Master-equation approach to the study of electronic transport in small semiconductor devices

Previously [J. Appl. Phys. 83, 270 (1998)] the Pauli master equation has been argued to constitute an equation suitable for the simulation of steady-state electron transport in semiconductor devices of length L smaller than the dephasing length ${\lambda }_{\phi }$ in the contacts. Here, the master equation is derived emphasizing the role played by the dissipative interactions of the Van Hove-type, by the Markov approximation, and by the Van Hove limit in establishing irreversibility. An extension of the method to realistic band structures is also presented. Finally, the approach is applied to simulate electron transport in a simple one-dimensional Si $\mathrm{nin}$ diode at 77 K.