Theory of band line-ups

Abstract

Natural band line-ups may be defined in terms of tight-binding energy bands, which place the bands for all materials on the same energy scale. These line-ups account quite well for the observed line-ups at semiconductor heterojunctions. However, for metal–semiconductor interfaces they place the metal Fermi energy a few electron volts above the conduction band edge in most cases, leading to Ohmic contacts. Corrections to the natural band line-ups from interface-bond dipoles are then added. They are found to be very small for heterojunctions, but can be of the order of an electron volt for metal–semiconductor interfaces; the latter were calculated replacing the metal by an ‘‘image lattice,’’ which should provide a good description of the interface. An additional shift due to tails of the metallic states in the semiconductor [Metal-induced gaps (MIGs)] are calculated analytically, including the effects of both light and heavy electron and hole bands; the heavy bands being seen to dominate. The resulting formula leads to a maximum shift of 0.4 eV in the case of metal–GaAs. The cell-averaged Green’s function is also calculated analytically for this system. It is seen to be dominated by the light bands and therefore not to represent well the interface dipole. It also does not address the size of the dipole, which we have found to be small. It is concluded that heterojunction band line-ups are consistent with ideal interface geometry, but defects at the interface are required to understand Schottky barriers at metal–semiconductor interfaces, many defects being required. The observed behavior at a metal–gallium arsenide interface is consistent with positive-U defects, such as arsenic antisites with a gallium antisite spectator; that of the metal–silicon interface is consistent with negative-U defects, such as silicon vacancies.