Mutual Interplay between the Break-Up of Spatial Order and the Onset of Low-Dimensional Temporal Chaos in an Exemplary Semiconductor System

  • Jürgen Parisi
Part of the NATO ASI Series book series (NSSB, volume 225)


Partially all branches of modern science ranging from physics through chemistry and biology to economics and sociology deal with complex nonlinear systems the dynamics of which may acquire a macroscopic spatial, temporal, or functional structure without specific interference from the outside. Such ubiquitous processes of spontaneous self-organization can in general be formulated as nonequilibrium order-disorder phase transitions. The basic idea for the underlying unifying approach stems from that of synergetics1 and information thermodynamics.2 It implies that we consider open systems capable of decomposing into a potentially large number of competing individual subparts. In our quest to understand how structures are generated by nature, the mutual interaction among these subsystems, or say variables, is of fundamental importance in the neighborhood of critical instability points where only a few collective degrees of freedom, often called order parameters, dominate the global system behavior. Those coherent variables force the subsystems to join an organized motion, just giving the total system its specific structure or order. Most characteristically, it turns out that the detailed nature of any particular subsystem becomes unessential, ensuing the universal character of pattern-forming processes.


Negative Differential Resistance Current Filament Semiconductor System Nonequilibrium Phase Transition Spontaneous Oscillation 
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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  1. 1.
    H. Haken, “Advanced Synergetics”, Springer, Berlin (1989).Google Scholar
  2. 2.
    H. Haken, “Information and Self-Organization”, Springer, Berlin (1988).MATHGoogle Scholar
  3. 3.
    Y. Abe, ed., “Nonlinear and Chaotic Transport Phenomena in Semiconductors”, special issue of Appl. Phys. A, vol. 48, pp. 93 – 191, Springer, Berlin (1989), and references therein.Google Scholar
  4. 4.
    R.P. Huebener, K.M. Mayer, J. Parisi, J. Peinke, and B. Röhricht, Chaos in semiconductors, Nucl. Phys. B (Proc. Suppl.) 2: 3 (1987).ADSCrossRefGoogle Scholar
  5. 5.
    K.M. Mayer, J. Peinke, B. Röhricht, J. Parisi, and R.P. Huebener, Spatial and temporal current instabilities in germanium, Physica Scripta T 19: 505 (1987).ADSCrossRefGoogle Scholar
  6. 6.
    J. Peinke, J. Parisi, B. Röhricht, K.M. Mayer, U. Rau, and R.P. Huebener, Spatio-temporal instabilities in the electric breakdown of p-germanium, Solid State Electron. 31: 817 (1988).ADSCrossRefGoogle Scholar
  7. 7.
    K.M. Mayer, J. Parisi, and R.P. Huebener, Imaging of self-generated multifilament ary current patterns in GaAs, Z. Phys. B — Condensed Matter 71: 171 (1988).ADSCrossRefGoogle Scholar
  8. 8.
    K.M. Mayer, J. Parisi, J. Peinke, and R.P. Huebener, Resonance imaging of dynamical filamentary current structures in a semiconductor, Physica D 32: 306 (1988).ADSCrossRefGoogle Scholar
  9. 9.
    E. Schöll, “Nonequilibrium Phase Transitions in Semiconductors”, Springer, Berlin (1987).CrossRefGoogle Scholar
  10. 10.
    R.P. Huebener, J. Peinke, and J. Parisi, Experimental progress in the nonlinear behavior of semiconductors, Appl. Phys. A 48: 107 (1989).ADSCrossRefGoogle Scholar
  11. 11.
    B. Röhricht, J. Parisi, J. Peinke, and O.E. Röss1er, A simple morphogenetic reaction-diffusion model describing nonlinear transport phenomena in semiconductors, Z. Phys. B — Condensed Matter 65: 259 (1986).ADSCrossRefGoogle Scholar
  12. 12.
    J. Parisi, J. Peinke, B. Röhricht, U. Rau, M. Klein, and O.E. Rössler, Comparison between a generic reaction-diffusion model and a synergetic semiconductor system, Z. Naturforsch. 42 a: 655 (1987).Google Scholar
  13. 13.
    J. Peinke, J. Parisi, B. Röhricht, K.M. Mayer, U. Rau, W. Clauß, R.P. Huebener, G. Jungwirt, and W. Prettl, Classification of current instabilities during low-temperature breakdown in germanium, Appl. Phys. A 48: 155 (1989).ADSGoogle Scholar
  14. 14.
    R.P. Huebener, Scanning electron microscopy at very low temperatures, in: “Advances in Electronics and Electron Physics”, vol. 70, p. 1, P.W. Hawkes, ed., Academic Press, New York (1988).CrossRefGoogle Scholar
  15. 15.
    J. Parisi, U. Rau, J. Peinke, and K.M. Mayer, Determination of electric transport properties in the pre- and post-breakdown regime of p-ger-manium, Z. Phys. B — Condensed Matter 72: 225 (1988).ADSCrossRefGoogle Scholar
  16. 16.
    J. Peinke, D.B. Schmid, B. Röhricht, and J. Parisi, Positive and negative differential resistance in electrical conductors, Z. Phys. B — Con-densed Matter 66: 65 (1987).ADSCrossRefGoogle Scholar
  17. 17.
    K.M. Mayer, R. Gross, J. Parisi, J. Peinke, and R.P. Huebener, Spatially resolved observation of current filament dynamics in semiconductors, Solid State Commun. 63: 55 (1987).ADSCrossRefGoogle Scholar
  18. 18.
    U. Rau, J. Peinke, J. Parisi, and R.P. Huebener, Switching behavior of current filaments in p-germanium connected in parallel, Z. Phys. B -Condensed Matter 71: 305 (1988).ADSCrossRefGoogle Scholar
  19. 19.
    J. Peinke, J. Parisi, A. Mühlbach, and R.P. Huebener, Different types of current instabilities during low-temperature avalanche breakdown in p-germanium, Z. Naturforsch. 42 a: 441 (1987).Google Scholar
  20. 20.
    J. Peinke, U. Rau, W. Clauß, R. Richter, and J. Parisi, Critical dynamics near the onset of spontaneous oscillations in p-germanium, Euro-phys. Lett. 9: 743 (1989).ADSCrossRefGoogle Scholar
  21. 21.
    J. Peinke, A. Mühlbach, R.P. Huebener, and J. Parisi, Spontaneous oscillations and chaos in p-germanium, Phys. Lett. 108 A: 407 (1985).ADSGoogle Scholar
  22. 22.
    J. Peinke, B. Röhricht, A. Mühlbach, J. Parisi, Ch. Nöldeke, R.P. Huebener, and O.E. Rössler, Hyperchaos in the post-break down regime of p-germanium, Z. Naturforsch. 40 a: 562 (1985).ADSGoogle Scholar
  23. 23.
    J. Peinke, J. Parisi, B. Röhricht, B. Wessely, and K.M. Mayer, Quasiperiodicity and mode locking of undriven spontaneous oscillations in germanium crystals, Z. Naturforsch. 42 a: 841 (1987).Google Scholar
  24. 24.
    U. Rau, J. Peinke, J. Parisi, R.P. Huebener, and E. Scholl, Exemplary locking sequence during self-generated quasiperiodicity of extrinsic germanium, Phys. Lett. 124 A: 335 (1987).ADSGoogle Scholar
  25. 25.
    J. Peinke, J. Parisi, R.P. Huebener, M. Duong-van, and P. Keller, Quasiperiodic behavior of d.c. biased semiconductor electronic breakdown, Europhys. Lett, (to be published).Google Scholar
  26. 26.
    R. Stoop, J. Peinke, J. Parisi, B. Röhricht, and R.P. Huebener, A p-Ge semiconductor experiment showing chaos and hyperchaos, Physica D 35: 425 (1989).ADSCrossRefGoogle Scholar
  27. 27.
    J. Parisi, J. Peinke, R.P. Huebener, R. Stoop, and M. Duong-van, Evidence of chaotic hierarchy in a semiconductor experiment, Z. Natür-forsch. a (to be published).Google Scholar
  28. 28.
    B. Röhricht, B. Wessely, J. Parisi, and J. Peinke, Crosstalk of the dynamical dissipative behavior between different parts in a current-carrying semiconductor, Appl. Phys. Lett. 48: 233 (1986).ADSCrossRefGoogle Scholar
  29. 29.
    B. Röhricht, J. Parisi, J. Peinke, and R.P. Huebener, Spontaneous resistance oscillations in p-germanium at low temperatures and their spatial correlation, Z. Phys. B — Condensed Matter 66: 515 (1987).ADSCrossRefGoogle Scholar
  30. 30.
    E. Scholl, J. Parisi, B. Röhricht, J. Peinke, and R.P. Huebener, Spatial correlations of chaotic oscillations in the post-breakdown regime of p-Ge, Phys. Lett. 119 A: 419 (1987).ADSGoogle Scholar
  31. 31.
    E. Schöll, H. Naber, J. Parisi, B. Röhricht, J. Peinke, and S. Uba, Resonance transition of the spatial correlation factor of self-generated oscillations in the post-breakdown regime of p-Ge, Z. Naturforsch, a (to be published).Google Scholar
  32. 32.
    B. Röhricht, R.P. Huebener, J. Parisi, and M. Weise, Nonequilibrium critical and multicritical phase transitions in low-tempe rature electronic transport of p-germanium, Phys. Rev. Lett. 61: 2600 (1988).ADSCrossRefGoogle Scholar
  33. 33.
    N. Rashevsky, An approach to the mathematical biophysics of biological self-regulation and of cell polarity, Bull. Math. Biophys. 2: 15 (1940);MathSciNetCrossRefGoogle Scholar
  34. 33a.
    N. Rashevsky, Further contributions to the theory of cell polarity and self-regulation, Bull. Math. Biophys. 2: 65 (1940);MathSciNetCrossRefGoogle Scholar
  35. 33b.
    N. Rashevsky, Physicomathematical aspects of some problems of organic form, Bull. Math. Biophys. 2: 109 (1940).CrossRefGoogle Scholar
  36. 34.
    A.M. Turing, The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. London B 237: 37 (1952).ADSCrossRefGoogle Scholar
  37. 35.
    B. Röhricht, J. Parisi, J. Peinke, and O.E. Rössler, Breakdown of symmetry in an exemplary Turing system, Dynamics and Stability of Systems (to be published).Google Scholar
  38. 36.
    E. Scholl, Nonequilibrium phase transitions and chaos in semiconductors, J. Phys. Chem. Solids 49: 651 (1988).ADSCrossRefGoogle Scholar
  39. 37.
    E. Scholl, Instabilities in semiconductors including chaotic phenomena, Physica Scripta T 29: 152 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Jürgen Parisi
    • 1
  1. 1.Physical InstituteUniversity of TübingenTübingenFed. Rep. Germany

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