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Classical Size Effect on In-plane Thermoelectric Transport at Low Dimension

Published online by Cambridge University Press:  21 March 2011

W. L. Liu  and
G. Chen
W. L. Liu
Affiliation:
Mechanical and Aerospace Engineering Department University of California at Los Angeles, CA 90095, USA
G. Chen
Affiliation:
Mechanical Engineering Department Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139
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Abstract

Previous models on low-dimensional thermoelectric investigation deal with the quasi twodimensional electron transport due to quantum confinement effect. The formation of sub-bands in quantum well requires that electron wave reflections or transmissions at the interface are strictly in the specular direction and the superimposed wave function keeps phase coherence. However, due to the interface non-ideality or roughness, electrons can lose coherence such that their transport will deviate from that described by two-dimensional quantum well limit theories. In this paper, we report a theoretical approach to investigate the classical size effect on in-plane thermoelectric transport at low dimensions. A theoretical model based on Boltzmann equation is established with interface scattering treated as partial specular and partial diffuse scattering boundary condition. With the infinite quantum well assumption, the classical size effect in the quantum-classical mixed regime is quantitatively demonstrated. Factors that affecting classical size effect, such as quantum well width and relaxation length, are discussed.

Keywords

ThermoelectricsSuperlatticesBoltzmann EquationThin Films
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 691: Symposium G – Thermoelectric Materials 2001--Research and Applications , 2001 , G8.28
Copyright
Copyright © Materials Research Society 2002

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References

REFERENCES

1 Hicks, L.D. and Dresselhaus, M. S., Phys. Rev. B, 47, 12727 (1993).Google Scholar
2 Hicks, L.D. and Dresselhaus, M. S., Phys. Rev. B, 47, 16631 (1993).Google Scholar
3 Sofo, J. O. and Mahan, G. D., Appl. Phys. Lett., 65, 2690 (1994).Google Scholar
4 Broido, D.A. and Reinecke, T.L., Appl. Phys. Lett., 70, 2834 (1997).Google Scholar
5 Koga, T., Sun, X., Cronin, S.B., and Dresselhaus, M.S., 1999, Appl. Phys. Lett., 75, 2438 (1999).Google Scholar
6 Harman, T.C., Spears, D.L., Calawa, D.R., Groves, S.H., and Walsh, M.P., Proceedings ICT'97, 416 (1997).Google Scholar
7 Koga, T., Cronin, S.B., Dresselhaus, M.S., Liu, J.L., and Wang, K.L, Appl. Phys. Lett., 77, 1490 (2000).Google Scholar
8 Mendez, E. E., Chang, L. L., Landgren, G., Ludeke, R., Esaki, L., and Pollak, F. H., Phys. Rev. Lett., 46, 1230 (1981)Google Scholar
9 Dow, J. D., Ren, S. Y., and Hess, K., Phys. Rev. B, 25, 6218 (1982).Google Scholar
10 N, Trivedi and Ashcroft, N. W., Phys. Rev. B, 35, 6084 (1987).Google Scholar
11 Tellier, C. R. and Tosser, A. J., Size Effects in Thin Films, Elsevier Scientific, New York (1982).Google Scholar
12This assumption is far away from the real band structure of Si/Ge. Due to the tunneling effect, the optimum ZT obtained with finite quantum well is much lower that with infinite quantum well, as has been pointed out in Refs. 3 and 4. The infinite quantum well assumption made here is to reduce complexity and focus on demonstrating classical size effect. However, the model developed can be extended to include finite barrier height and multi-band degeneracy. Some modeling results on Si/Ge superlattice under that strategy will be presented elsewhere.Google Scholar
13 Chen, G., J. Heat Trans., 119, 220 (1997).Google Scholar
14 Chen, G., Phys. Rev. B, 57, 14958 (1998).Google Scholar
15 Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Saunders College Publishing, Philadelphia (1976).Google Scholar
16 Sun, X., Chen, G., Wang, K. L., and Dresselhaus, M. S., ICT'98 Proceedings, p47 (1998)Google Scholar
17 X, Sun, The Effect of Quantum Confinement on the Thermoelectric Figure of Merit, Ph.D. Thesis, Massachusetts Institute of Technology, (1999)Google Scholar