On the band gap variation in CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$

TL;DR

This study uses advanced density-functional-theory calculations to analyze how the band gap in mixed halide perovskites varies with composition, revealing a quadratic-like behavior and supporting the presence of significant bowing.

Contribution

It provides detailed computational insights into the band gap variation and bowing parameter in CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$, clarifying discrepancies in experimental reports.

Findings

Band gap variation is quadratic-like with Br content.

Calculated band gaps match experimental values.

Supports significant bowing parameter in the material.

Abstract

The electronic structure and the band gap behavior of CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$ for $x$=0.25, 0.33, 0.50, 0.67, 0.75, 1.00 were studied using the full-relativistic density-functional-theory calculations. A combination of the parameter-free Armiento-K\"{u}mmel generalized gradient approximation exchange functional with the nonseparable gradient approximation Minnesota correlation functional was employed. The calculated band gap sizes for the CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$ series were found to be similar to the experimentally measured values. While the change of the optimized lattice parameter with an increasing Br content can be described by a linear fit, the calculated band gap variation exhibits rather a quadratic-like behavior over the $x$ region of the cubic crystal structure. While the experimental reports are divided on whether the bowing parameter value is being very small or significant, our calculated results support the latter case.