Advertisement

Scaling properties of noise-induced switching in a bistable tunnel diode circuit

  • Stephen W. TeitsworthEmail author
  • Matthew E. Olson
  • Yuriy Bomze
Regular Article
  • 35 Downloads
Part of the following topical collections:
  1. Topical issue: Non-Linear and Complex Dynamics in Semiconductors and Related Materials

Abstract

Noise-induced switching between coexisting metastable states occurs in a wide range of far-from-equilibrium systems including micro-mechanical oscillators, epidemiological and climate change models, and nonlinear electronic transport in tunneling structures such as semiconductor superlattices and tunnel diodes. In the case of tunnel diode circuits, noise-induced switching behavior is associated with negative differential resistance in the static current–voltage characteristics and bistability, i.e., the existence of two macroscopic current states for a given applied voltage. Noise effects are particularly strong near the onset and offset of bistable current behavior, corresponding to bifurcation points in the associated dynamical system. In this paper, we show that the tunnel diode system provides an excellent experimental platform for the precision measurement of scaling properties of mean switching times versus applied voltage near bifurcation points. More specifically, experimental data confirm that the mean switching time scales logarithmically as the 3/2 power of voltage difference over an exceptionally wide range of time scales and noise intensities.

Graphical abstract

References

  1. 1.
    H.B. Chan, C. Stambaugh, Phys. Rev. Lett. 99, 060601 (2007) ADSCrossRefGoogle Scholar
  2. 2.
    J. Aldridge, A. Cleland, Phys. Rev. Lett. 94, 156403 (2005) ADSCrossRefGoogle Scholar
  3. 3.
    W. Wernsdorfer, E.B. Orozco, K. Hasselbach, A. Benoit, B. Barbara, N. Demoncy, A. Loiseau, H. Pascard, D. Mailly, Phys. Rev. Lett. 78, 1791 (1997) ADSCrossRefGoogle Scholar
  4. 4.
    M. Rogozia, S. Teitsworth, H. Grahn, K. Ploog, Phys. Rev. B 64, 041308 (2001) ADSCrossRefGoogle Scholar
  5. 5.
    O. Tretiakov, T. Gramespacher, K. Matveev, Phys. Rev. B 67, 073303 (2003) ADSCrossRefGoogle Scholar
  6. 6.
    Y. Bomze, R. Hey, H. Grahn, S. Teitsworth, Phys. Rev. Lett. 109, 026801 (2012) ADSCrossRefGoogle Scholar
  7. 7.
    V. Lucarini, D. Faranda, M. Willeit, Nonlinear Process. Geophys. 19, 9 (2012) ADSCrossRefGoogle Scholar
  8. 8.
    M. Khasin, M.I. Dykman, Phys. Rev. Lett. 103, 068101 (2009) ADSCrossRefGoogle Scholar
  9. 9.
    E.M. Izhikevich, Dynamical Systems in Neuroscience (MIT Press, MA, 2007) Google Scholar
  10. 10.
    L. Esaki, Phys. Rev. 109, 603 (1958) ADSCrossRefGoogle Scholar
  11. 11.
    L. Chang, L. Esaki, R. Tsu, Appl. Phys. Lett. 24, 593 (1974) ADSCrossRefGoogle Scholar
  12. 12.
    J. Chen, M. Reed, A. Rawlett, J. Tour, J. Sci. 286, 1550 (1999) CrossRefGoogle Scholar
  13. 13.
    L.L. Bonilla, S.W. Teitsworth, Nonlinear Wave Methods for Charge Transport (Wiley VCH, Weinheim, 2010) Google Scholar
  14. 14.
    H. Xu, S.W. Teitsworth, J. Appl. Phys. 108, 043705 (2010) ADSCrossRefGoogle Scholar
  15. 15.
    A. Wacker, Phys. Rep. 357, 1 (2002) ADSCrossRefGoogle Scholar
  16. 16.
    L.L. Bonilla, H.T. Grahn, Rep. Prog. Phys. 68, 577 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    H. Grahn, R. Haug, W. Müller, K. Ploog, Phys. Rev. Lett. 67, 1618 (1991) ADSCrossRefGoogle Scholar
  18. 18.
    S. Lu, L. Schrottke, S. Teitsworth, R. Hey, H. Grahn, Phys. Rev. B 73, 033311 (2006) ADSCrossRefGoogle Scholar
  19. 19.
    H. Schneider, H.C. Liu, Quantum Well Infrared Photodetectors (Springer, Berlin, 2007) Google Scholar
  20. 20.
    M. Buckingham, Noise in Electronic Devices and Systems (John Wiley & Sons, NJ, 1985) Google Scholar
  21. 21.
    C. Gardiner, Stochastic Methods: A Handbook for the Natural and Social Sciences, Springer Series in Synergetics (Springer, Switzerland, 2009) Google Scholar
  22. 22.
    K. Luo, H. Grahn, K. Ploog, Phys. Rev. B 57, R6838 (1998) ADSCrossRefGoogle Scholar
  23. 23.
    M. Rogozia, S. Teitsworth, H. Grahn, K. Ploog, Phys. Rev. B 65, 205303 (2002) ADSCrossRefGoogle Scholar
  24. 24.
    M.H. Devoret, D. Esteve, J.M. Martinis, A. Cleland, J. Clarke, Phys. Rev. B 36, 58 (1987) ADSCrossRefGoogle Scholar
  25. 25.
    R. Victora, Phys. Rev. Lett. 63, 457 (1989) ADSCrossRefGoogle Scholar
  26. 26.
    M.I. Dykman, E. Mori, J. Ross, P. Hunt, J. Chem. Phys. 100, 5735 (1994) ADSCrossRefGoogle Scholar
  27. 27.
    M. Dykman, B. Golding, L. McCann, V. Smelyanskiy, D. Luchinsky, R. Mannella, P. McClintock, Chaos 11, 587 (2001) ADSCrossRefGoogle Scholar
  28. 28.
    R. Landauer, J. Appl. Phys. 33, 2209 (1962) ADSCrossRefGoogle Scholar
  29. 29.
    O. Tretiakov, K. Matveev, Phys. Rev. B 71, 165326 (2005) ADSCrossRefGoogle Scholar
  30. 30.
    P. Rodin, E. Schöll, J. Appl. Phys. 93, 6347 (2003) ADSCrossRefGoogle Scholar
  31. 31.
    A. Amann, E. Schöll, Phys. Rev. B 72, 165319 (2005) ADSCrossRefGoogle Scholar
  32. 32.
    S.H. Strogatz, Nonlinear Dynamics and Chaos:With Applications to Physics, Biology, Chemistry, and Engineering (CRC Press, Boca Raton, 2015) Google Scholar
  33. 33.
    M. Dykman, B. Golding, J. Kruse, L. McCann, D. Ryvkine, AIP Conf. Proc. 665, 428 (2003) ADSCrossRefGoogle Scholar
  34. 34.
    L. Lapidus, D. Enzer, G. Gabrielse, Phys. Rev. Lett. 83, 899 (1999) ADSCrossRefGoogle Scholar
  35. 35.
    W. Li, I. Reidler, Y. Aviad, Y. Huang, H. Song, Y. Zhang, M. Rosenbluh, I. Kanter, Phys. Rev. Lett. 111, 044102 (2013) ADSCrossRefGoogle Scholar
  36. 36.
    M. Alvaro, M. Carretero, L. Bonilla, Europhys. Lett. 107, 37002 (2014) ADSCrossRefGoogle Scholar
  37. 37.
    J. Kurkijärvi, Phys. Rev. B 6, 832 (1972) ADSCrossRefGoogle Scholar
  38. 38.
    M. Dykman, M. Krivoglaz, Physica A 104, 480 (1980) ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    H.A. Kramers, Physica 7, 284 (1940) ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    M.I. Freidlin, A.D. Wentzell, in Random Perturbations of Dynamical Systems, A Series of Comprehensive Studies in Mathematics (Springer, Switzerland, 2012) Google Scholar
  41. 41.
    M. Heymann, in Minimum Action Curves in Degenerate Finsler Metrics, Series Lecture Notes in Mathematics (Springer, Switzerland, 2015), Vol. 2134 Google Scholar
  42. 42.
    H. Okean, in Semiconductors and Semimetals (Elsevier, Amsterdam, 1971), Vol. 7, pp. 473–624 Google Scholar
  43. 43.
    S.W. Teitsworth, unpublished (2018) Google Scholar
  44. 44.
    O. Tretiakov, K. Matveev, Phys. Rev. B 73, 115302 (2006) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Stephen W. Teitsworth
    • 1
    Email author
  • Matthew E. Olson
    • 1
  • Yuriy Bomze
    • 1
  1. 1.Department of PhysicsDuke UniversityDurhamUSA

Personalised recommendations