Why is the band gap of GaP indirect while that of GaAs and GaN are direct?

Abstract

Many III-V semiconductors possess direct band gaps and are thus widely applied in optoelectronics. Although GaN (either in wurtzite phase or zinc blende phase), GaAs and GaSb are well-known direct gap semiconductors, GaP exhibits an indirect band gap nevertheless. This seems mysterious when considering that, P is between N and As among Group-VA elements and GaN has a direct gap even in the zinc blende structure. In this work, we analyze the generic rule of energy gaps in GaN, GaP and GaAs of the zinc blende phase, and study the trends of gap variation concerning the lattice constant and anion electronegativity. It is demonstrated that a compressed compound among the zinc blende III-V semiconductors is more likely to show an indirect band gap, while a tensed compound tends to possess a direct band gap. While GaP actually manifests a normal behavior, the reason why GaN surprisingly has a direct gap is analyzed through examining and perturbing its valence band as well as conduction band. It turns out that the conduction band electron shows a non-negligible probability to emerge near the N cores. The attractive nucleus potential pulls down the conduction band more strongly at Γ, which is in principle further supported through an analysis of the Kronig-Penney model. The difference between GaP and GaN in this respect is also analyzed in detail.