Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl${}_{3}$, CsSnBr${}_{3}$, and CsSnI${}_{3}$

Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl $_{3}$ , CsSnBr $_{3}$ , and CsSnI $_{3}$

Ling-yi Huang and Walter R. L. Lambrecht

Phys. Rev. B 88, 165203 – Published 17 October 2013

Abstract

The halide perovskites CsSn $X_{3}$ , with $X =$ Cl, Br, I, are investigated using quasiparticle self-consistent $G W$ electronic structure calculations. These materials are found to have an “inverted” band structure from most semiconductors with a nondegenerate $s$ -like valence band maximum (VBM) and triply degenerate $p$ -like conduction band minimum (CBM). The small hole effective mass results in high hole mobility, in agreement with recent reports for CsSnI $_{3}$ . The relatively small band gap changes from Cl to Br to I result from the intra-atomic Sn $s$ and Sn $p$ characters of the VBM and CBM, respectively. The latter is also responsible for the high oscillator strength of the optical transition in these direct-gap semiconductors and hence a strong luminescence and absorption. The band gap change with lattice constant is also anomalous. It increases with increasing lattice constant, and this results from the decreasing valence band width due to the decreased Sn $s$ with anion $p$ interaction. It leads to an anomalous temperature dependence of the gap. The changes in band gap in different lower-symmetry crystallographic phases is studied. The exciton binding energy of the free exciton, estimated from the Wannier-Mott exciton theory and the calculated dielectric constants and effective masses, is found to be two orders of magnitude smaller than previously claimed in literature, or of the order of 0.1 meV. The photoluminescence peak previously assigned to the free exciton is instead ascribed to an acceptor bound exciton. The phonons at the $Γ$ point are calculated as well as the related enhancement of the dielectric constants.