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

This paper is concerned with numerical algorithms for the bipolar quantum drift diiusion model. For the thermal equilibrium case a quasi-gradient method minimizing the energy functional is introduced and strong convergence is proven. The computation of current{voltage characteristics is performed by means of an extended Gummel{iteration. It is shown that the involved xed 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 diierential resistances is veriied for the rst time in a Quantum Drift Diiusion model.