Full-band-structure theory of high-field transport and impact ionization of electrons and holes in Ge, Si, and GaAs

The empirical pseudopotential band-structure of Ge, Si, and GaAs is used to compute the impact ionization (pair production) rate for electrons and holes. The constant-matrix-element and Kane's random-k approximations are also employed, to assess the importance of the energy-dependence of the Coulomb matrix element, of momentum conservation, and of the joint density of states. For electrons in Si and electrons and holes in Ge and GaAs, the latter is found to be dominant, while for holes in Si momentum conservation appears to be an important constraint on ionization processes near threshold. These results are then fitted to an isotropie ionization rate, function of carrier energy only. Full-band-structure Monte Carlo simulations are finally performed in order to calibrate the acoustic and nonpolar-optical deformation potentials. The low-energy deformation potentials are obtained from the usual
¹
fits to experimental velocity-field characteristics, while high-energy deformation potentials are determined from fits to experimental data on the ionization coefficients. The usual ambiguity of conventional Monte Carlo calibration of the scattering parameters ∼ using both carrier-phonon and impact ionization rates as fitting entities ∼ is thus removed, giving us better confidence on the final result. The deformation potentials so obtained are in good agreement with those reported in the literature, whenever a comparison is meaningful.