AVALANCHE MULTIPLICATION IN SEMICONDUCTORS - A MODIFICATION OF CHYNOWETHS LAW

A new theory is presented for calculating the avalanche multiplication factor M(x) in semiconductors. The integral equation, which determines M(x), takes into account that a particle has to gain a critical energy U(c) (threshold energy) from the electric field E(x) in order to be able to ionize lattice and impurity atoms. Therefore, our theory is also applicable to narrow junctions. The input to our theory are the mean free paths and the threshold energies of electrons (L(n), U(c)n) and holes (L(p), U(c)p), respectively. Approximations to the integral equation for M(x) lead to ionization rates alpha-n(E), alpha-p(E) for electrons and holes, respectively. The dependence of these ionization rates on the electric field is determined analytically and a correction to Chynoweth's law is found. In this paper we merely want to show that the field dependence of the ionization rates given by Chynoweth's law (alpha-s(c) = alpha-s(c) exp(-b(s)c/E) with s = {n,p}) is, in general, a crude approximation within our more general theory. Rather we shall derive an approximation of the following form: [GRAPHICS] We want to stress that the purpose of our paper is not to determine the physical parameters a(s), b(s) from multiplication factor measurements. Rather we want to convince the reader that our expression of the ionization rate is both a simple and, for narrow junctions, a necessary correction to Chynoweth's law. Considering abrupt p-n junctions with different doping concentrations it is shown that our dependence of ionization rate on electric field E(x) is valid in a range 2 x 10(5) < E < 6 x 10(5) V/cm. In contrast to the results by Van Overstraeten and De Man, no splitting of the constants a(s), b(s) in a high field and a low field range is required in order to obtain a correct multiplication factor. The arguments used are self contained.