## 3 Results and Discussion
### Carrier Transport Properties  
After absorbing the photons, the electrons transition from the VB to the CB, resulting in electrons and holes. We can better understand their PCE by calculating their effective masses and exciton binding energy. The calculation of effective mass satisfies the following formula:  
\[\frac{1}{\text{m}^{*}}=\frac{1}{\hbar^{2}}\frac{\partial^{2}E_{n}(\overset{ \rightarrow}{k})}{\partial k^{2}} \tag{5}\]  
As shown in Figure 10, we selected the curves of conduction band minimum and valence band maximum, combined Equation (5) and the software of origin, and obtained the effective masses of electrons and holes at the lowest point (G point) of the band gap; the calculated results are summarized in Table 2. According to Table 2, the electron effective mass is 0.27 m\({}_{0}\) and the hole effective mass is 0.34 m\({}_{0}\) at 0 GPa; the electron effective mass is 0.23 m\({}_{0}\) and the hole effective mass is 0.25 m\({}_{0}\) at \(-\)0.5 GPa. It can be seen that the effective mass of electrons and holes decreases correspondingly after applied pressure, which will lead to better migration efficiency and improve the PCE of solar cells. When looking into the literature, we did not find the experimental data, so we cannot compare with the experimental data, but our calculation provides a reference for future experiments.  
Figure 8: The conductivity of CsGeI\({}_{3}\) of (**a**) real and (**b**) imaginary under the pressure of 0 GPa and \(-\)0.5 GPa.  
Figure 9: The absorption of CsGeI\({}_{3}\) under the pressure of 0 GPa and \(-\)0.5 GPa.  
The exciton binding energy was calculated within the weak Mott-Wannier model, using the following formula [37]:  
\[E_{\text{b}}=13.56\frac{\mu}{\varepsilon_{s}^{2}} \tag{6}\]  
where \(\mu\) is the effective reduced mass, which satisfies the formula:  
\[\frac{1}{\mu}=\frac{1}{m_{e}^{*}}+\frac{1}{m_{h}^{*}} \tag{7}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\mathbf{m_{e}}\) & \(\mathbf{m_{h}}\) & \(\mathbf{\mu}\) & \(\mathbf{\varepsilon_{s}}\) & \(\mathbf{E_{b}}\) **(ev)** \\ \hline
0 GPa & 0.27 & 0.34 & 0.15 & 5.2 & 0.075 \\ \(-\)0.5 GPa & 0.23 & 0.25 & 0.12 & 5.5 & 0.054 \\ \hline \end{tabular}
\end{table}
Table 2: Effective masses and exciton binding energy calculated for CsGeI\({}_{3}\) under the pressure of 0 GPa and \(-\)0.5 GPa. Masses are given in units of the free electron mass m\({}_{0}\).  
Figure 10: Calculated of effective mass at Z point of conduction band bottom and valence band top of CsGeI\({}_{3}\) under the pressure of 0 GPa and \(-\)0.5 GPa.  
where \(\varepsilon_{s}\) is the static dielectric constant (as previously seen). It can be seen from Table 2 that the exciton binding energy is 0.075 eV without pressure, and 0.054 eV under applied pressure. The lower exciton binding energy means that photogenic carriers (electrons and holes) are more easily generated, which helps to improve photoelectric conversion efficiency.  
By calculating the effective mass and the exciton binding energy, we found that CsGeI\({}_{3}\) has a lower effective mass and lower exciton binding energy and can be used as efficient light absorbing material.