Abstract
A Fokker–Planck equation for carrier transport in semiconductors is derived from the Boltzmann transport equation by expanding in Legendre polynomials and assuming the phonon energy exchanged at momentum randomizing collisions is small compared with the mean carrier energy. The method is used to compute impact ionization probability distributions in space and time and the results agree well with those generated by an equivalent Monte Carlo model over a wide range of electric fields from 300 kV/cm to 1 MV/cm.
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