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Numerical approaches to the kinetic semiconductor equation

Zugäuge zur numerischen Berechnung der kinetischen Halbleitergleichung

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Abstract

In this paper we consider several methods for the numerical computation of carrier transport effects in semiconductors based on kinetic equations. We especially discuss the computational costs of the different algorithms, which in some cases prohibit their application to higher dimensional problems.

Zusammenfassung

In dieser Arbeit untersuchen wir mehrer Methoden zur numerischen Berechnung von Transportphänomenen in Halbleitern, die auf kinetischen Gleichungen basieren. Insbesondere betrachten wir den Aufwand an Rechenzeit für die verschiedenen Algorithmen, der in einigen Fällen die Anwendung auf höherdimensionale Probleme unmöglich macht.

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References

  1. Burkhard, R.: Ein finites Partikelverfahren für Elektron-Phonon-Streuung in Halbleitern. Diploma Thesis, Universität Kaiserslautern 1992.

  2. Burkhard, R., Motta, S., Wick, J.: The CRF-method in general coordinates. J. Comput. Phys. (submitted).

  3. Cottet, G. H., Raviart, P. A.: Particle methods for the 1-dimensional Vlasov-Poisson equations. SIAM J. Numer. Anal.21, 52–76 (1984).

    Article  Google Scholar 

  4. Geyer, T., Wick, J.: A deterministic particle-method solving the linearized Boltzmann equation. Computing43, 199–207 (1990).

    Article  Google Scholar 

  5. Jacoboni, C., Reggiani, L.: The Monte-Carlo-method for the solution of charge transport in semiconductors with applications to Covalent materials. Rev. Mod. Phys.55, 645–705 (1983).

    Article  Google Scholar 

  6. Mas-Gallic, S.: A deterministic particle method for the linearized Boltzmann equation. Trans. Theory Stat. Phys.16, 855–887 (1987).

    Google Scholar 

  7. Moock, H., Motta, S., Russo, G., Wick, J.: Point approximation of a space-homogeneous transport-equation. Numer. Math.56, 763–774 (1990).

    Google Scholar 

  8. Moock, H.: Ein deterministisches Teilchenverfahren zur Simulation der Boltzmann-Vlasov-Gleichung für Halbleiter. PhD-Thesis, Universität Kaiserslautern 1992.

  9. Motta, S., Wick, J.: A new numerical method for kinetic equations in several dimensions. Computing46, 223–232 (1991).

    Article  Google Scholar 

  10. Neunzert, H.: An introduction to the nonlinear Boltzmann-Vlasov equation. Preprint28, Universität Kaiserslautern 1981.

  11. Niclot, B., Degond, P., Poupaud, F.: Deterministic particle simulations of the Boltzmann transport equation of semiconductors. J. Comput. Phys.78, 313–349 (1988).

    Article  Google Scholar 

  12. Neunzert, H., Wick, J.: The convergence of simulation methods in plasma physics; mathematical methods of plasmaphysics (Oberwolfach, 1979) pp. 271–286; Methoden Verfahren Math. Phys. Vol. 20. Frankfurt: P. Lang 1980.

    Google Scholar 

  13. Pfau, J.: Ein finites Teilchenverfahren für eine nichtlineare 1-D Transportgleichung. Diploma Thesis, Universität Kaiserslautern 1991.

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Wick, J. Numerical approaches to the kinetic semiconductor equation. Computing 52, 39–49 (1994). https://doi.org/10.1007/BF02243395

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  • DOI: https://doi.org/10.1007/BF02243395

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