Inverse Design of Wavelength-Selective Film Emitter for Solar Thermal Photovoltaic System

Abstract

Solar photovoltaic (PV) technology is developing quickly due to the continual rise in demand for energy and environmental protection. Solar thermal photovoltaic (STPV) systems can break the Shockley–Queisser limit of conventional PV systems by reshaping the solar spectrum using selective absorbers and emitters. However, the traditional design method relies on the designer’s experience, which fails to achieve rapid designing of STPV devices and greatly improve the performance. In this paper, an STPV thin-film selective emitter is inversely designed based on a genetic algorithm. The optimized structure consists of SiO₂ and SiC layers alternately stacked on a Cr substrate, whose emissivity can reach 0.99 at 1.86 μm. When combined with an InGaAsSb cell, the power conversion efficiency can be up to 43.3% at 1673 K. This straightforward and easily scalable film emitter can be designed quickly and gain excellent efficiency, which promotes the practical application of STPV systems.

1. Introduction

With the increasing demand for energy and environmental protection, solar photovoltaic (PV) power generation has developed rapidly in recent years [1,2,3]. The efficiency of conventional solar cells is limited by the Shockley–Queisser (SQ) limit, i.e., the maximum conversion efficiency of an ideal single-junction cell cannot exceed 33% under one sun of normal incident radiation with a power of 100 mW/cm² [4]. The main reason for this limitation is the inherent spectral mismatch between solar radiation and the bandgap of PV cells [5,6]. Photons with energy lower than the bandgap of a PV cell cannot be absorbed, while photons with energy higher than the bandgap cannot be absorbed completely, with excess energy dissipated as heat [7]; both result in lower power conversion efficiency. At present, STPV systems are an effective solution to improve the power conversion efficiency of PV cells and then break the SQ limit [8,9]. STPV systems convert broadband solar radiation into narrowband thermal radiation above the cell bandgap through selective absorbers and emitters.

Due to its ability to improve the efficiency of STPV systems, the wavelength-selective emitter has attracted extensive attention in recent years and has been realized through metamaterials [10,11], metasurfaces [12,13], photonic crystals [14,15], etc. Yuan et al. [10] proposed a selective metamaterial emitter with a centrally symmetric tantalum strip, which can achieve 40.34% power conversion efficiency when matched with an InGaAsSb cell. Cui et al. [13] designed a Mo-based gratings emitter, resulting in a high PV cell efficiency of 41.8% around 1723 K. Abbas et al. [16] achieved 21% power conversion efficiency by using Cr nanocylindrical arrays to form a selective absorber and emitter. Rana et al. proposed selective absorbers and emitters composed of cross-shaped Ta [17] and Cr [11], achieving 41.8% and 43.2% photoelectric conversion efficiencies, respectively. However, these structures are complex, thereby requiring a high-precision and low-efficiency lithography fabrication process, hindering their practical applications. To address these challenges, researchers began to design multilayer emitters, which are a simpler and more scalable fabrication. Lin et al. [14] proposed a multilayer membrane selective emitter matched with InGaAs and realized an efficiency of 33.7% based on Tamm plasmon polaritons (TPPs) consisting of alternating layers of HfO₂ and SiO₂ stacked on a Mo substrate. Zhao et al. [15] proposed a double-junction thermophotovoltaic system based on multilayer membrane emitters of TPPs, achieving a maximum system efficiency of 19.36%. These multilayer film emitters not only exhibit excellent spectral control but also are cost-effective and scalable for large-area fabrication, making them a promising alternative to complex metasurface and metamaterial designs.

Nevertheless, these designs using metasurfaces or films predominantly rely on the traditional forward design method, which optimizes the structure based on empirical knowledge and time-consuming parameter sweeps. To break these limits, researchers have started to use deep learning and genetic algorithms (GAs) to design STPV systems automatically [18]. Noureen et al. [19] proposed a hybrid deep learning model to accurately design metasurface-based absorbers and emitters for wavelength selection. Jiang et al. [20] optimized a solar absorber with a double-layer cylindrical array embedded in a metasurface structure based on a GA, which achieved a high absorptivity of 93% in the solar spectrum and a low emissivity of 21% in the mid-infrared band. Hu et al. [21] optimized the thickness and arrangement order of the layers of an emitter by a machine learning algorithm. The inverse design process, eliminating the need for time-consuming parameter scanning and a strong theoretical analysis ability among researchers, instead automatically generates the optimal structural parameters based on the desired optical response. However, the materials in these structures are still chosen based on experience, which only achieves inverse design of structural dimension parameters for pre-specified materials. This restriction reduces the design freedom and may limit further performance improvement.

In this paper, we use a GA to inversely design a wavelength-selective film emitter for the STPV system. The material and thickness of each layer, the period of the distributed Bragg reflector (DBR) and the number of cavities can be optimized simultaneously. The optimal structure consists of SiO₂ and SiC layers alternately stacked on a Cr substrate. The emissivity is as high as 0.99 at 1.86 μm, and the power conversion efficiency is up to 43.3% when combined with an InGaAsSb cell under one sun of normal incident radiation. This simple and easily fabricated film emitter is designed quickly and gains excellent efficiency, which breaks the limits of experts’ experience and promotes the practical application of STPV systems.

2. Model and Method

2.1. Target Spectra and Structure

A schematic diagram of the STPV system is shown in Figure 1a, consisting of a concentrator, absorber, emitter, PV cell and thermal management system. First, the absorber absorbs the solar radiation concentrated by the concentrator and converts it into thermal energy. Then, the absorber and emitter are heated, and the emitter transfers thermal energy to the PV cell by re-emitting photons. Finally, the photovoltaic cell absorbs photons larger than the bandgap energy and forms electron–hole pairs to generate electrical energy. The InGaAsSb cell is used as an example in this study. The green curve in Figure 1b is the external quantum efficiency (EQE) [10,22] of the InGaAsSb cell, which indicates the probability that the PV cell absorbs photons with a wavelength of λ and produces electrons. The EQE increases rapidly with an increase in λ, reaching a maximum at 1.3 μm, and then slowly decreases in the range of 1.3–2.1 μm and rapidly decreases to 0 after 2.1 μm. It can be seen that the cut-off band of the InGaAsSb cell is about 2.3 μm. The blue and magenta dashed lines show the spectral emissive power of the blackbody at 1300 K and 1500 K, respectively, which is mainly concentrated in the near-infrared band. According to the EQE of the InGaAsSb cell, it is known that photons with wavelengths greater than 2.3 μm cannot be effectively used. Therefore, to match well with the InGaAsSb cell and achieve efficient conversion of the radiation energy, it is necessary to use a selective emitter to reshape the radiation spectrum so that the thermal radiation from the emitter can be concentrated below 2.3 μm [23]. The red curve shows the ideal spectrum of the emitter, which has a high emissivity of 1 in the wavelength range [λ₁, λ₂] below the bandgap wavelength of the PV cell and 0 outside of this range [22,24].

In an STPV system, a selective emitter is a key component for improving the power conversion efficiency of PV cells. Complex metasurface structures are not conducive to large-scale fabrication, so a multilayer thin-film emitter based on TPPs is designed in this paper. A schematic diagram of the Tamm plasmon film structure is shown in Figure 2, consisting of a highly reflective DBR, a cavity and a highly reflective metal substrate from top to bottom. The DBR consists of alternating layers with two different materials, m₁ and m₂. The material of the metal substrate is denoted by m₃. The period of the DBR is labeled as p, with a range from 1 to 10. The number of cavity layers is denoted by n, which is taken from 0 to 2. When n = 0, it denotes the conventional DBR structure. When n = 1 and n = 2, it denotes a monolayer cavity-enhanced and a bilayer cavity-enhanced Tamm plasmon (TP) structure, respectively [25].

Considering the high-temperature operating environment of the STPV system, all materials selected should have high-temperature stability. Therefore, we build a self-built material library including 10 alternative materials (Al₂O₃, AlN, HfO₂, Si₃N₄, SiC, SiO₂, TiO₂, ZrO₂, TiN and Cr₂O₃) for the DBR and 5 alternative materials (Cr, Mo, Re, Ta and W) for the metal substrate, which are labeled as the top material library (TML) and substrate material library (SML), respectively. These materials are commonly used and have high-temperature stability. The two materials of the top DBR are randomly chosen from the TML by randomly generating numbers between 1 and 10, which leads to $A_{10}^2$= 90 potential candidate material combinations. The material of the substrate is randomly chosen from the SML. The material of the cavity is the same as that of the DBR. The optical constants of the materials in the TML and SML were acquired from references [26,27,28,29,30,31,32,33] and references [22,34,35], and the data after interpolated processing are shown in Table S1 in the Supplementary Material. The substrate thickness should be greater than the skinning depth of the metal to ensure that the electromagnetic wave transmission is zero; it is set to 100 nm in this paper. The thicknesses of the two DBR materials are denoted by d₁ and d₂, the thickness of the monolayer cavity is denoted by d₃, and the thicknesses of the bilayer cavities are denoted by d₃ and d₄, respectively. The thicknesses d₁, d₂, d₃ and d₄ are randomly generated in the range between 100 nm and 500 nm.

2.2. Performance Evaluation

The performance of the STPV emitter is closely related to the power conversion efficiency of the PV cell. The efficiency of the PV cell, η_PVC, is affected by the photoelectric conversion process, the transport process of photogenerated carriers and the load matching. η_PVC is related to the spectral conversion efficiency U_eff, the depreciation factor V_eff and the impedance matching Im(V_op), and it is calculated as follows [4]:

(1)${\eta }_{\mathrm{PVC}}=U_{\mathrm{eff}}\cdot V_{\mathrm{eff}}\cdot \mathrm{Im}(V_{\mathrm{op}})$

During the photoelectric conversion process, only energy greater than the cell bandgap E_g can be converted into electron–hole pairs, where U_eff is the ratio of the useful power P_{emit, E≥Eg} to the total power P_emit emitted into the PV cell from the emitter [6]:

(2)$U_{\mathrm{eff}}={\displaystyle \frac{P_{\mathrm{emit}, E\ge E_{\mathrm{g}}}}{P_{\mathrm{emit}}}}={\displaystyle \frac{{\displaystyle {\int }_0^{2\pi }d\phi {\displaystyle {\int }_0^{\frac{\pi }{2}}\sin (\theta )\cos (\theta )d\theta {\displaystyle {\int }_{E_{\mathrm{g}}}^{\infty }{\epsilon }_{\mathrm{emit}}(E,\theta ,\phi )I_{\mathrm{BB}}(E,T_{\mathrm{emit}})\frac{E_{\mathrm{g}}}{E}dE}}}}{{\displaystyle {\int }_0^{2\pi }d\phi {\displaystyle {\int }_0^{\frac{\pi }{2}}\sin (\theta )\cos (\theta )d\theta {\displaystyle {\int }_0^{\infty }{\epsilon }_{\mathrm{emit}}(E,\theta ,\phi )I_{\mathrm{BB}}(E,T_{\mathrm{emit}})dE}}}}}$

where ε_emit(E,θ,φ) is the spectral emissivity of the emitter, and T_emit is the operating temperature of the emitter. I_BB(λ,T) = 2hc²/λ⁵/(e^hc/kT − 1) is the spectral radiance intensity of the blackbody, where h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant and T is the blackbody temperature.

During the transport process of photogenerated carriers, the open-circuit voltage V_op is the maximum voltage that can be output from the PV cell. When the temperature of the PV cell is 0 K, V_op = V_g [4]. V_g is the bandgap voltage of the PV cell, and V_g = E_g/q, where q is the electron charge. As the temperature increases, carrier recombination accelerates, the bandgap of the PV cell narrows and V_op decreases, resulting in open-circuit voltage loss V_eff [36,37]:

(3)$\begin{array}{c}{V}_{\mathrm{eff}}={\displaystyle \frac{V_{\mathrm{op}}}{V_{\mathrm{g}}}}={\displaystyle \frac{V_{\mathrm{c}}}{V_{\mathrm{g}}}}\ln ({\displaystyle \frac{f{P}_{\mathrm{emit}, E\ge E_{\mathrm{g}}}}{P_{\mathrm{c}, E\ge E_{\mathrm{g}}}}})\hfill \\ \hspace{1em} ={\displaystyle \frac{V_{\mathrm{c}}}{V_{\mathrm{g}}}}\ln \left[f{\displaystyle \frac{{\displaystyle {\int }_0^{2\pi }d\phi {\displaystyle {\int }_0^{\frac{\pi }{2}}\sin (\theta )\cos (\theta )d\theta {\displaystyle {\int }_{E_{\mathrm{g}}}^{\infty }{\epsilon }_{\mathrm{emit}}(E,\theta ,\phi )I_{\mathrm{BB}}(E,T_{\mathrm{emit}})\frac{E_{\mathrm{g}}}{E}dE}}}}{{\displaystyle {\int }_0^{2\pi }d\phi {\displaystyle {\int }_0^{\frac{\pi }{2}}\sin (\theta )\cos (\theta )d\theta {\displaystyle {\int }_{E_{\mathrm{g}}}^{\infty }{\epsilon }_{cell}(E,\theta ,\phi )I_{\mathrm{BB}}(E,T_{\mathrm{c}})\frac{E_{\mathrm{g}}}{E}dE}}}}}\right]\hfill \end{array}$

where T_c is the operating temperature of the PV cell, taken as 300 K. f is a non-ideal factor related to the planar geometry of the PV cell and emitter, taken as 0.5 [16,17].

When the PV cell is connected to the load, if the output impedance of the battery does not match the input impedance of the load, impedance matching loss will occur. The impedance matching factor Im(V_op) is the ratio of the maximum output power to the nominal power, which can be described as follows [37]:

(4)$\mathrm{Im}(V_{\mathrm{op}})={\displaystyle \frac{Z_{\mathrm{m}}^2}{(1+Z_{\mathrm{m}}-e^{-Z_{\mathrm{m}}})(Z_{\mathrm{m}}+\ln (1+Z_{\mathrm{m}}))}}$

where Z_m is related to Z_op by Z_op = Z_m + ln(1 + Z_m), and Z_op = V_op/V_c. V_c is the thermal voltage of the PV cell, and V_c = kT_c/q.

2.3. Inverse Design

GA is an optimization algorithm based on the concepts of evolution and natural selection [38,39,40,41], which has a great advantage in dealing with multi-objective optimization problems. In this study, we use MATLAB R2021b software to implement the GA-based inverse design of the STPV emitter, and a flowchart of the GA is sh own in Figure 3. (1) First, the size of the initial population, N, is set to 1000, and the population is randomly initialized. According to Section 2.1, there are nine parameters to be optimized. Each individual consists of three materials (m₁, m₂ and m₃), four thicknesses (d₁, d₂, d₃ and d₄, taken as 100 to 500 nm in steps of 5 nm), the period p of the DBR (taken as 1 to 10 in steps of 0.5) and the number of cavities n (taken as 0 to 2), selected randomly. Each individual is defined by a 46-bit binary string, in which the four thicknesses, the period p, the number of cavities n and the two materials of the DBR and substrate are represented by 7-bit × 4, 5-bit, 2-bit, 4-bit × 2 and 3-bit binary numbers, respectively. For example, as d₁ is changed from 100 nm to 500 nm with step sizes of 5 nm, there are 81 possible thickness values. The thickness d₁ is encoded by a 7-bit binary number, which can represent 2⁷ = 128 distinct values. Therefore, dd₁ = randi(81) is used to randomly generate an integer between 1 and 81. If dd₁ = 4, it is converted to a 7-bit binary number, 0000100, and added to the individual. (2) Second, the binary population is converted to a decimal population. For dd₁, for example, 0000100 is converted to 4. Then, it is mapped to the thickness d₁ = 100 + (dd₁ − 1) × 5. (3) Third, the emissivity is calculated by the transfer matrix method (TMM) based on the nine randomly generated parameters [21]. (4) Fourth, the key indicator of power conversion efficiency, η, is calculated based on the acquired emissivity, which is usually used to indicate the performance of solar thermal photovoltaic systems. But η increases a little as the temperature increases. To comprehensively evaluate the performance of the system and ensure quantitative comparisons between different designs in the inverse design, the figure of merit (FOM) is defined as the average power conversion efficiency of a PV cell when the operating temperature of the emitter changes from 1073 K to 1673 K with change intervals of 100 K; it is calculated as follows [21]:

(5)$\mathrm{FOM}={\overline{\eta }}_{\mathrm{PVC}}={\displaystyle \frac{{\displaystyle \sum _{i=1073K}^{1673K}{\eta }_{\mathrm{PVC}}\left(i\right)}}{\mathrm{Numbers} \mathrm{of} i}}$

This temperature range between 1073 K and 1673 K is the usual operating temperature of the emitter [13,16,42]. The higher the FOM is, the better the emitter and the solar thermal photovoltaic system are. Therefore, the FOM is set as the fitness function of the GA in this paper, which is utilized for quantitative comparisons and optimization. It is worth noting that the efficiency η just changes a little at different temperatures. Therefore, it is also feasible to use the efficiency η at a certain fixed temperature as a fitness function for the GA.

(5) Finally, a new generation of populations in binary is generated by genetic manipulation through roulette wheel selection, single-point crossover and basic bit mutation based on the FOM value. (i) Roulette wheel selection [43]: The probability of selecting an individual is proportional to its FOM value, ensuring that individuals with higher FOM values are more likely to be selected. The FOM of all individuals is cumulatively summated and then normalized. By repeatedly spinning the roulette wheel, individuals are chosen using stochastic sampling with replacement to fill the intermediate population. The operation progress is the same as that in Lipowski’s work [43]. (ii) Single-point crossover [44]: If a randomly generated number between 0 and 1 is less than the crossover probability, then single-point crossover is performed. The operation process of single-point crossover is the same as in Whitley’s work [44]. In our work, the pairwise crossover of the 1000 individuals requires 500 cycles. It is worth noting that each individual contains nine parameters, so the corresponding binary numbers need to be crossed separately at 9 randomly generated crossover points within every cycle. The crossover probability is set to 0.7. (iii) Basic bit mutation [45]: If a randomly generated number between 0 and 1 is less than the mutation probability, then the bit at the randomly generated mutation points is flipped. It is worth noting that this stochastic process is performed for each parameter of each individual. The mutation probability is set to 0.4. This introduces diversity into the population and helps avoid premature convergence to local optima.

When the maximum number of iterations of 100 is reached, or when the change in the FOM is less than 1 × 10⁻³ for 25 consecutive generations, the iteration is stopped and the optimal result is output.

3. Results

3.1. Results of Inverse Design

Considering all the parameters to be optimized, the emitter designed in this paper has 10 × 9 × 5 × 19 × (81² + 81³ + 81⁴) = 3.7 × 10¹¹ potential candidate structures. With an intel core i7-RTX3050Ti CPU, the optimal emitter was inversely designed after 14.25 h and 100 iterations and is shown in Figure 4a. The optimized emitter is a five-layer structure without a cavity (n = 0), consisting of SiO₂ and SiC layers alternately stacked on a Cr substrate. The period of the DBR structure is two. The thicknesses of the layers are d₁ = 165 nm and d₂ = 185 nm. The red line in Figure 4b is the emissivity of the optimized emitter, which has a peak with an emissivity of 0.99 and a full width at half-maximum (FWHM) of 550 nm at 1.86 μm. The emissivity gradually decreases after 1.86 μm and is lower than 0.2 after 2.6 μm, which means that the loss of sub-bandgap photon energy can be effectively reduced. The blue line in Figure 4b is the simulated result using the finite difference time domain (FDTD) method, which shows an excellent agreement with the result of the TMM and verifies its accuracy. Figure 4c shows that the max FOM gradually increased from 0.291 to 0.385 as the number of iterations increased, and it remained constant when the number of iterations was greater than 80. Figure 4d shows the emissivity in different generations. The initial population had an emissivity peak of 1.82 μm with an intensity of 0.41. As the number of iterations increased, the emissivity intensity gradually increased, with the peak wavelength shifting a little. The peak intensity values at 1.86 μm in the 20th generation, 1.82 μm in the 40th generation and 1.81 μm in the 60th generation were 0.62, 0.69 and 0.82, respectively. Finally, the peak stabilized at 1.86 μm with an emissivity of 0.99 after the 80th generation.

3.2. Electromagnetic Field and Robustness of the Structure

To further investigate the potential physical mechanisms, Figure 5 shows the normalized electric and magnetic field distributions in the x-z plane of the emitter at 1.86 μm. Figure 5a,b show that the electric field is localized in the SiC layer. Figure 5b,c indicate that the magnetic field concentrates at the interface between the metal substrate and the SiC layer. The nodes of the electric field coincide with the antinodes of the magnetic field and vice versa. The high absorptivity at 1.86 μm is attributed to resonant interference and the excitation of the highly localized resonance of the TPPs [46,47].

The macroscopic optical performance of multilayer devices is determined by the thickness of their layers, and errors are inevitable during the actual fabrication process. Therefore, it is important to study the influence of geometric parameter changes on the emitter’s performance. Figure 6 shows the emissivity and FOM of the emitter under different thicknesses. In Figure 6a, as the thickness of the SiO₂, d₁, increases from 145 nm to 185 nm while the thickness of the SiC, d₂, is fixed at 185 nm, the emission bandwidth and intensity are unchanged while the peak slightly redshifts. Figure 6b shows that the corresponding FOM value increases and then decreases, reaching a maximum value of 0.385 when d₁ = 165 nm. The FOM drops by only 1% when d₁ varies by ±20 nm. In Figure 6c, as the thickness of the SiC, d₂, increases from 165 nm to 205 nm while the thickness of the SiO₂, d₁, is fixed at 165 nm, the emission bandwidth remains essentially unchanged, but the emission intensity decreases a little and the emissivity peak redshifts. Figure 6d shows that the FOM decreases by 4% at most when d₂ varies by ±20 nm during fabrication. To further analyze the combined effects, Figure 6e,f present the dependence of the emissivity and FOM on variations in d₁ and d₂ simultaneously. In Figure 6e, the emission peak exhibits a redshift when d₂ increases, regardless of the variation in d₁. This indicates that d₂ plays a dominant role in determining the optical thickness and the resulting spectral response of the device. Figure 6f shows the FOM at different d₁ and d₂. The red star represents the largest FOM value of 0.385, corresponding to d₁ = 165 nm and d₂ = 185 nm. When d₁ and d₂ are 145 nm and 205 nm, respectively, the FOM reaches its minimum value of 0.367, with a 4.7% decrease compared to the largest value. This decrease is also acceptable and just a little bigger than 4% in Figure 6d. Therefore, the average efficiency FOM is hardly changed when the thickness d₁ or d₂ is varied by ±20 nm alone or simultaneously. This structure exhibits robustness regarding the interface quality, including non-ideal interface abruptness and interface roughness, with an error tolerance of within 20 nm, as shown in Section S2 in the Supplementary Materials.

3.3. Angle Independence of the Emitter

In practical applications, the robustness of the emitter to the angle of incidence and polarization is important. As shown in Figure 7a, the emissivity of the emitter remains constant at different polarization angles from 0 to 90°, showing good robustness. Figure 7b,c show the emissivity of the emitter at different incident angles in the transverse magnetic (TM) and transverse electric (TE) wave modes, respectively. As the angle of incidence increases to 60°, the bandwidth of the peak remains constant and the peak wavelength blueshifts slightly. The intensity of the emissivity peak is always higher than 0.9 when the angle of incidence is increased to 60°. Figure 7d shows that the FOM decreases with an increase in the incident angle but is always above 0.345. The maximum reduction rate is 9.6%. In general, the optimized film structure is very insensitive to incident and polarization angles, which is attributed to the symmetry of the structure and excitation of the TPP mode.

4. Discussion

Figure 8 reveals the efficiency of the designed emitter at different temperatures when combined with the InGaAsSb cell. It can be seen that V_eff, Im(V_op) and η_PVC all increase with increasing temperature, and Im(V_op) has the smallest variation. U_eff increases and then decreases with increasing temperature, reaching a maximum value of 0.624 at 1373 K. The average values of U_eff, V_eff, Im(V_op) and η_PVC between 1073 and 1673 K are 0.591, 0.826, 0.786 and 0.385, respectively. The power conversion efficiency is up to 43.3% when combined with an InGaAsSb cell under one sun of normal incident radiation. This high efficiency indicates the excellent spectral matching between our selective emitter and the InGaAsSb cell, which minimizes sub-bandgap photon losses and maximizes the conversion of solar energy into electrical energy. This is conducive to energy savings and environmental protection.

Table 1 presents a comprehensive comparison between the proposed emitter and those in previously reported works. Our proposed emitter features a high efficiency of 43.3%, only lower than that in Zhou’s work [48]. Compared with other structures [10,11,13,16,17,48,49,50,51,52], our designed film emitter is simpler, does not need high-precision lithography and is easy to fabricate and scale. This performance improvement can be attributed to the advanced inverse design method employed in this work, which simultaneously optimizes multiple parameters, including the material selection and geometric configuration. In Table 1, all the materials have high-temperature stability, but only some designs have incidence and polarization insensitivity.

5. Conclusions

In this paper, we used a GA to inversely design an STPV thin-film emitter by simultaneously optimizing the material, the thickness of each layer, the period of the DBR and the number of cavities. From searching in a huge space of about 3.7 × 10¹¹, the final optimized emitter consists of a five-layer structure with alternating SiO₂ and SiC stacked on a Cr substrate, which exhibits good selectivity with an emissivity of up to 0.99 at 1.86 μm. When the emitter is combined with an InGaAsSb cell, the power conversion efficiency at 1673 K is as high as 43.3%, which is better than the performance of metasurface emitters [11,13,16,17]. Additionally, this structure is insensitive to fabrication errors in the range of ±20 nm, the incident angle to 60° and the polarization angle to 90°. Compared with the Cr nanocylindrical array proposed by Abbas [16] in 2022, our efficiency has doubled. Besides this, our film emitter is as thin as 800 nm. The design method reduces the stringent requirements on the knowledge and experience of designers, and the optimized structure is not only simple and scalable with low-cost manufacturing but also easy to integrate into the STPV system; this improves the design efficiency and system performance and thus promotes the practical application of STPV systems.

Author Contributions

Conceptualization, W.L. and Y.L.; methodology, W.L.; software, W.L.; validation, Y.L., W.L. and Q.C.; formal analysis, W.L.; investigation, W.L.; resources, Q.C.; data curation, D.Y.; writing—original draft preparation, W.L.; writing—review and editing, Y.L.; visualization, D.Y.; supervision, Y.L. and Y.C.; project administration, Y.L. and Y.C.; funding acquisition, Y.L. and Y.C. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Table

Figure 1. (a) Schematic diagram of the STPV system; (b) EQE of the InGaAsSb cell, blackbody radiation spectra at different temperatures, and the ideal emissivity of the emitter.

Figure 2. A schematic diagram of the emitter to be optimized.

Figure 3. Flowchart for inverse design of STPV emitter based on GA.

Figure 4. (a) A structural diagram and (b) the emissivity of the final optimized emitter; (c) the max FOM of the population and (d) corresponding emissivity in different generations.

Figure 4. (a) A structural diagram and (b) the emissivity of the final optimized emitter; (c) the max FOM of the population and (d) corresponding emissivity in different generations.

Figure 5. (a) The electric field intensity distribution along the z-direction at 1.86 μm; (b) the normalized electric field and (c) magnetic field distribution in the x-z plane at 1.86 μm.

Figure 6. (a) The emissivity and (b) FOM of the emitter under different thicknesses d1 with fixed d2; (c,d) are for different thicknesses d2 with fixed d1; (e,f) are for different d1 and d2. The red star represents the largest FOM value at d1 = 165 nm and d2 = 185 nm.

Figure 7. (a) Emissivity at different polarization angles; emissivity for (b) TE mode and (c) TM mode at different incident angles and (d) corresponding values of FOM.

Figure 8. Efficiency of the emitter at different temperatures.

Table 1

Comparisons of the function of the proposed device with that of other previously published devices.

Ref.	Structure Type	Materials	η PVC	Insensitivity
				Incident Angle	Polarization Angle
[13]	Gratings	Mo	41.8% (1723 K)	×	×
[10]	Strip array	Ta and SiO2	40.34% (1500 K)	√	√
[11]	Cross-shaped	Cr and Cr2O3	43.2% (1597~2573 K)	√	√
[49]	Square array	W	Not reported	×	×
[48]	3-layer shaped Ta	Ta	43.5% (1673 K)	√	√
[50]	Nanocylinder	Ta	32.3% (1700 K)	√	√
[51]	Not reported	Not reported	33.93% (1700 K)	×	×
[16]	Nanocylinder arrays	Cr and SiO2	21% (1573 K)	√	√
[17]	Cross-shaped	Ta and SiO2	39.13% (1673 K)	√	√
[52]	Sphere arrays	W and SiO2	28.2% (1425 K)	×	×
This work	Multilayer film	Cr, SiC and SiO2	43.3% (1673 K)	√	√

“×” and “√” means sensitivity and insensitivity respectively.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/photonics12030286/s1. Figure S1: (a) The structure diagram after introducing the transition layer; (b) FOM at different thicknesses of the transition layer; Figure S2: (a) The simulation interface in FDTD for simulated roughness; (b) FOM at different RMS; Figure S3: (a,c) Emissivity and (b,d) FOM of the emitter under different period p of DBR and the numbers of the cavity n, respectively; Table S1a,b,c: The optical constants of the materials used in TML and SML; Table S2: Parameters of three transition layers of T₁, T₂, T₃.

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