Quantum Transport Theory of Resonant Tunneling Devices

  • William R. Frensley
Part of the NATO ASI Series book series (NSSB, volume 189)


The ability to fabricate semiconductor heterostructures on the scale of a few atomic layers has led to the development of devices which exploit the quantum-mechanical wave properties of electrons in their operation. The quantum device which has recieved the most attention recently is the quantum-well resonant-tunneling diode (RTD).1,2 This device shows a negative-resistance characteristic which is quantum-mechanical in origin, and is potentially a very fast device. Most of the theoretical work on this device has employed the formal theory of scattering, focusing on the behavior of pure quantum states which are asymptotically plane waves. While this approach should adequately describe the device under stationary conditions, it is poorly equipped to treat any sort of time-varying behavior. The reason for this is that the behavior of the RTD, and indeed any electronic device, is manifestly time-irreversible, and a proper notion of irreversibility cannot be introduced into pure-state quantum mechanics. A pure quantum state cannot evolve time-irreversibly. Models which attempt to introduce such behavior inevitably violate some fundamental physical law, usually the continuity equation. However, transitions between quantum states may proceed irreversibly if the system of interest interacts with an external system having a continuum of states. Such processes may be consistently described in terms of statistically mixed states, which are represented most simply by the single-particle density matrix.3 A description of a many-particle system in terms of such a single-particle distribution is generally termed a kinetic theory.4 The present paper describes such a theory of electron devices which incorporates quantum coherence effects (including tunneling).


Wigner Function Liouville Equation Liouville Operator Longitudinal Optical Pure Quantum State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. L. Chang, L. Esaki and R. Tsu, Appl. Phys. Lett. 24, 593 (1974).ADSCrossRefGoogle Scholar
  2. 2.
    T. C. L. G. Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker and D. D. Peck, Appl. Phys. Lett. 43, 588 (1983).ADSCrossRefGoogle Scholar
  3. 3.
    U. Fano, Rev. Mod. Phys. 29, 74 (1957).MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Kubo, R., M. Toda, and N. Hashitsume, Statistical Physics II. Nonequilibrium Statistical Mechanics. ( Springer-Verlag, Berlin, 1985 ).Google Scholar
  5. 5.
    W.R. Frensley, Phys. Rev. B36, 1570 (1987).ADSCrossRefGoogle Scholar
  6. 6.
    E. Wigner, Phys. Rev. 40, 749 (1932).ADSCrossRefGoogle Scholar
  7. 7.
    W.R. Frensley, Phys. Rev. Lett. 57, 2853 (1986).CrossRefGoogle Scholar
  8. 8.
    R. Tsu and L. Esaki, Appl. Phys. Lett. 22, 562 (1973).ADSCrossRefGoogle Scholar
  9. 9.
    D.D. Coon and H.C. Liu, Appl. Phys. Lett. 47, 172 (1985).ADSCrossRefGoogle Scholar
  10. 10.
    R.K. Mains and G.I. Haddad, “Numerical Considerations in the Wigner Function Modeling of Resonant-Tunneling Diodes,” to be published.Google Scholar
  11. 11.
    W.R. Frensley, Appl. Phys. Lett. 51, 448 (1987).Google Scholar
  12. 12.
    S. Ramo, Proc. IRE 27, 584 (1939).CrossRefGoogle Scholar
  13. 13.
    W. Shockley, J. Appl. Phys. 9, 635 (1938).ADSCrossRefGoogle Scholar
  14. 14.
    T.C.L.G. Sollner, E.R. Brown, W.D. Goodhue, and H.Q. Le, Appl.Phys. Lett. 50, 332 (1987).ADSCrossRefGoogle Scholar
  15. 15.
    K.S. Champlin, D.B. Armstrong, and P.D. Gunderson, Proc. IEEE 52, 677 (1964).CrossRefGoogle Scholar
  16. 16.
    W.R. Frensley, to be published in Superlattices and Microstructures.Google Scholar
  17. 17.
    I.B. Levinson, “Translational invariance in uniform fields and the equation of motion for the density matrix in the Wigner representation,” Soviet Physics JETP 30, 362–7 (1970).MathSciNetADSGoogle Scholar
  18. 18.
    J. Lin and L.C. Chi u, “Quantum theory of electron transport in the Wigner formalism,” J. Appl. Phys. 57, 1373–6 (1985).ADSCrossRefGoogle Scholar
  19. 19.
    E.M. Conwell, High Field Transport in Semiconductors,(Academic Press, New York, 1967) ch. 5.Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • William R. Frensley
    • 1
  1. 1.Central Research LaboratoriesTexas Instruments IncorporatedDallasUSA

Personalised recommendations