# Theory of avalanche breakdown in InSb and InAs

## Abstract

We have constructed a theory of avalanche breakdown for polar semiconductors such as InSb and InAs in which the primary electron-scattering mechanism is polar-optical-mode scattering. Because of the anisotropy of polar scattering, previous theories of avalanche breakdown involving the assumptions of an isotropic scattering probability and/or a nearly isotropic electron distribution should not be appropriate for polar semiconductors. We have assumed a very anisotropic electron distribution which is narrowly drawn out in the direction of the electric field. We also distinguish between small- and large-angle scattering, since for polar scattering, the probability of scattering to a state close to the initial state is much greater than the probability for scattering through a large angle, although the latter process results in a greater loss of energy, since it places the electron in a state in which it is decelerated by the field. The electron distribution function is obtained analytically, and from it the pair-generation rate and electron drift velocity are calculated for InSb and InAs. The pair-generation rate for InSb is obtained using the ionicity which best fits the low-field-mobility data and a hyperbolic conduction band, and it agrees very well with experimental data on the generation rate in InSb. The calculated drift velocity at fields above 200 V/cm is also in good agreement with the drift-velocity measurements by Glicksman and Hicenbothem, showing that the electron distribution is, indeed, highly anisotropic. © 1968 The American Physical Society.