Theory of Electron Transport In Small Semiconductor Devices Using the Pauli Master Equation

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 wavefunctions and with the approximate open boundary conditions, this transport equation removes some of the approximations which render the Boltzmann equation unsatisfactory at small length-scales, permitting the inclusion of tunneling, interference effects, arbitrary 'steep' potentials, and intra-collisional field effects. However, the master equation is based on the same weak scattering and long-time limits on which the Boltzmann 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 wavepackets injected from the contacts can be handled, and this constitutes the interesting range of sub-50nm devices. Three one-dimensional examples solved by a simple Monte Carlo technique are finally presented.