Unified theory of direct or indirect band-gap nature of conventional semiconductors

Although the direct or indirect nature of the band-gap transition is an essential parameter of semiconductors for optoelectronic applications, the reasons for why some of the conventional semiconductors have direct or indirect band gaps remains ambiguous. In this paper, we reveal that the existence of the occupied cation d bands is a prime element in determining the directness of the band gap of semiconductors through the s-d and p-d couplings, which push the conduction band energy levels at the X and L valley up, but leave the Gamma-valley conduction state unchanged. This unified theory unambiguously explains why diamond, Si, Ge, and Al-containing group III-V semiconductors, which do not have active occupied d bands, have indirect band gaps, and the remaining common semiconductors, except GaP, have direct band gaps. Besides s-d and p-d couplings, bond length and electronegativity of anions are two remaining factors regulating the energy ordering of the Gamma, X, and L valleys of the conduction band, and are responsible for the anomalous band-gap behaviors in GaN, GaP, and GaAs that have direct, indirect, and direct band gaps, respectively, despite the fact that N, P, and As are in ascending order of the atomic number. This understanding will shed light on the design of direct band-gap light-emitting materials.