IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v556y2020ics037843712030409x.html
   My bibliography  Save this article

Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors

Author

Listed:
  • Sabelfeld, Karl K.
  • Kireeva, Anastasya

Abstract

Stochastic simulation algorithms for solving transient nonlinear drift diffusion recombination transport equations are developed. The governing system of equations includes two drift–diffusion equations coupled with a Poisson equation for the potential whose gradient forms the drift velocity. A stochastic algorithm for solving nonlinear drift–diffusion equations is proposed here for the first time. In each time step, the method calculates the solution on a cloud of points using a new global Monte Carlo random walk and Cellular Automata algorithms. The Poisson equation is solved by a global version of the Random Walk on Spheres method which calculates both the solutions and the derivatives without using finite difference approximations. The method is also able to calculate fluxes to any desired part of the boundary, from arbitrary sources. For transient drift–diffusion equations we suggest a stochastic expansion from cell to cell algorithm for calculating the whole solution field. All new global random walk algorithms developed in this paper are validated by comparing the simulation results with exact solutions. Application of the developed method to solve a system of 2D transport equations for electrons and holes in a semiconductor is given.

Suggested Citation

  • Sabelfeld, Karl K. & Kireeva, Anastasya, 2020. "Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    • Handle: RePEc:eee:phsmap:v:556:y:2020:i:c:s037843712030409x
    DOI: 10.1016/j.physa.2020.124800
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712030409X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.124800?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. Sabelfeld Karl K., 2016. "Random walk on spheres method for solving drift-diffusion problems," Monte Carlo Methods and Applications, De Gruyter, vol. 22(4), pages 265-275, December.
    2. Sabelfeld Karl K., 2019. "A global random walk on spheres algorithm for transient heat equation and some extensions," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 85-96, March.
    3. Madalina Deaconu & Antoine Lejay, 2006. "A Random Walk on Rectangles Algorithm," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 135-151, March.
    4. Sabelfeld, Karl K., 2017. "A mesh free floating random walk method for solving diffusion imaging problems," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 6-11.
    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. Karl K. Sabelfeld & Anastasia E. Kireeva, 2022. "Stochastic Simulation Algorithms for Solving Transient Anisotropic Diffusion-recombination Equations and Application to Cathodoluminescence Imaging," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3029-3048, December.
    2. Sabelfeld Karl K., 2016. "Random walk on spheres method for solving drift-diffusion problems," Monte Carlo Methods and Applications, De Gruyter, vol. 22(4), pages 265-275, December.
    3. Lejay, Antoine & Maire, Sylvain, 2007. "Computing the principal eigenvalue of the Laplace operator by a stochastic method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 351-363.
    4. Gobet, Emmanuel & Menozzi, Stéphane, 2010. "Stopped diffusion processes: Boundary corrections and overshoot," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 130-162, February.
    5. Deaconu, M. & Herrmann, S. & Maire, S., 2017. "The walk on moving spheres: A new tool for simulating Brownian motion’s exit time from a domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 28-38.
    6. Bras, Pierre & Kohatsu-Higa, Arturo, 2023. "Simulation of reflected Brownian motion on two dimensional wedges," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 349-378.
    7. Maire, Sylvain & Nguyen, Giang, 2016. "Stochastic finite differences for elliptic diffusion equations in stratified domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 146-165.

    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:phsmap:v:556:y:2020:i:c:s037843712030409x. 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/physica-a-statistical-mechpplications/ .

    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.