Skip to main content

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

  • Chapter
Die Kunst of Phonons

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).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 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 

  • 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 

  • Butcher, P.N., 1990, Thermal and electric transport formalism for electronic microstructures with many terminals, J.Phys: Condens Matter 2: 4869.

    Article  ADS  Google Scholar 

  • 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 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Chamberlain, J.M., 1992, private communication.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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 

  • 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 

  • 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, Amsterdam

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Guenault, A.M., 1971, A physical picture of phonon drag thermoelectric power, J. Phys. F: Metal Phys. 1: 373.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Kittel, C, 1976, Introduction to Solid State Physics, John Wiley, New York.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Lyo, S.K. 1988, Low temperature phonon drag thermoelectric power in heterojunctions, Phys. Rev. B 38: 6345

    Article  ADS  Google Scholar 

  • Lyo, S.K., 1989, Magnetothermopower oscillations of the phonon drag thermoelectric power in heterojunctions, Phys. Rev. B 40: 6458

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Price, P.J., 1981, Two-dimensional electron transport in semiconducting layers, 1, phonon scattering, Ann. Phys. (N.Y.) 133: 217.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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: 1261a

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Walukiewicz, W., 1985, High mobility in modulation-doped heterostructures: GaAs-AlGaAs, Phys. Rev. B 31: 5557.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Ziman, J.M., 1989, “Principles of the Theory of Solids”, Cambridge University Press, Cambridge.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Plenum Press, New York

About this chapter

Cite this chapter

Butcher, P.N. et al. (1994). The Thermoelectric Behaviour of two Dimensional Electron and Hole Gases and Quantum Point Contacts. In: Paszkiewicz, T., Rapcewicz, K. (eds) Die Kunst of Phonons. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2455-7_22

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-2455-7_22

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-44677-1

  • Online ISBN: 978-1-4615-2455-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics