Skip to main content

A Wigner Potential Decomposition in the Signed-Particle Monte Carlo Approach

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11189)

Abstract

The description of the electron evolution, provided by the Wigner equation, involves a force-less Liouville operator, which is associated with particles moving over Newtonian trajectories, and a Wigner potential operator associated with generation of positive and negative particles. These concepts can be combined to develop stochastic algorithms for solving the Wigner equation, consolidated by the so-called signed particle approach. We investigate the option to split the Wigner potential into two parts and to approximate one of them by a classical force term. The purpose is two-fold: First, we search for ways to simplify the numerical complexity involved in the simulation of the Wigner equation. Second, such a term offers a way to a self-consistent coupling of the Wigner and the Poisson equations. The particles in the signed-particle approach experience a force through the classical component of the potential. A cellular automaton algorithm is used to update the discrete momentum of the accelerated particles, which is then utilized along with the Wigner-based generation/annihilation processes. The effect of the approximation on generic physical quantities such as current and density are investigated for different cut-off wavenumbers (wavelengths), and the results are promising for a self-consistent solution of the Wigner and Poisson equations.

Keywords

  • Wigner function
  • Potential splitting
  • Signed-particle approach

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-10692-8_29
  • Chapter length: 10 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   69.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-10692-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   89.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

References

  1. Ellinghaus, P.: Two-Dimensional Wigner Monte Carlo Simulation for Time-Resolved Quantum Transport with Scattering. Dissertation, Institute for Microelectronics, TU Wien (2016)

    Google Scholar 

  2. Gehring, A., Kosina, H.: Wigner function-based simulation of quantum transport in scaled DG-MOSFETs using a Monte Carlo method. J. Comput. Electron. 4(1–2), 67–70 (2005)

    CrossRef  Google Scholar 

  3. Nedjalkov, M., Querlioz, D., Dollfus, P., Kosina, H.: Wigner function approach. In: Vasileska, D., Goodnick, S. (eds.) Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling, pp. 289–358. Springer, New York (2011). https://doi.org/10.1007/978-1-4419-8840-9_5

    CrossRef  Google Scholar 

  4. Querlioz, D., Dollfus, P.: The Wigner Monte Carlo Method for Nanoelectronic Devices. A Particle Description of Quantum Transport and Decoherence. Wiley, Hoboken (2010)

    MATH  Google Scholar 

  5. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn, pp. 154–155. Prentice Hall, New York (2008)

    Google Scholar 

  6. Ellinghaus, P., Nedjalkov, M., Selberherr, S.: Optimized particle regeneration scheme for the Wigner Monte Carlo method. In: Dimov, I., Fidanova, S., Lirkov, I. (eds.) NMA 2014. LNCS, vol. 8962, pp. 27–33. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-15585-2_3

    CrossRef  Google Scholar 

  7. ViennaWD - Wigner Ensemble Monte Carlo Simulator. http://www.iue.tuwien.ac.at/software/viennawd

Download references

Acknowledgements

This research has been supported by the Austrian Science Fund through the project FWF-P29406-N30.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Majid Benam .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Benam, M., Nedjalkov, M., Selberherr, S. (2019). A Wigner Potential Decomposition in the Signed-Particle Monte Carlo Approach. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-10692-8_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10691-1

  • Online ISBN: 978-3-030-10692-8

  • eBook Packages: Computer ScienceComputer Science (R0)