Impact-ionization model consistent with the band structure of semiconductors

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Abstract
A new formula for calculating the impact-ionization probability for electrons in semiconductors is derived in terms of the density of states of semiconductors and thus takes into account the details of the realistic band structure. Applying this formula to Si, GaAs, InAs, and In0.53Ga0.47As yields ionization probabilities similar to those derived from the first principles under the constant matrix element approximation, and at high energies (ε≥3 eV) the magnitude and the energy dependence of the calculated ionization probability are similar for each of these materials.