Wigner Ensemble Monte Carlo: Challenges of 2D Nano-Device Simulation
We announce a two dimensional WIgner ENSemble (WIENS) approach for simulation of carrier transport in nanometer semiconductor devices. The approach is based on a stochastic model, where the quantum character of the carrier transport is taken into account
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Institute for Microelectronics, Technical University of Vienna Gusshausstrasse 27-29/E360, A-1040 Vienna, Austria 2 Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287-5706, USA
Abstract. We announce a two dimensional WIgner ENSemble (WIENS) approach for simulation of carrier transport in nanometer semiconductor devices. The approach is based on a stochastic model, where the quantum character of the carrier transport is taken into account by generation and recombination of positive and negative particles. The first applications of the approach are discussed with an emphasis on the variety of raised computational challenges. The latter are large scale problems, introduced by the temporal and momentum variables involved in the task.
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Introduction
The Wigner formulation of the quantum statistical mechanics provides a convenient kinetic description of carrier transport processes on the nanometer scale, characteristic of novel nanoelectronic devices. The approach, based on the concept of phase space considers rigorously the spatially-quantum coherence and can account for processes of de-coherence due to phonons and other scattering mechanisms using the models developed for the Boltzmann transport. Almost two decades ago the coherent Wigner equation has been utilized in a deterministic 1D device simulators [3,4,1]. The latter have been refined towards self-consistent schemes which take into account the Poisson equation, and dissipation processes have been included by using the relaxation time approximation. At that time it has been recognized that an extension of the deterministic approaches to two dimensions is prohibited by the enormous increase of the memory requirements, a fact which remains true even for todays computers. Indeed, despite the progress of the deterministic Boltzmann simulators which nowadays can consider even 3D problems, the situation with Wigner model remains unchanged. The reason is that, in contrast to the sparse Boltzmann scattering matrix, the counterpart provided by the Wigner potential operator is dense. A basic property of the stochastic methods is that they turn the memory requirements of the deterministic counterparts into computation time requirements. Recently two Monte Carlo methods for Wigner transport have been proposed [7,5]. The first one has been derived by an operator splitting approach. The Wigner function is presented by an ensemble of particles which are advanced in the phase space and carry I. Lirkov, S. Margenov, and J. Wa´ sniewski (Eds.): LSSC 2007, LNCS 4818, pp. 139–147, 2008. c Springer-Verlag Berlin Heidelberg 2008
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M. Nedjalkov, H. Kosina, and D. Vasileska
the quantum information via a quantity called affinity. The latter is updated at consecutive time steps and actually originates from the Wigner potential, whose values are distributed between particles according their phase space position. This ensemble method has been applied in a self-consistent scheme to resonanttunneling diodes (RTD’s), the scattering with phonons is accounted
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