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Zeitschrift für Physik B Condensed Matter

, Volume 81, Issue 2, pp 183–194 | Cite as

Nonlinear dynamics of breathing current filaments inn-GaAs andp-Ge

  • E. Schöll
  • D. Drasdo
Article

Abstract

A novel model is presented for spatio-temporal pattern formation in semiconductors. It leads to self-generated nonlinear current oscillations due to “breathing” current filaments in the regime of impurity impact ionization. The four qualitatively different regimes which have been observed in Ge with increasing current are consistently explained as: a stationary nonconducting state; bulkdominated oscillations; breathing filaments; stable filaments. The physical origin of the breathing oscillations is impact ionization coupled with transverse diffusion and longitudinal dielectric relaxation. A method is developed to derive simple nonlinear dynamic equations for the filament radius and the position of the peak transverse electric field by a nonlinear mode expansion.

Keywords

Dynamic Equation Pattern Formation Dielectric Relaxation Impact Ionization Physical Origin 
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.

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References

  1. 1.
    Haken, H.: Synergetics. An introduction. 3rd Edn. Berlin, Heidelberg, New York: Springer 1983Google Scholar
  2. 2.
    Thomas, H. (ed.): Nonlinear dynamics in solid state physics. Berlin, Heidelberg, New York: Springer 1990 (to be published)Google Scholar
  3. 3.
    Schöll, E.: Nonequilibrium phase transitions in semiconductors. In: Springer Series in Synergetics. Vol. 35. Berlin, Heidelberg, New York: Springer 1987Google Scholar
  4. 4.
    Abe, Y. (ed.): Nonlinear and chaotic transport in semiconductors. Appl. Phys. A (Special Issue)48, 93–191 (1989)Google Scholar
  5. 5.
    Schöll, E.: Solid-State Electr.32, 1129 (1989)Google Scholar
  6. 6.
    Aoki, K., Yamamoto, K.: Phys. Lett.98 A, 72 (1983)Google Scholar
  7. 7.
    Mayer, K.M., Parisi, J., Huebener, R.P.: Z. Phys. B—Condensed Matter71, 171 (1988)Google Scholar
  8. 8.
    Brandl, A., Völcker, M., Prettl, W.: Appl. Phys. Lett.55, 238 (1989)Google Scholar
  9. 9.
    Mayer, K.M., Gross, R., Parisi, J., Peinke, J., Huebener, R.P.: Solid State Commun.63, 55 (1987)Google Scholar
  10. 10.
    Jäger, D., Baumann, H., Symanczyk, R.: Phys. Lett. A117, 141 (1986); Baumann, H., Symanczyk, R., Radehaus, C., Purwins, H.-G., Jäger, D.: Phys. Lett. A123, 421 (1987)Google Scholar
  11. 11.
    Schöll, E.: Physica134B, 271 (1985)Google Scholar
  12. 12.
    Schöll, E.: Proceedings of the 19th International Conference on Physics of Semiconductors, Warsaw, 1988; Zawadzki, W. (ed.), pp. 1407. Warsaw: Institute of Physics, Polish Academy of Sciences, 1988Google Scholar
  13. 13.
    Mayer, K.M., Parisi, J., Peinke, J., Huebener, R.P.: Physica D32, 306 (1988)Google Scholar
  14. 14.
    Rau, U., Mayer, K.M., Parisi, J., Peinke, J., Clauss, W., Huebener, R.P.: Solid-State Electr.32, 1365 (19890Google Scholar
  15. 15.
    Mayer, K.M., Peinke, J., Röhricht, B., Parisi, J., Huebener, R.P.: Phys. Scr. T19, 505 (19870Google Scholar
  16. 16.
    Mayer, K.M., Parisi, J., Rau, U., Huebener, R.P.: Proceedings of the 19th International Conference on Physics of Semiconductors, Warsaw, 1988. Zawadzki, W. (ed.), pp. 1411. Warsaw: Institute of Physics, Polish Academy of Sciences, 1988Google Scholar
  17. 17.
    Mayer, K.M., Parisi, J., Rau, U., Peinke, J., Huebener, R.P.: Phys. Rev. B. (to be published 1990); Mayer, K.M.: Stromfilamente und deren raum-zeitliche Dynamik in Halbleitern. Ph. D. Thesis, Tübingen 1989Google Scholar
  18. 18.
    Rau, U., Clauss, W., Kittel, A., Lehr, M., Bayerbach, M., Parisi, J., Peinke, J., Huebener, R.P.: Phys. Rev B (to be published, 1990)Google Scholar
  19. 19.
    Brandl, A., Völcker, M., Prettl, W.: Solid State Commun.72, 847 (1989)Google Scholar
  20. 20.
    Brandl, A., Kröninger, W., Prettl, W., Obermair, G.: Phys. Rev. Lett.64, 212 (1990)Google Scholar
  21. 21.
    Aoki, K., Yamamoto, K., Mugibayashi, N.: Proceedings of the 19th. International Conference on Physics of Semiconductors, Warsaw, 1988. Zawadzki, W. (ed.), p. 145. Warsaw: Institute of Physics, Polish Academy of Sciences, 1988Google Scholar
  22. 22.
    Schöll, E.: Z. Phys. B—Condensed Matter46, 23 (1982); Schöll, E.: Solid State Electr.29, 687 (1986)Google Scholar
  23. 23.
    Dubitskij, A.L., Kerner, B.S., Osipov, V.V.: Sov. Phys. Semicond.20, 755 (1986)Google Scholar
  24. 24.
    Kerner, B.S., Osipov, V.V.: Sov. Phys. JETP52, 1122 (1980)Google Scholar
  25. 25.
    Kerner, B.S., Sinkevich, V.F.: Sov. Phys. JETP Lett. B6, 437 (1982)Google Scholar
  26. 26.
    Kardell, K., Radehaus, C., Dohmen, R., Purwins, H.-G.: J. Appl. Phys.64, 6336 (1988)Google Scholar
  27. 27.
    Schöll, E.: Phys. Rev. B34, 1395 (1986)Google Scholar
  28. 28.
    Shadrin, V.D., Kogan, Sh.M.: Sov. Phys. Solid State13, 845 (1971)Google Scholar
  29. 29.
    Drasdo, D.: Dynamik von Stromfilamenten in Halbleitern. Diplom Thesis, RWTH Aachen (1989)Google Scholar
  30. 30.
    Evans, D.A.: In: Solid state theory. Landsberg, P.T. (ed). New York: Wiley, 1969Google Scholar
  31. 31.
    Schöll, E.: Appl. Phys. A48, 95 (1989)Google Scholar
  32. 32.
    Schöll, E.: Phys. Scr. T29, 152 (1989)Google Scholar
  33. 33.
    Schlögl, F.: Z. Phys.253, 147 (1972)Google Scholar
  34. 34.
    Landolt-Börnstein. Vol. 3, 17a. Berlin, Heidelberg New York: Springer 1982Google Scholar
  35. 35.
    Westervelt, R.M., Teitsworth, S.W.: J. Appl. Phys.57, 5457 (1985)Google Scholar
  36. 36.
    Parisi, J., Rau, U., Peinke, J., Mayer, K.M.: Z. Phys. B—Condensed Matter72, 225 (1988)Google Scholar
  37. 37.
    Stillman, G.E., Wolfe, C.M., Dimmock, J.O.: Proceedings of the 3rd International Conference on Photoconductors, Stanford, 1969. p. 265. Oxford: Pergamon 1971; See also in Willardson, R.K., Beer, A.C. (eds.): Semiconductors and semimetals. Vol. 12, p. 200. New York: Academic Press 1977Google Scholar
  38. 38.
    Hüpper, G., Schöll, E., Reggiani, L.: Solid-State Electr.32, 1787 (1989)Google Scholar
  39. 39.
    Lauterborn, W., Suchla, E.: Phys. Rev. Lett.53, 2304 (1984)Google Scholar
  40. 40.
    van Kampen, N.G.: Phys. Rep.124, No. 2 (1985) 69Google Scholar
  41. 41.
    Schöll, E., Landsberg, P.T.: Z. Phys. B—Condensed Matter72, 515 (1988)Google Scholar
  42. 42.
    Ebeling, W., Feistel, R.: Physik der Selbstorganisation und Evolution. Berlin: Akademie-Verl. 1982Google Scholar
  43. 43.
    Schnakenberg, J.: Z. Phys. B—Condensed Matter68, 271 (1987)Google Scholar
  44. 44.
    Reggiani, L., Mitin, V.V.: Riv. Nuovo Cimento.11, no. 12, 1 (1989)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • E. Schöll
    • 1
  • D. Drasdo
    • 2
  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlin 12Germany
  2. 2.Institut für Theoretische PhysikRheinisch-Westfälische Technische Hochschule AachenAachenGermany

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