Electronic band structure trends of perovskite halides: Beyond Pb and Sn to Ge and Si

The trends in electronic band structure are studied in the cubic ABX₃ halide perovskites for A=Cs; B=Pb, Sn, Ge, Si; and X=I, Br, Cl. The gaps are found to decrease from Pb to Sn and from Ge to Si, but increase from Sn to Ge. The trend is explained in terms of the atom s levels of the group-IV element and the atomic sizes which changes the amount of hybridization with X-p and hence the valence bandwidth. Along the same series spin-orbit coupling also decreases and this tends to increase the gap because of the smaller splitting of the conduction band minimum. Both effects compensate each other to a certain degree. The trend with halogens is to reduce the gap from Cl to I, i. e. , with decreasing electronegativity. The role of the tolerance factor in avoiding octahedron rotations and octahedron edge sharing is discussed. The Ge containing compounds have tolerance factor t>1 and hence do not show the series of octahedral rotation distortions and the existence of edge-sharing octahedral phases known for Pb and Sn-based compounds, but rather a rhombohedral distortion. CsGeI₃ is found to have a suitable gap for photovoltaics both in its cubic (high-temperature) and rhombohedral (low-temperature) phases. The structural stability of the materials in the different phases is also discussed. We find the rhombohedral phase to have lower total energy and slightly larger gaps but to present a less significant distortion of the band structure than the edge-sharing octahedral phases, such as the yellow phase in CsSnI₃. The corresponding silicon based compounds have not yet been synthesized and therefore our estimates are less certain but indicate a small gap for cubic CsSiI₃ and CsSiBr₃ of about 0. 20. 2 eV and 0. 80. 6 eV for CsSiCl₃. The intrinsic stability of the Si compounds is discussed.