Quasi-rigid-band behavior and band gap changes upon isovalent substitution in Cs ₃ Bi ₂ Br _{9− <i>x</i>} I _<i>x</i>

Abstract The recently introduced approach, combining the parameter-free Armiento-Kümmel generalized gradient approximation exchange functional with the nonseparable gradient approximation Minnesota correlation functional, was used to calculate the electronic structure of the Cs 3 Bi 2 Br 9− x I x series within density functional theory including the spin–orbit coupling. The changes in the band gap size and its dependence on the x value was investigated. The band gap was found to be of indirect nature and it decreases with increasing I content as long as the system is in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>P</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>m</mml:mi> <mml:mn>1</mml:mn> </mml:math> phase. A clear non-linear dependence of the band gap size on x was established which is in qualitative and quantitative agreement with reported experimental data. The quasi-rigid band behavior of the states in the valence and conduction bands of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>P</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>m</mml:mi> <mml:mn>1</mml:mn> </mml:math> phase is discussed since no significant changes in the shape of the total density of unoccupied states were observed upon the isovalent substitution.