Open Submitted: 29 July 2022 Accepted: 23 October 2022 Published Online: 10 November 2022
Appl. Phys. Lett. 121, 193903 (2022); https://doi.org/10.1063/5.0116806
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• Gavin P. Forcade: Data curation (lead); Formal analysis (lead); Funding acquisition (supporting); Investigation (lead); Methodology (lead); Software (equal); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead).
• Christopher E. Valdivia: Funding acquisition (supporting); Supervision (equal); Writing – review & editing (equal).
• Sean Molesky: Methodology (supporting); Software (equal); Supervision (supporting); Writing – review & editing (supporting).
• Shengyuan Lu: Conceptualization (lead); Funding acquisition (lead); Investigation (supporting); Software (supporting); Supervision (supporting); Writing – review & editing (supporting).
• Alejandro W. Rodriguez: Conceptualization (equal); Funding acquisition (supporting); Software (supporting); Writing – review & editing (supporting).
• Jacob J. Krich: Methodology (supporting); Software (equal); Supervision (supporting); Writing – review & editing (equal).
• Raphael St-Gelais: Conceptualization (lead); Funding acquisition (lead); Investigation (supporting); Software (supporting); Supervision (supporting); Writing – review & editing (supporting).
• Karin Hinzer: Conceptualization (equal); Funding acquisition (supporting); Resources (equal); Supervision (lead); Writing – review & editing (supporting).

Waste heat is a free and abundant energy source, with 15% of global total energy use existing as waste heat above 600 K. For 600–900 K temperature range, near-field thermophotovoltaics (NFTPVs) are theorized to be the most effective technology to recycle waste heat into electrical power. However, to date, experimental efficiencies have not exceeded 1.5%. In this work, we optimize the efficiency of three modeled InAs/InAsSbP-based room-temperature NFTPV devices positioned 0.1 μm from a 750 K p-doped Si radiator. We couple a one-dimensional fluctuational electrodynamics model for the near field optics to a two-dimensional drift-diffusion model, which we validated by reproducing measured dark current–voltage curves of two previously published InAs and InAsSbP devices. The optimized devices show four to six times higher above-bandgap energy transfer compared to the blackbody radiative limit, yielding enhanced power density, while simultaneously lowering parasitic sub-bandgap energy transfer by factors of 0.68–0.85. Substituting InAs front- and back-surface field layers with InAsSbP show 1.5- and 1.4-times higher efficiency and power output, respectively, from lowered parasitic diffusion currents. Of our three optimized designs, the best performing device has a double heterostructure with an n–i–p doping order from front to back. For radiator-thermophotovoltaic gaps of 0.01–10 μm and radiators within 600–900 K, this device has a maximum efficiency of 14.2% and a maximum power output of 1.55 W/cm2, both at 900 K. Within 600–900 K, the efficiency is always higher with near- vs far-field illumination; we calculate up to 3.7- and 107-times higher efficiency and power output, respectively, using near-field heat transfer.
Waste heat above 600 K represents 15% of global total energy use,11. C. Forman, I. K. Muritala, R. Pardemann, and B. Meyer, Renewable Sustainable Energy Rev. 57, 1568 (2016). https://doi.org/10.1016/j.rser.2015.12.192 and recycling this waste heat to electrical power with solid-state modules could be a general solution to improve energy-use efficiency. For 600–900 K heat sources, existing commercial waste-heat-to-electricity solid-state converters, thermoelectric generators (TEGs), have high power densities of 2 W/cm2 but suffer from low efficiencies less than 12%.22. See https://thermoelectric-generator.com/ for thermoelectric generators (2022). Conversely, thermophotovoltaic (TPV) systems have high theoretical efficiencies up to 45% but low power densities of 0.2 W/cm2.33. I. A. Okanimba Tedah, F. Maculewicz, D. E. Wolf, R. Schmechel, I. A. O. Tedah, F. Maculewicz, D. E. Wolf, and R. Schmechel, J. Phys. D: Appl. Phys. 52, 275501 (2019). https://doi.org/10.1088/1361-6463/ab1833 Near-field thermophotovoltaic (NFTPV) systems, which position a heat source (radiator) and a TPV cell in extreme proximity, present both high theoretical efficiency and power density, up to 40% and 10 W/cm2 for practical devices.3,43. I. A. Okanimba Tedah, F. Maculewicz, D. E. Wolf, R. Schmechel, I. A. O. Tedah, F. Maculewicz, D. E. Wolf, and R. Schmechel, J. Phys. D: Appl. Phys. 52, 275501 (2019). https://doi.org/10.1088/1361-6463/ab18334. B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, Nano Energy 41, 344 (2017). https://doi.org/10.1016/j.nanoen.2017.09.054 Although NFTPV systems with cells operating at room temperature have experimentally achieved 40-fold increases in power density over TPV systems,55. A. Fiorino, L. Zhu, D. Thompson, R. Mittapally, P. Reddy, and E. Meyhofer, Nat. Nanotechnol. 13, 806 (2018). https://doi.org/10.1038/s41565-018-0172-5 they have not exceeded 1.5% efficiency for 600–900 K radiator temperatures. This low efficiency is due to the use of TPV cells that were not optimized for near-field operation5,65. A. Fiorino, L. Zhu, D. Thompson, R. Mittapally, P. Reddy, and E. Meyhofer, Nat. Nanotechnol. 13, 806 (2018). https://doi.org/10.1038/s41565-018-0172-56. G. R. Bhatt, B. Zhao, S. Roberts, I. Datta, A. Mohanty, T. Lin, J. M. Hartmann, R. St-Gelais, S. Fan, and M. Lipson, Nat. Commun. 11, 2545 (2020). https://doi.org/10.1038/s41467-020-16197-6 or InGaAs-based cells with larger-than-optimal bandgaps (0.73 eV at 300 K).7,87. T. Inoue, T. Koyama, D. D. Kang, K. Ikeda, T. Asano, and S. Noda, Nano Lett. 19, 3948 (2019). https://doi.org/10.1021/acs.nanolett.9b012348. R. Mittapally, B. Lee, L. Zhu, A. Reihani, J. W. Lim, D. Fan, S. R. Forrest, P. Reddy, and E. Meyhofer, Nat. Commun. 12, 4364 (2021). https://doi.org/10.1038/s41467-021-24587-7 Conversely, Lucchesi et al. designed a low bandgap (0.23 eV at 77 K) InSb-based NFTPV cell that was cooled to 77 K and measured a 14% efficiency with a power density of 0.75 W/cm2 with a 732 K radiator.99. C. Lucchesi, D. Cakiroglu, J. P. Perez, T. Taliercio, E. Tournié, P. O. Chapuis, and R. Vaillon, Nano Lett. 21, 4524 (2021). https://doi.org/10.1021/acs.nanolett.0c04847 Although they reached a high efficiency, these cells only function properly when cooled to cryogenic temperatures, making them impractical for most situations.
In the present work, we investigate the performance of NFTPV cells based on InAs, which has an ideal bandgap (0.353 eV at 300 K) for 600–900 K radiator temperatures and proven room temperature operating performance.40–4640. Q. Lu, X. Zhou, A. Krysa, A. Marshall, P. Carrington, C. H. Tan, and A. Krier, Sol. Energy Mater. Sol. Cells 179, 334 (2018). https://doi.org/10.1016/j.solmat.2017.12.03141. A. Krier, M. Yin, A. Marshall, and S. E. Krier, J. Electron. Mater. 45, 2826 (2016). https://doi.org/10.1007/s11664-016-4373-042. A. Krier, M. Yin, A. R. J. Marshall, M. Kesaria, S. E. Krier, S. McDougall, W. Meredith, A. D. Johnson, J. Inskip, and A. Scholes, Infrared Phys. Technol. 73, 126 (2015). https://doi.org/10.1016/j.infrared.2015.09.01143. B. A. Matveev, V. I. Ratushnyi, and A. Y. Rybal'chenko, Tech. Phys. 64, 1164 (2019). https://doi.org/10.1134/S106378421908014044. V. A. Gevorkyan, V. M. Aroutiounian, K. M. Gambaryan, I. A. Andreev, L. V. Golubev, and Y. P. Yakovlev, Tech. Phys. Lett. 34, 69 (2008). https://doi.org/10.1134/S106378500801021545. E. V. Kunitsyna, I. A. Andreev, V. V. Sherstnev, T. V. L'Vova, M. P. Mikhailova, Yu. P. Yakovlev, M. Ahmetoglu, G. Kaynak, and O. Gurler, Opt. Mater. (Amst.) 32, 1573–1577 (2010). https://doi.org/10.1016/j.optmat.2010.06.01046. V. P. Khvostikov, L. S. Lunin, V. V. Kuznetsov, V. I. Ratushny, V. Oliva, O. A. Khvostikova, and M. Z. Shvarts, Tech. Phys. Lett. 29, 851 (2003). https://doi.org/10.1134/1.1623867 We optimize the coupled electrical and optical properties of three NFTPV designs, all with back reflectors and two with InAs/InAsSbP double-heterostructures, by maximizing their efficiency under the illumination of a 750 K p-doped Si radiator separated by 0.1 μm. We compare their performances to a baseline design on a 500 μm substrate, shown in Fig. 1(a). We further investigate the performance for the highest-efficiency design for radiator temperatures from 600 to 900 K and with radiator-TPV gaps from 0.01 to 10 μm.
We propose three designs, presented in Figs. 1(b)–1(d). The pin and pin-Q cell designs have a p–i–n doping order from top to bottom. Conversely, the nip-Q design reverses this order to reduce lateral sheet resistance in the front-surface field (FSF) layer since electron mobilities are higher than hole mobilities (see Sec. 1 of the supplementary material). The pin-Q and nip-Q designs include the quaternary (Q) InAsxSb0.31(1-x)P0.69(1-x) lattice matched to InAs with bandgap up to 0.495 eV at 300 K4747. S. Adachi, Handbook on Physical Properties of Semiconductors, 1st ed. (Springer, New York, 2017). in the FSF and base layers to reduce undesirable diffusion currents, but at the cost of higher growth complexity. All cells have a uniform temperature of 300 K (see Sec. 2 of the supplementary material) and are illuminated by high-temperature 5 × 1018 cm−3 p-type silicon radiators, separated by vacuum. The distance between gridlines is dG-G while the distance between the bottom of the radiator and the top of the FSF layer is dR-FSF. For comparison, we consider the baseline design [Fig. 1(a)], which is based on the fabricated TPV cell from Lu et al.4040. Q. Lu, X. Zhou, A. Krysa, A. Marshall, P. Carrington, C. H. Tan, and A. Krier, Sol. Energy Mater. Sol. Cells 179, 334 (2018). https://doi.org/10.1016/j.solmat.2017.12.031 In contrast to the baseline design, we added cap and back-surface field (BSF) layers to each new design to minimize contact resistance48–5048. A. Baraskar, V. Jain, M. A. Wistey, U. Singisetti, Y. J. Lee, B. Thibeault, A. Gossard, and M. J. W. Rodwell, in International Conference on Indium Phosphide and Related Materials ( IPRM, 2010),p. 481. https://doi.org/10.1109/ICIPRM.2010.551626949. A. Katz, S. N. G. Chu, and B. E. Weir, J. Vac. Sci. Technol. B 8, 1125 (1990). https://doi.org/10.1116/1.58492950. W. Lu, B. R. Bennett, J. B. Boos, and J. A. Del Alamo, Electron. Lett. 36, 546 (2000). https://doi.org/10.1049/el:20000436 and reduce undesirable minority diffusion currents. In addition, our three proposed designs have their substrates removed, increasing fabrication complexity but minimizing parasitic sub-bandgap (SBG) photon absorption. Substrate-less devices with a back reflector (BR) layer reflect SBG photons for re-absorption within the radiator, increasing efficiency, and decreasing cooling requirements for the TPV cell.
Our coupled optoelectronic model simulates the radiative thermal transport and the electrical response of the NFTPV device by combining the results of two software packages. We model radiation transport using a custom fluctuational electrodynamics solver51,5251. M. T. H. Reid, A. W. Rodriguez, and S. G. Johnson, Proc. IEEE 101, 531 (2013). https://doi.org/10.1109/JPROC.2012.219174952. S. Molesky and S. Lu, “ heatSlabs” (2020). https://Github.Com/SeanMolesky/HeatSlabs that treats the devices as laterally infinite layered structures. We compute depth- and frequency-resolved radiation transfer, separated by the physical absorption mechanism, allowing us to calculate the depth-resolved electron-hole generation rate from interband absorption and total heat transfer from lattice, free-carrier, and interband processes (see Sec. 3 of the supplementary material for model details). We verify the optical model by reproducing the spectral absorption calculated in Ref. 88. R. Mittapally, B. Lee, L. Zhu, A. Reihani, J. W. Lim, D. Fan, S. R. Forrest, P. Reddy, and E. Meyhofer, Nat. Commun. 12, 4364 (2021). https://doi.org/10.1038/s41467-021-24587-7; the results are shown in Sec. 4 of the supplementary material.
We model the electrical transport for the NFTPV device using Synopsys TCAD Sentaurus. This software solves Poisson's equation coupled with electron and hole drift and diffusion equations to determine the TPV cell current–voltage curves as well as depth-resolved recombination rate profiles including radiative, Auger, Shockley–Read–Hall (SRH), and surface recombinations.2727. M. M. Wilkins and K. Hinzer, Handbook of Optoelectronic Device Modeling and Simulation ( CRC Press, 2017). We apply the 1D electron–hole pair generation rate profiles, extracted from the optical model, uniformly across the illuminated portion of the 2D TPV cell, with no generation directly below the top contacts. We assume no contact and sheet resistance for both top and bottom electrodes, as they can be designed to be negligible.48–5048. A. Baraskar, V. Jain, M. A. Wistey, U. Singisetti, Y. J. Lee, B. Thibeault, A. Gossard, and M. J. W. Rodwell, in International Conference on Indium Phosphide and Related Materials ( IPRM, 2010),p. 481. https://doi.org/10.1109/ICIPRM.2010.551626949. A. Katz, S. N. G. Chu, and B. E. Weir, J. Vac. Sci. Technol. B 8, 1125 (1990). https://doi.org/10.1116/1.58492950. W. Lu, B. R. Bennett, J. B. Boos, and J. A. Del Alamo, Electron. Lett. 36, 546 (2000). https://doi.org/10.1049/el:20000436 We calculate radiative and Auger recombination coefficients following the method in Ref. 5353. A. Rogalski and Z. Orman, Infrared Phys. 25, 551 (1985). https://doi.org/10.1016/0020-0891(85)90028-4, providing Auger coefficients for InAs (Cn = 0.48 × 10−26 and Cp = 1.01 × 10−26 cm6/s) within the experimental uncertainties of Ref. 5454. S. Marchetti, M. Martinelli, and R. Simili, J. Phys: Condens. Matter 14, 3653 (2002). https://doi.org/10.1088/0953-8984/14/13/321. We employ a constant SRH lifetime (3.7 × 10−7 s) for both n- and p-type InAs, which provided the best fit to the measured dark-I–V curve of the TPV cell from Ref. 4040. Q. Lu, X. Zhou, A. Krysa, A. Marshall, P. Carrington, C. H. Tan, and A. Krier, Sol. Energy Mater. Sol. Cells 179, 334 (2018). https://doi.org/10.1016/j.solmat.2017.12.031. Subtracting Auger and radiative contributions from the total lifetime of Ref. 5555. G. A. Sukach, A. B. Bogoslovskaya, P. F. Oleksenko, Y. Y. Bilynets, and V. N. Kabacij, Infrared Phys. Technol. 41, 299 (2000). https://doi.org/10.1016/S1350-4495(00)00046-3 using Matthiessen's rule, we estimate the SRH lifetime of InAsxSb0.31(1-x)P0.69(1-x) for x ≠ 1 to be 3.2 × 10−8 s. We include a doping-dependent surface recombination velocity at the vacuum/FSF interface, discussed further in Sec. 5 of the supplementary material. Due to the low conduction band density of states of InAs and InAsSbP lattice matched to InAs, we use a non-parabolic band model to calculate the electron quasi-Fermi level.5656. A. Raymond, J. L. Robert, and C. Bernard, J. Phys. C 12, 2289 (1979). https://doi.org/10.1088/0022-3719/12/12/014 We employ the model and parameters from Ref. 5757. M. Grigoryev, E. Ivanov, and K. Moiseev, Semiconductors 45, 1334 (2011). https://doi.org/10.1134/S1063782611100071 to calculate the bandgap and electron affinity for all stoichiometric compositions of InAsSbP. The energy band diagrams of baseline and optimized nip-Q cells at maximum power point voltage (Vmpp) are presented in Fig. 2, including conduction band (EC) and valence band (EV) edges and the Fermi levels of electrons (EFe) and holes (EFh). Figure 2(b) shows abrupt band offsets at the heterojunctions with the FSF and BSF layers, which effectively block parasitic hole and electron transport, respectively. We validate the electrical model, comparing measured and simulated dark current–voltage curves of p–i–n InAs4040. Q. Lu, X. Zhou, A. Krysa, A. Marshall, P. Carrington, C. H. Tan, and A. Krier, Sol. Energy Mater. Sol. Cells 179, 334 (2018). https://doi.org/10.1016/j.solmat.2017.12.031 and p-InAsSbP/n-InAs/n+-InAs4141. A. Krier, M. Yin, A. Marshall, and S. E. Krier, J. Electron. Mater. 45, 2826 (2016). https://doi.org/10.1007/s11664-016-4373-0 devices, with the results given in Sec. 6 of the supplementary material.
With a goal to efficiently recover 600–900 K waste heat while considering achievable radiator-TPV gaps (dR-FSF) of present NFTPV devices,5–9,585. A. Fiorino, L. Zhu, D. Thompson, R. Mittapally, P. Reddy, and E. Meyhofer, Nat. Nanotechnol. 13, 806 (2018). https://doi.org/10.1038/s41565-018-0172-56. G. R. Bhatt, B. Zhao, S. Roberts, I. Datta, A. Mohanty, T. Lin, J. M. Hartmann, R. St-Gelais, S. Fan, and M. Lipson, Nat. Commun. 11, 2545 (2020). https://doi.org/10.1038/s41467-020-16197-67. T. Inoue, T. Koyama, D. D. Kang, K. Ikeda, T. Asano, and S. Noda, Nano Lett. 19, 3948 (2019). https://doi.org/10.1021/acs.nanolett.9b012348. R. Mittapally, B. Lee, L. Zhu, A. Reihani, J. W. Lim, D. Fan, S. R. Forrest, P. Reddy, and E. Meyhofer, Nat. Commun. 12, 4364 (2021). https://doi.org/10.1038/s41467-021-24587-79. C. Lucchesi, D. Cakiroglu, J. P. Perez, T. Taliercio, E. Tournié, P. O. Chapuis, and R. Vaillon, Nano Lett. 21, 4524 (2021). https://doi.org/10.1021/acs.nanolett.0c0484758. R. St-Gelais, L. Zhu, S. Fan, and M. Lipson, Nat. Nanotechnol. 11, 515 (2016). https://doi.org/10.1038/nnano.2016.20 we optimize the three NFTPV designs of Figs. 1(b)–1(d) for a radiator temperature of 750 K and dR-FSF = 0.1 μm. We calculate the total optical power density absorbed by the TPV cell (Pin) and its maximum power point density (Pmpp), with power densities defined as power divided by the illuminated area. We then optimize the device structure to maximize device efficiency, η = Pmpp/Pin, using an iterative optimizer with parameter domain sampling defined by the face-centered central composite method.5959. Sentaurus TCAD User's Manual ( Synopsys, Inc., 2021). We optimize for efficiency as opposed to power as it increases waste heat use while also lowering cell cooling requirements.
To speed up the optimization, we hold constant the parameters with fixed values listed in Fig. 1. This includes the cap and BSF layer doping concentrations, which are set at readily achievable values48–5048. A. Baraskar, V. Jain, M. A. Wistey, U. Singisetti, Y. J. Lee, B. Thibeault, A. Gossard, and M. J. W. Rodwell, in International Conference on Indium Phosphide and Related Materials ( IPRM, 2010),p. 481. https://doi.org/10.1109/ICIPRM.2010.551626949. A. Katz, S. N. G. Chu, and B. E. Weir, J. Vac. Sci. Technol. B 8, 1125 (1990). https://doi.org/10.1116/1.58492950. W. Lu, B. R. Bennett, J. B. Boos, and J. A. Del Alamo, Electron. Lett. 36, 546 (2000). https://doi.org/10.1049/el:20000436 to maximize current collection and quench contact resistance. This choice necessitates a thin BSF layer to minimize free-carrier absorption. We employ an intrinsic InAs absorber layer to maximize absorption3131. D. Milovich, J. Villa, E. Antolin, A. Datas, A. Marti, R. Vaillon, and M. Francoeur, J. Photonics Energy 10, 025503 (2020). https://doi.org/10.1117/1.JPE.10.025503 while minimizing the Auger recombination that dominates in cells using p-InAs.4040. Q. Lu, X. Zhou, A. Krysa, A. Marshall, P. Carrington, C. H. Tan, and A. Krier, Sol. Energy Mater. Sol. Cells 179, 334 (2018). https://doi.org/10.1016/j.solmat.2017.12.031 See Sec. 7 of the supplementary material for effects of varying Cap and BSF layer thickness and doping on performance.
We consider the radiator to be semi-infinite, but instead using a 500-μm thickness decreases total radiation transfer by less than 1%. A separate optimization showed that our chosen radiator doping of 5 × 1018 cm−3 maximizes above-bandgap (ABG) radiation transfer for realistic radiator thicknesses (on the order of a typical 500 μm Si substrate or less). Thinner radiators demand higher doping concentrations to maximize ABG radiation transfer, but such radiators also increase SBG radiation transfer, which hurts efficiency.
Layer thicknesses and doping not specified in Fig. 1 are included as parameters for optimization. The optimization domain and results for all designs illuminated by a 750 K radiator with dR-FSF = 0.1 μm are given in Table I. The optimized As mole fraction (x) of InAsxSb0.31(1-x)P0.69(1-x), for the FSF and base layers of the pin-Q and nip-Q designs, respectively, reached the lower bound of 0.4, which we constrained to high quality compositions60,6160. I. A. Andreev, O. Y. Serebrennikova, N. D. Il'inskaya, A. A. Pivovarova, G. G. Konovalov, E. V. Kunitsyna, V. V. Sherstnev, and Y. P. Yakovlev, Semiconductors 49, 1671 (2015). https://doi.org/10.1134/S106378261512002761. E. Tournie, J. L. Lazzari, H. Mani, F. Pitard, C. L. Alibert, and A. F. Joullie, Proc. SPIE 1361, 641 (1991). https://doi.org/10.1117/12.24427 outside the miscibility gap.6262. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001). https://doi.org/10.1063/1.1368156 The p-type doping concentration for the FSF layer of the pin design reached the upper bound of 1019 cm−3, which we limited to readily achievable concentrations for these devices.49–5149. A. Katz, S. N. G. Chu, and B. E. Weir, J. Vac. Sci. Technol. B 8, 1125 (1990). https://doi.org/10.1116/1.58492950. W. Lu, B. R. Bennett, J. B. Boos, and J. A. Del Alamo, Electron. Lett. 36, 546 (2000). https://doi.org/10.1049/el:2000043651. M. T. H. Reid, A. W. Rodriguez, and S. G. Johnson, Proc. IEEE 101, 531 (2013). https://doi.org/10.1109/JPROC.2012.2191749 These bounded values minimize parasitic electron diffusion; the lower bound Q has the largest bandgap with favorable band-alignment as a p-type material (see Fig. 2) while the pin design requires high p-doping to perform the same task.
TABLE I. Optimized NFTPV cell structure for a 750 K p-Si radiator and dR-FSF = 0.1 μm, with their optimization bounds and performance metrics.
ParameterUnitsRangeBaselineapinpin-Qnip-Q
InputdG-Gμm20–300206494978
FSF thicknessμm0.005–2.02.00.00531.10.0089
FSF InAsxSb0.31(1-x)P0.69(1-x)x =0.4–1.01.01.0a0.40.46
FSF dopingcm−36 × 1014–1019p = 1018p = 1019p = 2 × 1017n = 4 × 1015
Absorber thicknessμm0.1–3.010.00.720.770.77
Base thicknessμm0.005–2.02.00.0620.0550.10
Base InAsxSb0.31(1-x)P0.69(1-x)x =0.4–1.01.01.0a0.760.4
Base dopingcm−36 × 1014–1019n = 1018n = 6 × 1014n = 7 × 1016p = 2 × 1015
OutputJscA cm−21.752.392.462.36
VocV0.0650.1080.1430.145
PmppmW cm−234121204203
$η$%0.294.88.09.0
aFixed at a given value.
The FSF conductivity effects can only be captured with 2+ dimension drift-diffusion solvers, highlighting the importance of our electrical model. To minimize lateral series resistance, the p-type FSF layer must be thick and moderately doped (pin-Q) or thin and highly doped (pin). The n-type FSF layer of the nip-Q device further reduces top sheet resistance, since electron mobility is higher than hole mobility, allowing for a thin and moderately doped FSF layer with 60% larger dG-G, increasing power output density.
Comparing parameters of the optimized designs to the baseline design, the optimized designs have smaller dG-G values and are composed of much thinner layers. Thinner cells improve device performance due to higher carrier collection efficiency and lower parasitic free carrier absorption but reduce current generation. However, the thin designs have higher Jsc than the baseline due to shorter penetration depth of evanescent vs propagating waves and high reflection at the gold BR layer. The base layers optimally reached lower doping concentrations to reduce SBG power transfer (PSBG) originating from free-carrier absorption.
Our optical model calculates a significant enhancement of useful ABG power transfer (PABG) over the blackbody radiative limit for all devices. Figure 3 shows the layer-resolved spectral absorbed energy flux for each device. A 750 K blackbody radiative spectrum represented by the solid black line is included for comparison, along with a vertical dashed black line denoting the bandgap of InAs (0.353 eV). The optimized devices have PSBG approximately 10% of that in the baseline design. PSBG is not converted to useful power and instead raises the TPV cooling requirements. PSBG could be further reduced with a more reflective BR.16,6316. T. Inoue, T. Suzuki, K. Ikeda, T. Asano, and S. Noda, Opt. Express 29, 11133 (2021). https://doi.org/10.1364/OE.41952963. D. Fan, T. Burger, S. McSherry, B. Lee, A. Lenert, and S. R. Forrest, Nature 586, 237 (2020). https://doi.org/10.1038/s41586-020-2717-7 The optimized designs [Figs. 3(b)–3(d)] have 4–6 times higher total PABG and 0.68–0.85 times lower PSBG compared to the blackbody limit. Although PABG of the efficiency-optimized designs are about 70% of the baseline design, we see much higher efficiency and power output (Table I) due to order-of-magnitude thinner absorption layers, which improves current collection.
Up to 80% of available current is collected at Vmpp for the optimized designs compared to just 39% for the baseline, highlighting the importance of optimizing electronic device properties for near-field operation. Figure 4 shows the current–voltage characteristics, normalized to the total photo-generated current (Jph), of the four designs. We include extracted current (J), surface recombination at the vacuum/FSF and electrode/semiconductor interfaces (Jsurf), as well as Auger (JAug,l), radiative (Jrad,l), and Shockley–Read–Hall (JSRH,l) recombination currents in layer l. All currents that contribute less than 1.5% to Jph at Vmpp are combined into Jother. Auger recombination is the main electrical loss mechanism for all designs, consuming 8%–54% of Jph at Vmpp. However, the devices could be further improved using higher quality absorber layer material, i.e., lowering SRH recombination. Comparing Figs. 4(b) and 4(c), we find that the introduction of the quaternary InAsSbP in the FSF and base layers reduces surface recombination by two-third and eliminates recombination in all but the absorber layer, contributing to a 45% larger Vmpp. Designs with InAsSbP, nip-Q and pin-Q, have similar normalized current–voltage characteristics [see Figs. 4(c) and 4(d)]; therefore, nip-Q's performance enhancement (Table I) is due to better PSBG management and larger dG-G.
Using our best design, the optimized nip-Q device, we explore the impact of radiator temperature and dR-FSF on the power output and efficiency in Fig. 5. The star represents the parameter values used during the nip-Q device optimization. We calculate a significant power output enhancement from near-field energy transfer for all radiator temperatures investigated, with the largest enhancement being 107-fold larger than the far-field (dR-FSF = 10 μm), occurring with dR-FSF = 0.01 μm and a 600 K radiator. We also calculate an improved efficiency under near-field illumination for all radiator temperatures within 600–900 K, reaching up to a 3.7-fold increase with a 600 K radiator and dR-FSF = 0.12 μm compared to a far-field device.
The maximum efficiency for a given radiator temperature varies with dR-FSF. The optimal dR-FSF decreases as temperature increases, going from 0.12 to 0.09 μm for a 600–900 K radiator, respectively. This shift toward smaller dR-FSF occurs because there is proportionally less near-field PSBG transfer to the FSF layer for higher radiator temperatures. Finally, the dip in efficiency at dR-FSF $≈$ 1 μm is caused by a lowered PABG relative to PSBG due to propagative wave interference effects. Since the relative fraction of PABG vs PSBG increases with radiator temperature, the highest efficiency and power output of 14.2% and 1.55 W/cm2 occur at 900 K. PABG increases as dR-FSF decreases, but PSBG absorbed in the FSF layer also increases rapidly below 0.1 μm, which reduces efficiency without impacting power output. Therefore, the maximum efficiency and power output occur at different dR-FSF of 0.09 and 0.01 μm (lower limit), respectively.
Simulation of our optimized nip-Q design significantly outperforms the simulated p-InAs/n-InAs design studied in Ref. 3131. D. Milovich, J. Villa, E. Antolin, A. Datas, A. Marti, R. Vaillon, and M. Francoeur, J. Photonics Energy 10, 025503 (2020). https://doi.org/10.1117/1.JPE.10.025503. At 800 K and with dR-FSF = 0.1 μm, we calculate approximately 2.7- and 3.3-times higher efficiency and power density relative to that device (compared to their efficiency that assumes no absorption in the substrate). The nip-Q device performance enhancement is attributed to our BR layer, use of Q material, and n–i–p doping configuration.
In summary, three NFTPV cell designs containing InAs and/or InAsSbP were optimized and compared under near-field illumination by a 750 K p-Si radiator at dR-FSF = 0.1 μm, using a validated optoelectronic model solving full 2D drift-diffusion equations and fluctuational electrodynamics. The optimized devices have 4–6 times higher above-bandgap and 0.68–0.85 times less sub-bandgap radiation transfer than the blackbody limit. Over the 600–900 K radiator temperature range, we calculate up to 14.2% efficiency and 1.55 W/cm2 power output for the best performing device design. According to these results, our best design could significantly outperform the best measured NFTPV device for the conversion of 600–900 K waste heat, providing important guidelines for the design of future NFTPV cells.
See the supplementary material for further details and validation of the optical and electrical model, the calculated temperature gradient of the device, and the impact on device performance of parameters that were fixed during optimization.
The authors thank University of Ottawa colleagues C. Zhang and M. Giroux for discussions on this topic. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (No. NSERC CGS-D) and by the New Frontiers in Research Fund (No. NFRFE-2019-00334). They are also grateful to CMC Microsystems for providing access to the Synopsys Sentaurus software (vS-2021.06).
The authors have no conflicts to disclose.
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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