IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v107y2015icp108-119.html
   My bibliography  Save this article

A comparison of approaches for the solution of the Wigner equation

Author

Listed:
  • Sellier, J.M.
  • Nedjalkov, M.
  • Dimov, I.
  • Selberherr, S.

Abstract

As nowadays semiconductor devices are characterized by active lengths on the nanometer scale, it is important to use models including fully the quantum mechanical effects. In this paper we focus on the Wigner equation, a convenient reformulation of the Schrödinger equation in terms of a phase-space, and present a Monte Carlo technique to solve it, based on signed particles. Then we adapt the concept of potential decomposition, widely utilized to simplify the numerical treatment of the Wigner equation, to our method. Both approaches are compared to the direct solution of the Schrödinger equation. We show that excellent agreement is reached with our Monte Carlo technique which is also computationally efficient. The numerical experiment chosen for the comparisons consists of a Gaussian wave packet tunneling through a realistic source-to-drain potential profile. This is a technologically relevant situation for today's semiconductor devices for which quantum mechanical effects are prominent.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:107:y:2015:i:c:p:108-119
    DOI: 10.1016/j.matcom.2014.06.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475414001530
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2014.06.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sellier Jean Michel & Dimov Ivan & Nedjalkov Mihail & 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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 Jean Michel & Dimov Ivan & Nedjalkov Mihail & 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:107:y:2015:i:c:p:108-119. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.