The Stationary Current-Voltage Characteristics of the Quantum Drift-Diffusion Model

Abstract

This paper is concerned with numerical algorithms for the bipolar quantum drift-diffusion model. For the thermal equilibrium case, a quasi-gradient method minimizing the energy functional is introduced and strong convergence is proved. The computation of current-voltage characteristics is performed by means of an extended Gummel-iteration. It is shown that the involved fixed point mapping is a contraction for small applied voltages. In this case the model equations are uniquely solvable and convergence of the proposed iteration scheme follows. Numerical simulations of a one-dimensional resonant tunneling diode are presented. The computed current-voltage characteristics are in good qualitative agreement with experimental measurements. The appearance of negative differential resistances is verified for the first time in a quantum drift-diffusion model.