First-Principles Calculations of Barrier Heights and Valence-Band Offsets

Abstract

The local-density approximation to the density-functional theory or, for short, LDA-DF theory is the most powerful and widely used tool for theoretical studies of the ground-state properties of solids. However, excitation energies such as, for example, the width of the energy gaps between the valence and conduction bands of semiconductors cannot be correctly obtained from such calculations. The fundamental band gaps of the elemental semiconductors C, Si, and Ge as well as of the III–V and II–VI compounds are notoriously underestimated by 25 to 50%. However, it became possible to compute quasi-particle energies and band gaps of semiconductors from first principles by using the so called GW approximation for the electron self-energy which was pioneered by Hybertsen and Louie [1986] and by Godby et al. [1988]. The resulting band-gap energies agree to within 0.1 to 0.3 eV with the experimental values. Bechstedt and DelSole [1988, 1990], Zakharov et al. [1994] and Grossner et al. [1999] calculated the quasi-particle shifts of the valence-band maxima of the III–V and the II–VI compound semiconductors in the GW approximation. The quasi-particle corrections move the valence band-maxima to lower energies and, on the average, the GW correction accounts for 63 ± 2% of the quasi-particle widening of the LDA-DFT band gaps. To mention the most important point first, it is obviously much more demanding to calculate the barrier heights of Schottky contacts than the valence-band offsets of heterostructures even if the most advanced theoretical tools, ab initio LDA-DFT plus GW corrections, are employed.