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A benchmark study of the Wigner Monte Carlo method

Author

Listed:
  • Sellier Jean Michel

    (IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. 25A, 1113 Sofia, Bulgaria)

  • Nedjalkov Mihail

    (Institute for Microelectronics, TU Wien, Gußhausstraße 27–29/E360, 1040 Wien, Austria)

  • Dimov Ivan

    (IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. 25A, 1113 Sofia, Bulgaria)

  • Selberherr Siegfried

    (Institute for Microelectronics, TU Wien, Gußhausstraße 27–29/E360, 1040 Wien, Austria)

Abstract

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.

Suggested Citation

  • Sellier Jean Michel & Nedjalkov Mihail & Dimov Ivan & Selberherr Siegfried, 2014. "A benchmark study of the Wigner Monte Carlo method," Monte Carlo Methods and Applications, De Gruyter, vol. 20(1), pages 43-51, March.
    • Handle: RePEc:bpj:mcmeap:v:20:y:2014:i:1:p:43-51:n:4
    DOI: 10.1515/mcma-2013-0018
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    References listed on IDEAS

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    1. Nedjalkov M. & Vasileska D. & Dimov I. & Arsov G., 2007. "Mixed initial-boundary value problem in particle modeling of microelectronic devices," Monte Carlo Methods and Applications, De Gruyter, vol. 13(4), pages 299-331, November.
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    Cited by:

    1. Dimov, I. & Savov, M., 2020. "Probabilistic analysis of the Single Particle Wigner Monte-Carlo method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 173(C), pages 32-50.
    2. Sellier, J.M. & Nedjalkov, M. & Dimov, I. & Selberherr, S., 2015. "A comparison of approaches for the solution of the Wigner equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 108-119.

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    1. Sellier, J.M. & Nedjalkov, M. & Dimov, I. & Selberherr, S., 2015. "A comparison of approaches for the solution of the Wigner equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 108-119.

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