Theory of electron transport in small semiconductor devices using the Pauli master equation

Abstract

It is argued that the Pauli master equation can be used to simulate electron transport in very small electronic devices under steady-state conditions. When written in a basis of suitable wave functions and with the appropriate open boundary conditions, this transport equation removes some of the approximations which render the Boltzman equation unsatisfactory at small length scales, permitting the inclusion of tunneling, interference effects, arbitrary "steep" potentials, and intracollisional field effects. However, the master equation is based on the same weak-scattering and long-time limits on which also the Boltzman equation rests and cannot provide the complete solution of time dependent quantum transport problems. The main problems consist in describing the interaction of the system with the reservoirs - here treated phenomenologically - and in assessing the range of validity of the equation: Only devices smaller than the size of the electron wave packets injected from the contacts can be handled, and this constitutes the interesting range of sub-50 nm devices. Three one-dimensional examples solved by a simple Monte Carlo technique are finally presented. © 1998 American Institute of Physics.