Theoretical Analysis of InGaN Solar Energy Converters Based on Photon-Enhanced Thermionic Emission

Abstract

Photon-enhanced thermionic emission (PETE) is an efficient solar energy conversion mechanism that combines photovoltaic effects and thermionic emissions. In this study, a diffusion–emission model of electrons for the InGaN cathode was deduced based on one-dimensional continuity equations. The temperature dependence of the excess electron concentration, current density, and conversion efficiency at different cathode electron affinities was simulated, and the performance of the PETE converter under isothermal and nonisothermal state was compared. The results show that the improvement in conversion efficiency under isothermal condition was limited by the increase in anode temperature and reached the maximum of ~22% at an electron affinity of 0.56–0.59 eV and the operating temperature of 710–740 K. When the anode temperature was 500 K, the conversion efficiency increased with the increase in the electron affinity and exceeded the maximum value of the isothermal state at 0.6 eV. We explored the behavior of the converter at bias voltages as well as the determination of the maximum conversion efficiency point. The open-circuit voltage in the isothermal state was lower than that in the nonisothermal state, and the output voltage at the maximum conversion efficiency was eventually greater than the flat-band voltage.

1. Introduction

Solar energy is one way to replace traditional energy, and improving its conversion efficiency is a key research field. Photovoltaic power generation and solar thermal power generation are two widely studied conversion technologies in this field, but their conversion efficiencies are limited by the inherent characteristics of their own structures and materials [1,2]. The direct combination of a photovoltaic system and a solar heat converter has been found to achieve a theoretical efficiency of more than 60% [3]. However, the two technologies conflict in operating temperature, which makes them difficult to implement in practice [4,5].

In order to solve the above problems and improve solar energy conversion, it is necessary to combine the photovoltaic effect with thermionic emission. In 2004, Smestad proved that both light and heat from solar energy can be converted into electricity at the same time through illustrative experiments using vacuum diodes [6]. In 2010, Schwede et al. proposed the photon-enhanced thermionic emission (PETE) conversion concept in order to combine the two conversion mechanisms into a single physical process [7]. Using a structure similar to the vacuum thermionic energy converter (VTEC) and using a semiconductor cathode, the PETE converter could effectively take advantage of the thermal loss caused by low-energy photons in the solar spectrum, theoretically breaking the Shockley–Queisser (SQ) limit and achieving an efficiency of over 40% [7,8].

Since the PETE theory was proposed, researchers have continually explored the structure of the PETE converter in order to optimize its performance. Segev et al. designed a multistage series solar cell based on PETE, which could achieve an efficiency of 30–40% in isothermal state, and was better than the thermionic converter, which needed to maintain the temperature difference between the anode and the cathode [9]. They also demonstrate that the ultimate efficiency of single-bandgap PETE converters in the isothermal state is still limited by the SQ limit, which can be exceeded by nonisothermal operation [10]. Wang et al. explored the limitation of the space charge effect on the PETE converter and found that the conversion efficiency can be effectively improved with a suitable interelectrode space [11,12]. Qiu et al. combined the PETE converter with a Stirling heat engine and modeled the hybrid system with full consideration of optical, electrical, and thermodynamic processes. Through simulation analysis, for 500 solar concentrations, the output power of the hybrid system could reach 162.65 KW/m² with a conversion efficiency of 32.77% [13].

Regarding the selection of cathode materials, previous studies have shown that III–V semiconductors have good PETE properties but are concentrated on GaAs-based materials [14,15,16,17]. Both GaN and InN have been applied to PETE converter cathodes, while cathodes based on InGaN ternary compounds have not yet been attempted [7,18]. The bandgap of InN is 0.7 eV, and that of GaN is 3.4 eV [19]. The ternary compound InGaN formed by these two compounds can achieve an adjustable bandgap of 0.7–3.4 eV by changing the composition of In, which can cover most of the solar spectra [20]. Additionally, InGaN is widely studied in the field of high-temperature solar cells. Huang et al. found that InGaN-based solar cells would have a self-cooling effect at high temperatures, which is helpful for improving performance [21]. Moses et al. explored the performance of InGaN solar cells at high solar concentrations and high temperatures. Through experimental research, for 300 solar concentrations, the conversion efficiency peaked at 623–723 K, and InGaN maintained good stability at high temperature [22]. In addition, InGaN has a high absorption coefficient and can effectively utilize sunlight [23]. Based on the above characteristics, InGaN was selected as the cathode for the PETE converter.

In this study, the structure of a vacuum PETE converter was used to establish the temperature difference between anode and cathode. Based on the one-dimensional steady-state continuity equation, the performance of converters in isothermal and nonisothermal operations was analyzed and compared. In the calculation, we considered the change in the bandgap of the InGaN cathode with temperature and simulated the temperature dependence of excess electron concentration, current density, and conversion efficiency for different cathode electron affinities. In addition, the reason why the open-circuit voltage of the converter was higher than that of the nonisothermal operation is analyzed. We investigate the behavior of the PETE converter under applied bias at different cathode temperatures and further determine the point of maximum conversion efficiency.

2. Theoretical Model

2.1. Structure and Principle

Figure 1a shows the structure of the PETE solar converter. The cathode and the anode are arranged in a thermionic converter structure, parallel to the vacuum chamber, and sunlight is concentrated on the cathode through the Fresnel lens. It is assumed that there is a functional layer on the surface of the cathode that can absorb photons with less energy than the cathode bandgap so as to raise the temperature of the cathode and thermalize the conduction band electrons [5,24]. In the case of flat-band voltage, the external load is connected to the cathode and the anode, forming a complete loop. In addition, the load can be replaced by an applied bias. When the anode is connected to the positive electrode and the cathode is connected to the negative electrode, the converter operates in the negative bias state; when configured conversely, the converter operates in the positive bias state.

When the vacuum levels of the cathode and the anode are in the same position, the energy band diagram of the PETE converter is as shown in Figure 1b. The PETE conversion process can be divided into three steps: (ⅰ) at the incident interface, the low-energy photon is absorbed by the functional layer and provides infrared thermal energy to the cathode, while the high-energy photons excite the valence band electrons to the conduction band and rapidly relax to the conduction band minimum, which increases the electron concentration at the incident interface; (ⅱ) the uneven distribution of conduction band electrons in the cathode creates a concentration difference, driving electrons to the emission surface, a process that is accompanied by the recombination of electrons and holes; and (ⅲ) at the emission surface, the thermal energy transferred by the functional layer enables electrons to overcome the electron affinity of the cathode and be emitted into the vacuum, and finally the electrons are collected by the anode.

2.2. Calculation Model

Under the condition of low injection, the concentration of excess electron is less than the equilibrium concentration of the hole in the cathode, and the analytical solution exists in the one-dimensional steady state model. Although the one-dimensional continuity model is also suitable for medium-high-injection conditions, approximate solutions can only be obtained by numerical solutions; thus, the PETE converter was assumed to operate under low injection conditions in the simulation [18,25].

The solar converter can reduce optical loss before entering the cathode using an antireflective film; therefore, the effect of reflectivity was not considered in the calculation. When sunlight shines on an incident interface, the cathode absorbs photons in an exponential manner, resulting in the uneven distribution of photo-generated carrier concentration. In the cathode, due to the action of the concentration gradient, the photo-generated carrier diffuses and drifts and can be described by the one-dimensional continuity equation [26]:

$$D_n\frac{d^{2}n\left(x\right)}{d{x}^2}-\frac{n\left(x\right)}{\tau }+G\left(x\right)=0$$

(1)

Here, n(x) represents the photo-generated carrier of the cathode, which is also called the excess electron concentration; it depends on the cathode thickness, x. D_n is the diffusion coefficient of the cathode, and τ is the lifetime of the electron. G(x) represents the production rate of the excess electron concentration, which can be simplified, based on [17], as:

$$G\left(x\right)=I\left(x\right)\alpha$$

(2)

$$I\left(x\right)=I_{0}exp\left({{\displaystyle \int }}_0^x-\alpha dx\right)$$

(3)

where I(x) represent the relationship between photon flux and thickness. I₀ and α represent the initial photon flux of the incident interface and the absorption coefficient of the cathode, respectively.

For the InGaN cathode, the absorption coefficient can be expressed by the characteristic equation based on [27]:

$$\alpha =1\times {10}^5\sqrt{C\left(h\nu -E_g\left(T_c\right)\right)+D{\left(h\nu -E_g\left(T_c\right)\right)}^2}, h\nu >E_g$$

(4)

where C and D are the characteristic parameters of In_yGa_1−yN, which are related to the In composition y [28,29], and hυ corresponds to photon energy at different wavelengths. T_c is the temperature of the cathode, and E_g(T_c) represents the change of the bandgap of the cathode with T_c. The relationship is as follows, based on [30]:

$$E_g\left(T_c\right)=E_g\left(300 K\right)+{\alpha }_T\left(\frac{{300}^2}{300+{\beta }_T}-\frac{T_c}{T_c+{\beta }_T}\right)$$

(5)

where α_T = 9.09 × 10⁻⁴ eV/K and β_T = 650 K are the Varshni coefficients of In_yGa_1−yN and are applicable to any In composition, y [30]. E_g(300 K) represents the bandgap of In_yGa_1−yN at room temperature, and its expression is as follows, based on [20]:

$$E_g\left(300 K\right)=y{E}_g\left(InN\right)+\left(1-y\right)E_g\left(GaN\right)-by\left(1-y\right)$$

(6)

Here, E_g(InN) = 0.7 eV, E_g(GaN) = 3.4 eV, and b = 1.43 eV is the bending parameter.

According to the above equation, the excess electron concentration of the cathode conduction band can be calculated as:

$$n\left(x\right)=C_{1}exp\left(\frac{x}{L_n}\right)+C_{2}exp\left(-\frac{x}{L_n}\right)+\frac{\tau G\left(x\right)}{1-L_n^2{\alpha }^2}$$

(7)

where C₁ and C₂ are constants, and L_n is the diffusion length of the electron. As shown in Figure 2, when sunlight is irradiated on the cathode, surface recombination occurs at the incident interface (x = 0), and the initial condition of the one-dimensional continuity equation can be expressed as:

$$D_n{\left.\frac{dn\left(x\right)}{dx}\right|}_{x=0}={\left.S_{1}n\left(x\right)\right|}_{x=0}$$

(8)

After the excess carriers reach the emission surface, some of them are recombined at the interface, while the others reach the anode after overcoming the obstruction of the reverse current; therefore, the boundary conditions can be written as:

$$D_n{\left.\frac{dn\left(x\right)}{dx}\right|}_{x=d}={\left.-S_{2}n\left(x\right)\right|}_{x=d}-\frac{J_{PE}-J_a}{q}$$

(9)

Above, S₁ and S₂ are the compound velocities corresponding to the incident and emission interfaces, respectively. J_PE represents the current density generated by photon enhancement in the cathode, and J_a represents the reverse thermal current density generated by the anode. Their expression can be written in the following form [31]:

$$J_{PE}=\left\{\begin{array}{c}{A}_c{T}_c^{2}exp\left(-\frac{{\phi }_c}{k_B{T}_c}\right)\frac{n\left(d\right)}{n_{eq}}, V\le V_{fb}\\ A_c{T}_c^{2}exp\left(-\frac{{\phi }_c+q\left(V-V_{fb}\right)}{k_B{T}_c}\right)\frac{n\left(d\right)}{n_{eq}}, V>V_{fb}\end{array}\right.$$

(10)

$$J_a=\left\{\begin{array}{c}{A}_a{T}_a^{2}exp\left(-\frac{{\phi }_a+q\left(V_{fb}-V\right)}{k_B{T}_a}\right), V\le V_{fb}\\ A_a{T}_a^{2}exp\left(-\frac{{\phi }_a}{k_B{T}_a}\right), V>V_{fb}\end{array}\right.$$

(11)

$$V=V_{fb}+V_{bias}$$

(12)

where A_c and A_a represent the Richardson constants of the cathode and the anode. T_a is the temperature of the anode. V is the output voltage. $V_{bias}<0$ is negative bias, and $V_{bias}>0$ is positive bias. $V_{fb}=\left({\phi }_C-{\phi }_A\right)/q$ is flat-band voltage, and n_eq is the equilibrium electron concentration in the cathode conduction band.

The PETE solar converter operates under a synergistic effect of light and heat, and the cathode current density J_c is equal to the PETE current density J_PETE, including J_PE and thermal current J_T.

$$J_c=J_{PETE}=J_{PE}+J_T$$

(13)

In addition, J_T follows the Richardson–Dushman thermoelectric emission formula [7]

$$J_T=\left\{\begin{array}{c}{A}_c{T}_c^{2}exp\left(-\frac{{\phi }_c}{k_B{T}_c}\right), V\le V_{fb}\\ A_c{T}_c^{2}exp\left(-\frac{{\phi }_c+q\left(V-V_{fb}\right)}{k_B{T}_c}\right), V>V_{fb}\end{array}\right.$$

(14)

The output power P_out and conversion efficiency η of the PETE converter are expressed as

$$P_{out}=\left(J_c-J_a\right)\times V$$

(15)

$$\eta =\frac{P_{out}}{P_{solar}}$$

(16)

where P_solar is the power of sunlight.

3. Results and Analysis

In the simulation, the In composition of the cathode is set as 0.6, and the bandgap is 1.44 eV according to Equation (6), which is within the optimal range of PETE effect and can cover most visible wavelengths of the AM1.5G spectrum [7]. InGaN materials are usually grown on sapphire or GaN substrates, which have a wide bandgap; thus, the absorption of incident light by the substrates is ignored. The InGaN with high In components is usually thin in thickness. In this study, the cathode thickness was set as 0.2 μm, and the p-type doping concentration was set as 1 × 10¹⁸ cm⁻³ [32,33,34]. To simplify the calculation, the diffusion coefficient and the electron lifetime were treated as constants independent of temperature. D_n = 63.6 cm²/s corresponds to In_0.6Ga_0.4N, which can be obtained by the formula in [35]. The electron lifetime of the cathode is 1 ns, so the diffusion length can be obtained by $L_n=\sqrt{D_n\tau }$ [27]. The composite velocity of the incident interface was set as S₁ = 1 × 10⁵ cm/s [36,37]. For the emission interface, the composite velocity, S₂, can be reduced by passivation treatment and was set to 10³ cm/s [38]. The anode was phosphorus-doped diamond, and the work function, φ_a, was 0.9 eV [39]. The AM1.5G solar spectrum was used in the calculation, and the PETE solar converter operated at 1000 solar concentrations (P_solar = 100 W/cm²).

The performance of PETE converters based on the In_0.6Ga_0.4N cathode was calculated using the above analytical model. The bandgap of the cathode decreased with increasing temperature; therefore, the electron affinity, χ, increased from 0.4 eV to keep the cathode work function, φ_c, greater than the anode work function, φ_a. When the anode and the cathode were isothermal, the variation trend in excess electron concentration, n(d), at the emission interface with different electron affinities was as shown in Figure 3a. There was a slow increase and then a sharp decline in the number of excess electrons. The reason is that at low temperatures, excess electrons do not have enough energy to overcome the electron affinity and accumulate at the emission interface. The heat generated by the rising temperature allows these electrons to overcome the electron affinity and reach the anode in the form of thermionic emission. The number of excess electrons eventually decreases to reach a certain value as the temperature continues to rise, and this value is positively correlated with the electron affinity. This is because as the electron affinity increases, the excess electron concentration becomes greater at the emission interface, and the temperature required to provide more energy for the electron emission is higher. In the case of isothermal cathodes and anodes, the reverse thermal current of the anode increases with increasing temperature, which undoubtedly increases the excess electron concentration of the cathode, making it unable to drop to zero. This effect is particularly significant at electron affinities above 0.4 eV.

Figure 3b shows the photon-enhanced current, thermal current, and photon-enhanced thermal current as functions of temperature at an electron affinity of 0.4 eV. The figure can be simply divided into three regions: the photoelectric emission region, the photon-enhanced thermionic emission region, and the thermoelectric emission region. When the temperature is below 550 K, the PETE converter mainly relies on the photoelectric emission mechanism. The current density starts at zero and then increases rapidly, which corresponds to the accumulation stage and the emission stage in Figure 3a. Above 950 K, the thermoelectric emission mechanism plays a dominant role. Above 850 K, the thermoelectric emission mechanism plays a dominant role, and the current density rises rapidly for a second time. In the region of 550–850 K, the photoelectric emission tends to saturate and the influence of photon enhancement is greatest, while the thermoelectric emission is obscured at this time, and the current density of the cathode remains constant. By way of a saturated photocurrent boosting the initial current of thermoelectric emission, the PETE mechanism combines the two, which enables the converter to adapt to a wider temperature range and make better use of solar energy.

Figure 3c shows the variation in output current density with temperature under isothermal conditions. The output current densities of the converters operating at different electron affinities show similar trends as in Figure 3b. There is a phase of slow increase in current density between two rapid increases, that is, the saturation region. According to Figure 3a, the number of excess electrons that can be emitted decreases with the increase in electron affinity; thus, the saturation current also decreases, and the saturation region is shortened. When the electron affinity exceeds 0.6 eV, the saturation region of the output current density begins to become less obvious, as shown in the inset. The temperature dependence of the current tends to be the thermal current state. At this time, the PETE converter behaves as a thermionic converter. This indicates that the PETE mechanism cannot be fully utilized at high barriers when the converter is isothermal.

Figure 3d shows the variation in conversion efficiency with temperature. With the increase of electron affinity, the maximum conversion efficiency first increases and then decreases. The increment in efficiency is 1.52% as the electron affinity changes from 0.4 eV to 0.5 eV, whereas it is only 0.52% as the electron affinity continues to rise to 0.6 eV. At 0.7 eV, the conversion efficiency drops directly to 17.94%. The reason is that the decrease in saturation current will eventually be greater than the increase in electron affinity. This indicates that there is an optimal range of electron affinities that maximizes the performance of PETE converters under isothermal conditions.

In order to further determine the optimal range of electron affinity and temperature of the PETE solar converter under isothermal conditions, their effects on the conversion efficiency are plotted as shown in Figure 4a,b. When the electron affinity potential is constant, the conversion efficiency first increases and then decreases with increasing temperature. The same trend holds for a given temperature. Overall, the conversion efficiency is maximized when the electron affinity potential is 0.45–0.52 eV and the operating temperature is 645–705 K. Although the PETE converter can generate a net current under the influence of electron affinity when the cathode and the anode are isothermal, it is still limited by the reverse current caused by the hot anode at high temperatures.

The anode can be cooled by connecting it to an external thermal cycle, and the waste heat can be reused to convert electricity, further improving the conversion efficiency. Therefore, in the following discussion, the anode temperature is set at 500 K, which is the same as the hypothesis in a previous study [7]. In this case, the cathode temperature increased from 500 K to keep the PETE converter in nonisothermal operation. Figure 5a shows the relationship between the excess electron concentration and the cathode temperature. When the electron affinity was 0.4–0.6 eV, the excess electron concentration decreased monotonously with the increase in cathode temperature, and the slow accumulation of electrons in the conduction band of the emission surface could be observed at 0.7 eV. However, unlike the isothermal case, the decline in excess electrons at different electron affinities tended to be consistent in the nonisotherm case. This is because the anode temperature is 500 K, and it can be calculated from Equation (11) that the reverse thermal current without bias is only 0.026 A/cm², which has negligible influence on the electron emission. The excess electrons at different affinities are eventually emitted, resulting in an electron concentration of almost zero.

For an anode temperature of 500 K, the output current density with the change in cathode temperature is shown in Figure 5b. Compared with Figure 3c, with the increase in electron affinity, the anode maintained a low temperature to avoid deterioration of the saturation current and tended to be the same numerically. At low electron affinity, the output current had a better temperature response, reaching saturation value at lower temperature. However, for an anode work function of 0.9 eV, the decrease in the electron affinity potential affected the cathode work function, resulting in a decrease in the output voltage at zero bias. Therefore, the lower electron affinity was not better for PETE converters.

Figure 5c depicts the relationship between the conversion efficiency and the cathode temperature. For the given electron affinity, the conversion efficiency reached the maximum when the current entered the saturation region and then began to decline. This can be explained as the difference between the work functions of the cathode and the anode decreases due to the influence of temperature on the bandgap; this decrease is greater than the increase in current. However, when thermoelectric emission was dominant, the current increased exponentially, and the effect of the drop in the difference of the work function was completely outweighed, causing the conversion efficiency to grow again. When the electron affinity was 0.6 eV, the maximum conversion efficiency exceeded the ultimate efficiency of the isothermal state. According to Figure 3d and Figure 5c, at 0.7 eV, the optimal operating temperature of the nonisothermal converter was reduced by 10 K compared to the isothermal state. This indicates that the temperature response of cathodes with high electron affinity is affected by the increase in anode temperature. With the increase in electron affinity, the maximum conversion efficiency increased linearly, and the cathode needed to operate at a higher temperature. The efficiency of the converter was numerically predicted to exceed 30% at the electron affinity of 1 eV, but the optimum operating temperature was over 1000 K.

The relationship between the output current and the applied bias under isothermal and nonisothermal operation of the converter is shown in Figure 6a. The temperature of the cathode was 740 K, which is almost the optimal temperature at 0.6 eV. The figure is divided into two regions: negative bias (V_bias ≤ 0, V ≤ V_fb) and positive bias (V_bias > 0, V > V_fb). The external electric field created by applying a negative bias to the converter helped the electrons of the cathode move towards the anode and limited the increase in the reverse current caused by heating of the anode, resulting in the same output current at different anode temperatures. However, the negative bias was close to zero, and the limiting effect of the electric field on the reverse current was weakened; thus, the output current under the isothermal condition began to decline in advance. When the anode temperature was 500 K, the reverse current could be ignored, and the output current remained constant throughout the negative bias region. In the positively biased region, the external electric field severely impeded the emission of electrons from the cathode, causing the output current to drop exponentially. With the increase in positive bias, the output current finally dropped to zero, and the converter reached the open-circuit state. The open-circuit voltage under isothermal conditions was less than that under nonisothermal conditions. The bandgap diagrams are given to illustrate the reasons for the differences in open-circuit voltages.

Figure 6b shows the band diagram with the converter at zero bias. For the sake of illustration, the Fermi level at T_a = T_c = 740 K is taken as the reference, and B_a1 represents the barrier that the anode electron needs to overcome to reach the cathode from the Fermi level at this time. When the anode temperature decreases from 740 K to 500 K, the barrier B_a1 increases to B_a2; thus, the positions of the vacuum and Fermi levels of the anode are shown by the blue line. When the cathode is irradiated by sunlight, the Fermi level is raised to the quasi-Fermi level. B_c represents the barrier that the cathode electrons need to overcome to reach the vacuum level. The band diagram at positive bias is shown in Figure 6c. When the Fermi level of the anode reaches the same position as the quasi-Fermi level of the cathode, the barrier that the anode electron needs to overcome to reach the cathode is B_a = B_a1 − V₁ = Ba₂ − V₂ = B_c. V₁ and V₂ represent the open-circuit voltage in the isothermal and nonisothermal states, respectively. At this time, no net current is generated inside the converter. Due to B_a1 < B_a2, V₁ < V₂ can be obtained; that is, the open-circuit voltage is greater under nonisothermal conditions. This means that there is a larger potential difference between the anode and the cathode in the nonisothermal case than in the isothermal case, so electrons can more easily reach the anode.

Figure 7a shows the relationship between current density and output voltage at different cathode temperatures. When the output voltage is lower than the flat-band voltage (indicated with “+”), the output current increases with temperature and follows the same trend as that shown in Figure 5b. As the temperature of the cathode increases, the bandgap narrows and the Fermi level rises, resulting in the difference between the work function of the cathode and the anode decreasing, that is, “+” shifting to the left. The inset shows the open-circuit voltage of the converter at different temperatures. The greater the current, the greater the positive bias required for the converter to reach the open-circuit state; therefore, the open-circuit voltage increases as the temperature of the cathode increases. The relationship between the conversion efficiency and the output voltage at different cathode temperatures is shown in Figure 7b. Under the impact of applied bias pressure, the maximum conversion efficiency is positively correlated with temperature. However, according to Figure 5c, when the converter operates at zero bias voltage, the maximum conversion efficiency decreases at 800–900 K. This indicates that an appropriate bias voltage can help compensate for the deterioration of conversion efficiency caused by the decrease in the difference between the anode and the cathode work functions.

In order to determine the maximum conversion efficiency point,

Table 1. At different temperatures, the flat-band voltage V_fb and the output voltage V_m. (V_m represents the output voltage at the maximum conversion efficiency).

Tc (K)	Vfb (V)	Vm (V)
600	0.794	0.794
700	0.684	0.684
800	0.569	0.699
900	0.450	0.730

lists flat-band voltages V_fb and output voltages V_m (indicated with “×”) at different temperatures. As the cathode temperature increases, the output voltage V_m decreases at first and then increases. The reason is that when the applied positive bias begins to increase, the current at temperatures of 600 K and 700 K is small and is greatly affected by the bias, and V_m is equal to V_fb and consistent with its trend. However, when the temperature is 800–900 K, the current density is already in the saturation region and slowly increasing. When the positive bias voltage is applied, the current no longer drops instantly but instead undergoes a slow decline process; thus, V_m obviously exceeds V_fb. The result shows that with the increase in temperature, the conversion efficiency will eventually reach the maximum at an output voltage greater than the flat-band voltage.

In studies of InGaN single-junction solar cells, the conversion efficiency can be increased from 14.5% to 22.7% by polarization engineering, increasing the back-surface field and window layer and adjusting the doping concentration and thickness optimization [40,41,42]. However, photovoltaic cells have a low utilization of thermal energy from sunlight. In our study, the structure of anode and cathode separation is adopted, and the cathode can simultaneously absorb light and heat in solar energy through PETE effect so as to optimize performance. After cooling the anode, the conversion efficiency can be further improved and linearly increases with electron affinity. Therefore, the PETE converter can make more efficient use of solar energy.

4. Conclusions

In this study, we used an InGaN cathode to simulate the performance of the photon-enhanced thermionic emission (PETE) energy converter. In the process of using the one-dimensional continuity equation to describe the electron diffusion–emission model, we considered the temperature dependence of the bandgap and added the Varshni equation. By exploring the influence of operating temperature on the excess electron concentration, output current, and conversion efficiency, the performance of the PETE converter in isothermal nonisothermal state was compared. The results show that the rise in anode temperature increases the reverse current, hinders the emission of excess electrons, reduces the output current, and deteriorates the conversion efficiency. Thus, the conversion efficiency of PETE converters operating under isothermal conditions is limited to less than 22%. However, when the anode is kept at 500 K, the conversion efficiency and the cathode temperature increase linearly with the electron affinity. Through applied bias, the converter can reach the open-circuit state. In the nonisothermal state, there is a larger potential difference between the anode and the cathode, so the open-circuit voltage is higher than the isothermal state. We also determined the maximum efficiency point at different temperatures and found that the output voltage at maximum efficiency exceeded the flat-band voltage. Finally, this study broadens the selection of cathode materials and provides further insights into solar energy utilization.