New Solution to High-Field Transport in Semiconductors: II. Velocity Saturation and Ballistic Transmission

Abstract

High-field transport in semiconductor diodes at room temperature is analyzed in the reflection–transmission regime. The pseudo-one-dimensional Boltzmann equation with a constant electric field is transformed into a pair of carrier flux equations. They are analytically solved neither with the relaxation time approximation nor with the perturbation expansion. The carrier energy relaxation due to optical phonon emission is essential in high-field transport. The current- and velocity-field characteristics are closely related to flux transmission through a specific layer, in which the elastic scattering is dominant and the optical phonon emission is absent. If the transmission coefficient is much less than unity, the proportionality of the current to the field results as the Ohm's law in high-field range. The current and velocity tend to saturate when the coefficient approaches unity (ballistic transmission). This result provides simple insight into transport in nanoscale devices.