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Feynman Path Integral Approach to Resonant Tunneling

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Resonant Tunneling in Semiconductors

Part of the book series: NATO ASI Series ((NSSB,volume 277))

Abstract

A path integral formulation is developed for resonant tunneling in a double barrier quantum well structure. Analysis is carried out in detail for a case where scattering in the well is strong. It is shown that sequential tunneling through quasi-bound states in the well is an alternative description of resonant tunneling, and that resonant transmission and resonant tunneling time delay are significantly reduced for the strong scattering case.

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References

  1. L.L. Chang, L. Esaki, and R. Tsu, Resonant tunneling in semiconductor double barriers, Appl. Phys. Lett. 24: 593(1974).

    Article  ADS  Google Scholar 

  2. See, for example, E.E. Mendez, Physics of resonant tunneling in semiconductors, in: “Physics and Applications of- Quantum Wells and Superlattices”, edited by E.E. Mendez and K. von Klitzing, Plenum, New York, (1987).

    Google Scholar 

  3. F. Capasso, K. Mohammed, and A.Y. Cho, Resonant tunneling through double barriers, Perpendicular quantum transport phenomena in superlatties, and their device applications, IEEE J. Quantum Electron. QW-22: 1853 (1986).

    Article  ADS  Google Scholar 

  4. S. Luryi, Frequency limit of double-barrier resonant-tunneling oscillators, Appl. Phys. Lett. 47: 490 (1985).

    Article  ADS  Google Scholar 

  5. B. Ricco and M. Y. Azbel, Physics of resonant tunneling, The one-dimensional double barrier case, Phys. Rev. B 29: 1970 (1984).

    Article  ADS  Google Scholar 

  6. Y. Zohta, K. Tsuda and Y.S. Hiraoka, Anomalous I - V characteristics of semiconductor heterojunction diode due to transmission resonance, J. Vac. Sci. Technol. B 4: 658 (1986).

    Article  Google Scholar 

  7. Y. Zohta, Analysis of thermionic emission current over the Aℓx Ga1-x As barrier in a GaAs/A ℓ xGa1-x As/GaAs (x>0.45) structure, Jpn, J. Appl. Phys. Pt.2. 27: L906 (1988).

    Article  Google Scholar 

  8. Y. Zohta, T. Nozu, and M. Obara, Resonant tunneling spectroscopy of two coupled quantum wells, Phys. Rev. B 39:1375 (1987).

    Article  Google Scholar 

  9. A.D. Stone and P.A. Lee, Effect of inelastic processes on resonant tunneling in one dimension, Phys. Rev. Lett, 54:1196 (1985).

    Article  ADS  Google Scholar 

  10. M. Jonson and A. Grincwaig, Effect of inelastic scattering on resonant and sequential tunneling in double barrier heterostructures, Appl. Phys. Lett. 51:1729 (1987).

    Google Scholar 

  11. B. Gu, C. Coluzza, M. Mangiantini, and A. Frova, Scattering effects on resonant tunneling in double-barrier heterostructures, J. Appl. Phys. 65: 3510 (1989).

    Article  ADS  Google Scholar 

  12. Y. Zohta, Path-integral approach to resonant tunneling, Phys. Rev. B 41: 7879 (1990).

    Article  ADS  Google Scholar 

  13. Y. Zohta, Scattering effect on resonant tunneling: Feynman path integral approach, Solid State Commun. 72: 931 (1989).

    Article  ADS  Google Scholar 

  14. Y. Zohta, Scattering matrix theory of resonant tunneling Jpn. J. Appl. Phys. Pt.2. 28: L2144 (1989).

    Article  Google Scholar 

  15. Y. Zohta, Resonant tunneling time delay studied by Feynman path integrals, Solid State Commun. 73: 847 (1990).

    Article  ADS  Google Scholar 

  16. R.P. Feynman and A.R. Hibbs, “Quantum Mechanics and Path Integrals”, McGraw-Hill, New York, (1965).

    MATH  Google Scholar 

  17. L.S. Schulman, “Techniques and Applications of Path Integration”, Wiley, New York, (1981).

    Book  MATH  Google Scholar 

  18. M.C. Gutzwiller, Phase-integral approximation in momentum space and the bound states of an atom, J. Math. Phys. 8: 1979 (1967); 10:1004 (1969); 11: 1971 (1970); 12: 343 (1971).

    Google Scholar 

  19. K.F. Freed, Path integral and semiclassical tunneling, wave functions, and energies, J. Chem. Phys. 56; 692 (1972).

    Article  ADS  Google Scholar 

  20. D.W. McLaughlin, Complex time, countour independent path integrals and barrier penetration, J. Math, Phys. 13:1099 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  21. R.A. Webb, S. Washburn, A.D. Benoit, C.P. Umbach and R.B. Laibowitz, Conductance fluctuations in disordered sub-micron wires and rings, Jpn. J. Appl. Phys. 26, Suppl. 26–3: 1926 (1987).

    Google Scholar 

  22. A. Sommerfeld, “Optics”, Academic, New York, (1954) p. 180.

    MATH  Google Scholar 

  23. D. Bohm, “Quantum Theory”, Prentice-Hall, Englewood Cliffs, NJ, (1951) p. 290.

    Google Scholar 

  24. T.C.L.G. Sollner, W.D. Goodhue, P.E. Tannenwald, C.D. Parker, and D.D. Peck, Resonant tunneling through quantum wells at frequencies up to 2.5 THz, Appl. Phys. Lett. 43: 588 (1983).

    Article  ADS  Google Scholar 

  25. H. Feshbach, C.E. Porter, and V.F. Weisskopf, Model for nuclear reactions with neutrons, Phys. Rev. 96: 448 (1954); See also, L.D. Landau, and Ya. Smorodinsky, “Lectures on Nuclear Theory”, Plenum, New York, (1959).

    Google Scholar 

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Zohta, Y., Nakamura, K., Ezawa, H. (1991). Feynman Path Integral Approach to Resonant Tunneling. In: Chang, L.L., Mendez, E.E., Tejedor, C. (eds) Resonant Tunneling in Semiconductors. NATO ASI Series, vol 277. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3846-2_27

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  • DOI: https://doi.org/10.1007/978-1-4615-3846-2_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6716-1

  • Online ISBN: 978-1-4615-3846-2

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