Space-charge striations

The non-local nature of impact ionization is modelled using lucky-drift theory with the assumption that the relevant electric field is the average field, but that the relevant drift velocity is that associated with the local field. The carrier density relevant for impact ionization is also taken to be non-local. The model is applied to the case of a thin film insulator with Fowler-Nordheim injections of electrons at the cathode. For clarity's sake we avoid considering the excitation of holes and limit attention to the ionization of a set of occupied deep-level states present in high concentration. We show that the non-local nature of the ionization process reduces the local field markedly, resulting in a pile-up of free electrons to maintain current continuity in the rest of the film. This is contrasted to the prediction of local-impact-ionization theory, in which the field is reduced merely to that necessary to sustain a small level of ionization. Under certain circumstances space-charge striations are produced analogous to the situation in gas discharge, and for some film thicknesses a NDR occurs.