A new simplified approach to the problem of "soft" threshold energy in impact ionization in semiconductors is presented. The model used is entirely classical and leads to a simple exact formula for the ionization rate as a function of energy. This result is used as the basis for modifying the "lucky drift" model of impact ionization, as has been done previously for other models of the "soft" threshold. The final analytic relations show excellent agreement with the available experimental data for the ionization coefficients in GaAs but indicate that the impact ionization process may involve three (or more) incident particles rather than two as previously thought.
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R.C. Woods (1987) studied this question.