A comprehensive simulation study of multi-junction solar cell

This study conducts comprehensive simulation analysis of typical triple-junction solar cells using Silvaco ATLAS. Initially, modeling and simulation of the typical triple-junction solar cells under the AM1.5 solar spectrum at 300 K are performed to characterize various performance parameters of the cells under one sun illumination. Subsequently, the impact of the thickness of the top and middle cell layers on the efficiency of the cells is analyzed. Additionally, the influence of doping concentration errors in individual sub-cells on the overall power deviation of the cells is investigated. Moreover, Al0.9Ga0.1As is employed to replace AlInP as the top FSF (Front Surface Field). Furthermore, the study analyzes the variation of internal radiation efficiency of the top and middle sub-cells of the solar cells with concentration factor and bias voltage. Finally, an assessment is made on the effects of different positions and densities of interface defects, as well as the introduction of class-acceptor Gaussian distribution state levels induced by defects, on the performance of the solar cells. The results indicate that this study provides valuable insights for optimizing multi-junction solar cells and analyzing internal physical phenomena.


Introduction
In recent years, solar energy has emerged as a focal point in energy production transition as a renewable energy source [1].In comparison to traditional silicon-based solar cells, multi-junction solar cells exhibit higher efficiency and were classified as third-generation solar cells by Green in 2001 [2][3][4].Multi-junction(MJ) solar cells originated from stacking p-n junctions with different bandgaps, arranged in ascending order of bandgap width from bottom to top.This arrangement enables high-energy photons to be absorbed in the wide bandgap p-n junctions at the upper layer, while low-energy photons are absorbed in the narrow bandgap p-n junctions at the lower layer.Through selective absorption of different regions of the solar spectrum, MJ solar cells achieve effective enhancement in conversion efficiency [1,5,6].Currently, III-V compound materials are considered ideal for MJ solar cells [7,8].Relevant literature has demonstrated that MJ solar cells fabricated from III-V compound materials have achieved a conversion efficiency of up to 46% under high solar concentration [9,10].GaInP, InGaAs, and Ge triple-junction(TJ) solar cells have been extensively researched due to their excellent bandgap alignment in the lattice matching system [10].GaInP and InGaAs junctions feature large bandgap front and back surface fields, which facilitate the connection of minority carriers within the junction region [11].Each layer of p-n junctions is interconnected by tunnel diodes, and these structures are grown on Ge substrates via metal-organic chemical vapor deposition (MOCVD) [12].The typical layered structure of a GaInP/InGaAs/Ge TJ solar cell and its simple equivalent circuit model are illustrated in figures 1 and 2.
Research on multi-junction solar cells is continuously advancing.In previous studies, such as those conducted by Salem [13] and Zhu [14], The former study proposed a method for assessing the performance of InGaP/GaAs dual-junction (DJ) solar cells under a standard AM1.5 solar spectrum at 300 K and 1-sun conditions.Initially, it investigated the impact of the top window thickness, top base thickness, and bottom BSF thickness and doping concentration on the efficiency of DJ solar cells.Subsequently, the study replaced the original AlGaAs top window with AlGaInP, optimizing the aluminum (Al) mole fraction in AlGaInP.This optimization resulted in an enhanced efficiency of the InGaP/GaAs DJ solar cells, reaching η = 38.53%,which represents a 4% improvement compared to previous results.However, this research lacked an analysis of the thickness of the top cell emitter layer, BSF layer, and other layers of the bottom cell besides the BSF layer.Additionally, it only examined the doping concentration of the bottom BSF layer, neglecting the influence of doping concentrations in other layers on the overall performance of the solar cell.The latter study conducted theoretical calculations and analyses on the relationship between internal radiation efficiency and conversion efficiency of MJ solar cells under the AM1.5 solar spectrum.It confirmed that the internal radiation efficiency of solar cells is a critical parameter for evaluating the performance of MJ solar cells.Furthermore, the study emphasized the optimization of internal radiation efficiency to enhance the conversion efficiency of MJ solar cells.Zhu's research provided a detailed theoretical framework for understanding the regularities of internal radiation efficiency in MJ solar cells.However, it lacked further validation of these regularities using TCAD tools.Additionally, the analysis only focused on the overall internal radiation efficiency of MJ solar cells, neglecting a detailed investigation into the individual sub-cells of MJ solar cells.
In this study, we conducted comprehensive simulations and theoretical investigations on a typical TJ solar cell using TCAD tools.We analyzed the effects of different thicknesses of layers in the top and middle subcells on the efficiency of the TJ solar cell.Furthermore, we examined the impact of doping concentration errors in each subcell on the overall power mismatch of the solar cell.To achieve higher efficiency, we replaced AlInP with the optimal alloy ratio of AlGaAs (Al 0.9 Ga 0.1 As) as the top FSF layer.Additionally, we analyzed the variation of  internal radiation efficiency of the cell with bias voltage and concentration ratio.Lastly, inspired by Chouhan's research on perovskite solar cell [15], we modeled the effects of interface defects at different positions and densities within the TJ solar cell on its internal performance.This work provides valuable insights for optimizing MJ solar cells and analyzing internal mechanisms.

Modeling process and theoretical frameworks
In this section, we first introduce the modeling process and theoretical foundation of the Silvaco ATLAS software.Subsequently, we provide a detailed explanation of the main steps involved in simulating triplejunction solar cells using this software, including the physical models and material parameters utilized.

Modeling process and theoretical foundations
When simulating multi-junction solar cells using Silvaco ATLAS, the electronic characteristics of the devices are predicted by simulating the transport of carriers through a two-dimensional grid.To input the structure and composition of the solar cells into the Silvaco ATLAS software, a two-input three-output scheme is employed for simulation [16].
Below, we outline the key steps involved in the simulation process.Figure 3 illustrates the theoretical framework of the required steps for typical simulation work.
In this simulation, the AM1.5 standard solar spectrum (H 0 = 1000 W m −2 ) is utilized.Equation (1) represents the generation rate of photo-generated carriers in the solar cell under illumination.Equation (2) denotes the Poisson equation, which illustrates the relationship between the electrostatic potential and spatial charge density.Equations (3) and (4) represent the carrier continuity equations, describing the time partial derivatives of electron concentration and hole concentration, respectively.Equations (5) and (6) depict the driftdiffusion equations.
Where, F( ) l represents the photon flux, , x ( ) a l denotes the optical absorption coefficient, R denotes the surface reflectance of the solar cell, and x represents the penetration depth of photons.e is the local dielectric constant, j is the electrostatic potential, and r is the local spatial charge density.n and p represent the electron and hole concentrations, respectively.G n and G p denote the generation rates of electrons and holes, while R n and R p represent the recombination rates of electrons and holes.J n and J p represent the electron and hole current densities, respectively, and q is the electron charge constant.n m and p m represent the electron and hole mobilities, respectively, while E n and E p represent the quasi-Fermi levels.By solving the aforementioned set of fundamental equations, the characteristic parameters of the triple-junction solar cell can be obtained.

Structural design and meshing
Reference to Wilkins [11], figure 4 illustrates the MJ solar cell structure required for the current modeling and simulation.To enhance the performance of the structure, each subcell is composed of tunnel diodes.Since tunnel diodes do not absorb any incident solar radiation, they can be defined as electrodes with a certain resistance during the modeling process.The presence of tunnel junctions provides a low-resistance path for carrier flow, thereby improving the efficiency of the multi-junction solar cell [11].
Silvaco ATLAS is a grid-based simulation tool, meaning that device characteristics are computed at grid points.The number of grid points or the density of the grid determines the accuracy of the simulation, the speed of simulation, and whether the results converge [16,17].This directly relates to the numerical method used in the simulation process.Therefore, grid partitioning is one of the most critical steps in device modeling using Silvaco ATLAS.

Physical models and materials
In utilizing the Silvaco ATLAS tool for simulating multi-junction solar cells, careful selection of the physical models used in the simulation is essential to effectively optimize and simulate the performance of the solar cells.The primary physical models employed for designing any solar cell include the concentration-dependent mobility model, optical recombination model, Shockley-Read-Hall recombination model, Auger recombination model, and Fermi-Dirac statistics model [13,16].Table 1 summarizes the physical models utilized in the Silvaco ATLAS tool for designing multi-junction solar cells in this study.
In order to achieve superior performance of the designed solar cell, meticulous selection of materials for each layer and determination of their required material parameters are crucial.This presents one of the biggest challenges in designing a multi-junction solar cell, particularly evident for ternary and quaternary materials.Due to the potential need for material composition optimization, multiple material parameters may be required [11].
For the material of each FSF layer, its lattice constant needs to match that of the emitter material, and it should possess a larger bandgap than the emitter material.Additionally, the selection of emitter and base materials results in a decreasing bandgap width of each subcell from top to bottom, where the upper cells can absorb short-wavelength spectra from solar radiation, while the lower cells absorb long-wavelength spectra.Furthermore, the material selection for the BSF layer should satisfy the surface recombination between the passivation of the upper base and the emitter of the lower tunnel diode.The material parameters listed in table 2 are the ones required for simulating the TJ solar cell using the Silvaco ATLAS simulator in this study.

Simulation results
For a clearer understanding of the performance and operational characteristics of this solar cell, the main parameters extracted in this study are: efficiency (η), open-circuit voltage (V oc ), short-circuit current density (J sc ), fill factor (FF), maximum power density (P max ), J-V curve, P-V curve, and external quantum efficiency of the subcells.
Table 3 summarizes the electrical performance parameters of the triple-junction solar cell studied in this research.Figure 5 respectively depict the extracted J-V and P-V curves of the overall solar cell from the simulation.Figure 6 illustrate the J-V curves of each subcells, while figure 7 presents the external quantum efficiency of each subcells.
It can be observed that in the current simulation, the fill factor (FF) of the overall solar cell reached approximately 91.58%, with a conversion efficiency (η) of 31.46%.The short-circuit current density (J sc ) attained 11.72 mA cm −2 , and the maximum output power (P max ) was measured at 31.47 mW cm −2 , with an open-circuit voltage (V oc ) of 2.93 V.For the top cell, the maximum current density (J sc ) was 11.72 mA cm −2 , with an open-circuit voltage (V oc ) of 1.45 V.In the middle cell, the maximum current density (J sc ) was 14.99 mA cm −2 , with an open-circuit voltage (V oc ) of 1.11 V. Finally, for the bottom cell, the maximum current density (J sc ) measured 15.01 mA cm −2 , with an open-circuit voltage (V oc ) of 0.36 V.

FSF layer thickness
In the design of triple-junction solar cells, the main role of the FSF layer in the top cell is to reduce surface recombination, enhance carrier collection and transport, and facilitate the absorption of the entire input solar radiation spectrum, thereby improving the overall photoelectric conversion efficiency of the cell [18,19].To investigate the impact of different FSF layer thicknesses in the top and middle cells on the overall cell conversion efficiency, numerical analyses were conducted on the FSF layer thickness.Keeping other parameters constant, as shown in the figure 8(a), the FSF layer thickness of the top cell was varied from 10 nm to 45 nm.The maximum conversion efficiency of the cell was achieved at an FSF layer thickness of 40 nm, reaching 32.18%.Similarly, as depicted in the figure 8(b), the FSF thickness of the middle cell varied from 10 nm to 60 nm, with the optimal thickness being 20 nm, resulting in a cell conversion efficiency of 31.48%.

Emitter layer thickness
The emitter layer, a crucial component of the solar cell structure, plays a vital role in solar cells, primarily involving electron emission and the collection of photogenerated carriers.It serves as one of the key layers in photovoltaic conversion [20].To analyze the impact of different thicknesses of the emitter layer in the top and middle cells on the overall efficiency of the solar cell, numerical analyses were conducted while keeping other parameters constant.As shown in the figure 9(a), the thickness of the emitter layer in the top cell varied from 40 nm to 180 nm.The maximum efficiency of the solar cell was achieved at an emitter layer thickness of 160 nm, reaching 31.75%.Similarly, as depicted in the figure 9(b), the thickness of the emitter layer in the middle cell ranged from 60 nm to 110 nm, with the optimal thickness being 70 nm, resulting in a maximum efficiency of 31.5% for the cell.

BSF layer thickness
The BSF layer, located at the back of the solar cell, serves to passivate the rear surface of the solar cell to minimize carrier recombination effects, thereby enhancing the cell's efficiency.To enhance light absorption, the BSF layer   must have a relatively high thickness, theoretically absorbing all incident light with a certain thickness of the BSF layer [21,22].While keeping other parameters constant, this study extensively analyzed the impact of BSF layer thickness on the overall conversion efficiency of the solar cell for both the top and middle cells.As shown in the figure 10(a), for the top cell, the BSF layer thickness ranged from 10 nm to 130 nm.It was observed that thicker BSF layers resulted in higher cell conversion efficiency, reaching a maximum efficiency of 34.42% at a BSF layer thickness of 130 nm.However, further increasing the thickness led to a decrease in cell efficiency.Similarly, as depicted in the figure 10(b), the optimal BSF thickness for the middle cell was 50 nm, resulting in a cell conversion efficiency of 31.51%.Decreasing or increasing the thickness beyond this optimal value resulted in a decrease in cell efficiency.

Base layer thickness
The role of the base layer in solar cells primarily involves photovoltaic conversion and carrier transport, serving as the region for photovoltaic conversion and the pathway for electron and hole conduction.Its thickness significantly impacts the conversion efficiency of solar cells.Typically, in solar cell design, the optimal base thickness should be smaller than the carrier diffusion length.This ensures that the carriers generated by light can be separated and collected by the p-n junction of the solar cell before recombination occurs [23,24].While keeping other parameters constant, this study analyzed the impact of different thicknesses of the base layer in both the top and middle cells on the conversion efficiency of the solar cell.For the top cell (figure 11(a)), the base layer thickness ranged from 450 nm to 1650 nm.The conversion efficiency of the cell initially increased with increasing base layer thickness, reaching a maximum efficiency of 32.93% at a thickness of 1550 nm.However, as the thickness continued to increase beyond this point, the efficiency of the cell began to decrease.In the case of the middle cell, the base layer thickness ranged from 2200 nm to 2800 nm (figure 11(b)).The  conversion efficiency peaked at 31.52% for a thickness of 2300 nm.Further increases in base layer thickness resulted in a decreasing trend in efficiency.

Doping concentration errors discussion
The production and processing of solar cells inevitably introduce errors that may result in deviations from the theoretically designed cells, such as variations in doping concentration across different layers of the cell.Doping serves to adjust the band structure of materials, enhancing their ability to absorb energy within the visible light spectrum.Appropriate doping levels can improve carrier mobility, reduce carrier traps, and enhance overall cell performance [25][26][27].This section primarily investigates the impact of doping concentration errors on the power output of the overall triple-junction solar cell, considering the top, middle, and bottom cell layers.
When analyzing the impact of doping concentration errors on the power output of one junction cell, the doping concentrations of the other two junction cells are held constant.As shown in the figure 12(a), setting the error rate range from 4% to 20% aims to obtain more sample data for greater precision in the final results.Arranging the doping concentration error rates for each layer in descending order based on their impact on power mismatch reveals the order: bottom cell > middle cell > top cell.Since the doping concentration error in the bottom cell significantly affects its power output, further analysis is conducted on the doping concentration effects on power for each layer of the bottom cell.
As shown in the figure 12(b), arranging the doping concentration error rates for each layer in descending order based on their impact on power mismatch, we observe that Substrate > BSF > Buffer, FSF, Emitter.Moreover, compared to the Substrate and BSF layers, the impact of doping errors in the Buffer, FSF, and Emitter layers on the power output of the cell is negligible.

Using AlGaAs as the top FSF layer
In this section, AlGaAs was utilized as a replacement for the original AlInP material in the top FSF layer, and the optimization of the Al alloy composition ratio was studied.Achieving the optimal alloy composition ratio (x) is crucial for compound semiconductors to ensure lattice matching between different semiconductors [28,29].The refractive index (n) and extinction coefficient (k) of compound semiconductors vary with changes in the alloy composition ratio [30].To enhance the performance of solar cells, the alloy composition ratio of compound semiconductors must be optimized.Six alloy composition ratios of AlGaAs were investigated, and the efficiency of GaInP/InGaAs/Ge triple-junction solar cells was extracted for each composition ratio.As depicted in the figure 13, the maximum efficiency of 32.8% was achieved when x = 0.9, resulting in an overall efficiency improvement of 1.34% compared to TJ solar cells using AlInP as the top FSF layer.Therefore, Al 0.9 Ga 0.1 As, providing the maximum efficiency for this TJ solar cell, is identified as the optimal alloy composition ratio.

TJ solar cell internal radiation efficiency discussion
In solar cells, internal radiation efficiency plays a crucial role in determining the performance and energy conversion efficiency of the device.In previous studies, Shockley and Queisser incorporated the impact of nonradiative recombination processes on the performance of single-junction cells into the external radiation efficiency (η ext ), defined as the ratio of externally emitted radiation-generated recombination current to the total recombination current [31].Chan [32], considering non-radiative Shockley-Read-Hall (SRH) recombination, calculated the optimal bandgap for 1 to 3-junction solar cells using a dual-diode model while accounting for the influence of η ext .Although η ext values can reflect the quality of the cell material, they are also influenced by factors such as cell structure, surface reflectivity, and material thickness.In contrast, internal radiation efficiency (η int ) is a more appropriate attribute, defined as the ratio of internal radiation recombination rate to the total recombination rate, providing a direct reflection of material quality and being less susceptible to factors like cell structure [33].Following Jia's [34] definition, the internal radiation efficiency of multi-junction solar cells is defined by the equation (7) Where J rad, J1 represents the radiation recombination current of the first junction, and J rec, J1 denote the total recombination current of the first junction.Therefore, η int can typically be considered proportional to J rad, J1 /J rec, J1 .As depicted in the figures 14(a) and (b), the internal radiation efficiency of GaInP and InGaAs subcells in the TJ solar cell was studied as a function of concentration ratio.
From the figure 14(a), it can be observed that the internal radiation efficiency of the GaInP sub-cell remains nearly constant in the low bias voltage region (0-2 V), where J rad, J1 /J rec, J1 exhibits minimal variation with voltage and can be approximated as a constant.As the voltage approaches the maximum power point, J rad, J1 /J rec, J1 gradually decreases and reaches a minimum near the maximum power point.Subsequently, with further increase in voltage, J rad, J1 /J rec, J1 begins to increase.From the figure 14(b), it can be observed that the internal radiation efficiency of the InGaAs sub-cell exhibits a behavior similar to that of the GaInP sub-cell.In the low bias voltage region (0-2 V), J rad, J2 /J rec, J2 remains nearly constant.As the voltage gradually increases towards the vicinity of the maximum power point, J rad, J2 /J rec, J2 starts decreasing until it reaches a minimum, and eventually, with further voltage increase, J rad, J2 /J rec, J2 gradually increases.Comparison of figures 14(a) and (b), it is evident that the internal radiation efficiency of the InGaAs sub-cell is more susceptible to the concentration factor of the TJ solar cell.

Effect of interfacial defects on the performance of TJ solar cell
In this section, following the approach by Chouhan [15] in perovskite solar cells, we introduced defects by inserting interface defect layers with a thickness of 1 nm between the FSF and emitter layers of both the top and middle cells of the TJ solar cell, as illustrated in figure 15(L1) and (L2).The effects of different regions of interface defects and varying interface defect densities on the performance of the solar cell were investigated.

Interface defects in L1
During the simulation process, interface defects with a thickness of 1 nm were introduced between AlInP and GaInP layers in the top cell, while keeping other parameters constant.The interface defect densities varied within the range of 10 8 cm −2 to 10 14 cm −2 .As shown in the figure 16(a), the presence of interface defects resulted in a relatively small decrease in V oc , from 2.93 V to 2.8 V.However, there was a significant decrease in J sc and Efficiency, especially when the interface defect density reached 10 10 cm −2 .At this density, J sc decreased to 8.47 mA cm −2 , and Efficiency decreased to 22.06%.Subsequently, the decreasing trend of both parameters gradually slowed down.

Interface defects in L2
In the middle cell, interface defects with a thickness of 1 nm were introduced between AlGaAs and InGaAs layers (figure 16(b)), while keeping other parameters constant.The interface defect density varied between 10 8 cm −2 and 10 14 cm −2 .The change in interface defect density had a minimal effect on V oc ; when the defect density ranged from 10 8 cm −2 to 10 13 cm −2 , J sc and Efficiency remained almost unchanged.However, when the defect density reached 10 14 cm −2 , there was a drastic decrease in both J sc and Efficiency.Jsc plummeted to 0.76 mA cm −2 , and Efficiency dropped sharply to 1.08%.

Interface defects in L3
In the top cell, interface defects with a thickness of 1 nm are introduced between the emitter and base layers (figure 16(c)).While keeping other parameters constant, the interface defect density gradually increases from 10 8 cm −2 to 10 14 cm −2 .As the defect density varies, V oc decreases gradually from 2.92 V to 2.14 V.With defect densities ranging from 10 8 cm −2 to 10 11 cm −2 , J sc remains relatively unchanged.However, when the defect density reaches 10 12 cm −2 , J sc starts to decrease gradually, dropping abruptly to 7.9 mA cm −2 .Meanwhile, the efficiency shows a continuous downward trend with the increase in defect density, decreasing from 31.24% to 14%.

Interface defects in L4
In the middle cell, interface defects with a thickness of 1 nm are introduced between the emitter and base layers (figure 16(d)).While keeping other parameters constant, the interface defect density gradually increases from  8 cm −2 to 10 14 cm −2 .As the defect density varies, V oc gradually decreases from 2.92 V to 2.66 V, with a minor decline.However, J sc exhibits a slightly larger decline compared to V oc , decreasing slowly from 11.68 mA cm −2 to 10.2 mA cm −2 .Regarding efficiency, when the defect density reaches 10 14 cm −2 , the efficiency drops to 22%, which is 9.29% lower than the efficiency at a density of 10 -8 cm −2 .This analysis underscores the impact of varying defect densities on the performance metrics of the solar cell.

local energy level parameter
In the previous section, a Gaussian distribution of localized energy levels was introduced to simulate defects.In this section, we investigate the influence of localized energy level parameters on the short-circuit current density, open-circuit voltage, fill factor, and efficiency of the solar cell.It was observed in the previous section that when interface defects are located between the middle cell FSF and emitter, the efficiency of the cell experiences the most significant decline with increasing defect density.Therefore, we focus on analyzing the L2 defect, keeping other parameters unchanged, with an interface defect density of 10 13 cm −2 .Specifically, we examine the impact of the peak energy of the Gaussian distribution of the pseudo-donor states (E GA ) and the standard deviation of the Gaussian distribution of pseudo-donor states (W GA ) on the performance of the solar cell.

Standard deviation of Gaussian distribution of acceptor-like states
The simulated parameters of the cell are illustrated in the figure 17(a) The range of W GA is 0.1 to 0.7 eV, while the interface defect density is maintained at 10 13 cm −2 , and E GA is kept at 0.5 eV.As the value of W GA changes, J sc remains constant at 11.68 mA cm −2 , and V oc almost remains unchanged, ranging from 2.88 V to 2.87 V.However, when W GA exceeds 0.5 eV, both FF and efficiency significantly decrease, with FF dropping to 81.6% and efficiency reducing to 27.4%.Overall, it can be inferred that the variation in W GA is unlikely to have an impact on the current density and open-circuit voltage of the multi-junction solar cell.

Peak energies of Gaussian distributions of acceptor-like states
The simulated parameters of the cell are depicted in the figure 17(b).The range of E GA is 0.1 to 0.7 eV, while the interface defect density is maintained at 10 13 cm −2 , and E GA is kept at 0.5 eV.As the value of E GA varies, both J sc and V oc remain constant, at 11.68 mA cm −2 and 2.88 V, respectively.However, when E GA exceeds 0.5 eV, both FF and efficiency notably decrease, with FF dropping to 66.7% and efficiency reducing to 22.4%.Overall, it can be inferred that the variation in E GA does not impact the current density and open-circuit voltage of the multijunction solar cell.In comparison to the previous section, the influence of increasing E GA on the performance of this solar cell is significantly greater than the impact of increasing W GA .It can be concluded that while the peak energy of the class of Gaussian distribution (E GA ) and the standard deviation of the Gaussian distribution (W GA ) have minimal effects on the current density (J sc ) and open-circuit voltage (V oc ) of this solar cell, they have a considerable impact on FF and efficiency.

Conclusions
In summary, (1) the optimal thicknesses for the FSF layer in the top and middle cells are 40 nm and 20 nm, respectively; for the emitter layer, the optimal thicknesses are 160 nm and 70 nm, respectively; the BSF layer thicknesses are 130 nm and 50 nm, respectively; and the optimal thicknesses for the base layer are 1550 nm and 2300 nm, respectively.(2) The overall doping concentration error of the bottom cell has the greatest impact on the power deviation of the TJ solar cell.(3) When utilizing Al 0.9 Ga 0.1 As as the top FSF layer for this TJ solar cell, the conversion efficiency of the cell improved by 1.34%.(4) Compared to the top cell, the internal radiation efficiency of the middle cell is more susceptible to the concentration ratio.(5) Compared to V oc , J sc , and Efficiency, defects have a greater impact, especially when the interface defects are located in the top cell, where at a defect density of 10 10 cm −2 , J sc and Efficiency begin to decrease sharply.When located in the middle cell, a density of 10 14 cm −2 leads to a sudden drop in J sc and Efficiency, and when the interface defects are located between the emitter and base of the top and middle cells, V oc , J sc and efficiency are all affected to different degrees.(6) Through the investigation of introducing defect states characterized by a Gaussian distribution of pseudo-acceptor levels, it was found that the peak energy (E GA ) and standard deviation (W GA ) of the Gaussian distribution of pseudo-acceptor states have minimal impact on the J sc and V oc of the cell, while they exert a significant influence on the FF and efficiency.
In future research, we will continue to offer various theoretical analyses for other multi-junction solar cells, thereby reducing the complexity and cost of improving and optimizing solar cell technologies.

Figure 5 .
Figure 5. TJ solar cell JV and PV curves.

Figure 11 .
Figure 11.(a) Top cell base layer thickness.(b) middle cell base layer thickness.

Figure 12 .
Figure 12.(a) Subcells doping error and power.(b) doping error and power of each layer of the bottom cell.

Figure 13 .
Figure 13.AlGaAs with different alloy ratios as top FSF layer.

Figure 14 .
Figure 14.(a) Internal radiation efficiency of middle cell with bias pressure and concentration multiple.(b) Internal radiation efficiency of top cell with bias pressure and concentration multiple.

Figure 15 .
Figure 15.Location of interfacial defects in the top and middle cells.

Figure 16 .
Figure 16.(a) Defects in the TJ solar cell parameters at L1.(b) defects in the TJ solar cell parameters at L2. (c) Defects in the TJ solar cell parameters at L3.(d) Defects in the TJ solar cell parameters at L4.

Figure 17 .
Figure 17.(a) Effect of W GA on solar cell performances.(b) effect of E GA on solar cell performances.

Table 1 .
Physical models used for simulation.

Table 3 .
TJ solar cell performance parameters.