Classical and quantum transport calculations for elastically scattered free electron gases in 2D nanostructures when B=0

  • P. N. Butcher
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 477)


The Boltzmann equation in the relaxation time approximation is used to calculate formal expressions for the local electrical, thermal and thermoelectric transport coefficients of a strictly 2D, elastically scattered, free electron gas. The terminal transport coefficients for the same gas confined in a quantum wire are also calculated using the Landauer-Buttiker formalism. Both calculations are valid in a quantum wire structure when its width w is much greater than the Fermi wavelength and its length l is much greater than the classical mean free path. Comparison shows that the sum of all the transmission coefficients through the system at the Fermi energy ɛ is therefore given by T(ɛ)=(w/l)ɛ/Δɛ where Δɛ=ħ/τ(ɛ) is the uncertainty in ɛ arising from the classical relaxation time τ(ɛ). A new way of calculating T(ɛ) using wave functions is outlined. Numerical results for both T(ɛ) and scattering wave functions are presented for two nanonstructures: (i) a quantum wire with one hard wall finger pushed in and (ii) a quantum wire with two hard wall fingers pushed in so as to create a quantum dot.


Wave Function Transmission Coefficient Quantum Wire Evanescent Mode Scatter Wave Function 
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.
    Butcher P.N., 1973 Electrons in Crystalline Solids, 1973 (IAEA, Vienna).Google Scholar
  2. 2.
    Madelung O., 1978, Introduction to Solid State Theory, p. 193 (Springer-Verlag, Berlin).Google Scholar
  3. 3.
    Butcher, P.N., J. Phys.: Condens. Matter 3, 4896 (1990).Google Scholar
  4. 4.
    Buttiker M., 1992, Nanostructure Systems, Ed. M. Reed, p. 191 (Academic Press, New York).Google Scholar
  5. 5.
    Butcher, P.N., 1993, Physics of Low-dimensional Semiconductor Structures, Eds. P.N. Butcher, N.H. March and M.P. Tosi, p. 95 (Plenum Press, New York).Google Scholar
  6. 6.
    D.S. Fisher, A. MacKinnon, E. Castonao and G. Kirczenow, 1992, Handbook on Semiconductors vol. 1, ed. P.T. Landsberg (Amsterdam: North-Holland) p. 863.Google Scholar
  7. 7.
    A. MacKinnon, Z. Phys. B 59, 385 (1985).CrossRefADSGoogle Scholar
  8. 8.
    H.U. Baranger and A.D. Stone, Phys. Rev. B 40, 8169 (1989).ADSGoogle Scholar
  9. 9.
    H.U. Baranger, D.P. DiVicenzo, R.A. Jalabert and A.D. Stone, Phys. Rev. B 44, 10637 (1991).ADSGoogle Scholar
  10. 10.
    P.N. Butcher and J.A. McInnes, J. Phys.: Condens. Matter 7, 745–758 (1995).CrossRefADSGoogle Scholar
  11. 11.
    P.N Butcher and J.A. McInnes, J. Phys. Condens. Matter 7, 6717–6726 (1995).CrossRefADSGoogle Scholar
  12. 12.
    A.D. Stone and A. Szafar, Phys. Rev. Lett 62, 300 (1990).ADSGoogle Scholar
  13. 13.
    B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouenhoven, D. van der Marel and C.J. Foxon, Phys. Rev. Lett. 60, 848 (1988).CrossRefADSGoogle Scholar
  14. 14.
    L.W. Moulenkamp, Th. Gravier, H. van Houten, O.J.A. Buijk, M.A.A. Mabusoone, Moulenkamp et al, Phys. Rev. Lett. 68, 3765 (1992).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • P. N. Butcher
    • 1
  1. 1.Department of PhysicsUniversity of WarwickCoventryU.K.

Personalised recommendations