A benchmark study of the Wigner Monte Carlo method

Jean Michel Sellier 1 , Mihail Nedjalkov 2 , Ivan Dimov 1  and Siegfried Selberherr 2
  • 1 IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. 25A, 1113 Sofia, Bulgaria
  • 2 Institute for Microelectronics, TU Wien, Gußhausstraße 27–29/E360, 1040 Wien, Austria


The Wigner equation is a promising full quantum model for the simulation of nanodevices. It is also a challenging numerical problem. Two basic Monte Carlo approaches to this model exist exploiting, in the time-dependent case, the so-called particle affinity and, in the stationary case, integer particle signs. In this paper we extend the second approach for time-dependent simulations and present a validation against a well-known benchmark model, the Schrödinger equation. Excellent quantitative agreement is demonstrated by the compared results despite the very different numerical properties of the utilized stochastic and deterministic approaches.

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This quarterly published journal presents original articles on the theory and applications of Monte Carlo and Quasi-Monte Carlo methods. Launched in 1995 the journal covers all stochastic numerics topics with emphasis on the theory of Monte Carlo methods and new applications in all branches of science and technology.