The Background to Resonant Tunnelling Theory

  • G. A. Toombs
  • F. W. Sheard
Part of the NATO ASI Series book series (NSSB, volume 231)


The concept of tunnelling is almost as old as quantum mechanics itself. Oppenheimer (1928) wrote a paper on a hydrogen atom in an electric field as early as 1927. He calculated the rate of dissociation of the hydrogen atom and developed a method for determining the transition probabilities between two almost orthogonal states of the same energy. This method was to be rediscovered years later by Bardeen (1961) and applied to many particle tunnelling between two metals separated by a thin oxide layer. It is normally referred to as the Bardeen transfer hamiltonian method and it is important in tunnelling theory. The most familiar example of tunnelling is undoubtedly the radioactive decay of a nucleus by α-particle emission. The enormous range of lifetimes observed experimentally for radioactive decay is a consequence of the sensitivity of the transmission coefficient to variations in the tunnel barrier. For the same reason, a wide range of lifetimes should also be expected for tunnelling in semiconductors even though the potential barriers are much smaller.


Transmission Coefficient Landau Level Schrodinger Equation Resonant Tunnelling Negative Differential Resistance 
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  1. Alves, E.S., Eaves, L., Henini, M., Hughes, O.H., Leadbeater, M.L., Sheard, F.W., Toombs, G.A., Hill, G., Pate, M.A., 1988, Observation of intrinsic bistability in resonant tunnelling devices, Electronic Letters. 24: 1190.Google Scholar
  2. Bando, H., Nakagawa, T., Tokumoto, H., Ohta, K., Kajimura, K., 1987, Resonant magnetotunneling in AlGaAs/GaAs triple barrier diodes, Japan J. Appl. Phys. 26, Suppl. 26 - 3: 765.Google Scholar
  3. Chan, K.S., Eaves, L., Maude, D.K., Sheard, F.W., Snell, B.R., Toombs, G.A., Alves, E.S., Portal, J.C., Bass, S., 1988, Electron tunnelling into interfacial Landau states in single-barrier n-type (InGa)As/InP/(InGa)As heterostructures, Solid-State Electronics. 31: 711.Google Scholar
  4. Dicke, R.H., Wittke, J.P., 1960, “Introduction to Quantum mechanics”, Addison-Wesley, Reading.MATHGoogle Scholar
  5. Duke, C.B., 1969, “Tunneling in Solids”, Academic Press, New York.Google Scholar
  6. Goldman, V.J. Tsui, D.C., Cunningham, J.E., 1987c, Evidence for LO-phonon-assisted tunneling in double-barrier heterostructures, Phys. Rev. B., 36: 7635.ADSGoogle Scholar
  7. Kane, E.O., 1969, Basic concepts in tunneling, in: “Tunneling Phenomena in Solids”, E. Burstein and S. Lindqvist, ed., Plenum, New York.Google Scholar
  8. Leadbeater, M.L., Alves, E.S., Eaves, L., Henini, M., Hughes, O.H., Sheard, F.W., Toombs, G.A., Magnetic field and capacitance studies of intrinsic bistability in double-barrier structures, 1989a, Superlattices and Microstructures. 6: 59.Google Scholar
  9. Leadbeater, M.L., Alves, E.S., Eaves, L., Henini, M., Hughes, O.H., Celeste, A., Portal, J.C., Hill, G., Pate, M.A., 1989b, Magnetic field studies of elastic scattering and optic-phonon emission in resonant tunneling devices, Phys. Rev. B. 39: 3438.ADSCrossRefGoogle Scholar
  10. Mendez, E.E., 1988, Physics of resonant tunneling in semiconductors, in “Physics and Applications of Quantum Wells and Superlattices”, E.E. Mendez and K. von Klitizing, ed.,Plenum, New York.Google Scholar
  11. Morkoc, H. Chen, J., Reddy, U.K., and Henderson, T., 1986, Observation of a negative differential resistance due to tunneling through a single barrier into a quantum well, Appl. Phys. Lett.. 49: 70.ADSGoogle Scholar
  12. Payling, C.A., Alves, E.S., Eaves, L., Foster, T.J., Henini, M., Hughes, O.H., Simmonds, P.E., Sheard, F.W., Toombs, G.A., Portal, J.C., 1988, Evidence for sequential tunnelling and charge build-up in double barrier resonant tunneling devices, Surface Science. 196: 404.Google Scholar
  13. Price, P.J., 1988, Theory of resonant tunneling in heterostructures, Phys. Rev. B. 38: 1944.Google Scholar
  14. Ricco, B., Azbel, M. Ya., 1984, Physics of resonant tunneling:the one-dimensional double-barrier case, Phys. Rev. B. 29: 1970.Google Scholar
  15. Sheard, F.W., Chan, K.S., Toombs, G.A., Eaves, L., and Portal, J.C., 1988, Magnetotunnelling in single-barrier III-V semiconductor heterostructures, in:“Gallium Arsenide and Related Components 1987”, A. Christou and H.S. Rupprecht, ed., Institute of Physics, Bristol.Google Scholar
  16. Sheard, F.W., and Toombs G.A., 1988, Space charge buildup and bistability in resonant-tunneling double-barrier structures, Appl. Phys. Lett.. 52, 1228.Google Scholar
  17. Toombs G.A., Alves, E.S, Eaves, L., Foster, T.J., Henini, M., Hughes, O.H., Leadbeater, M.L., Payling, C.A., Sheard, F.W., Claxton, P.A., Hill, G., Pate, M.A., and Portal, J.C., 1988, Magnetic field studies of resonant tunnelling double barrier structures, in: “Gallium Arsenide and Related Compounds 1987”, A. Christou and H.S. Rupprecht, ed., Institute of Physics, Bristol.Google Scholar
  18. Van de Walle, C.G., and Martin, R.M., 1987, Theoretical study of band offsets at semiconductor interfaces, Phys. Rev. B. 35: 8154.ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • G. A. Toombs
    • 1
  • F. W. Sheard
    • 1
  1. 1.Department of PhysicsUniversity of NottinghamNottinghamEngland

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