Impact ionisation rate and soft energy thresholds for anisotropic parabolic band structures

The effect of anisotropic parabolic energy bands and of indirect parabolic energy bands (conduction and valence band extrema at different points in wavevector space) on the transition probability per unit time for impact ionisation is investigated. The resulting direction-dependent threshold energy is described by introducing a threshold ellipsoid. It is found that for the 'lucky-drift' model for impact ionisation in an electric field the transition probability rate which is applicable increases from zero above the energy threshold with a cubic power for anisotropic or indirect parabolic bands, or, in special circumstances a 5/2 power compared with the more usual square law of the Keldysh result for direct isotropic parabolic band structures.