When electrons and holes traverse a semiconductor depletion region under large reverse bias they can acquire enough energy to impact ionize a secondary carrier. This effect, known as avalanche multiplication, has been widely investigated for the more commonplace semiconductors, such as Si, Ge, and GaAs. The modeling [87-89] of avalanche multiplication has been primarily phenomenological, and it is based on considerations of the electron distribution function obtained from equating the energy gained by the carrier from the applied electric field to the energy lost by interaction with optical phonons. The distribution function obtained in this way then has a fraction of carriers with sufficient energy to impact ionize electron-hole pairs. The probability of impact ionization is assumed to be a function of applied electric field only and in no way depends on the position or history of the carrier. The band structure of the specific semiconductor is essentially ignored.
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