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Gauge-Invariant Formulation of Fermi's Golden Rule and Its Application to High-Field Transport in Semiconductors

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Abstract

A gauge-invariant formulation of Fermi's Golden rule is proposed. We shall revisit the conventional description of carrier-phonon scattering in the presence of high electric fields by means of a gauge-invariant density-matrix approach. We show that the so called intracollisional field effect, as usually accounted for, has been always overestimated due to the neglect of the time variation of the basis states, which in turn leads to a ill-defined Markov limit in the carrier-phonon interaction process. This is confirmed by our fully three-dimensional simulations of charge transport in state-of-the-art semiconductor superlattices.

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References

  1. F. Bloch, Z. Phys., 52, 555 (1928).

    Google Scholar 

  2. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer, Berlin, 1996).

    Google Scholar 

  3. W.V. Houston, Phys. Rev., 57, 184 (1940).

    Google Scholar 

  4. G.H. Wannier, Rev. Mod. Phys., 34, 645 (1962).

    Google Scholar 

  5. F. Rossi, in Theory of Transport Properties of Semiconductor Nanostructures, edited by E. Schöll (Chapman & Hall, London, 1998), p. 283.

    Google Scholar 

  6. T. Meier, F. Rossi, P. Thomas, and S.W. Koch, Phys. Rev. Lett., 75, 2558 (1995); F. Rossi, A. Di Carlo, and P. Lugli, Phys. Rev. Lett. 80, 3348 (1998); B. Rosam et al., Phys. Rev. Lett., 86, 1307 (2001).

    Google Scholar 

  7. I.B. Levinson and Y. Yasevichyute, Sov. Phys. JETP, 35, 991 (1972).

    Google Scholar 

  8. J.F. Barker and D.K. Ferry, Phys. Rev. Lett., 42, 1779 (1979).

    Google Scholar 

  9. R. Brunetti, C. Jacoboni, and F. Rossi, Phys. Rev., B 39, 10781 (1989).

    Google Scholar 

  10. R. Bertoncini and A.P. Jauho, Phys. Rev., B44, 3655 (1991).

    Google Scholar 

  11. M. Herbst, V.M. Axt, T. Kuhn, and J. Schilp, Phys. Stat. Sol.,(b) 204, 358 (1997).

    Google Scholar 

  12. C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulations (Springer, Wien, 1989).

    Google Scholar 

  13. L. Reggiani, P. Lugli, and A.P. Jauho, Phys. Rev., B36, 6602 (1987) and references therein.

    Google Scholar 

  14. Theneed for a gauge-invariant formulation of the problem was originally pointed out by Bertoncini and Jauho in [10].

  15. F. Rossi and T. Kuhn, Rev. Mod. Phys., 74, 895 (2002).

    Google Scholar 

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Authors and Affiliations

  1. Istituto Nazionale per la Fisica della Materia (INFM) and Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Emanuele Ciancio, Rita C. Iotti & Fausto Rossi

Authors
  1. Emanuele Ciancio
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  2. Rita C. Iotti
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  3. Fausto Rossi
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Ciancio, E., Iotti, R.C. & Rossi, F. Gauge-Invariant Formulation of Fermi's Golden Rule and Its Application to High-Field Transport in Semiconductors. Journal of Computational Electronics 2, 173–176 (2003). https://doi.org/10.1023/B:JCEL.0000011420.01771.18

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  • DOI: https://doi.org/10.1023/B:JCEL.0000011420.01771.18

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