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Instabilities in semiconductors: Domains, filaments, chaos

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Festkörperprobleme 26

Part of the book series: Advances in Solid State Physics ((ASSP,volume 26))

Abstract

Bulk negative differetial conductivity in semiconductors can be induced by negative differential mobility as well as by non-equilibrium generation and recombination processes, in particular impact ionization of impurities. The, resulting instabilities lead to the spontaneous formation of dissipative structures: dipole field domains, current filaments, periodic or chaotic oscillations. We discuss these different types of non-linear dynamics and their bifurcation behaviour, and derive analytical conditions for their onset in a phenomenological macroscopic theory. In particular, anomalous domain formation in SNDC elements and self-generated oscillations and chaos in semiconductors are discussed.

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References

  1. F. Stöckmann, in: Festkörperprobleme: Advances in Solid State Physics, ed. by O. Madelung (Vieweg, Braunschweig 1969), Vol. IX, p. 138

    Google Scholar 

  2. A. F. Volkov and Sh. M. Kogan, Sov. Phys. Usp. 11, 881 (1969)

    Article  ADS  Google Scholar 

  3. H. Hartnagel, Semiconductor Plasma Instabilities (Elsevier Publishing Company, New York 1969)

    Google Scholar 

  4. H. Thomas, in: Synergetics, ed. by H. Haken (Teubner, Stuttgart 1973), p. 87. H. Thomas, in: Cooperative Effects, ed. by H. Haken (North Holland, Amsterdam 1974), pp. 171

    Google Scholar 

  5. V. L. Bonch-Bruevich, I. P. Zvyagin, and A. G. Mironov, Domain Electrical Instabilities in Semiconductors (Consultant Bureau, New York 1975)

    Google Scholar 

  6. M. P. Shaw, H. L. Grubin and P. Solomon, The Gunn Hilsum Effect (Academic Press, New York 1979)

    Google Scholar 

  7. J. Pozhela, Plasma and Current Instabilities in Semiconductors (Pergamon press, Oxford 1981)

    Google Scholar 

  8. M. Asche, Z. S. Gribnikow, V. V. Mitin, and O. G. Sarbei, Hot Electrons in Many-Valley Semiconductors (in Russ.) (Naukova Dumka, Kiev 1982)

    Google Scholar 

  9. M. P. Shaw and N. Yildirim, Adv. Electr. Electron Phys. 60, 307 (1983)

    Google Scholar 

  10. C. L. Dick and B. Ancker-Johnson, Phys. Rev. B5, 526 (1972)

    Article  ADS  Google Scholar 

  11. E. Schöll, Nonequilibrium Phase Transitions in Semiconductors (Springer Series in Synergetics, Berlin, Heidelberg) to be published

    Google Scholar 

  12. B. K. Ridley, Proc. Phys. Soc. 82, 954 (1963)

    Article  ADS  Google Scholar 

  13. E. Schöll, Proc. 17th Int. Conf. Physics of Semiconductors, San Francisco 1984, ed. by J. D. Chadi and W. Harrison (Springer New York 1985) p. 1353; Z. Phys. B—Condensed Matter 62, 245 (1986)

    Google Scholar 

  14. P. R. Solomon, M. P. Shaw, and H. L. Grubin, J. Appl. Phys. 43, 159 (1972)

    Article  ADS  Google Scholar 

  15. M. P. Shaw, H. L. Grubin, and I. J. Gastman, IEEE Trans. Electron Dev. ED-20, 169 (1973)

    Article  Google Scholar 

  16. M. A. Lampert and P. Mark, Current Injection in Solids (Academic Press, New York 1970)

    Google Scholar 

  17. P. T. Landsberg, D. J. Robbins, and E. Schöll, Phys. stat. sol. (a) 50, 423 (1978); 65, 353 (1981)

    Article  ADS  Google Scholar 

  18. E. Schöll, J. Physique Colloque C7, 57 (1981); Z. Phys. B46, 23 (1982), B48, 153 (1982), B52, 321 (1983)

    Google Scholar 

  19. K. Seeger, Solid State Comm. 53, 219 (1985)

    Article  ADS  Google Scholar 

  20. F. G. Bass, Yu. G. Gurevich, S. A. Kostylev, and N. A. Terent'eva, Sov. Phys. Semicond. 17, 808 (1983)

    Google Scholar 

  21. P. T. Landsberg, in Festkörperprobleme: Advances in Solid State Physics, ed. by O. Madelung (Vieweg, Braunschweig 1966) Vol. VI, p. 174 H. J. Hoffmann and F. Stöckmann, in Festkörperprobleme: Advances in Solid State Physics, ed. by J. Treusch (Vieweg, Braunschweig 1979), Vol. XIX, p. 271 P. T. Landsberg, in: Handbook on Semiconductors, ed. by T. S. Moss, Vol. I, Ch. 8 (North Holland, Amsterdam 1982)

    Google Scholar 

  22. R. S. Crandall, J. Phys. Chem. Solids 31, 2069 (1970); Phys. Rev. B1, 730 (1970)

    Article  ADS  Google Scholar 

  23. A. A. Kastalskij, phys. stat. sol. (a) 15, 599 (1973)

    Article  ADS  Google Scholar 

  24. A. G. Zabrodskij and I. S. Shlimak, Sov. Phys. Solid State 16, 1528 (1975)

    Google Scholar 

  25. W. Pickin, Solid State Electr. 21, 309, 1299 (1978)

    Article  ADS  Google Scholar 

  26. W. G. Proctor, P. Lawaetz, Y. Marfaing, and R. Triboulet, phys. stat. sol. (b) 110, 637 (1982)

    Article  ADS  Google Scholar 

  27. A. A. Sukhanov, Sov. Phys. Semiconductors 5, 1160 (1972)

    Google Scholar 

  28. M. Büttiker and H. Thomas, Phys. Rev. A24, 2635 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  29. H. L. Grubin, M. P. Shaw, and P. R. Solomon, IEEE Trans. Electr. Dev. ED-20, 63 (1973)

    Article  Google Scholar 

  30. E. Schöll, Physica 134B, 271 (1985); Phys. Rev. B, to be published (1986)

    Google Scholar 

  31. H. Lueder, W. Schottky, and E. Spenke, Naturwissenschaften 24, 61, (1936)

    Article  ADS  Google Scholar 

  32. P. N. Butcher, Phys. Lett. 19, 546 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  33. D. Adler, M. S. Shur, M. Silver, and S. R. Ovshinsky, J. Appl. Phys. 51, 3289 (1980)

    Article  ADS  Google Scholar 

  34. E. Schöll, Solid-State Electron n. 29, to be published (1986)

    Google Scholar 

  35. A. M. Barnett, Semicond. Semimetals 6, 141 (1970)

    Article  MathSciNet  Google Scholar 

  36. W. Prettl, private communication

    Google Scholar 

  37. H. Baumann, T. Pioch, H. Dahmen, and D. Jäger, BEDO 18, 133 (1985); SEM (to be published 1986); D. Jäger, H. Baumann, and R. Symanczyk, Phys. Lett. A, to be published

    Google Scholar 

  38. R. P. Huebener, private communication

    Google Scholar 

  39. K. Aoki, T. Kobayashi, and K. Yamamoto, J. Physique Colloque C7, 51 (1981); J. Phys. Soc. Jap. 51, 2373 (1982); Physica 134B, 288 (1985)

    Google Scholar 

  40. G. N. Maracas, W. Porod, D. A. Johnson, D. K. Ferry, and H. Goronkin, Physica 134B, 276 (1985)

    Google Scholar 

  41. S. W. Teitsworth, R. M. Westervelt, and E. E. Haller, Phys. Rev. Lett. 51, 825 (1983)

    Article  ADS  Google Scholar 

  42. G. A. Held, C. Jeffries, and E. E. Haller, Phys. Rev. Lett. 52, 1037 (1984); G. A. Held and C. Jeffries, Phys. Rev. Lett. 55, 887 (1985); 56, 1183 (1986); in: Springer Series in Synergetics Vol. 32, ed. by G. Mayer-Kress (Springer, Berlin, Heidelberg, New York 1986)

    Article  ADS  Google Scholar 

  43. S. W. Teitsworth and R. M. Westervelt, Phys. Rev. Lett. 53, 2587 (1984); 56, 516 (1986)

    Article  ADS  Google Scholar 

  44. J. Peinke, A. Mühlbach, R. P. Huebener, and J. Parisi, Phys. Lett. 108A, 407 (1985); J. Peinke, B. Röhricht, A. Mühlbach, J. Parisi, Ch. Nöldeke, R. P. Huebener, and O. E. Rössler, Z. Naturforsch. 40a, 562 (1985); B. Röhricht, B. Wessely, J. Parisi, and J. Peinke, Appl. Phys. Lett. 48, 233 (1986); B. Röhricht, B. Wessely, J. Peinke, A. Mühlbach, J. Parisi, and R. P. Huebener, Physica 134B, 281 (1985)

    ADS  Google Scholar 

  45. S. B. Bumeliene, Yu. K. Pozhela, K. A. Pyragas, and A. V. Tamaševičius Physica 134B, 293 (1985)

    Google Scholar 

  46. D. G. Seiler, C. L. Littler, R. J. Justice, and P. W. Milonni, Phys. Lett. 108A, 462 (1985)

    ADS  Google Scholar 

  47. K. Nakamura, Progr. Theoret. Phys. 57, 1874 (1977)

    Article  ADS  Google Scholar 

  48. J. M. Wersinger, J. M. Finn, and E. Ott, Phys. Fluids 23, 1142 (1980)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  49. K. A. Pyragas, Sov. Phys.-Semicond. 17, 652 (1983) [Fiz. Tekh. Poluprov. 17, 1035 (1983)]

    Google Scholar 

  50. E. Schöll, to be published

    Google Scholar 

  51. D. J. Robbins and P. T. Landsberg, J. Phys. C13, 2425 (1980); V. V. Mitin, Appl. Phys. A39, 123 (1986)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Rheinisch-Westfälische Technische Hochschule, D-5100, Aachen, Federal Republic of Germany

    Eckehard Schöll

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  1. Eckehard Schöll
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P. Grosse

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© 1986 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

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Schöll, E. (1986). Instabilities in semiconductors: Domains, filaments, chaos. In: Grosse, P. (eds) Festkörperprobleme 26. Advances in Solid State Physics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107802

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  • DOI: https://doi.org/10.1007/BFb0107802

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  • Print ISBN: 978-3-528-08032-7

  • Online ISBN: 978-3-540-75359-9

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