Thermodynamic Stability and Structural Insights for CH$_3$NH$_3$Pb$_{1-x}$Si$_x$I$_3$, CH$_3$NH$_3$Pb$_{1-x}$Ge$_x$I$_3$, and CH$_3$NH$_3$Pb$_{1-x}$Sn$_x$I$_3$ Hybrid Perovskite Alloys: A Statistical Approach from First Principles Calculations.

The recent reaching of 20% of conversion efficiency by solar cells based on metal hybrid perovskites (MHP), e.g., the methylammonium (MA) lead iodide, CH3NH3PbI3 (MAPbI3), has excited the scientific community devoted to the photovoltaics materials. However, the toxicity of Pb is a hindrance for large scale commercial of MHP and motivates the search of another congener eco-friendly metal. Here, we employed first-principles calculations via density functional theory combined with the generalized quasichemical approximation to investigate the structural, thermodynamic, and ordering properties of MAPb1-xSixI3, MAPb1-xGexI3, and MAPb1-xSnxI3 alloys as pseudo-cubic structures. The inclusion of a smaller second metal, as Si and Ge, strongly affects the structural properties, reducing the cavity volume occupied by the organic cation and limitating the free orientation under high temperature effects. Unstable and metaestable phases are observed at room temperature for MAPb1-xSixI3, whereas MAPb1-xGexI3 is energetically favored for Pb-rich in ordered phases even at very low temperatures. Conversely, the high miscibility of Pb and Sn into MAPb1-xSnxI3 yields an alloy energetically favored as a pseudo-cubic random alloy with tunable properties at room temperature.