Abstract
Spectral absorptance of a metal-semiconductor-metal (MSM) thin-multilayer structured thermo-photovoltaic cell was experimentally investigated. A MSM consists of a thin GaSb-semiconductor sandwiched between a top fishnet-type electrode and a flat backside electrode made of gold. A thin GaSb layer was grown on a substrate made of InAs using molecular beam epitaxy, and then all of the InAs substrate was removed using wet etching. The GaSb film was bonded on a surface of gold, which was sputtered on a Si substrate, using a van der Waals bonding method. The top fishnet-type electrode was made using electron beam lithography and a lift-off process. In the case of a 115 nm thick GaSb layer and a square fishnet aperture of a 300 nm × 310 nm size, the spectral absorptance of MSM reached a local peak (95%) at a wavelength of 1.66 µm, which is similar to spectra predicted by numerical simulation. Moreover, the equivalent resonance cavity model and LC circuit model functioned well to indicate the wavelength of several distinct peaks of absorptance.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Thermo-photovoltaic (TPV) power generation has been developed to harvest radiative energy from unused thermal resources such as the thermal radiation from high-temperature steel manufacturing processes. Molten steel at a temperature of 1500–1800 K is a convenient radiation source for photocurrent generation since most of the TPV cells have high quantum efficiencies at wavelengths shorter than approximately 2.5 µm. Fabrication processes of low-bandgap semiconductors, such as gallium antimonide (GaSb), have been developed since the end of the 20th century to promote industries relating to TPV power generation [1 –3]. Wang et al. showed a TPV cell made of GaInAsSb/GaSb with a bandgap energy level of 0.5 eV that realized a high internal quantum efficiency (IQE) of 90% at a wavelength of 1.6 µm [4]. Several researchers proposed a thin-film TPV cell with several hundred nanometers to reduce the bulk non-radiative carrier recombination loss after photocurrent generation, resulting in improved IQE and a lower saturation current [5 –8]. Simultaneously, the reduction of surface recombination loss is predicted with a well-formed passivation layer on the thin-film TPV cell. In addition to developing the TPV cell, enhancement of the irradiation intensity is an essential issue to improve the power generation density of TPV [9]. Simultaneously, spectral control of incident radiation using optical metamaterials has been progressing to increase conversion efficiency and reduce cooling costs for the TPV cell. This is because each TPV cell has suitable external quantum efficiencies for a specific wavelength range [4,10 –12]. A perfect blackbody [13] and a selective thermal emitter [14 –16] were studied, among others, as optical metamaterials. These optical metamaterials consist of micrometer- or nanometer-sized structures, which are smaller than the wavelength of incident light. Thus, they have spectral absorptance and reflectance values that do not exist in nature [16 –18]. A metal–insulator–metal (MIM) multilayer, in which the insulator layer is between a substrate and top metal layers, is an optical metamaterial that can absorb or emit radiation only at a specific wavelength [16,19]. A metal–dielectric–metal (MDM) multilayer, in which the insulator layer of a MIM is replaced with a dielectric layer, has similar spectral absorptance to MIMs [20]. Here, the intermediate layer must be transparent to excite resonant modes originating from magnetic polariton (MP) and Fabry–Pérot interference. These are the dominant mechanisms of absorption. With this requirement, a metal–semiconductor–metal (MSM) multilayer has also been proposed as a metamaterial-TPV cell through numerical simulations [8,21]. A photovoltaic semiconductor such as GaSb is sandwiched between the top and substrate metal electrodes. The GaSb thickness is reduced to several hundred nanometers to conserve fabrication materials and diminish thermal resistance. Moreover, the top electrode has a shape with periodic islands, a one-dimensional grating, or a periodic fishnet, which excite resonant modes. Then, incident light with a specified wavelength is trapped inside the MSM due to MP or cavity resonance. Consequently, the incident light is converted into electricity at the depletion layer of the GaSb with a high spectral efficiency of nearly unity. A resonant phenomenon related to a thin-film TPV cell has a potential to significantly enhance the power generation density. Its theoretical performance using far- or near-field radiation as incident radiation was calculated in past studies [5,6,8]. In this work, a MSM thin-multilayer consisting of a gold fishnet-type top electrode, a thin GaSb layer, and a gold backside electrode (fishnet MSM) was manufactured using nanofabrication technology to initiate the formation of a metamaterial-TPV cell. Its normal spectral absorptance at near-infrared wavelengths was measured to demonstrate high absorptance only around a specific wavelength. Moreover, the experimental results were compared with those of simulations to validate the analytical model that indicates the peak wavelengths of the fishnet-MSM. Then, the contributions of several absorption modes, i.e., the cavity resonance, MP, and Fabry–Pérot interference, were evaluated to reveal the requirement for the electrode width of the fishnet.
2. Methodology of sample fabrication
In the current study, the MSM thin-multilayer structure depicted in Fig. 1 was manufactured for measurement of spectral absorption to confirm the analytical model of previous work [21]. The thickness of the GaSb layer should be greater than 100 nm because it is reported that the thickness of the depletion layer of the p–n junction is approximately 100 nm [22]. Usually, an undoped or a zinc-doped GaSb is used as the p-type GaSb semiconductor [23,24], while a tellurium- or a sulfur-doped GaSb serves as the n-type GaSb semiconductor [25,26]. Additionally, a gold–germanium (Au–Ge) alloy is always used for the flat backside electrode to make ohmic contact with the n-type GaSb semiconductor [27 –29]. For evaluating the simulation result experimentally with a simple manufacturing process, only an undoped p-type GaSb semiconductor with a thickness of about 100 nm was grown because the optical absorptance of p-type GaSb is much the same as that of the n-type material. The real parts of both of their refractive indices are within 5% of each other [30]. Additionally, pure gold, which has a lower reflectance compared with that of Au–Ge [29], is used for the backside electrode. For the top fishnet-type gold electrode, a square aperture size in the x- and y- directions is defined as wx × wy, the pitch lengths of the fishnet in x- and y-directions are Λx and Λy, and the height of the electrode is h.
Figure 1 also illustrates a fabrication process of the MSM thin-multilayer structure with a gold electrode, p-GaSb semiconductor, and backside gold electrode. In the first step, as shown in Fig. 1(a), an undoped GaSb crystal layer was grown to a thickness of 100 nm on an indium arsenide (InAs) substrate with a thickness of 500 µm using molecular beam epitaxial (MBE) equipment modified from a vacuum evaporator (VX-30; Eiko Corporation, Tokyo, Japan). It is impossible to have epitaxial growth of the GaSb layer directly on the gold electrode surface, while it is possible to do this on the InAs crystals due to a negligible mismatch (less than 0.6%) between the GaSb and InAs crystal lattice constants [31,32]. For the future development of the manufacturing process to form a p–n junction inside the ultra-thin GaSb layer, n-GaSb will need to be grown to a thickness of 50 nm on InAs before growing a p-GaSb layer to 50 nm. Additionally, a reactive ion etching using BCl3, Cl2 and Ar gases will be required to precisely adjust the total thickness of the GaSb layer [33]. In the second step, depicted in Fig. 1(b), an acid-resist wax (Apiezon Wax W; M&I Materials, Manchester, United Kingdom) layer with a 3 mm thickness was made on the p-GaSb surface to support a thin GaSb film after removal of the InAs substrate. A droplet of a liquid wax solution made from 5 g of wax dissolved in 20 ml of trichloroethylene (TCE), was deposited and spread uniformly on the surface of the p-GaSb. After that, the liquid solution was dried at room temperature for 30 minutes. Then, another droplet was deposited and spread uniformly on the surface of the previous wax layer. This procedure was repeated until the wax thickness exceeded 3 mm. This wax layer was baked at 100 °C to completely volatilize TCE. In the third step, shown in Fig. 1(c), the InAs substrate was entirely removed with a wet etching process using a 37% hydrochloric acid (HCl), since there is a significant difference in the etching rates for InAs, 120 µm/h, and GaSb, 0.005 µm/h [32,34]. In the next step, depicted in Fig. 1(d), the surface of the thin GaSb layer supported on a thick resist wax substrate was bonded to the surface of a 200 nm thick layer of sputtered gold on a silicon substrate using a van der Waals (VDW) bonding method [35]. In the fifth step, shown in Fig. 1(e), the thick resist wax substrate was entirely removed using TCE. Figure 2(a) shows an image of a thin GaSb–gold bilayer manufactured by the abovementioned procedure. The thin GaSb layer was bonded on a part of gold–silicon substrate. In the subsequent step, illustrated in Fig. 1(f), the surface of the GaSb was coated using an electron beam (EB) resist (ZEP520A-7; Zeon Corporation, Tokyo, Japan) using a spin-coater, and then, the resist was baked for 5 minutes. Using an EB writer (F7000-VD02; Advantest Corporation, Tokyo, Japan), a fishnet pattern was made as an EB mask through an EB lithography process, where the pitch lengths, Λx and Λy, and the square aperture size, wx × wy, were designed to be 400 nm and 300 nm, respectively. This aperture size was sufficient to set the first resonant peak at 1.6 µm, where GaSb has high internal quantum efficiency. After the lithography, an inverse pattern of the fishnet structure was made using a developer (ZED-N50; Zeon Corporation, Tokyo, Japan) and a rinse (ZMD-B; Zeon Corporation, Tokyo, Japan). Next, as shown in Fig. 1(g), gold was deposited on the mask with an inverse pattern of the fishnet structure using an EB vapor deposition process. Finally, the mask was lifted off using N-methyl-2-pyrrolidone and an ultrasonic cleaner. Through these processes, a fishnet-structured gold electrode was manufactured on a thin GaSb semiconductor, as shown in Fig. 2(b) and 2(c).
3. Numerical simulation
In order to estimate the absorptance of the MSM thin-multilayer, numerical simulations using a finite difference time domain (FDTD) method were conducted. In the FDTD method, Maxwell’s electromagnetic field equations [36] were numerically solved. Only one period of the cyclic fishnet MSM thin-multilayer, i.e., one cavity, was modelled in the computational area. A planar Gaussian wave was irradiated perpendicular to the surface of the multilayer because of small angular dependency [8,18]. Then, the absorptance was estimated by dividing the intensity of the absorbed wave by that of the incident wave [21]. The spatial and time resolution of the current simulations were 5 nm and 5.0 × 10−18 s, respectively. A second-order perfectly matched layer (PML) condition [37,38] was applied to both the top and bottom ends of the computational area, while other side boundaries were set to a periodic boundary condition to express planes with semi-infinite areas. Optical properties, i.e., the complex permittivities of gold [39] and undoped p-GaSb [40], were introduced into the simulation using a piecewise linear recursive convolution (PLRC) method [41]. The complex permittivity of gold was fitted to the Drude model with the same parameters described in the previous study [21]. Figure 3 shows a comparison of the complex refractive indices of GaSb with a reference value [40] and a fitting model used in the simulation. In the current simulation using the PLRC method, the complex permittivity, i.e., the square of the complex refractive index, of GaSb, ɛ GaSb, needed to be fitted to the Lorentz oscillator model as shown below:
4. Surface measurement of the sample
Figure 2(c) shows a field emission-scanning electron microscopic (FE-SEM) image of the fishnet structure. The bright portion of the image corresponds to the fishnet structure made of gold. Due to the backscattering and proximity effects of EB in the lithography process [42], the length of one side of a square cavity appears slightly smaller than 300 nm, and the corners of the fishnet apertures are rounded. In this work, compensation for these effects during the EB lithography could not be perfectly achieved.
The surface distribution of the fishnet was observed using atomic force microscopy (AFM) to determine the geometric parameters of the fishnet MSM thin-multilayer for the numerical simulation. Figure 4(b) shows the detailed displacements of cantilevers on two line segments A–B and C–D in Fig. 4(a). From the relative vertical displacement, the thickness of the fishnet electrode was found to be about 30 nm, although both the ceilings of the fishnet and the surface of GaSb were rough. In the horizontal direction, it was found that the cyclic fishnet structure period in the A–B direction was about 3% longer than that of C–D direction. This warping was not intended in the design process and originated from thermal expansion of the substrate or lattice orientation of GaSb. Moreover, the sidewalls of the fishnet became sloped with widths of approximately 30 nm. Here, the radius of curvature of the cantilever of AFM (OMCL-TR800PSA-1; Olympus Corporation, Tokyo, Japan) was about 15 nm at its tip. Since the tip radius was smaller than the fishnet height, physical interference between the ceiling of the fishnet and the tip caused slightly larger displacement in vertical direction at distant points from the sidewall. Thus, the sidewalls of the fishnet structure were estimated as vertical walls. Finally, the geometric parameters of the manufactured fishnet structure on the GaSb layer were found to be wx = 300 nm, wy = 310 nm, Λx = 400 nm, Λy = 410 nm, and h = 30 nm. It was better to deposit a thicker electrode than 30 nm to enhance the cavity resonance mode; however, it is still acceptable to utilize its function to control the absorptance. Furthermore, the thickness of the GaSb layer, d, was measured using a step gauge and found to be approximately 115 nm.
5. Results and discussion
Figure 5(a) compares four absorptances obtained from sample measurements and numerical simulations. The absorptance measurements were conducted using a spectrophotometer (MSV-370; JASCO Corporation, Tokyo, Japan). In the simulation, the geometric parameters of a MSM thin-multilayer were equal to the results of AFM measurements. The corners and edges of the cavities were assumed to have an ideal rectangular shape. The black and red lines express the spectral absorptance obtained from the experiment without and with a fishnet electrode. Without a fishnet electrode, only a peak originating from the interference of thin-film at 0.75 µm is apparent. With a fishnet electrode, there are three peaks, at 0.72, 0.91, and 1.66 µm. In this work, we focus on two notable peaks at 1.66 and 0.72 µm (the first and second peaks). The most significant peak at 1.66 µm, which the fishnet electrode emphasized, reaches an absorptance of 0.95. It has a high absorptance at the peak while it diminishes to less than 0.2 at wavelengths greater than 2.0 µm.
There is a discrepancy in the peak wavelength of the simulation results depicted by the green line and the experimental results in Fig. 5(a). This inconsistency primarily comes from the optical properties of the p-GaSb grown in the experiment. The precise refractive index of the p-GaSb cannot be measured due to the complicated fabrication process of the fishnet-MSM. Alternatively, the carrier density of p-GaSb was measured, which was 2.646 × 1019 cm−3 and the mobility was 2.34 × 102 cm2/Vs in these experiments. The real part of the refractive index of p-GaSb tends to become smaller with increasing carrier density [30]. Here, this carrier density was ∼10 to ∼ 100 times higher than in other studies [30,43]. This is because the rate of epitaxial growth was too fast to make high quality GaSb. Considering the relationship between the carrier density and refractive index [30], the refractive index in the experiment was possibly about 10% lower than the simulation. The magnitude of the estimation of the refractive index is comparable to the errors of the first and second peak wavelengths, approximately 9%. The light blue line shows another simulation result roughly considering a reduced refractive index. Here, the parameter ɛ ∞ in Eq. (1) was taken as 6.100. Despite the approximated adjustment to the refractive index, the first peak wavelength drastically shifted closer to the experimental result. This indicates the cause of the difference between experimental and original simulation results.
We discuss an equivalent physical model to describe the absorbing mechanism for the first and second peaks. Here, the fishnet electrode has a topologically identical structure to a bundle of square waveguides. Moreover, when one side of the square waveguide is closed, it can be regarded as a resonance cavity with an open end. From these associations, the equivalent cavity model depicted in Fig. 5(b) was proposed to describe the peak wavelength [18,21,44]. In the model, the p-GaSb fills the open cavity made of gold. The resonant wavelength of the cavity mode, λ Resonant, is derived as follows:
The resonant cavity model also suggests a peak at 0.72 µm in the experiments. The wavelength of the second resonant mode of the resonance cavity model (CM2) calculated using Eq. (2) is 0.74 µm when the combination of the orders of the resonant modes (Nx, Ny, Nz) are (1, 0, 3) or (0, 1, 3) and n GaSb is 4.25. These combinations of the order numbers were chosen because the resonant modes (1, 0, Nz) or (0, 1, Nz) tend to be apparent in the resonance of a cavity with an open end [44]. While the absorptances at each peak are smaller than the first peak, both experimental and simulation results correspond to the indicated wavelength within a 3% error. Although the geometric conditions were of an ideal resonant cavity and fishnet-MSM dimensions, the correspondence of the wavelength for these two modes confirms the effectiveness of the equivalent resonance cavity model. The model has been shown useful in approximate estimation of distinct absorptance peaks of the fishnet-MSM.
This imperfection in the cavity resonance also affected the experimental results. The red line in Fig. 5(a) depicts a small shoulder beside the first peak at 1.3 µm. This shoulder implies another absorption mode. Here, the available range of the equivalent resonant cavity mode was examined through additional simulation. Figure 6 shows the relationship among absorptance, wavelength of the incident wave and electrode width, Λ − w, with a constant cavity width wx = wy = 300 nm. In this examination, the GaSb thickness, d, and the fishnet electrode thickness, h, were both set to 100 nm. When Λ − w is larger than the thickness of the GaSb layer, the first peak at 1.5 µm split into three peaks.
The peak at the longest wavelength is excited by the MP originating from an equivalent LC circuit resonance [8,16,46]. Figure 7(a) shows a schematic diagram of the LC circuit model for the fishnet-MSM, consisting of two capacitors and inductors formed at the GaSb layer and the space inside the gold aperture. For the transverse magnetic (TM) mode with an angular frequency of ω, the mutual and kinetic inductances between the bottom gold and y directional top electrodes, L m1 and L k1, are defined as follows:
The capacitance values between top and bottom gold layer, C m, and between two y directional electrodes, C g, are defined as follows:
When Z total(ω r) becomes zero, an electromagnetic wave at the resonant frequency, ω r, will be significantly absorbed.
Figure 7(b) shows the distribution of an electromagnetic field surrounding the fishnet MSM at the resonant wavelength, 2.25 µm, for the electrode width, Λ − w, of 190 nm. The arrows correspond to the electric field vectors, while the contour depicts the logarithmic intensity of y-directional magnetic fields. The magnetic field is localized and enhanced so that is ten times stronger than the incident wave in the GaSb region between the top and bottom gold layers. Simultaneously, the left and the right sides of the electrode at the center of the image are positively and negatively charged, respectively. The tips of the vectors near the right bottom corner of the center electrode point to the corner. It is also seen that the left and the right sides of the gold substrate just below the top electrode are negatively and positively charged, respectively. Moreover, the distribution of electric charges alternatively switches at an interval of a half the period of the electric wave. These electric charges come from movement of free electrons inside the gold layer, and promotes two capacitors, C m, at the right and left halves of the electrode. Thus, the equivalent circuit was established and radiation at 2.25 µm was absorbed due to magnetic resonance.
The second peak for the electrode width of 190 nm in Fig. 6 corresponds to optical interference inside the GaSb layer. Here, a part of the incident wave diffracts at the bottom corner of the electrode and propagates as a surface wave in a direction parallel to the gold surface. For the electrode width, Λ − w, of 190 nm, the central peak stands at 1.73 µm. Here, the refractive index of GaSb at 1.73 µm is approximately 3.82. Thus, it corresponds to the wavelength of 453 nm inside the GaSb layer. The shortened wavelength is close to the pitch lengths of the fishnet, Λ = 490 nm. Similarity is also observed in the results with a longer pitch length. Therefore, the wavelength of the interference peak increases linearly. This trend implies that the surface wave interferes with itself, depending on the pitch length of the periodic structure.
The third peak for the electrode width of 190 nm in Fig. 6 corresponds to CM1, whose resonant wavelength was affected by the reflection peak of the interference mode, and shifted so that it became slightly shorter than 1.6 µm. Figure 7(c) shows the distribution of an electromagnetic field around the fishnet-MSM at the resonant wavelength, 1.38 µm, for an electrode width, Λ − w, of 190 nm. Contrary to the case of MP, a strong magnetic field is observed at the center of the equivalent cavity. Its intensity is more than ten times greater than that of the incident wave. Additionally, an electric field is also promoted at the center, while it is comparably weak below the fishnet electrode. Thus, the abovementioned imaginary conductive wall is formed below the fishnet electrode to confine the electromagnetic energy inside the fishnet-MSM.
However, these separated peaks were attenuated with increasing electrode width. It is considered that these peaks dissipated due to their overlap with each other’s resonant mode, especially the horizontal interference mode excited around the strip-wired gold structure [21]. Furthermore, the larger the area occupied by the gold wire, the less radiation contributed to cavity resonance. Therefore, an electrode having a width of 100 nm with d = 115 nm was suitable for making the separated peaks inconspicuous while keeping the principal peak apparent.
6. Conclusions
As a metamaterial-TPV cell, a fishnet-MSM thin-multilayer was manufactured using wet etching, VDW bonding, EB lithography, and liftoff techniques. Then, its normal absorptance was measured to validate the equivalent cavity resonance absorption model for the fishnet-MSM. Although the square cavity of the top fishnet electrode shrunk slightly and became rounded because of backscattering and the proximity effect during EB lithography, the top fishnet electrode was shaped as designed, and the methodology to fabricate the fishnet-MSM was established. Here, the experimental absorptance spectra slightly departed from the FDTD simulation results, especially for the two distinct peak wavelengths. Another simulation result with an adjusted refractive index revealed that the cause was a decreased refractive index of the experimentally grown GaSb. An equivalent resonance cavity model was proposed to clarify the principle of absorbing radiation at two distinct peak wavelengths. The first and second eigenmode wavelengths indicated by the model roughly corresponded to the two peaks in the simulation results. Through further simulation, the equivalent resonance cavity model hardly functioned as indicator of the resonant wavelength with the fishnet electrode width broader than the GaSb thickness. This was because the magnetic resonance and interference of the surface wave surrounding electrode partially canceled the cavity resonance. Consequently, the model was verified as a useful indicator of the peak wavelength for a fishnet-MSM, when its fishnet electrode width is narrow.
Funding
Japan Society for the Promotion of Science (17H03184, 20H02084).
Acknowledgements
The authors would like to thank the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant in Aide (Number: 17H03184, 20H02084) for their financial support. A part of this work was conducted at the Takeda Sentanchi Supercleanroom, The University of Tokyo, supported by “Nanotechnology Platform Program” of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, Grant Number JPMXP09F19UT0144. The absorptance measurements were conducted at the Center for Analytical Instrumentation Chiba University. Additionally, surface analysis using AFM was conducted at the Open Facility Center, Material Analysis Division, Tokyo Institute of Technology. All simulations in this study were conducted using the TSUBAME 3.0 supercomputer provided by Global Scientific Information and the Computing Center at Tokyo Institute of Technology.
Disclosures
The authors declare no conflicts of interest.
References
1. T. J. Coutts, Thermophotovoltaic principles, potential, and problems, AIP Conference Proceedings, 404, 217 (1997).
2. T. J. Coutts, “An overview of thermophotovoltaic generation of electricity,” Sol. Energy Mater. Sol. Cells 66(1-4), 443–452 (2001). [CrossRef]
3. L. Fraas and L. Minkin, TPV History from 1990 to Present & Future Trends, AIP Conference Proceedings, 890, 17 (2007).
4. C. A. Wang, H. K. Choi, S. L. Ransom, G. W. Charache, L. R. Danielson, and D. M. DePoy, “High-quantum-efficiency 0.5 eV GaInAsSb/GaSb thermophotovoltaic devices,” Appl. Phys. Lett. 75(9), 1305–1307 (1999). [CrossRef]
5. J. K. Tong, W. C. Hsu, Y. Huang, S. V. Boriskina, and G. Chen, “Thin-film ‘Thermal Well’ emitters and absorbers for high-efficiency thermophotovoltaics,” Sci. Rep. 5(1), 10661 (2015). [CrossRef]
6. A. Karalis and J. D. Joannopoulos, “‘Squeezing’ near-field thermal emission for ultra-efficient high-power thermophotovoltaic conversion,” Sci. Rep. 6(1), 28472 (2016). [CrossRef]
7. T. Burger, D. Fan, K. Lee, S. R. Forrest, and A. Lenert, “Thin-film architectures with high spectral selectivity for thermophotovoltaic cells,” ACS Photonics 5(7), 2748–2754 (2018). [CrossRef]
8. Q. Ni, H. Alshehri, Y. Yang, H. Ye, and L. Wang, “Plasmonic light trapping for enhanced light absorption in film-coupled ultrathin metamaterial thermophotovoltaic cells,” Front. Energy 12(1), 185–194 (2018). [CrossRef]
9. A. Datas, D. L. Chubb, and A. Veeraragavan, “Steady state analysis of a storage integrated solar thermophotovoltaic (SISTPV) system,” Sol. Energy 96, 33–45 (2013). [CrossRef]
10. N. J. Ekins-Daukes, K. W. J. Barnham, J. P. Connolly, J. S. Roberts, J. C. Clark, G. Hill, and M. Mazzer, “Strain-balanced GaAsP/InGaAs quantum well solar cells,” Appl. Phys. Lett. 75(26), 4195–4197 (1999). [CrossRef]
11. L. G. Ferguson and L. M. Fraas, “Theoretical study of GaSb PV cell efficiency as a function,” Sol. Energy Mater. Sol. Cells 39(1), 11–18 (1995). [CrossRef]
12. X. Y. Gong, T. Yamaguchi, H. Kan, T. Makino, T. Iida, T. Kato, M. Aoyama, Y. Hayakawa, and M. Kumagawa, “Room temperature InAsxP1-x-ySbyInAs photodetectors with high quantum efficiency,” Jpn. J. Appl. Phys. 36, 2614–2616 (1997). [CrossRef]
13. M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013). [CrossRef]
14. X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011). [CrossRef]
15. S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic power generation,” Appl. Phys. Lett. 83(2), 380–382 (2003). [CrossRef]
16. A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transfer 149, 33–40 (2014). [CrossRef]
17. H. Yu, D. Liu, Z. Yang, and Y. Duan, “Simple rectangular gratings as a near-field “Anti-Reflection” pattern for GaSb TPV cells,” Sci. Rep. 7(1), 1026 (2017). [CrossRef]
18. S. Maruyama, T. Kashiwa, H. Yugami, and M. Esashi, “Thermal radiation from two-dimensionally confined modes in microcavities,” Appl. Phys. Lett. 79(9), 1393–1395 (2001). [CrossRef]
19. Y. B. Chen and F. C. Chiu, “Trapping mid-infrared rays in a lossy film with the Berreman mode, epsilon near zero mode, and magnetic polaritons,” Opt. Express 21(18), 20771 (2013). [CrossRef]
20. T. Liu and J. Takahara, “Ultrabroadband absorber based on single-sized embedded metal-dielectric-metal structures and application of radiative cooling,” Opt. Express 25(12), A612 (2017). [CrossRef]
21. K. Isobe and K. Hanamura, “Selective absorption of a thermophotovoltaic cell using a thin semiconductor and a top fishnet-structured electrode,” Int. J. Heat Mass Transfer 134, 807–814 (2019). [CrossRef]
22. N. Shibata, S. D. Findlay, H. Sasaki, T. Matsumoto, H. Sawada, Y. Kohno, S. Otomo, R. Minato, and Y. Ikuhara, “Imaging of built-in electric field at a p-n junction by scanning transmission electron microscopy,” Sci. Rep. 5(1), 10040 (2015). [CrossRef]
23. A. B. Djurišić, E. H. Li, D. Rakić, and M. L. Majewski, “Modeling the optical properties of AlSb, GaSb, and InSb,” Appl. Phys. A 70(1), 29–32 (2000). [CrossRef]
24. O. V. Sulima and A. W. Bett, “Fabrication and simulation of GaSb thermophotovoltaic cells,” Sol. Energy Mater. Sol. Cells 66(1-4), 533–540 (2001). [CrossRef]
25. B. B. Kosicki and A. Jayaraman, “Conduction-band structure of GaSb from pressure experiments to 50 kbar,” Phys. Rev. 172(3), 764–769 (1968). [CrossRef]
26. G. Stollwerck, O. V. Sulima, and A. W. Bett, “Characterization and simulation of GaSb device-related properties,” IEEE Trans. Electron Devices 47(2), 448–457 (2000). [CrossRef]
27. A. W. Bett and O. V. Sulima, “GaSb photovoltaic cells for applications in TPV generators,” Semicond. Sci. Technol. 18(5), S184–S190 (2003). [CrossRef]
28. A. G. Milnes and D. L. Feucht, Heterojunctions and Metal-Semiconductor Junctions. Academic Press, New York, 1972.
29. M. L. Theye, V. N. Van, and S. Fission, “Validity of the free-electron model for Ag-Ge and Au-Ge amorphous metallic alloys,” Philos. Mag. B 47(1), 31–50 (1983). [CrossRef]
30. P. P. Paskov, “Refractive indices of InSb, InAs, GaSb, InAsxSb1-x, and In1-xGaxSb: Effects of free carriers,” J. Appl. Phys. 81(4), 1890–1898 (1997). [CrossRef]
31. M. Yokoyama, H. Yokoyama, M. Takenaka, and S. Takagi, “Ultrathin body GaSb-on-insulator p-channel metal-oxide-semiconductor field-effect transistors on Si fabricated by direct wafer bonding,” Appl. Phys. Lett. 106(7), 073503 (2015). [CrossRef]
32. L. Song, S. Degroote, K. H. Choi, G. Borghs, and P. Heremans, “Release of epitaxial layers grown on InAs substrates,” Electrochem. Solid-State Lett. 6(2), G25 (2003). [CrossRef]
33. K. Swaminathan, P. E. Janardhanan, and O. V. Sulima, “Inductively coupled plasma etching of III–V antimonides in BCl3/SiCl4 etch chemistry,” Thin Solid Films 516(23), 8712–8716 (2008). [CrossRef]
34. D. H. Van Dorp, S. Arnauts, F. Holsteyns, and S. De Gendt, “Wet-chemical approaches for atomic layer etching of semiconductors: Surface chemistry, oxide removal and reoxidation of InAs (100),” ECS J. Solid State Sci. Technol. 4(6), N5061–N5066 (2015). [CrossRef]
35. E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, and J. P. Harbison, “Van der Waals bonding of GaAs epitaxial liftoff films onto arbitrary substrates,” Appl. Phys. Lett. 56(24), 2419–2421 (1990). [CrossRef]
36. J. R. Howell, R. Siegel, and M. P. Mengüç, Thermal Radiation Heat Transfer –. 5th Edition, CRC Press, New York, 2011.
37. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]
38. D. Correia and J. M. Jin, “On the development of higher-order PML,” IEEE Trans. Antennas Propag. 53(12), 4157–4163 (2005). [CrossRef]
39. E. D. Palik, Handbook of Optical Constants of Solids: Volume 1. Academic Press, San Diego, California, 1985.
40. S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66(12), 6030–6040 (1989). [CrossRef]
41. D. F. Kelley, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antennas Propag. 44(6), 792–797 (1996). [CrossRef]
42. G. Owen and P. Rissman, “Proximity effect correction for electron beam lithography by equalization of background dose,” J. Appl. Phys. 54(6), 3573–3581 (1983). [CrossRef]
43. R. Ferrini, M. Patrini, and S. Franchi, “Optical functions from 0.02 to 6 eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84(8), 4517–4524 (1998). [CrossRef]
44. F. Kusunoki, T. Kohama, T. Hiroshima, S. Fukumoto, J. Takahara, and T. Kobayashi, “Narrow-band thermal radiation with low directivity by resonant modes inside tungsten microcavities,” Jpn. J. Appl. Phys. 43(8A), 5253–5258 (2004). [CrossRef]
45. K. Isobe, D. Hirashima, and K. Hanamura, “Spectrally enhanced near-field radiation transfer using nanometer-sized pillar array structured surfaces,” Int. J. Heat Mass Transfer 115, 467–473 (2017). [CrossRef]
46. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620 (2006). [CrossRef]
47. N. W. Ashcroft and N. D. Mermin, Solid State Physics. Saunders College Publishing, Philadelphia, 1976.