## 3 Results and Discussion
### Electronic Structure  
In order to study the effect of pressure on the electronic structure, we studied the effect of band structure and density of states (DOS) under pressure. We obtained the band gap value of 0.97 eV when no pressure was applied, which is similar to most theoretical calculations [31], but much smaller than the experimental result of 1.60 eV [32]. Although the theoretical calculation is smaller than the experimental value, it does not affect our study on its properties. Therefore, we continued to use DFT-PBE to study the changes of photoelectric properties of perovskite CsGeI\({}_{3}\) after applied pressure. We applied pressure from \(-0.5\) GPa to 0.5 GPa to the material and found that the band gap gradually decreased from 1.37 eV to 0.72 eV, as shown in Figure 3. It was found that when the material is applied with pressure, the band gap gradually decreases, while when the material is applied with tension, the band gap gradually increases. When the tension is 0.5 GPa, the band gap value is 1.37 eV, between 1.3-1.4 eV. According to the Shockley-Queisser theory, this is the band gap value with the best photoelectric efficiency of perovskite materials [33]. As can be seen from Figure 3, the band gap value changed significantly after applied pressure, which is due to the change in the electronic structure of the material. It can be seen from Figure 2 that the cell angle of CsGeI\({}_{3}\) and the bond length of Ge-I all changed significantly.  
Figure 2: The structure parameters of CsGeI\({}_{3}\) under different pressure conditions. (**a**) The curve of energy. (**b**) The curve of the lattice constant. (**c**) The curve of volume. (**d**) The curve of cell angle. (**e**) The curve of bond length of Ge-I. (**f**) The curve of the strain.  
We focused on the comparative study of band structure and DOS when the pressure is \(-0.5\) GPa and \(0\) GPa. As shown in Figures 4 and 5, the band structure and DOS barely changed after the pressure was applied. It can be seen from the figure of band structure that CsGeI\({}_{3}\) is still a direct band gap semiconductor, and the conduction band becomes a little flatter after applied pressure. From Figure 5, it can be seen that the Ge-4p orbital mainly contributes to the conduction band minimum (CBM), and valence band maximum (VBM) was mainly contributed by I-5p orbital. The Cs atom mainly plays a role in the 5p electron orbital, but its DOS is mainly in the deep energy level above \(6\) eV and below \(-6\) eV, and its contribution to the Fermi surface is almost zero. However, Cs atom is very important to stabilize the structure of CsGeI\({}_{3}\).  
Figure 4: The band structure of CsGeI\({}_{3}\) under the pressure of (**a**) \(0\) GPa and (**b**) \(-0.5\) GPa.  
Figure 5: The DOS of CsGeI\({}_{3}\) under the pressure of (**a**) \(0\) GPa and (**b**) \(-0.5\) GPa.  
Figure 3: The band gap of CsGeI\({}_{3}\) under different pressure conditions.  
To further understand the electrons under pressure, we also studied the charge transfer in CsGeI\({}_{3}\), as shown in Figure 6. When the pressure changed from \(-0.5\) GPa to \(0.5\) GPa, the charges of Cs and Ge gradually decrease from \(0.61\) e and \(0.22\) e to \(0.56\) e and \(0.08\) e, respectively. According to the law of conservation of charge, the charge of I also decreased. The calculation shows that the charge of I decreased from \(-0.28\) e to \(-0.21\) e.