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First-Principles Study on Material Properties and Stability of Inorganic Halide Perovskite Solid Solutions CsPb(I$_{1-x}$Br$_x$)$_3$ towards High Performance Perovskite Solar Cells

All-inorganic halide perovskites have attracted a great interest as a promising light harvester of perovskite solar cells due to their enhanced chemical stability. In this work we investigate the material properties of solid solutions CsPb(I$_{1-x}$Br$_x$)$_3$ in cubic phase by applying the virtual crystal approximation approach within a density functional theory framework. First we check the validity of constructed pseudopotentials of the virtual atoms (X = I$_{1-x}$Br$_x$) by verifying that the lattice constants follow the linear function of mixing ratio. We then suggest an idea of using the hybrid HSE functional with linear increasing value of exact exchange term as increasing the Br content x, which produces the band gaps of CsPbX3 in good agreement with the available experimental data. The calculated light absorption coefficients and reflectivity show the systematic varying tendency to the Br content. We calculate the phonon dispersions of CsPbX3, CsX and PbX2 as slightly changing their volumes, revealing the phase instability of CsPbX3 and calculating the thermodynamic potential function differences. By projecting Gibbs free energy differences onto the plane of G = 0, we determine the P - T diagram for CsPbX3 to be stable against the chemical decomposition, highlighting that the area of being stable extends gradually as the Br content increases.