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Although the direct or indirect nature of the bandgap transition is anessential parameter of semiconductors for optoelectronic applications, theunderstanding why some of the conventional semiconductors have direct orindirect bandgaps remains ambiguous. In this Letter, we revealed that theexistence of the occupied cation d bands is a prime element in determining thedirectness of the bandgap of semiconductors through the s-d and p-d couplings,which push the conduction band energy levels at the X- and L-valley up, butleaves the {\Gamma}-valley conduction state unchanged. This unified theoryunambiguously explains why Diamond, Si, Ge, and Al-containing group III-Vsemiconductors, which do not have active occupied d bands, have indirectbandgaps and remaining common semiconductors, except GaP, have direct bandgaps.Besides s-d and p-d couplings, bond length and electronegativity of anions aretwo remaining factors regulating the energy ordering of the {\Gamma}-, X-, andL-valley of the conduction band, and are responsible for the anomalous bandgapbehaviors in GaN, GaP, and GaAs that have direct, indirect, and directbandgaps, respectively, despite the fact that N, P, and As are in ascendingorder of the atomic number. This understanding will shed light on the design ofnew direct bandgap light-emitting materials.

Unified theory of the direct or indirect bandgap nature of conventional semiconductors