## 4 Conclusions  
Based on the first-principles, the physical properties of CsGeI\({}_{3}\) were studied under hydrostatic pressure from \(-0.5\) GPa to \(0.5\) GPa with an interval of \(0.1\) GPa in this paper. The results showed that its geometric structure, electronic structure, and elastic properties changed significantly. When the hydrostatic pressure was \(-0.5\) GPa, the optical band gap value of CsGeI\({}_{3}\) increased from \(0.97\) eV to \(1.37\) eV, reaching the optimal band gap value. This paper focused on the properties of CsGeI\({}_{3}\) when the pressure was \(0\) GPa and \(-0.5\) GPa, and the results are as follows:  
1. CsGeI\({}_{3}\) is still a direct band gap semiconductor. The band structure and DOS of CsGeI\({}_{3}\) hardly changed after applied pressure, but the conduction band became a little flatter. When the pressure changed from \(-0.5\) GPa to \(0.5\) GPa, the charge transfer number of Cs\({}^{+}\), Ge\({}^{2+}\), and \(\Gamma\) decreased.
2. The dielectric, conductivity, and absorption coefficient of CsGeI\({}_{3}\) under pressure of \(-0.5\) GPa were higher than that without pressure. Three peaks appeared simultaneously in the imaginary part of the dielectric function, the real part of the conductivity, and the absorption coefficient, located around \(4.0\) eV, \(6.5\) eV, and \(8.5\) eV. In either visible light or an ultraviolet region, the absorption peak was slightly larger after applied pressure than that without applied pressure, and the absorption light had a blue shift phenomenon under pressure.
3. Both the effective mass and exciton binding energy were reduced after the application of pressure, indicating that photogenic carriers were more likely to be generated after pressure, and that carriers had better migration efficiency, which was conducive to improving the photoelectric conversion efficiency.  
Figure 12: The thermodynamic properties of CsGeI\({}_{3}\) of (**a**) Debye temperature, (**b**) heat capacity, and (**c**) enthalpy, temperature-entropy, and free energy under the pressure of \(0\) GPa and \(-0.5\) GPa.  
Though multiple calculations of the Born-Huang stability criterion, the tolerance factor T, and phonon spectrum with or without virtual frequency, it was found that CsGeI\({}_{3}\) was stable under both pressure conditions. We also calculated the elastic modulus of both pressure conditions and found that they were both soft, ductile, and anisotropic, and the values of B, B/G, and A decreased after applying pressure.
* It was found that the Debye temperature and heat capacity increased with the increase of thermodynamic temperature, and the Debye temperature increased rapidly after pressure, while the heat capacity increased slowly and eventually stabilized. Through the calculation of enthalpy, entropy, and Gibbs free energy of CsGeI\({}_{3}\), it was found that the Gibbs free energy of CsGeI\({}_{3}\) decreases faster with the increase of temperature without pressure, which indicates that CsGeI\({}_{3}\) has higher stability without pressure.  
Conceptualization, Formal analysis, Methodology, and Writing--Original draft, L.-K.G.; Funding acquisition, Supervision, Y.-L.T.; Writing--Review and editing, Y.-L.T., X.-F.D. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the National Natural Science Foundation of China Program (Grant No.11164004, 61835003), Guizhou Provincial Photonic Science and Technology Innovation team (Qianke Joint talents team [2015]4017) and the Industrial Research Project of Guizhou Province (GY[2012]3060).  
The authors declare no conflict of interest.