Semi-classical balance equations for the first four moments of the Boltzmann equation are derived, including impact ionisation of hot carriers. The authors calculate the impact ionisation rate and the resulting energy and momentum relaxation rates as functions of the mean energy per carrier, and show that impact ionisation leads to a novel, threshold-like nonlinear energy relaxation rate which becomes important for high carrier energies.
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Schöll et al. (1987) studied this question.
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