The intra-collisional field effect in semiconductors. II. Numerical results

For pt.I see ibid., vol.15, p.5411 (1982). Numerical calculations appropriate to intra-valley scattering in silicon using the Airy function formalism of Herbert and Till validate the predictions about field suppression of Airy-Airy scattering made by these authors, but to discuss band-tail scattering it is essential to consider scattering from electron wavepackets. These calculations with exact Airy functions indicate that the field-induced band-tail scattering rates closely compensate the field-suppressed Airy-Airy scattering with the result that the total scattering rate is independent of electric field at high kinetic energy. The formulation has been extended to consider a simple inter-valley scattering model and the scattering rates are found to have a similar field dependence to those for intra-valley scattering. The effective mass in the satellite valley scales the scattering rates in the way predicted by the theory and the principal effect of the energy difference of the valley minima is to set a field-dependent threshold for the onset of inter-valley scattering. The parameters have been chosen so that the calculations are relevant to the Gamma to L transition in GaAs.