Avalanche multiplication factors in Ge and Si abrupt junctions

Analytical approximations for the multiplication factors M
n
and M
p
in Ge and Si one-sided abrupt junctions are given. The resulting expressions account for different α and β ionization rates and are quite accurate. With further approximations on the ionization integrals, very simple expressions of 1 -- 1/M both for electron and holes in the range of very low multiplication are obtained, depending from a single ionization rate.