Nonlocality of Carrier Multiplication in Semiconductor Depletion Layers

Analytical and numerical calculations of multiplication coefficients in the Schottky junctions are performed with inhomogeneity of the electric field taken into account. It is shown that in the thin depletion layers distribution functions of electrons and holes and their impact ionization (II) coefficients is nonlocal, i.e. they depend not only upon the electric field strength at a certain point but also on the fields in the vicinity of the point. In such nonlocal cases the introduction of the II coefficients is justified only for small multiplication coefficients, for the large ones they make no sence. If one assumes that the carriers — holes and electrons — differ from each other by the sign of the charge only, the nonlocality effect does not change just the values of the II coefficients obtained in the local approximation, but provides as well the difference between the electron and hole multiplication coefficients. This is due to the electric field asymmetry in the depletion layer.