Accurate Band Gaps for Semiconductors from Density Functional Theory

TLDR

Designing semiconductor devices for photovoltaics and thermoelectrics requires materials with suitable band gaps and dopant level alignment, yet conventional LDA and GGA functionals typically underestimate gaps and can misclassify metals, whereas hybrid functionals that incorporate exact Hartree–Fock exchange are known to perform better. The study demonstrates that for CuInSe₂, LDA and GGA predict near‑zero gaps while B3PW91 yields 1.07 eV, close to the experimental 1.04 eV, and across 27 related semiconductors, B3PW91 achieves a mean absolute deviation of only 0.09 eV, outperforming all contemporary hybrid functionals.

Abstract

An essential issue in developing semiconductor devices for photovoltaics and thermoelectrics is to design materials with appropriate band gaps plus the proper positioning of dopant levels relative to the bands. Local density (LDA) and generalized gradient approximation (GGA) density functionals generally underestimate band gaps for semiconductors and sometimes incorrectly predict a metal. Hybrid functionals that include some exact Hartree−Fock exchange are known to be better. We show here for CuInSe2, the parent compound of the promising CIGS Cu(InxGa1−x)Se2 solar devices, that LDA and GGA obtain gaps of 0.0−0.01 eV (experiment is 1.04 eV), while the historically first global hybrid functional, B3PW91, is surprisingly better than B3LYP with band gaps of 1.07 and 0.95 eV, respectively. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a mean average deviation (MAD) of only 0.09 eV, which is substantially better than all modern hybrid functionals.