Stochastic Algorithm for Solving the Wigner-Boltzmann Correction Equation

  • M. Nedjalkov
  • S. Selberherr
  • I. Dimov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6046)


The quantum-kinetics of current carriers in modern nanoscale semiconductor devices is determined by the interplay between coherent phenomena and processes which destroy the quantum phase correlations. The carrier behavior has been recently described with a two-stage Wigner function model, where the phase-breaking effects are considered as a correction to the coherent counterpart. The correction function satisfies a Boltzmann-like equation.

A stochastic method for solving the equation for the correction function is developed in this work, under the condition for an a-priori knowledge of the coherent Wigner function. The steps of an almost optimal algorithm for a stepwise evaluation of the correction function are presented. The algorithm conforms the well established Monte Carlo device simulation methods, and thus allows an easy implementation.


Wigner Function Stochastic Algorithm Coherent Phenomenon Newton Trajectory Dimensional Space Formulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Querlioz, D., Dollfus, P.: The Wigner Monte Carlo Method for Nanoelectronic Devices - A particle description of quantum transport and decoherence (ISTE-Wiley) (2010)Google Scholar
  2. 2.
    Kosina, H., Nedjalkov, M., Selberherr, S.: The stationary Monte Carlo method for device simulation - Part I: Theory. J. Appl. Phys. 93(6), 3553–3563 (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Nedjalkov, M., Kosina, H., Selberherr, S., Ringhofer, C., Ferry, D.K.: Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices. Physical Review B 70(11), 115319–115335 (2004)CrossRefGoogle Scholar
  4. 4.
    Schwaha, P., Baumgartner, O., Heinzl, R., Nedjalkov, M., Selberherr, S., Dimov, I.: Classical approximation of the scattering induced Wigner correction equation. In: 13th International Workshop on Computational Electronics Book of Abstracts, IWCE-13, Beijing, China, pp. 177–180. IEEE, Los Alamitos (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • M. Nedjalkov
    • 1
  • S. Selberherr
    • 1
  • I. Dimov
    • 2
  1. 1.Institute for MicroelectronicsTU WienViennaAustria
  2. 2.Institute for Parallel ProcessingBulgarian Academy of SciencesSofiaBulgaria

Personalised recommendations