Calculation of semiconductor band bending due to a superficial zone including electronic states: Application to Schottky diodes

Abstract

A very simple and general method for calculating band bending profiles due to electronic states in semiconductors is proposed. In the present study, states are assumed to be close to the semiconductor surface, their densities decreasing from the surface to the bulk. Two cases are considered. The first is the case of the free semiconductor surface. Some simple examples are presented in order to demonstrate that the penetration depth of the states is also an important parameter that can account for experimental behaviour. The other is the metal-semiconductor contact. Assuming Schottky-Mott interface conditions, the proposed examples show that a Schottky barrier independent of metal work function can only be obtained if the states spread far enough from the interface. The general conclusion, of particular interest for studies devoted to the interaction of semiconductor surfaces with metals or other materials, is that the fact that the states can penetrate into the semiconductor must be considered in any attempt to explain experimental results.