Normalized representation of the avalanche breakdown behaviour in one-sided abrupt junctions

Abstract

Analytical solutions for the avalanche breakdown voltage, U b , as a function of the net doping concentration, N, in one-sided abrupt junctions and its temperature dependence are presented. The results are based on a broken rational approximation function for the field dependence of the impact ionization coefficient, α( F), and on the assumption that the impact ionization coefficient of the electrons and holes are related by a constant ratio γ. Application to the α( F) relations introduced by Chynoweth and Wolff yields normalized curves applicable to arbitrary semiconductor materials covering the familiar (d U b /d N) < 0) and anomalous ((d U b /d N) > 0) ranges of avalanche breakdown behaviour predicted in a previous paper. It is shown that the anomaly is correlated with an anomalous temperature coefficient (d U b /d T) < 0. The temperature dependence is expected to be at its lowest for that doping, N min, at which U b ( N) reaches a minimun values. The normalized curves are in good agreement with published theoretical and experimental results. Taking into account the tunneling breakdown mechanism, the anomaly is in general restricted to narrow energy band gap materials at low temperatures. This is confirmed experimentally for InSb by investigations on Schottky barrier diodes presented in this paper and published results obtained from p- n junctions.