ELECTRON-DRIFT AND DIFFUSION IN A HIGH-ELECTRIC-FIELD

The Fokker-Planck framework is used to investigate electron transport in a uniform electric field in a solid, under the assumption that the electron be drifting. The drift velocity and diffusion tensor at an ar bitrary field strength are expressed as simple integrals involving the exact band structure and electron-lattice interaction. The position-d ependent energy distribution is obtained explicitly, and it is found t hat the leading edge of a carrier packet is hotter than the trailing e dge. The predictions are in quantitative agreement with a Monte Carlo simulation of transport in the absence of any adjustable parameter. In addition, Ohmic transport is retrieved within the Fokker-Planck forma lism in the limit of a vanishing field strength. It can be envisioned as ''unlucky drift'' in the sense that the field cannot bring about a significant departure from equilibrium statistics. It is further argue d that the connection between equilibrium and high-field statistics in grained in thermodynamic approaches is the reason for their inadequacy in solid-state electronics.