Origin of the variation of exciton binding energy in semiconductors

Excitonic effects are crucial to optical properties, and the exciton binding energy E(b) in technologically important semiconductors varies from merely a few meV to about 100 meV. This large variation, however, is not well understood. We investigate the relationship between the electronic band structures and exciton binding energies in semiconductors, employing first-principles calculations based on the density functional theory and the many-body perturbation theory using Green's functions. Our results clearly show that E(b) increases as the localization of valence electrons increases due to the reduced electronic screening. Furthermore, E(b) increases in ionic semiconductors such as ZnO because, contrary to the simple two-level coupling model, it has both conduction and valence band edge states strongly localized on anion sites, leading to an enhanced electron-hole interaction. These trends are quantized by electronic structures obtained from the density functional theory; thus, our approach can be applied to understand the excitonic effects in complex semiconducting materials.