## 3 Results and Discussion
So, the \(J_{01}/J_{02}\) ratio can be written as:  
\[\frac{J_{01}}{J_{02}}=\frac{\left(J_{sc}-J_{m}\right)\exp\frac{V_{\infty}}{n_{ 2}V_{T}}-J_{sc}\exp\frac{V_{m}+I_{m}R_{s}}{n_{2}V_{T}}}{J_{sc}\exp\frac{V_{m}+ I_{m}R_{s}}{n_{1}V_{T}}-\left(J_{sc}-J_{m}\right)\exp\frac{V_{\infty}}{n_{1}V_{T}}}. \tag{8}\]  
If the current density-voltage relationships of an Al-BSF solar cell and a PERC solar cell can be measured under different injection levels, the relationships between \(J_{01}/J_{02}\) and open-circuit voltage, short-circuit current, and fill factor can be obtained according to Equation (8). In our analytical method, the root mean square error (RMSE) of current density was used to compare the variation in simulation accuracy. The RMSE of current density is defined as follows:  
\[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{m}\left(j_{mass}^{i}-j_{\alpha l}^{i} \right)^{2}}{m}} \tag{9}\]  
where \(j_{mass}^{i}\) and \(j_{cal}^{i}\) are the measured and calculated values of output current density in point \(i\), respectively, and \(m\) is the number of points. Figure 3 illustrates the flowchart to find \(J_{01}\) and \(J_{02}\) under different injection levels. In this work, \(R_{s}\) and \(R_{sh}\) under different injection levels are given by the measured values. It is necessary to assign good initial values for solving the above nonlinear Equations (1)-(8). When the root mean square error (RMSE) of current density gets to its minimum, the accuracy of the entire curve is satisfied, and the calculated \(J_{01}\) and \(J_{02}\) under different injection levels are derived. \[J_{d1}=J_{01}\bigg{(}\exp\frac{V+JR_{s}}{n_{1}V_{T}}-1\bigg{)} \tag{2}\]0 Flowchart to find the \(J_{01}\) and \(J_{02}\) under different injection levels. Table 2 shows the \(J_{01},J_{02}\), and RMSE of current density for an Al-BSF solar cell at typical injection levels. Table 3 lists the \(J_{01},J_{02}\), and RMSE of current density for a PERC solar cell at typical injection levels. From Tables 2 and 3, it is found that the RMSE of current density is less than 1% for the Al-BSF solar cell and the PERC solar cell at typical injection levels. These results suggest that the difference between calculated and experimental data is very small, and the obtained \(J_{01}\) and \(J_{02}\) values could reveal the recombination behavior of the diffusion region and depletion region for Al-BSF solar cells and PERC solar cells at typical injection levels. Figure 4 displays a comparison of the RMSE of current density for an Al-BSF solar cell and a PERC solar cell under different injection levels. From Figure 4, it can be seen that the RMSEs of current density for the Al-BSF solar cell and the PERC solar cell are nearly the same according to our analytical method under different injection levels. The results show that \(J_{01}\) and \(J_{02}\  
Investigation into the Recombination Parameters of the Diffusion Region and Depletion Region for a PERC Silicon Solar Cell and an Al-BSF Silicon Solar Cell under Different Injection Levels  
The relationship between \(J_{01}\) and the injection level at 25 \({}^{\circ}\)C and AM1.5G for the Al-BSF solar cell and the PERC solar cell is depicted in \[J_{d1}=J_{01}\bigg{(}\exp\frac{V+JR_{s}}{n_{1}V_{T}}-1\bigg{)} \tag{2}\]1 From Figure 5, it is found that the \(J_{01}\) of a PERC solar cell is always lower than that of an Al-BSF solar cell no matter how much the injection level changes. These results suggest that a PERC solar cell has higher carrier collection efficiency under different injection levels compared with an Al-BSF solar cell. As observed, the \(J_{01}\) of the Al-BSF solar cell was \(1.54\times 10^{-12}\) A/cm\({}^{2}\) under STC, but the \(J_{01}\) of the PERC solar cell was only \(1.89\times 10^{-13}\) A/cm\({}^{2}\) under STC. This is because a PERC solar cell with AlOx and SiNx:H rear passivation has a lower back surface recombination velocity compared with an Al-BSF solar cell. This result agrees with other authors' works [42; 43; 44].