Abstract
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 barrier variation between p- and n-type semiconductors. Interface contamination is predicted to have a very small effect on the barrier height provided the dopant occurs within the range of the tunneling electrons. If the dopant is deeper, however, and converts the semiconductor type, the effective barrier height, charge storage and photosensitivity are radically changed. It is shown that this phenomenon creates effective Schottky barrier configurations that have softer reverse current-voltage characteristics than an uncontaminated barrier. These conclusions are reinforced by measurements on Hf-n-type-Si Schottky barriers.