## 1 Introduction  
Organic-inorganic hybrid halide perovskites and related materials have attracted much attention in the past decade due to their high absorption coefficient, appropriate band gap width, excellent carrier mobility, long carrier life, and low cost [1; 2; 3; 4; 5; 6]. Recent studies have shown that they have a high photoelectric conversion efficiency (PCE) of more than 25% [7]. They have been widely used in solar cells, photon emitters, photodetectors, and other photoelectric devices [8; 9; 10; 11]. In general, the most used perovskite materials are organic methylammonium lead iodide and formamidinium lead iodide due to their excellent PCE. However, the organic cations methylammonium cation (MA\({}^{+}\)) and formamidinium cation (FA\({}^{+}\)) are easily decomposed due to sun and rain exposure after prolonged exposure to the air. At present, inorganic perovskite has attracted research attention, among which Cs\({}^{+}\) is the most studied substitute for MA\({}^{+}\) and FA\({}^{+}\). In fact, Cs\({}^{+}\) (1.67 A) has a smaller ionic radius than MA\({}^{+}\) (1.80 A) or FA\({}^{+}\) (1.90 A), and the tolerance factor of CsGeI\({}_{3}\) is 0.81 calculated by the Goldschmidt formular [12; 13]. Due to its high thermal stability, researchers have studied the inorganic perovskite CsPbI\({}_{3}\)[14; 15; 16; 17], in which the PCE of quantum dot devices [16] is as high as 13.4%, and that of thin films [15] is as high as 15.1%. The search for non-toxic PSCs materials has become a research hotspot because CsPbI\({}_{3}\) contains the toxic element Pb. We know that Ge, Sn, and Pb are in the same main group, and that they have similar properties. For example, they have similar electron shells and their outermost shell is composed of two electrons. As an efficient hole transport material, CsGeI\({}_{3}\) can be applied to solar cells due to its small effective hole mass, without low-energy deep hole trap and the suitable band offset with solar absorber materials such as dye molecules and methylammonium lead iodide [18]. [PERSON] et al. synthesized CsGeI\({}_{3}\) in their experiment and studied its PCE. They found that the PCE reached 11% and showed good stability [19].  
Most researchers improve PCE by doping materials. However, the application of pressure can change the structure of PSCs, thus changing their photoelectric properties. Many experiments have been carried out to apply pressure to methylammonium lead iodide to change its electronic structure and photoelectric properties [20; 21]. [PERSON] and [PERSON] studied the geometry and band structures of CsGeBr\({}_{3}\) and CsGeCl\({}_{3}\) under pressure [22; 23]. [PERSON] et al. studied the photoelectric properties of CsPbI\({}_{3}\) at different pressure by the first-principles and found that when the pressure was 1.4 GPa, it had an optimal band gap value of 1.34 eV [24].  
However, there are few studies on the photoelectric properties of CsGeI\({}_{3}\) under pressure. Although [PERSON] et al. studied some photoelectric properties of CsGeI\({}_{3}\) under hydrostatic pressure through first-principles, we still do not know enough about it [25]. Based on the first-principles, the change of photoelectric property of CsGeI\({}_{3}\) was explored at the hydrostatic pressure from \(-\)0.5 GPa to 0.5 GPa. It has been found that its geometric structure, electronic structure, and elastic properties have changed significantly. When the applied pressure is \(-\)0.5 GPa, it has an optimal band gap value of 1.37 eV. Therefore, we focused on the comparative study of the electronic structure, optical properties, carrier migration properties, elastic properties, and thermodynamic properties when the pressure is \(-\)0.5 GPa and 0 GPa. Through the comparative analysis of these photoelectric properties, we found that CsGeI\({}_{3}\) after applied pressure is a good photoelectric material and suitable for PSC material.