Current Instabilites in the Interplay Between Chaos and Semiconductor Physics

  • J. Peinke


To get a theoretical understanding of experimentally observed current instabilities in a semiconductor system, the experimentalist will first of all be guided by the desire to explain the whole system by a single appropriate model. In such an approach, one would like to start with elementary semiconductor physics and end up with a comprehensive understanding, without requiring the experimentalist to exclude any experimental facts from his mind. This article intends to show how far it is possible to explain the instabilities on the basis of semiconductor physics, and to point out where this becomes impossible with present knowledge. In contrast to the ansatz based on semiconductor physics, different models based on nonlinear dynamics are presented that explain and predict nonlinear features of current instabilities.


Charge Carrier Lyapunov Exponent Phase Portrait Free Charge Carrier Semiconductor Physic 
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  1. 1.
    H. Haken: Advanced Synergetics, in Springer Ser. Syn., Vol. 20 (Springer, Berlin 1983)Google Scholar
  2. I. Prigogine, R. Lefever: “Theory of Dissipative Structures”, in Synergetics, ed. by H. Haken (Teubner, Stuttgart 1973) pp. 124–135Google Scholar
  3. 2.
    I.L. Ivanov, S.M. Ryvkin: Sov. Phys. Techn. Phys. 3, 722 (1958)Google Scholar
  4. 3.
    B. Ancker-Johnson: “Plasmas in Semiconductors and Semimetals”., in Semicond. and Semimetals, Vol. 1, ed. by R.K. Willardson and A.C. Beer (Academic Press, New York 1966) pp. 379–481CrossRefGoogle Scholar
  5. 4.
    H. Hartnagel: Semiconductor Plasma Instabilities (Heinemann Educational Books, London 1969)Google Scholar
  6. 5.
    M. Glicksman: “Plasma in Solids”, in Solid State Phys., Vol. 26, ed. by H. Ehrenreich, F. Seitz, and D. Turnbell (Academic Press, New York 1971) pp. 275–427Google Scholar
  7. 6.
    V.L. Bonch-Bruevich, I.P. Zvyagin, A.G. Mironov: Domain Electrical Instabilities in Semiconductors (Consultants Bureau, New York 1975)Google Scholar
  8. 7.
    J. Pozhela: Plasma and Current Instabilities in Semiconductors (Pergamon, Oxford 1981)Google Scholar
  9. 8.
    E. Schöll: Nonequilibrium Phase Transition in Semiconductors, Springer Ser. Syn., Vol. 35 (Springer, Berlin, Heidelberg 1987)CrossRefGoogle Scholar
  10. 9.
    M. Cardona, W. Ruppel: Jour. Appl. Phys. 31, 1826 (1967)CrossRefADSGoogle Scholar
  11. 10.
    Y. Abe (ed.): Nonlinear and Chaotic Transport Phenomena in Semiconductors, Applied Physics, Vol. A48, No. 2 (Springer, Heidelberg 1989)Google Scholar
  12. 11.
    R.P. Huebener, J. Peinke, J. Parisi: Appl. Phys. A48, 107 (1989)ADSGoogle Scholar
  13. 12.
    J. Peinke, J. Parisi, B. Röhricht, K.M. Mayer, U. Rau, W. Clauß, R.P. Huebener, G. Jungwirt, W. Prettl: Appl. Phys. A48, 155 (1989)ADSGoogle Scholar
  14. 13.
    W. Clauß, U. Rau, J. Parisi, J. Peinke, R.P. Huebener, H. Leier, A. Forchel: J. Appl. Phys. 67, 2980 (1990)CrossRefADSGoogle Scholar
  15. 14.
    J. Parisi, U. Rau, J. Peinke, K.M. Mayer: Z. Phys. B72, 225 (1988)CrossRefADSGoogle Scholar
  16. 15.
    U. Rau, K.M. Mayer, J. Parisi, J. Peinke, W. Clauß, R.P. Huebener: Proc. 6th Int. Conf. on Hot Carriers in Semicond., Scottsdale 1989; Solid State Electron. 32, 1365 (1989)CrossRefADSGoogle Scholar
  17. 16.
    R.P. Huebener: Rep. Prog. Phys. 47, 175 (1984)CrossRefADSGoogle Scholar
  18. 17.
    K.M. Mayer, R.P. Huebener, U. Rau: J. Appl. Phys. 67, 1412 (1990)CrossRefADSGoogle Scholar
  19. 18.
    K.M. Mayer, R. Gross, J. Parisi, J. Peinke, R.P. Huebener: Solid State Commun. 63, 55 (1987)CrossRefADSGoogle Scholar
  20. 19.
    K.M. Mayer, J. Parisi, J. Peinke, R.P. Huebener: Physica D32, 306 (1988)CrossRefADSGoogle Scholar
  21. 20.
    E. Schöll: Proc. 19th Int. Conf. Phys. of Semicond., Warsaw 1988, ed. by W. Zawadzki; Inst. of Physics, Polish Academy of Sciences (1988)Google Scholar
  22. 21.
    J. Peinke, J. Parisi, U. Rau, W. Clauß, B. Röhricht, R.P. Huebener, R. Stoop: “Experimental Progress on the Ladder Towards Higher Chaos”, in A Chaotic Hierarchy, ed. by M. Klein and G. Baier (World Scientific, Singapore 1991) pp. 317–340Google Scholar
  23. 22.
    J. Peinke, U. Rau, W. Clauß, R. Richter, J. Parisi: Europhys. Lett. 9, 743 (1989)CrossRefADSGoogle Scholar
  24. 23.
    R. Stoop, J. Peinke, J. Parisi, B. Röhricht, R.P. Huebener: Physica D35, 425 (1989)ADSGoogle Scholar
  25. 24.
    F. Takens: “Detecting Strange Attractors in Turbulence”, in Dynamical Systems and Turbulence, ed. by D.A. Rand and L.-S. Young, Springer Lect. Notes in Math., Vol. 898 (Springer, New York 1981) pp. 366–381CrossRefGoogle Scholar
  26. N. H. Packard, J.P. Crutchfield, J.D. Farmer, and R.S. Shaw: Phys. Rev. Lett. 45, 712 (1980)CrossRefADSGoogle Scholar
  27. 25.
    H.G. Schuster: Deterministic Chaos (Physik Verlag, Weinheim, 1984)MATHGoogle Scholar
  28. 26.
    H.B. Stewart: Z. Naturforsch. 41a, 1412 (1986)ADSGoogle Scholar
  29. 27.
    F.T. Arecchi, A. Lapucci, R. Meucci, J.A. Roversi, P.H. Coullet: Europhys. Lett. 6, 677 (1988)CrossRefADSGoogle Scholar
  30. 28.
    J.-P. Eckmann, D. Ruelle: Rev. Mod. Phys. 57, 617 (1985)MathSciNetCrossRefADSGoogle Scholar
  31. 29.
    R. Badii, A. Politi: J. Stat. Phys. 40, 725 (1985)MathSciNetMATHCrossRefADSGoogle Scholar
  32. 30.
    O.E Rössler: Z. Naturforsch. 38a, 788 (1983)ADSGoogle Scholar
  33. 31.
    R. Stoop, P.F. Meier: J. Opt. Soc. Am. B5, 1037 (1988)ADSGoogle Scholar
  34. R. Stoop, J. Parisi, J. Peinke: “Lyapunov Exponent Calculations in High Dimensional Embedding Space, a Singular Value Approach”, in A Chaotic Hierarchy, ed. by M. Klein and G. Baier (World Scientific, Singapore 1991) pp. 341–352Google Scholar
  35. 32.
    P. Grassberger: in Chaos, ed. by A.V. Holden (Manchester Univ. Press, Manchester 1986) p. 291ffGoogle Scholar
  36. K. Pawelzik, H.G. Schuster: Phys. Rev. A35, 2207 (1987)Google Scholar
  37. 33.
    J.L. Kaplan, J.A. Yorke: in Lecture Notes in Mathematics, Vol. 730, ed. by H.O. Peitgen and H.O. Walther (Springer, Berlin 1979) p. 204Google Scholar
  38. 34.
    G. Mayer-Kress (ed.): Dimensions and Entropies in Chaotic Systems, in Springer Ser. Syn., Vol.32 (Springer, Berlin 1986)Google Scholar
  39. 35.
    J. Peinke, B. Röhricht, A. Mühlbach, J. Parisi, Ch. Nöldeke, R.P. Huebener, O.E. Rössler: Z. Naturforsch. 40a, 562 (1985)ADSGoogle Scholar
  40. 36.
    J. Peinke, A. Mühlbach, B. Röhricht, B. Wessley, J. Mannhart, J. Parisi, R.P. Huebener: Physica 23D, 176 (1986)ADSGoogle Scholar
  41. J. Parisi, J. Peinke, B. Röhricht, K.M. Mayer: Z. Naturforsch. 42a, 329 (1987)Google Scholar
  42. J. Peinke, J. Parisi, B. Röhricht, B. Wessley, K.M. Mayer: Z. Naturforsch. 42a, 841 (1987)Google Scholar
  43. U. Rau, J. Peinke, J. Parisi, R.P: Huebener: Z. Phys. B71, 305 (1988)CrossRefADSGoogle Scholar
  44. 37.
    E. Schöll, J. Parisi, B. Röhricht, J. Peinke, R.P. Huebener: Phys. Lett. 119A, 419 (1987)ADSGoogle Scholar
  45. E. Schöll, H. Naber, J. Parisi, B. Röhricht, J. Peinke, S. Uba: Z. Naturforsch. 44a, 1139 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • J. Peinke
    • 1
  1. 1.C.N.R.S.-Centre de Recherches sur les Très Basses TempératuresGrenoble CedexFrance

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