Advertisement

The Kubo Formula and Linear Response

  • David K. Ferry
Part of the Physics of Solids and Liquids book series (PSLI)

Abstract

In much of semiconductor transport theory, it is our main aim to calculate the response of the distribution of electrons, within our device or bulk semiconductor sample, to an applied perturbation. While this perturbation is usually an electric field, it may also be a magnetic field, temperature gradient, density gradient, pressure, or any combination of these generalized forces. Energy from these forces is coupled to the electrons and subsequently decays to the lattice via interaction with the phonons. In small semiconductor devices, we would like to know the entire time dependence of the appropriate interactions, and usually we use some form of kinetic theory based upon the Boltzmann transport equation, which itself is not valid on the short time scales. The response is directly related to the nature of the scattering of the electrons by the lattice, and is often characterized in terms of relaxation times, such as the momentum relaxation time and the energy relaxation time. In turn, these averaged quantities are the macroscopic effects of the microscopic fluctuations introduced by the scattering processes themselves. As a consequence, it is possible to relate them directly to the averaged response to the spectrum of the fluctuations themselves—the traditional fluctuation-dissipation theorem.

Keywords

Density Matrix Linear Response Boltzmann Transport Equation Kubo Formula Velocity Operator 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Kuso, J. Phys. Soc. Jpn. 12, 570 (1957).ADSCrossRefGoogle Scholar
  2. 2.
    S. Doniach and E. H. Sondheimer, Green’s Functions for Solid State Physicists, Benjamin/Cummings, Reading, MA (1974).Google Scholar
  3. 3.
    G. D. Mahan, Many-Particle Physics, Plenum Press, New York (1981).Google Scholar
  4. 4.
    S. W. Lovesey, Condensed Matter Physics: Dynamic Correlations, Benjamin/Cummings, Reading, MA (1980).Google Scholar
  5. 5.
    N. F. Morr, Phil Mag. 22, 7 (1970).ADSCrossRefGoogle Scholar
  6. 6.
    D. S. Fisher and P. A. Lee, Phys. Rev. B 23, 6851 (1981); Phys. Rev. Lett. 47, 882 (1981).Google Scholar
  7. 7.
    E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).ADSCrossRefGoogle Scholar
  8. 8.
    G. Czycholl and B. Kramer, Sol State Commun. 32, 945 (1979).ADSCrossRefGoogle Scholar
  9. 9.
    D. J. Thouless and S. Kirkpatrick, J. Phys. C 14, 235 (1981).ADSCrossRefGoogle Scholar
  10. 10.
    P. W. Anderson, Phys. Rev. 109, 1492 (1958).ADSCrossRefGoogle Scholar
  11. 11.
    R. Mezenner and D. K. Ferry, unpublished.Google Scholar
  12. D. N. Zubarev, Usp. Fiz. Nauk 71,71 (1960) [translation in Soy. Phys. Uspekhi. 3, 320 (1960)]; also, Nonequilibrium Statistical Mechanics,consultants Bureau, New York (1974).Google Scholar
  13. 13.
    V. P. Kalashnikov, Physica 48, 93 (1970).MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    D. K. Ferry, J. Physique (CoBog.) 42, C7–253 (1981).Google Scholar
  15. 15.
    U. Fano, Rev. Mod Phys. 29, 74 (1957).MathSciNetADSMATHCrossRefGoogle Scholar
  16. N. N. Bogoliubov, Problemi dinam. teorii u stat. Fiz., Moscow (1946); also, in Studies in Statistical Mechanics, Vol. 1 (J. de Boer and G. E. Uhlenbeck, eds.), p.11, North-Holland, Amsterdam (1962).Google Scholar
  17. 17.
    J. J. Niez and D. K. Ferry, Phys. Rev. B 28, 1988 (1983).ADSCrossRefGoogle Scholar
  18. 18.
    W. Pötz and D. K. Ferry, in: Proc. 17th Intern. Conf Physics of Semiconductors (J. D. Chadi and W. A. Harrison, eds.), p. 1329, Springer-Verlag, New York (1985).Google Scholar
  19. 19.
    D. K. Ferry and J. R. Barker, J. Phys. Chem. Solids 41, 1083 (1980).ADSCrossRefGoogle Scholar
  20. 20.
    A. P. Jauho and J. W. Wilkins, Phys. Rev. B 29, 1919 (1984).ADSCrossRefGoogle Scholar
  21. 21.
    A. R. Vasconcellos and R. Luzzi, Phys. Rev. B 27, 3874 (1983).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • David K. Ferry
    • 1
  1. 1.Center for Solid State Electronics Research, College of Engineering and Applied SciencesArizona State UniversityTempeUSA

Personalised recommendations