Zeitschrift für Physik B Condensed Matter

, Volume 48, Issue 2, pp 153–165 | Cite as

Current layers and filaments in a semiconductor model with an impact ionization induced instability

  • E. Schöll


Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.


Mode Instability Dissipative Structure Soft Mode Cylindrical Geometry Current Layer 
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.
    Schöll, E.: Z. Phys. B—Condensed Matter46, 23 (1982)Google Scholar
  2. 2.
    Ridley, B.K.: Proc. Phys. Soc.82, 954 (1963)Google Scholar
  3. 3.
    Thomas, H.: Lecture notes: Conf. on Fluctuation Phenomena. Chania, Crete (1969)Google Scholar
  4. 4.
    Bonch-Bruevich, V.L., Zvyagin, I.P., Mironov, A.G.: Domain electrical instabilities in semiconductors. New York: Consultant Bureau 1975Google Scholar
  5. 5a.
    Volkov, A.F., Kogan, Sh.M.: Sov. Phys. JETP25, 1095 (1967)Google Scholar
  6. 5b.
    Takeyama, K., Kitahara, K.: J. Phys. Soc. Jpn.39, 125 (1975)Google Scholar
  7. 6a.
    e.g. Schlögl, F.: Phys. Rep.62, 267 (1980)Google Scholar
  8. 6b.
    Schlögl, F.: On the statistical background of the Glansdorff-Prigogine criterion. In: Thermodynamics and regulation of biological processes. Zotin, A.I. (ed.). Moscow: Nauka (to appear)Google Scholar
  9. 7a.
    Knight, B.W., Peterson, G.A.: Phys. Rev.155, 393 (1967)Google Scholar
  10. 7b.
    Pytte, E., Thomas, H.: Phys. Rev.179, 431 (1969)Google Scholar
  11. 8.
    Shaw, M.P., Grubin, H.L., Solomon, P.: The Gunn-Hilsum effect. New York: Academic Press 1979Google Scholar
  12. 9.
    Büttiker, M., Thomas, H.: Solid-State Electron.21, 95 (1978); Z. Phys. B—Condensed Matter33, 275 (1979),34, 301 (1979)Google Scholar
  13. 10.
    Volkov, A.F., Kogan, Sh.M.: Sov. Phys. Usp.11, 881 (1969)Google Scholar
  14. 11.
    Shaw, M.P., Yildirim, N.: Thermal and Electrothermal Instabilities in Semiconductors. Advan. Electr. Electron Phys. (to be published 1982)Google Scholar
  15. 12.
    Adler, D., Shur, M.S., Silver, M., Ovshinsky, S.R.: J. Appl. Phys.51, 3289 (1980)Google Scholar
  16. 13.
    Landsberg, P.T., Pimpale, A.: J. Phys. C9, 1243 (1976)Google Scholar
  17. 14a.
    Schöll, E., Landsberg, P.T.: Proc. R. Soc. London Ser. A365, 495 (1979)Google Scholar
  18. 14b.
    Landsberg, P.T., Robbins, D.J., Schöll, E.: Phys. Status Solidi (a)50, 423 (1978)Google Scholar
  19. 14c.
    Robbins, D.J., Landsberg, P.T., Schöll, E.: Phys. Status Solidi (a)65, 353 (1981)Google Scholar
  20. 15a.
    Haken, H.: Synergetics. Berlin, Heidelberg, New York: Springer 1977Google Scholar
  21. 15b.
    Nicolis, G., Prigogine, I.: Self-Organization in nonequilibrium systems. New York: Wiley 1977Google Scholar
  22. 16.
    Schöll, E.: J. Physique C3, 57 (1981): 3rd Int. Conf. Hot Carriers in SemiconductorsGoogle Scholar
  23. 17.
    Kirchgässner, K.: In: Synergetics. Haken, H. (ed.), p. 34. Berlin, Heidelberg, New York: Springer 1977Google Scholar
  24. 18.
    Schlögl, F.: Z. Phys.253, 147 (1972)Google Scholar
  25. 19.
    Thom, R.: Structural stability and morphogenesis. New York: Benjamin 1975Google Scholar
  26. 20.
    Stillman, G.E., Wolfe, C.M., Dimmock, J.O.: Semicond. Semimet.12, 169 (1977)Google Scholar
  27. 21.
    Poehler, T.O.: Phys. Rev. B4, 1223 (1971)Google Scholar
  28. 22.
    Barnett, A.M.: Semicond. Semimet.6, 141 (1970)Google Scholar
  29. 23.
    Büttiker, M., Thomas, H.: Phys. Rev. A24, 2635 (1981)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • E. Schöll
    • 1
  1. 1.Institut für Theoretische Physik BRheinisch-Westfälische Technische HochschuleAachenFederal Republic of Germany

Personalised recommendations