Effect of Compensation on Breakdown Fields in Homogeneous Semiconductors

Abstract

Using Bloch and hydrogen-like functions, the impact-ionization coefficient has been calculated for processes in which an electron in a band collides with an electron on an impurity so as to ionize it. The problem is solved in the zero-order approximation, which is valid for trap depths large compared to $k{T}_e$. Estimates of impact-ionization cross sections obtained this way are in good agreement with exact numerical calculations for the range relevant to this paper. The theory is applied to study the effect of doping on breakdown electric fields in bulk materials at low temperatures. Comparison with experimental work done by Lambert on $p$-type germanium yields satisfactory agreement with the theory. Graphs of the impact-ionization coefficient as a function of electron temperature have also been obtained for several trap depths. Finally, we present a framework for predicting breakdown fields if donor and acceptor concentrations are known.