Augmented Fokker-Planck equation for electron transport in arbitrary electric fields

Electron transport in a solid subjected to an arbitrary electric field is analyzed in the energy-position manifold instead of phase space. In the absence of deeply inelastic electron-lattice scattering, the spectral carrier density satisfies a differential equation of the Fokker-Planck type. Subsumption of deeply inelastic events results in an integrodifferential equation which agrees exactly with Monte Carlo simulations in the limit of a vanishing drift-to-instantaneous velocity ratio. Reasonable agreement is found for ratios as high as 0.4, enabling the augmented Fokker-Planck equation to tackle a number of transport issues at a much lower cost than Monte Carlo simulations. (C) 1999 American Institute of Physics. [S0021-8979(99)05724-2].