Impact ionization coefficient and energy distribution function at high fields in semiconductors

Impact ionization coefficients in semiconductors are numerically calculated following Keldysh’s method [Sov. Phys. JETP 21, 1135 (1965)]. This requires deriving expressions for an energy-dependent mean free path l(ε) and an energy-dependent impact ionization scattering rate rii(ε). In the derivation of rii(ε), a nonparabolic ε-k relation as well as a smooth transition from the phonon-assisted impact ionization to the phononless impact ionization are considered. Numerically calculated impact ionization coefficients for electrons and holes in Ge, Si, and GaAs agree very well with experimental data. The calculated Keldysh energy distribution function is also compared with the standard Maxwellian distribution. The average mean free path l̄, which is a function of the electric field, has values within the range often quoted in the literature.