## 3 Calculation Results and Analysis
### Analysis of the Optical-Electrical-Thermal Coupling Effect of Output Characteristics
#### 3.3.2 Open-Circuit Voltage  
The change in the open-circuit voltage along the optical axis is shown in Figure 7b. It can be seen that a minimum of the open-circuit voltage near the focal plane also exists, and the maximum on both sides (\(Z=108\) mm, 114.5 mm) is about 3% higher than it, which is related to the optical-electrical-thermal coupling effect caused by the non-uniform focusing. Figure 10a shows the change in the open-circuit voltage of the InGaP, InGaAs and Ge sub cells along the optical axis without considering the temperature. It can be seen that the open-circuit voltages of the InGaP, InGaAs and Ge sub cells of the triple-junction cell reach minimum at the position of \(Z=110\) mm, 111 mm and 112 mm, respectively. The non-uniformity of the focusing and the mismatch between the sub cells will decrease the open-circuit voltage. Due to the non-uniformity of illumination, the carrier concentration is non-uniform and a potential difference on the surface of the emission region exists, resulting in transverse current on the cell surface [43]. It can be seen from the diode model of the solar cell that the greater the transverse potential difference on the cell surface, the smaller the open-circuit voltage of the cell. The open-circuit voltage changes exponentially with the radiation power. Therefore, when the concentration heterogeneity increases, the carrier concentration gradient on the surface of the cell increases thus increasing the surface  
Figure 9: (**a**) Short-circuit current of three sub cells; (**b**) Minimum short-circuit current of sub cells and short-circuit current of triple-junction solar cell.  
potential difference. Figure 10b compares the sum of the open-circuit voltage of the InGaP, InGaAs and Ge sub cells with the open-circuit voltage of the triple-junction solar cell. The sum of the open-circuit voltage of the sub cells basically coincides with the curve of the triple-junction cell, indicating that the open-circuit voltage of the triple-junction solar cell is mainly the result of the non-uniform irradiance.  
In order to analyze the influence of optic-electric-thermal coupling on the open-circuit voltage specifically, a photoelectric conversion simulation without considering coupled effect is set in this paper in which the temperature of the cell along the optical axis is set as a fixed value for calculation. Figure 11 shows the comparison of the open-circuit voltage characteristics of each sub cell and the whole cell with coupling and no coupling. When there is no coupling effect, the maximum open-circuit voltage of triple-junction cells is 2.675 v at Z = 108 mm, which is 0.047 v greater than the minimum value of 2.628 v at Z = 112 mm. When considering the optical-electrical-thermal coupling, the maximum voltage is 2.702 v at Z = 108 mm, which is 3% higher than the minimum. Compared with no coupling, the difference between the maximum and minimum of open-circuit voltage increases by 57.4%. The change in the open-circuit voltage along the optical axis cannot be ignored due to the optical-electrical-thermal coupling caused by the non-uniform irradiance. The minimum of open-circuit voltage near the focal plane is caused by the strongest optical non-uniformity and the optical-electrical-thermal coupling exacerbates the decrease in open-circuit voltage. On the contrary, at the position slightly away from the focal plane, due to the great improvement of the non-uniformity, the photoelectric conversion efficiency is improved and the boundary heat source is reduced. Under the same conditions of heat dissipation, the temperature at the position slightly away from the focal plane is reduced, which further improves the output performance of the cell and the optical-electrical-thermal coupling further increases the open-circuit voltage.