Advertisement

The Thermoelectric Behaviour of two Dimensional Electron and Hole Gases and Quantum Point Contacts

  • P. N. Butcher
  • T. M. Fromhold
  • R. R. Barraclough
  • P. R. Rogers
  • B. L. Gallagher
  • R. P. Oxley
  • M. Henini
Chapter

Abstract

Considerable progress has been made over the last ten years in understanding the thermoelectric behaviour of low dimensional transport systems. There are two regimes to consider. At low temperatures (below about 1K) the effect of phonons is negligible. This is the “diffusion” thermopower regime which we discuss briefly for 2D electron gases (2DEGS) in Section 2. In Section 3 we discuss a particularly interesting aspect of the formalism for 2DEGS which is that it may be modified easily to apply to the quantisation effects observed recently in quantum point contacts (van Wees et al, 1988; Wharam et al, 1988; van Houten et al, 1992; Molenkamp et al 1992).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barraclough, R.J., Fromhold, T.M., Rodgers, P.J., Gallagher, B.L., Jezierski, A., Henini, M., Butcher, P.N., and Hill, G., 1993, in preparation for Phys. Rev. B. Google Scholar
  2. Beenakker, C.W.J, and van Houten, H., 1991, Quantum transport in semiconductor nanostructures in Solid State Physics Vol 44, Ehrenreich and Turnball, eds, Academic Press, New York.Google Scholar
  3. Butcher, P.N., 1990, Thermal and electric transport formalism for electronic microstructures with many terminals, J.Phys: Condens Matter 2: 4869.ADSCrossRefGoogle Scholar
  4. Butcher, P.N., 1992, Theory of electron transport in low dimensional structures, in Physics of Low -Dimensional Semiconductor Structures, P.N. Butcher, N.H. March and M.P. Tosi, eds, Plenum, New York.Google Scholar
  5. Cantrell, D.G. and Butcher, P.N., 1985, Lifetime broadening of the subband structure in the thermopower of narrow channel systems, J. Phys. C: Solid State Phys. 18: 6639.ADSCrossRefGoogle Scholar
  6. Cantrell, D.G. and Butcher, P.N., 1987, A calculation of the phonon drag contribution to the thermopower of quasi-2D electrons coupled to 3D phonons J. Phys. C: Solid State Phys. 20: 1985, 1993.ADSCrossRefGoogle Scholar
  7. Chamberlain, J.M., 1992, private communication.Google Scholar
  8. Fletcher, R., Harris, J.J. and Foxon, CT., 1991, The effect of second subband occupation on the thermopower of a high mobility GaAs-Al0.33 Ga0.33 As heterojunction, Semicond. Sci. Technol. 6: 54.ADSCrossRefGoogle Scholar
  9. Fletcher, R., Maan, J.C., Ploog, K., and Weimann, G., 1986, Thermoelectric properties of GaAs-Ga1-xA1xAs heterojunctions at high magnetic fields, Phys. Rev. B 33: 7122.ADSCrossRefGoogle Scholar
  10. Fromhold, T.M., Butcher, P.N., Qin, G., Mulimani, B.G., Oxley, J.P., and Gallagher, B.L., 1992, 180° phase shift of phonon drag magnetothermopower oscillations in high mobility 2DEGS, Surf. Sci. 263: 183.Google Scholar
  11. Fromhold, T.M., Butcher, P.N., Qin, G., Mulimani, B.G., Oxley, J.P., and Gallagher, B.L., 1993, Phonon drag magnetothermopower oscillations in GaAs/AlGaAs heterojunctions, submitted to Phys. Rev. B.Google Scholar
  12. Gallagher, B.L. and Butcher, P.N., 1992, Classical transport and thermoelectric effects in low dimensional and mesoscopic semiconductor structures, in Handbook on Semiconductors Vol. 1, P.T. Landsberg, ed., North Holland, AmsterdamGoogle Scholar
  13. Gallagher, B.L., Oxley, J.P., Smith, M.J. and Butcher, P.N., 1990, The phonon drag and diffusion thermopower of a Si inversion layer, J. Phys.: Condens. Matter 2: 775.ADSCrossRefGoogle Scholar
  14. Guenault, A.M., 1971, A physical picture of phonon drag thermoelectric power, J. Phys. F: Metal Phys. 1: 373.ADSCrossRefGoogle Scholar
  15. Hayden, R.K., Maude, D.K., Eaves, L., Valadares, E.C., Henini, M., Sheard, F.W., Hughes, O.H., Portal, J.C., and Cury, L., 1991, Probing the hole dispersion curves of a quantum well using resonant magnetotunneling spectroscopy, Phys. Rev. Lett. 66: 1749.ADSCrossRefGoogle Scholar
  16. Kittel, C, 1976, Introduction to Solid State Physics, John Wiley, New York.Google Scholar
  17. Kubakaddi, S.S., Butcher, P.N. and Mulimani, B.G., 1989, Phonon drag thermopower of a 2D electron gas in a quantising magnetic field, Phys. Rev. B. 40: 1377.ADSCrossRefGoogle Scholar
  18. Lyo, S.K. 1988, Low temperature phonon drag thermoelectric power in heterojunctions, Phys. Rev. B 38: 6345ADSCrossRefGoogle Scholar
  19. Lyo, S.K., 1989, Magnetothermopower oscillations of the phonon drag thermoelectric power in heterojunctions, Phys. Rev. B 40: 6458ADSCrossRefGoogle Scholar
  20. Molenkamp, C.W., Gravier, Th., van Houten, H., Buijk, O.J.A. and Mabesoone, M.A.A., 1992, Peltier coefficient and thermal conductance of a quantum point contact, Phys. Rev. Lett. 68: 3765.ADSCrossRefGoogle Scholar
  21. Price, P.J., 1981, Two-dimensional electron transport in semiconducting layers, 1, phonon scattering, Ann. Phys. (N.Y.) 133: 217.ADSCrossRefGoogle Scholar
  22. Qin, G., Fromhold, T.M., Butcher, P.N., Mulimani, B.G., Oxley, J.P., and Gallagher, B.L., 1993, Magnetothermopower in silicon MOSFETS, J. Phys.: Condens. Matter 5: 1355.ADSCrossRefGoogle Scholar
  23. Ruf. C, Brummeil, M.A., Gmelin, E. and Ploog, K. 1989, The influence of subband structure on the thermopower of GaAs-AlxGa1-xAs heterostructures, Superlat, and Microstruct. 6: 175.ADSCrossRefGoogle Scholar
  24. Smith, M.J., and Butcher, P.N., 1989a, A calculation of the effect of screening on phonon-drag thermoelectric power in a Si MOSFET, J. Phys.: Condens. Matter 1: 1261aADSCrossRefGoogle Scholar
  25. Smith, M.J. and Butcher, P.N., 1989b, Inelastic scattering and the temperature dependence of thermoelectric power in quasi-2D systems, J. Phys. C: Condens. Matter 1: 4859.ADSCrossRefGoogle Scholar
  26. van Houten, H., Molenkamp, L.W., Beenakker, C.W.J, and Foxon, CT., 1992, Thermo-electric properties of quantum point contacts, Semicond. Sci. Technol. 7: B215.CrossRefGoogle Scholar
  27. van Wees, B.J., von Houten, H., Beenakker, C.W., Williamson, J.G., Kouwenhoven, L.P., van der Marel, D. and Foxon, C.T., 1988, Quantised conductance of point contacts in a two-dimensional electron gas, Phys. Rev. Letts, 60: 848.ADSCrossRefGoogle Scholar
  28. Walukiewicz, W., 1985, High mobility in modulation-doped heterostructures: GaAs-AlGaAs, Phys. Rev. B 31: 5557.ADSCrossRefGoogle Scholar
  29. Wang, W.I., Mendez, E.E., Iye, Y., Lee, B., Kim, M.H., and Stillman G.E., 1986, High mobility two-dimensional hole gas in an Al0.26Ga0.74As/GaAs heterojunction, J. Appl. Phys. 60: 1834.ADSCrossRefGoogle Scholar
  30. Wharam, D.A., Thornton, T.J., Newbury, R., Pepper, M., Ahmed, H., Frost, J.E.F., Hasko, D.G., Peacock, D.C., Ritchie, D.A. and Jones, G.A.C., 1988, One dimensional transport and the quantisation of the ballistic resistance, J. Phys. C: Solid State Phys. 21: L209.ADSCrossRefGoogle Scholar
  31. Ziman, J.M., 1989, “Principles of the Theory of Solids”, Cambridge University Press, Cambridge.Google Scholar

Copyright information

© Plenum Press, New York 1994

Authors and Affiliations

  • P. N. Butcher
    • 1
  • T. M. Fromhold
    • 2
  • R. R. Barraclough
    • 2
  • P. R. Rogers
    • 2
  • B. L. Gallagher
    • 2
  • R. P. Oxley
    • 2
  • M. Henini
    • 2
  1. 1.Department of PhysicsUniversity of WarwickCoventryUK
  2. 2.Department of PhysicsUniversity of NottinghamNottinghamUK

Personalised recommendations