New Solution to High-Field Transport in Semiconductors: I. Elastic Scattering without Energy Relaxation

Abstract

High-field transport in a semiconductor diode structure at room temperature is newly analyzed in a reflection–transmission regime. The Boltzmann equation with a constant electric field E is applied to a semiconductor channel of length L, and a pair of flux equations is analytically solved. For applied fields larger than ∼500 V/cm for silicon, the energy relaxation by the acoustic phonon scattering hardly catches up with the energy gain from the field, and the kinetic energy accumulates generating hot carriers. As a limiting case, in this paper we analyze carrier transport with elastic scattering and without energy relaxation. Current density proportional to √E/L is derived for a wide electric field range. At much higher fields, the ballistic transmission of carriers through the channel occurs, and current density tends to saturate. The result will find its application in sufficiently small systems, where energy relaxation by optical phonon scattering is not dominant.