A simplified self-consistent model for image force and interface charge in Schottky barriers

Some qualitative features are shown for an electrostatically self-consistent solution, initially without correlation and exchange forces, for the effect of electrons which tunnel from the metal of a Schottky barrier into the energy band gap of the semiconductor. The effect of an incremental electric field in the bulk semiconductor is deduced from a simple analytical treatment. In covalent semiconductors most of the incremental electric field terminates in the semiconductor in a manner almost independent of the nature of the metal, i.e., the effective “metal” electrode exists inside the bulk semiconductor. This is not true for ionic semiconductors. When the “metal” electrode location is used as the origin for the image force, a normal square root of the field dependence of the Schottky image force lowering is predicted at low electric fields and a linear dependence is predicted at high electric fields, both as reported recently by Andrews. The model also predicts the order of magnitude of the very small ba...