THEORY OF ELECTRON-TRANSPORT IN SMALL SEMICONDUCTOR-DEVICES USING THEPAULI MASTER EQUATION

It is argued that the Pauli master equation can be used to simulate el ectron transport in very small electronic devices under steady-state c onditions. When written in a basis of suitable wave functions and with the appropriate open boundary conditions, this transport equation rem oves some of the approximations which render the Boltzmann equation un satisfactory at small length scales, permitting the inclusion of tunne ling, interference effects, arbitrary ''steep'' potentials, and intrac ollisional field effects. However, the master equation is based on the same weak-scattering and long-time limits on which also the Boltzmann equation rests and cannot provide the complete solution of time depen dent quantum transport problems. The main problems consist in describi ng the interaction of the system with the reservoirs-here treated phen omenologically-and in assessing the range of validity of the equation: Only devices smaller than the size of the electron wave packets injec ted from the contacts can be handled, and this constitutes the interes ting range of sub-50 nm devices. Three one-dimensional examples solved by a simple Monte Carlo technique are finally presented. (C) 1998 Ame rican Institute of Physics.