Optimization of the Deterministic Solution of the Discrete Wigner Equation

The development of novel nanoelectronic devices requires methods capable to simulate quantum-mechanical effects in the carrier transport processes. We present a deterministic method based on an integral formulation of the Wigner equation, which considers the evolution of an initial condition as the superposition of the propagation of particular fundamental contributions. Major considerations are necessary, to overcome the memory and time demands typical for any quantum transport method. An advantage of our method is that it is perfectly suited for parallelization due to the independence of each fundamental contribution. Furthermore, a dramatic speed-up of the simulations has been achieved due to a preconditioning of the resulting equation system. To evaluate this deterministic approach, the simulation of a Resonant Tunneling Diode, will be shown.