar conversion efficiency and electrode temperatures as a function of the interelectrode gap width. The data are shown for a Si and b GaAs at MPP under a solar concentration ratio of 100. The symbols with subscript E and C represent the emitter and collector temperatures, respectively. Fig. 5 Performance metrics of different gap-optimized thermionic solar converters. a MPP current density and the corresponding photon enhancement factor (n/n ) for different semiconductor materials as a function of solar concentration ratio. n and n represent the conduction band electron density at eq eq the emitter surface under steady-state and equilibrium conditions, respectively. b MPP output power density and solar conversion efficiency for different semiconductor materials as a function of solar concentration ratio. The performance of a tungsten device is also shown for comparison between metal and semiconductor thermionics. concentration levels may not be achievable in practice as that materials considered (Fig. 6b). Regarding the trend versus gap material begins to decompose well below its melting point. width, for Si, the excess carrier contribution is negligible over most To gain further insight into these two materials’ different behaviors of the gap range (a signature of the pure thermionic mode of concerning the photon enhancement effect, in Fig. 6a, b we show the operation), whereas for GaAs, this contribution, while still being trends in steady-state conduction band electron density at the positive, gradually decreases with increasing gap width. We emitting surface together with the contribution from photogeneration attribute these differences to the varying degrees of thermal (under MPP), as a function of both the gap width and the solar generation enhancement and the associated increase in recombina- concentration level. It is worth noting that the dependence of the tion probability as well as the different thickness optimization mode of operationongap widthisnot trivial. As the gap width is criteria for these two materials. The trends with increasing solar increased, the cathode temperature increases (see Fig. 4a, b) due to concentration level can be explained by similar reasoning. The the net result of the interplay among the energy exchange channels. combined effect of the gap width and solar concentration level on This will increase the thermal generation of electron-hole pairs and the photon enhancement factor is shown in Fig. 6c, d). the associated recombination probability, which ultimately determine the steady-state carrier density in the cathode at the emitting surface, Micro-gap and macro-gap device performance comparison. whichinturn informs themodeof operation. Finally, we note that there exist alternative TEC structures that also Interestingly, while the total carrier concertation shows an mitigate the space charge effect: the vapor TEC involves the + 31 upward trend for both materials (for the trend with gap width, this inclusion of positive ions (such as Cs ) , which will neutralize the is due to a stronger thermal generation at elevated temperatures negative charge of the transiting electrons, while the triode TEC with the increase of gap width; for the trend with solar uses a gate electrode between emitter and collector to prevent the concentration, this is due to both higher photon flux and increased 36,37 buildup of a negative charge cloud . These structures, although thermal generation with increasing concentration level), the excess involving their own specific loss mechanisms, do not need small carrier contribution shows completely different trends for the two interelectrode gaps and hence do not incur near-field radiative loss. NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 5 -2 (%) J (A cm ) max MPP T (K) n/n eq MPP (%) -2 MPP P (W cm ) max (%) T (K) max MPP ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 Fig. 6 Trends of conduction band electron density and contributions from photogeneration at the emitter surface with gap width and solar concentration ratio. a Conduction band electron density (equilibrium (n ) and steady-state (n)) and the associated photon enhancement factor (n/n )as eq eq a function of interelectrode gap width. The data are shown at MPP and for a solar concentration ratio of 100. b Steady-state and excess carrier density (δn) in the conduction band for different semiconductor materials as a function of solar concentration ratio at MPP. Photon enhancement factor for c Si and d GaAs as a function of interelectrode gap width and solar concentration ratio. The data are shown at MPP and the dash-dotted line indicates the boundary between the PETE and pure thermionic regimes. Therefore, it is in principle possible for them to enable higher Figure 7 also shows that, under optimal operation and for performance compared to micro-gap devices. Within our model, we different device structures, the realistic thermionic solar cell can gain insight into the upper limit of performance for these efficiencies for the two semiconductors studied (which are also devices by neglecting the loss mechanisms associated with space widely used in photovoltaics) are comparable to those of charge and its mitigation strategy. For the materials studied in this commercial single-junction photovoltaic cells at the higher work, the performance improvement resulting from such macro- concentration levels. To further improve the device performance, gap architectures was found to be marginal (Fig. 7) (this indicates a second thermal cycle can be implemented, which would utilize that, in fact, for these two materials, at the optimal gap size, the the waste heat released from the collector. This second stage can near-field radiative coupling in the micro-gap structure was already be a thermoelectric, thermophotovoltaic or any other type of heat minimal). It is worth noting that these alternatives also involve engine. With such hybrid operation, the conversion efficiency can other challenges. For example, a vapor TEC’s lifetime is limited by be comparable to the multijunction and CPV performance and the availability of the ions, and ion deposition might result in can exceed the Shockley-Queisser limit . This hybrid generation unwanted secondary electron emission sources; in a triode TEC, capability is an additional advantage of thermionic and PETE gate leakage can reduce conversion efficiency and the device also devices due to their high temperature operation. requires additional circuitry to set up the gate voltage and magnetic fields to prevent electrons from striking the gate . Note that the results shown in Fig. 7 are based on a best-case estimate for macro- Discussion gap devices, and even then these devices do not present a significant Based on the above results and analyses, we conclude that while advantage over the micro-gap device for the materials considered. thermionic conversion using semiconducting emitters is a 6 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE Overall, the concept of semiconductor thermionics is still in early stages and much remains to be investigated on the experi- mental front. However, such experimental and design efforts also require a comprehensive understanding of this conversion mechanism and its underlying physics. Therefore, in this work, we revealed the effects of these materials and device physics, providing realistic performance estimates for devices based on widely used semiconductors. Methods Overview of the modeling approach. For the analysis of the semiconductor thermionic solar cell carried out in this work, we took into account the spatial dependence of optical absorption and transport of the photogenerated carriers within the emitter. Charge carrier transport inside the cathode, in general, involves both drift and diffusion. However, in cases where the electric field inside the cathode is negligible, the drift component can be neglected and the carrier balance is dictated by the diffusion mechanism. A discussion on these mechanisms as Fig. 7 Performance comparison between different thermionic device relevant to the present study can be found in Supplementary Note 1. Electron transport in the interelectrode space and the associated space charge effect were configurations. At each solar concentration ratio, the data are shown at incorporated using a phase space formalism. The interelectrode radiative exchange MPP, and the optimal interelectrode gap width was chosen for the micro- was calculated using fluctuational electrodynamics and the electrode temperatures gap devices. For macro-gap devices, the interelectrode gap width is of the were calculated using complete energy balance. An overview of the implementation order of a millimeter. of these physics is discussed below, and the detalied formulation is presented in the Supplementary Information. Cathode. The absorption profile of the solar spectrum and the associated spatial promising path and can address the thermal limitation of pho- variations of the photogenerated electron-hole pairs in the semiconductor emitter tovoltaics, its overall performance is still directly limited by were analyzed using the particle continuity equation that governs the generation, materials and physics-related challenges. Moreover, beyond those recombination and transport of the charge carriers. The various radiative and fundamental issues, additional difficulties need to be overcome nonradiative recombination mechanisms were implemented using theories that are valid under both low and high injection levels. The associated recombination for thermionics to compete with photovoltaics. Here we point out coefficients and lifetimes were taken from the literature. The detailed imple- these issues and possible solutions to both fundamental and mentation of the cathode model is discussed in Supplementary Note 1. For Si practical challenges, in order to provide a broader perspective as (where the solar conversion performance monotonically improves with the well as to motivate further research into semiconductor thickness), the material’s thickness was taken to be 20 µm (this thickness was chosen so that at least 80% of the solar spectrum is absorbed). Also, the resulting thermionics. efficiency almost saturates at this thickness, justifying saving on additional com- First, the high temperature stability of various electrodes, surface putational expenses associated with larger thicknesses. For GaAs, the thickness was coatings and electrical contacts needs to be ensured (in addition, taken at its optimal value (Fig. 2b) for the doping level considered. For emitter contact geometry needs to be optimized for maximum access to electron affinity, we considered a value of 1 eV (obtainable through appropriate −2 −2 surface coating) and the theoretical value of 120 Acm K was used for sunlight; the contact design technologies from existing CPV systems Richardson’s constant for thermionic current calculations. may be of help in this regard). Also, the emission and collection For incident solar radiation, we considered the AM 1.5 direct plus circumsolar probability of the thermally excited electrons need to be increased as spectrum concentrated by different concentration ratios used in this study. The much as possible, and surface treatment may provide a solution. For upper level of the solar concentration ratio used (500x) is based on practically example, the Richardson constant of nitrogen-incorporated diamond achievable values, as shown in both commercial and laboratory-based CPV systems . We have chosen p-type doping in the emitter to maximize the photon films was improved by four orders of magnitude via hydrogen 39 enhancement effect in case this mode occurs during the solar cell’s operation. For plasma treatment . Additionally, surface recombination needs to be the collector, we considered a heavily n-type doped semiconductor made of the minimized(unless thedeviceisoperating in thepurethermionic same material as the emitter. For the analyses shown in Figs. 3–7, we considered a 18 −3 mode). This may be achieved by adding an energy barrier near the p-type doping level of 10 cm in the cathode. The anode work function was taken to be 1 eV. For the study of metal thermionics, we considered tungsten emitting surfacesuchasbycreatingaheterostructure . In addition, electrodes due to the material’s high melting point. As the intrinsic work function trap-assisted recombination can be detrimental to the photon of tungsten is too high to obtain significant thermionic emission at practically enhancement effect. This carrier loss mechanism strongly depends on achievable temperatures, we assumed a barium-activated tungsten cathode and a the growth process of the material and material handling during Cs-activated tungsten anode . The heat transfer coefficient of the anode to the 41 −2 heat sink was taken as 0.1 Wcm , which represents the upper limit of cooling by device fabrication steps , and needs to be minimized. free convection. Manipulating the material dimensionality via micro- and nano-fabrication techniques may result in improved material Space charge and near-field radiative coupling. The space charge effect was properties such as increased optical absorption, higher electron treated by solving the coupled Poisson-Vlasov equations. The related phase space emission probability, reduced thermal conductivity, etc. For analysis of the thermionically emitted electrons in the space charge mode is dis- example, carbon nanotube arrays with long-range alignment cussed in the Supplementary Note 2. The interelectrode thermal radiative coupling (CNT forests), grown using chemical vapor deposition, exhibit was calculated using fluctuational electrodynamics. This ab initio method accounts for the near-field coupling of the evanescent waves as well as the far-field propa- near-perfect optical absorption over a wide spectral range and 43,44 gating waves, and the interference of the thermally generated electromagnetic efficient heating and multiphoton photothermal emission . waves in the device’s interelectrode space. The detailed implementation of this Semiconducting CNTs that may exploit the PETE mechanism can model is discussed in the Supplementary Note 3. be created by controlling the nanotube chirality. However, the CNT work function is typically above 4.5 eV and needs to be Semiconductor material properties. The semiconductor material’s properties 45,46 reduced through coatings with high temperature stability . such as spectral absorptivity, reflectivity and electron and hole mobilities were Vertically aligned III–V nanowire arrays have also shown low taken from various experimentally validated models considering their temperature and doping dependencies. The dielectric permittivities (which are needed for reflectance over the visible spectrum, which can be tuned by optical absorption and thermal radiation calculations) of the materials were taken 47 48 adjusting the nanowire diameter or the growth time . The from various empirical models considering their temperature and doping depen- ultimate challenge is to combine all the desired properties into a dencies. These dielectric models are discussed in the Supplementary Note 4. 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Eng. 157, 113758 (2019). 8 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24891-2 ARTICLE 49. Littau, K. A. et al. Microbead-separated thermionic energy converter with Additional information enhanced emission current. Phys. Chem. Chem. Phys. 15, 14442–14446 (2013). Supplementary information The online version contains supplementary material 50. Rahman, E. & Nojeh, A. Interplay between near-field radiative coupling and available at https://doi.org/10.1038/s41467-021-24891-2. space-charge effects in a microgap thermionic energy converter under fixed heat input. Phys. Rev. Appl. 14, 024082 (2020). Correspondence and requests for materials should be addressed to E.R. 51. Rahman, E. & Nojeh, A. Semiconductor thermionics for next generation solar Peer review information Nature Communications thanks Gideon Segev and the other, cells: photon enhanced or pure thermionic? https://doi.org/10.6084/m9. anonymous, reviewer(s) for their contribution to the peer review of this work. figshare.14818590.v1 (2021). Reprints and permission information is available at http://www.nature.com/reprints Acknowledgements Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in We acknowledge financial support from the Natural Sciences and Engineering Research published maps and institutional affiliations. Council of Canada (Grants No. RGPIN-2017-04608 and No. RGPAS-2017-507958). This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program. Ehsanur Rah- Open Access This article is licensed under a Creative Commons man thanks the Natural Sciences and Engineering Research Council of Canada for a Attribution 4.0 International License, which permits use, sharing, Vanier Canada Graduate Scholarship and the University of British Columbia for an adaptation, distribution and reproduction in any medium or format, as long as you give International Doctoral Fellowship and Faculty of Applied Science Graduate Award. appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless Author contributions indicated otherwise in a credit line to the material. If material is not included in the E.R. conceived and designed the project, performed the study, analyzed the data and article’s Creative Commons license and your intended use is not permitted by statutory composed the initial draft. A.N. provided technical guidance, directed the project and regulation or exceeds the permitted use, you will need to obtain permission directly from analyzed the data. E.R. and A.N. wrote the manuscript. the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. Competing interests The authors declare no competing interests. © The Author(s) 2021 NATURE COMMUNICATIONS | (2021) 12:4622 | https://doi.org/10.1038/s41467-021-24891-2 | www.nature.com/naturecommunications 9

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