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Abstract
The methylammonium lead iodide (CH3NH3PbI3)-germanium (Ge) heterojunction with a layer of periodic nanospheres was numerically studied to achieve improved performance over broadband from 300 nm to 1600 nm by the 3D finite element method (FEM). Under AM 1.5 g illumination, the total absorbed power increased 14% in heterojunction photodetectors assisted by an Al2O3 antireflection (AR) array, after optimizing the thickness of perovskite and Ge, as well as the radius, period and material type (metal or dielectric permittivity) of nanosphere array by genetic algorithm, with reference to a corresponding device without nanospheres. The enhanced optical properties were further elaborated and demonstrated by comparatively analyzing broadband absorptance, electric field distributions, absorbed power distributions and the optical generation rate of charge carriers in the two photodetector models. The proposed perovskite-Ge heterojunction with spheres shows great promise for optoelectronic devices.
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1. Introduction
Photodetectors, with the capacity to capture photons in a certain spectrum range and convert them to electronic signals, have important applications in various fields, such as environmental pollution monitoring, medicine, optical communication, and thermal imaging [1–4]. The spectrum range and light absorption of a photodetector are two crucial factors for its detection application. The spectrum range are generally determined by the specific bandgap of used active layer in a device. Methylammonium lead iodide (CH3NH3PbI3) perovskite material can efficiently absorb visible light from 300 nm to 770 nm due to its bandgap of ∼1.5 eV [5,6], and have already attracted great attentions in visible light detection for the advantages of long charge carrier diffusion length, high absorption coefficient and low fabrication cost [7–10].
To improve detection ability, on one hand, heterojunction devices based on perovskite and semiconductor material have been proposed and demonstrated [11–14]. Su et al. explored a perovskite - ZnO heterojunction for the photon sensing from the UV to the green band [11], with improved light absorption efficiency and detector responsivity. But such heterojunction did not expand the detection spectrum. Cao et al proposed perovskite-TiO2-Si tri-layer heterojunction structure [12], which achieved a response spectrum from 300 nm to 1150 nm. Moreover, the 2D materials such as graphene or MoS2 have also been explored together with perovskite to capture more photons [13,14]. Still, the above-mentioned heterojunction photodetectors are unable to detect photons with energy below Si bandgap of ∼1.12 eV, corresponding to a wavelength range beyond ∼1100 nm [15]. The limited response spectrum of considered photodetectors would hinder its commercial application [16]. In the near infrared range, the inorganic semiconductor Germanium (Ge), with cutoff wavelength ∼1600 nm, has been considered as promising materials for photodetectors because of the excellent carrier mobility and compatibility with complementary metal-oxide-semiconductor (CMOS) technology [17,18]. A heterojunction photodetector based on CH3NH3PbI3 perovskite and Ge was successfully fabricated and demonstrated by Xue et al. [19], with enhanced performance and broader bandwidth from visible to near infrared light. Nonetheless, the perovskite layer was mainly designed to act as an antireflection (AR) coating for a single wavelength 1550 nm.
On the other hand, sub-wavelength metal or dielectric nanostructures have been extensively used for light absorption improvements in a variety of scenarios, such as solar cells and photodetectors [20–26]. Localized surface plasmon resonance (LSPR) effects and/or scattering effects of metal nanospheres are mainly utilized to enhance absorptions in near field and/or far field. Chen et al [21] comparatively studied perovskite absorption based on LSPR after separately introducing Au, Ag or Al nanoparticles. Yang et al [22] demonstrated a CsPbBr3 microwire based photodetector, decorated with Au nanoparticles, achieving improved properties by LSPR effect and piezo-phototronic effect. Nevertheless, dielectric nanostructures may be more preferred due to low intrinsic loss. Fu et al [24] explored scattering properties of InP nanoparticles for absorption enhancement of InGaAs photodetectors over the wavelength range between 1.0 µm and 1.7 µm. Mann et al [25] numerically studied absorption of visible light in organic solar cells after embedding dielectric nanoparticles at anode. However, in these previous works, the material type of nanostructures was usually an invariant, which can seldom be regarded as a degree of freedom during designs and optimizations.
In this work, we numerically investigated CH3NH3PbI3 - Ge heterojunction photodetectors by the full-vector Finite Element Method (FEM). The constructed heterojunction photodetectors with perovskite layer and Ge layer showed wide detection spectrum range from 300 nm to 1600 nm. A square array of nanospheres, had already been studied numerically [24–28] and fabricated successfully [29] in recent years, was suggested to boost the detection efficiency of heterojunction among the wide spectrum. Genetic algorithm (GA) was adopted to optimize total absorption under AM 1.5 g normal illumination, provided that, multiple variables, i.e., thickness of Ge and perovskite layer, as well as period, radius and permittivity (Air, Al2O3, TiO2, SiO2, Au, Ag, Au) of nanospheres, were involved. The maximum total absorption reached 802.2W/m2 for the optimized perovskite - Ge photodetectors assisted by a periodic Al2O3 nanosphere array, which indicated 14% improvement with reference to the corresponding flat heterojunction, and 55% improvement compared with the previous reported ∼516.70W/m2 based on the single perovskite device with a periodic array [28]. Furthermore, the wavelength-dependent electric field and absorbed power were also calculated for five typical wavelengths (400 nm, 700 nm, 1000 nm, 1300 nm, 1600 nm) to further elaborate and confirm the improved performance of proposed heterojunction photodetectors. The maximal electric field and absorbed power of heterojunction device with Al2O3 spheres was 79.8 V/m and 6.6 × 108 W/m2, respectively, which is 5.25 and 20.6 times that of flat structure. The performance of proposed detectors was evaluated under oblique incidence as well, and the absorbed power was improved 13% - 15% with reference to flat case, for every incident angle varied from 0° to 80° with a step of 10°.
2. Methodology
2.1 Modelling of heterojunction photodetectors
The optical properties of the CH3NH3PbI3-Ge photodetectors were numerically investigated by full-vector Finite Element Method (FEM), which was implemented via the commercial RF module of COMSOL Multiphysics. The constructed 3D unit model of concerned heterojunction structures [19] was schematically shown in Fig. 1. From top to bottom section, the square cell with period P consists of a nanosphere with radius R and permittivity ɛ, CH3NH3PbI3 perovskite thin film with thickness h1, a Ge layer with thickness h2, and a 100 nm thick SiO2 substrate. The surrounding material on the top and at the bottom is air in the simulation domain. The nanosphere could be dielectric or noble metal, both of which could be well handled and analyzed by FEM. Especially, when the dielectric material of nanosphere is air, the model is a flat case without any nanospheres. The real and imaginary parts of permittivity of CH3NH3PbI3 and Ge were obtained from previous literature [30,31], while the remaining used materials were directly extracted from the COMSOL database. The incident plane wave with y polarization was normally irradiated along + z direction from the input port [32] on the top boundary. The incident wavelength range was from 300 nm to 1600 nm with interval space 5 nm. Floquet periodicity conditions were performed along x- and y- axis, while perfect match layer (PML) was applied along z direction to avoid spurious reflection at the bottom boundary.
2.2 Analysis of heterojunction photodetectors
The electronic fields in the unit cell could be calculated by solving Helmholtz equation in FEM:
Herein, k0 is the wave vector of incident light, ${\varepsilon _\textrm{r}}$ is the relative permittivity of the medium which is related to complex refractive index of materials. The average time-harmonic electromagnetic power absorbed [33,34] in any materials Pabs depends on the divergence of the Poynting vector S:
with a simple deduction, for nonmagnetic materials, the absorbed power per unit volume Pabs inside considered device can be further calculated as following [35–37]:2.3 Optimizations of heterojunction photodetectors
To obtain the maximal absorbed power, genetic algorithm (GA) [28,39,40] was employed to optimize the structure parameters, i.e., thickness of perovskite h1 and Ge h2, as well as period P and radius R of the nanosphere array. Moreover, the material type (Air, Al2O3, TiO2, SiO2, Au, Ag, or Au) of nanospheres with permittivity $\varepsilon (\lambda )$ were also considered in GA optimization. The whole GA flowchart was shown in Fig. 2. At the beginning of GA, a population with coded chromosomes containing variable information of [$\varepsilon (\lambda )$, h1, h2, P, R] was randomly generated in predefined value ranges. The fitness of each chromosome was calculated, after the total absorption of corresponding structure model was evaluated by FEM. A classic strategy of rank-based roulette wheel selection [39] was then adopted to assign the selection probability to each individual, resulting the chromosomes with larger fitness have more chances to be selected as parent. Double-point crossover [39] was performed for randomly paired couples to produce new offspring, followed by mutation operation for all current chromosomes. An updated population with new chromosomes was formed for evaluations by FEM again in the GA cycle. Besides, Elitism [39] was applied in each GA iteration, which means that the best chromosome with the largest fitness will always be specially chosen to directly transmit to next generation and replace the worst individual with the smallest fitness in the next population. The GA optimization recycling would not stop until a predefined condition was met.
3. Results and discussion
The optical performance of the perovskite-Ge photodetectors with a periodic nanosphere array was numerically investigated by 3D FEM and globally optimized by GA. For the device model, the value of h1 and h2 were between 40 nm and 1000 nm. The period P of nanosphere array varied from 300 nm to 1000 nm. The radius R of nanosphere was set to smaller than half of the period. Moreover, the material of nanospheres was randomly chosen by GA to be one of the seven types: Air, Al2O3, TiO2, SiO2, Au, Ag, Au. The whole structure would be regarded as a flat case when the material type of the nanospheres is air. During the optimization of GA, the chromosome number of population was 40, crossover and mutation probabilities were 80% and 0.1%, respectively. The iteration number of GA was set to 50 after multiple tests.
3.1 Total absorbed power and absorptance
The maximum absorbed power of heterostructure detector represented by encoded chromosome with best fitness in each generation of GA was shown in Fig. 3(a). The maximum power increased monotonically as the GA evolved because the elitism was adopted [39]. The power converges to 802.2W/m2, when the thickness of two thin film h1, h2 were 930.1 nm, 929 nm, and the nanosphere array was Al2O3 with period P and radius R of 828.7 nm and 353.4 nm. The corresponding absorptance was plotted in Fig. 3(b), from which, it could be noticed that the heterojunction structure displayed a broad absorption spectrum spanned from 300 nm to 1600 nm. This attributed to the underlying mechanisms - the top perovskite layer with band gap of ∼1.5 eV absorbed light range from 300 nm to 770 nm, while Ge layer with band gap of ∼0.67 eV exhibited excellent light absorption ability at near infrared from 750 nm to 1600 nm. Meanwhile, compared to the corresponding flat case without nanospheres, it was demonstrated that the Al2O3 nanosphere array, as an AR layer, contributed to evident absorption enhancement in the wide spectrum range. An 14% improvement of total power absorbed by heterojunction with Al2O3 nanosphere array was achieved with reference to the corresponding flat devices. Additionally, for a period variation of ±5%, it was verified that the total absorbed power would decrease no more than 0.3% after 3D FEM calculations, which indicated excellent robustness of designed heterostructure detector with nanosphere array.
Fig. 3. The maximum absorbed power in each GA iteration (a), and normalized absorption spectra (b) of optimized heterostructure detector.
3.2 Electric field distributions
The improvement of total absorption can be well understood from Eq. (3) and (4), which is related to electric field distributions in the device. The electric field distributions calculated by 3D FEM at five typical wavelengths (400 nm, 700 nm, 1000 nm, 1300 nm, 1600 nm) along propagation direction (+z direction) of the incident light were plotted, for heterojunction photodetectors with Al2O3 layer (Fig. 4(a)) and flat case (Fig. 4(b)). The electric fields were largely enhanced in the perovskite layer (with thickness h1) of heterojunction assisted by nanospheres. At short wavelength 400 nm and 700 nm, the maximum amplitude of electric fields of considered photodetector with Al2O3 layer was 79.8 V/m and 68 V/m on the top surface of perovskite, respectively, which was 5.25 and 3.7 times that of corresponding flat device. However, electric fields drastically decreased along propagation direction, which indicated poor penetration ability for incident wavelength of 400 nm and 700 nm. For longer wavelength, such as 1000 nm, 1300 nm and 1600 nm, the electric fields did not focus on the top surface of the perovskite, and more fields transmitted to the bottom Ge of heterojunction photodetectors. For these three long wavelengths, the maximum amplitude of electric fields was 26.7 V/m, 17.5 V/m and 13.8 V/m, respectively, which is 1.5, 1.8 and 1.3 times that of flat structure. Such enhancement of electric fields at typical five wavelengths attributes to Al2O3 nanosphere array acting as an AR layer. Fig. 4(c) and Fig. 4(d) further showed the 3D electric field map of the photodetectors with and without with Al2O3 layer, respectively, at wavelength 400 nm and 1600 nm.
Fig. 4. |E| profiles along (x, y, z) = (0, 0, h) of optimized heterojunction with (a) and without (b) Al2O3 nanospheres at five typical incident wavelengths. The 3D |E| map of heterojunction with (c) and without (d) nanosphere layer for incident wavelength 400 nm and 1600 nm.
3.3 Absorbed power distributions
Absorbed power distributions within photodetectors structure depend on both corresponding electric field and imaginary part of material permittivity. The absorbed power Pabs distribution of the photodetectors with Al2O3 layer and flat structure along the light propagation for considered wavelengths were plotted in Fig. 5(a) and Fig. 5(b), respectively. For incident wavelength 400 nm, the maximum Pabs of both flat and the optimized Al2O3 device are observed on the top surface of perovskite layer. The maximum Pabs for the device with Al2O3 layer was evaluated to be 6.6 × 108W/m3, which is 20.6 times that of the flat device. Then the power drastically decayed in the perovskite layer, which indicates strong absorption ability of perovskite. For wavelength of 700 nm, the maximum Pabs of photodetectors with Al2O3 layer and flat structure were 4.8 × 107W/m2 and 3.1 × 106W/m2. At infrared regime, the bandgap of perovskite limited light absorption. Hence for wavelength 1000 nm, 1300 nm and 1600 nm, the absorbed power of perovskite layer was nearly zero. The maximum Pabs were 4.4 × 106W/m3 and 3.9 × 106W/m3 obtained in the Ge layer for the device with Al2O3 layer, which is 2.75 and 9.5 times that of flat case. At wavelength 1600 nm, the maximum Pabs dramatically decreased to 98.6W/m3 and 83.8W/m3, respectively. The 3D distributions of absorbed power in heterojunction photodetectors with and without Al2O3 layer at wavelength 400 nm and 1600 nm were depicted in Fig. 5(c) and Fig. 5(d), respectively.
Fig. 5. Absorbed power distributions along (x, y, z) = (0, 0, h) of optimized heterojunction with (a) and without (b) Al2O3 nanospheres at five wavelengths. The 3D power distributions of heterojunction with (c) and without (d) nanospheres for wavelength 400 nm and 1600 nm.
The responsivity of photodetectors, defined as the ratio of photocurrent to the incident radiant power [19], exists an upper bound, which is determined by the optical generation rate (OGR) of charge carriers. Assume each absorbed photon excites an electron-hole pair, the OGR is equivalent to the photon absorption rate ${{{P_{\textrm{abs}}}} / {({\hbar \omega } )}}$ [28], from which, it could be learnt that the wavelength-dependent optical generation rate and absorbed power were equally enhanced in heterojunction detectors assisted by nanospheres, compared with that in flat case.
3.4 Oblique incidence
The influences of incident angle (the angle between incident direction and + z axis in the x = 0 plane) on total absorbed power and absorptance of optimized heterostructure detector with spheres were also analyzed. For 10° incident angle, the total absorbed power was reduced to 742.6W/m2. As the incident angle continued to increase to 80°, it rapidly decreased to 420.1W/m2, as shown in Fig. 6(a). Nevertheless, the absorbed power of heterostructure detector assisted by sphere array were still improved 13% - 15% compared with that of flat case for corresponding incident angles from 0° to 80°. It could be further noticed that, when the incident angle became larger, the deteriorated absorptances of optimized heterostructure detector with spheres accounted for the decreased absorbed power, although the wide absorption spectrum ranges were well maintained, as indicated in Fig. 6(b).
Fig. 6. For incident angle from 0° to 80°, total absorbed power and improvements (a) of detector with spheres, compared with flat case; absorptance (b) of detector with spheres.
4. Conclusion
The photodetector based on CH3NH3PbI3 - Ge heterojunction was numerically investigated by 3D full-vector Finite Element Method (FEM), to achieved enhanced optical performance among a broad detection bandwidth from 300 nm to 1600 nm. A layer of periodic metal (Au, Ag, or Au) or dielectric (Al2O3, TiO2, or SiO2) nanosphere array was utilized to improve the performance of heterojunction photodetectors. The maximal total absorption of optimized heterojunction device with spheres by GA was 802.2W/m2 under AM 1.5 g normal illumination, when the thickness of perovskite and Ge was 930.1 nm and 929 nm, respectively, and the period and radius of Al2O3 nanosphere was 828.7 nm and 353.4 nm, which indicated a 14% increasement compared to that of corresponding flat case. The absorptance was improved among broadband from ∼400 nm to ∼1500 nm. Besides, for five typical wavelengths (400 nm, 700 nm, 1000 nm, 1300 nm, 1600 nm) among the broadband range, the maximal electric field and absorbed power of optimized heterojunction device with Al2O3 spheres was 79.8 V/m and 6.6 × 108 W/m2, respectively, which is 5.25 and 20.6 times that of corresponding flat structure. The performance of proposed detectors was further evaluated under oblique incidence, and the absorbed power was improved 13% - 15% with reference to flat case, when incident angle varied from 0° to 80°. The detection properties of CH3NH3PbI3-Ge heterojunction with Al2O3 nanospheres were largely improved in a broadband range, because the nanosphere array acted as an antireflection layer and thus more light could enter perovskite layer and Ge layer. The proposed perovskite-Ge heterojunction assisted by a periodic nanosphere array shows great promising for novel optoelectronic devices.
Funding
Henan Provincial Major Project of Science and Technology (221100210200).
Disclosures
The authors declare no known conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. B. Liu, R. R. Gutha, B. Kattel, et al., “Using silver nanoparticles-embedded silica metafilms as substrates to enhance the performance of perovskite photodetectors,” ACS Appl. Mater. Interfaces 11(35), 32301–32309 (2019). [CrossRef]
2. X. Xu, Y. Dong, Y. Zhang, et al., “High-definition colorful perovskite narrowband photodetector array enabled by laser-direct-writing,” Nano Res. 15(6), 5476–5482 (2022). [CrossRef]
3. B. G. Kim, W. Jang, J. H. Lim, et al., “Physical engineering of anti-solvents in perovskite precipitation for enhanced photosensitive affinity,” Int J Energy Res 46(7), 9748–9760 (2022). [CrossRef]
4. M. Xu, X. Wang, J. Weng, et al., “Ultraviolet-to-infrared broadband photodetector and imaging application based on a perovskite single crystal,” Opt. Express 30(22), 40611 (2022). [CrossRef]
5. Z. Xie, S. Sun, X. Xie, et al., “Influence of TiO2 layer on ultimate efficiencies for planar and nano-textured CH3NH3PbI3 solar cells,” Mater. Res. Express 6(11), 115516 (2019). [CrossRef]
6. X. Ziang, L. Shifeng, Q. Laixiang, et al., “Refractive index and extinction coefficient of CH3NH3PbI3 studied by spectroscopic ellipsometry,” Opt. Mater. Express 5(1), 29 (2015). [CrossRef]
7. Z. Shi, D. Zhou, X. Zhuang, et al., “Light Management through Organic Bulk Heterojunction and Carrier Interfacial Engineering for Perovskite Solar Cells with 23.5% Efficiency,” Adv. Funct. Mater. 32(35), 1 (2022). [CrossRef]
8. M. I. Hossain, W. Qarony, M. Shahiduzzaman, et al., “Optics in high efficiency perovskite tandem solar cells,” in Comprehensive Guide on Organic and Inorganic Solar Cells: Fundamental Concepts to Fabrication Methods (2021).
9. A. Touré, A. Bouich, B. M. Soucasse, et al., “Investigation of the optoelectronics properties and stability of Formamidinium lead mixed halides perovskite,” Opt. Mater. 135, 113334 (2023). [CrossRef]
10. F. Mei, D. Sun, S. Mei, et al., “Recent progress in perovskite-based photodetectors: The design of materials and structures,” Adv. Phys.: X 4(1), 1592709 (2019). [CrossRef]
11. L. Su, T. Li, and Y. Zhu, “A vertical CsPbBr3/ZnO heterojunction for photo-sensing lights from UV to green band,” Opt. Express 30(13), 23330 (2022). [CrossRef]
12. F. Cao, Q. Liao, K. Deng, et al., “Novel perovskite/TiO2/Si trilayer heterojunctions for high-performance self-powered ultraviolet-visible-near infrared (UV-Vis-NIR) photodetectors,” Nano Res. 11(3), 1722–1730 (2018). [CrossRef]
13. A. M. Alamri, S. Leung, M. Vaseem, et al., “Fully inkjet-printed photodetector using a graphene/perovskite/graphene heterostructure,” IEEE Trans. Electron Devices 66(6), 2657–2661 (2019). [CrossRef]
14. F. Liu, J. Wang, L. Wang, et al., “Enhancement of photodetection based on perovskite/MoS2 hybrid thin film transistor,” J. Semicond. 38(3), 034002 (2017). [CrossRef]
15. W. Shao, J. Hu, and Y. Wang, “Five-layer planar hot-electron photodetectors at telecommunication wavelength of 1550 nm,” Opt. Express 30(14), 25555 (2022). [CrossRef]
16. F. P. García De Arquer, A. Armin, P. Meredith, et al., “Solution-processed semiconductors for next-generation photodetectors,” Nat. Rev. Mater. 2(3), 16100 (2017). [CrossRef]
17. S. Assefa, F. Xia, S. W. Bedell, et al., “CMOS-integrated high-speed MSM germanium waveguide photodetector,” Opt. Express 18(5), 4986 (2010). [CrossRef]
18. J. Hossain, M. M. A. Moon, B. K. Mondal, et al., “Design guidelines for a highly efficient high-purity germanium (HPGe)-based double-heterojunction solar cell,” Opt. Laser Technol. 143, 107306 (2021). [CrossRef]
19. W. Hu, H. Cong, W. Huang, et al., “Germanium/perovskite heterostructure for high-performance and broadband photodetector from visible to infrared telecommunication band,” Light: Sci. Appl. 8(1), 106 (2019). [CrossRef]
20. N. K. Pathak and R. P. Sharma, “Study of broadband tunable properties of surface plasmon resonances of noble metal nanoparticles using mie scattering theory: plasmonic perovskite interaction,” Plasmonics 11(3), 713–719 (2016). [CrossRef]
21. Y. X. Chen, C. L. Du, L. Sun, et al., “Plasmon nanoparticle effect to improve optical properties of perovskite thin film,” Photonics Nanostruct 43, 100888 (2021). [CrossRef]
22. Z. Yang, M. Jiang, L. Guo, et al., “A high performance CsPbBr3 microwire based photodetector boosted by coupling plasmonic and piezo-phototronic effects,” Nano Energy 85, 105951 (2021). [CrossRef]
23. B. Ai, Z. Fan, and Z. J. Wong, “Plasmonic–perovskite solar cells, light emitters, and sensors,” Microsyst. Nanoeng. 8(1), 5 (2022). [CrossRef]
24. D. Fu, J. Liu, X. Zhu, et al., “Exploring the effective photon management by InP nanoparticles: Broadband light absorption enhancement of InP/In0.53Ga0.47As/InP thin-film photodetectors,” J Appl Phys 117(20), 1 (2015). [CrossRef]
25. V. Mann and V. Rastogi, “FDTD simulation studies on improvement of light absorption in organic solar cells by dielectric nanoparticles,” Opt. Quantum Electron. 52(5), 233 (2020). [CrossRef]
26. D. Sharma, P. Kumari, A. Srivastava, et al., “Comparative Numerical Analysis of Broadband Light Trapping Structures Based on Plasmonic Metals Nanosphere and Silicon Nanopillar Arrays for Thin Solar Cells,” Plasmonics 18(2), 701–710 (2023). [CrossRef]
27. J. Wang, C. Chen, Y. Shao, et al., “Study of Extinction Characteristics of Au–Ag Nanosphere Periodic Array,” Lecture Notes in Electrical Engineering 543, 964–972 (2019). [CrossRef]
28. Y. Chen, C. Du, L. Sun, et al., “Improved optical properties of perovskite solar cells by introducing Ag nanopartices and ITO AR layers,” Sci. Rep. 11(1), 14550 (2021). [CrossRef]
29. B. Jose, R. K. Vijayaraghavan, L. Kent, et al., “Tunable metallic nanostructures using 3D printed nanosphere templates,” Electrochem. Commun. 98, 106–109 (2019). [CrossRef]
30. J. S. Manser, M. I. Saidaminov, J. A. Christians, et al., “Making and Breaking of Lead Halide Perovskites,” Acc. Chem. Res. 49(2), 330–338 (2016). [CrossRef]
31. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983). [CrossRef]
32. J. Wang and Y. Sheng, “Thin Metal Superlens Imaging in Nanolithography,” Int J Opt 2019, 1–6 (2019). [CrossRef]
33. A. D. Yaghjian, “Internal energy, Q-energy, Poynting’s theorem, and the stress dyadic in dispersive material,” IEEE Trans. Antennas Propag. 55(6), 1495–1505 (2007). [CrossRef]
34. V. E. Ferry, L. A. Sweatlock, D. Pacifici, et al., “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008). [CrossRef]
35. K. Aydin, V. E. Ferry, R. M. Briggs, et al., “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2(1), 517 (2011). [CrossRef]
36. H. Kocer, S. Butun, Z. Li, et al., “Reduced near-infrared absorption using ultra-thin lossy metals in Fabry-Perot cavities,” Sci. Rep. 5(1), 8157 (2015). [CrossRef]
37. S. Haque, M. J. Mendes, O. Sanchez-Sobrado, et al., “Photonic-structured TiO 2 for high-efficiency, flexible and stable Perovskite solar cells,” Nano Energy 59, 91–101 (2019). [CrossRef]
38. ASTM, “Standard Tables for Reference Solar Spectral Irradiances : Direct Normal and Hemispherical on 37° Tilted Surface,” G173-23 (Reapproved), (2023).
39. J. Wang and Y. Sheng, “Computer-Generated Very Large Space-Bandwidth Product Binary Hologram for Laser Projector,” IEEE Trans. Ind. Inf. 12(1), 179–186 (2016). [CrossRef]
40. L. Sun, R. X. Zhang, C. L. Du, et al., “Optical optimization of ultra-thin crystalline silicon solar cells by a co-simulation approach of FEM and GA,” Appl. Phys. A 127(7), 558 (2021). [CrossRef]
