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Fig. 2 shows a schematic diagram of the electronic energy band structure for bismuth nanowires in comparison to bulk bismuth, which is a semimetal with electrons in 3 carrier pockets at the L points in the rhombohedral Brillouin zone and holes in a single carrier pocket at the T point, and the band overlap of bulk Bi is 38 meV [20]. For Bi nanowires oriented along the bisectrix direction, there are two electron pockets in which the electrons have a heavy cyclotron Figure 1. Dependence of Z2DT and Z1DT on quantum well and effective mass (mh) and one electron pocket with a light quantum wire widths dW for the layers of the Bi quantum wells c normal to the trigonal direction and the Bi wire axis along the cyclotron effective mass (ml ), where the cyclotron mass is c trigonal direction. an average for the in-plane motion. Fig. 2, b, and c show , 1999, 41, . 758 M.S. Dresselhaus, G. Dresselhaus, X. Sun, Z. Zhang, S.B. Cronin, T. Koga schematically the calculated ground state energies of the [3] H.J. Goldsmid. Electronic Refrigeration. Pion, London (1986).

[4] A.F. Ioffe, S.V. Airapetyants, A.V. Ioffe, N.V. Kolomoets, heavy electron and light electron subbands and also the L.S. Stilbans. Dokl. Akad. Nauk SSSR 102, 981 (1956).

hole subband for a Bi wire oriented along the bisectrix [5] L.D. Hicks, T.C. Harman, X. Sun, M.S. Dresselhaus. Phys. Rev.

direction with a diameter of 100 nm and 50 nm, respectively, B53, 10493 (1996).

in comparison to the bulk Bi band structure shown in [6] L.D. Hicks, M.S. Dresselhaus. Phys. Rev. B47, 12727 (1993).

fig. 2, a [24]. Here we see that the lowest heavy electron [7] M.S. Dresselhaus, T. Koga, X. Sun, S.B. Cronin, K.L. Wang, subband lies lower than the corresponding light electron G. Chen. In 16th Int. Conf. on Thermoelectrics: Proceedings, subband. The figure further shows that the 100 nm wire is a ICT97; Dresden, Germany / Ed. by A. Heinrich and J. Schusemimetal with a small band overlap of 3 meV, and thermal mann, p. 1220.

energy (25 meV) is sufficient to cause significant occupation [8] M.S. Dresselhaus, X. Sun, S.B. Cronin, T. Koga, G. Dresof the light electron subband. However, the 50 nm diameter selhaus, K.L. Wang. In: Thermoelectric Materials - New wire along the bisectrix direction is a semiconductor and Directions and Approaches: MRS Symposia Proceedings, thermal excitation excites only heavy electrons. Thus, we San Francisco. 478 / Ed. by T.M. Tritt, M.G. Kanatzidis, can expect rather different transport properties for a 100 nm H.B. Lyon, Jr., G.D. Mahan, Materials Research Society Press, Pittsburgh, PA, (1997). P. 55.

and a 50 nm diameter wire.

[9] L.D. Hicks, M.S. Dresselhaus. Phys. Rev. B47, 16631 (1993).

Experimental transport studies are in progress to verify [10] Lyndon D. Hicks. The effect of quantum-well superlattices on the predictions of the model for semiconducting bismuth the thermo-electric figure of merit. PhD thesis, Massachusetts for small wire diameters. In the semiconducting regime, Institute of Technology (1996). Department of Physics.

work is in progress to estimate the thermoelectric properties [11] L.D. Hicks, T.C. Harman, M.S. Dresselhaus. Appl. Phys. Lett.

of the bismuth nanowires theoretically and to measure 63, 3230 (1993).

them experimentally, focusing on the conditions needed for [12] Shu Yuan, H. Krenn, G. Springholz, G. Bauer. Phys. Rev. B47, realizing an enhancement in ZT.

7213 (1993).

[13] G. Springholz, G. Ihninger, G. Bauer, M.M. Oliver, J.Z. Pastalan, S. Romaine, B.B. Goldberg. Appl. Phys. Lett. 63, 5. Conclusions (1993).

[14] T.C. Harman, D.L. Spears, D.R. Calawa, S.H. Groves, Some of the recent achievements that have been made M.P. Walsh. In: 16th Int. Conf. on Thermoelectrics: Proceedin the use of low dimensional materials for thermoelectric ings, ICT97; Dresden, Germany / Ed. by A. Heinrich and applications include a ZT 1.2 within n-type PbTe quantum J. Schumann. P. 416.

wells at room temperature [5]. Higher values are expected [15] X. Sun, G. Chen, K. Wang, M.S. Dresselhaus. In: 17th for this system at higher temperatures. The highest value of Int. Conf. on Thermoelectrics: Proceedings, ICT98; Nagoya, ZT for any thermoelectric material under any conditions Japan / Ed. by Kunihito Koumoto. Institute of Electrical and (ZT > 1.9) was achieved for a PbTe/PbSe0.98Te0.02/Te Electronics Engineers, Inc., Piscataway (1998).

superlattice at 570 K [18] where the system showed no [16] R. Venkatasubramanian. In: 17th Int. Conf. on Thermoelectrics: Proceedings, ICT98; Nagoya, Japan / Ed. by quantum confinement effects. Since research in this field Kunihito Koumoto. Institute of Electrical and Electronics is still at an early stage of development, significantly more Engineers, Inc., Piscataway (1998).

progress in enhancing ZT further is expected for the [17] T. Koga, X. Sun, S.B. Cronin, M.S. Dresselhaus. Appl. Phys.

future. It is thus appropriate to review recent progress on Lett., in press.

thermoelectric materials in celebration of the 80th birthday [18] T. Harman et al. In: The 40th Electronic Materials Conference.

of the Ioffe Institute, which has made so many important Charlottesville, VA, USA, (1998), abstract.

historical contributions to the field of thermoelectricity.

[19] H. Kato, A. Yamamoto, M. Takimoto, T. Ohta, K. Sakamoto, K. Miki, L. Whitlow, K. Kamisako, T. Matsui. In: 17th Int. Conf. on Thermoelectrics: Proceedings, ICT98; Nagoya, Acknowledgments Japan / Ed. by Kunihito Koumoto. Institute of Electrical and Electronics Engineers, Inc., Piscataway (1998).

The authors would like to thank T.C. Harman, J.P. Here[20] V.S. Edelman. Adv. Phys. 25, 555 (1976).

mans, G. Chen, J. Ying and K.L. Wang for valuable [21] K.F. Cuff, R.B. Horst, J.L. Weaver, S.R. Hawkins, C.F. Kooi, discussions.

G.M. Enslow. Appl. Phys. Lett. 2, 145 (1963).

The authors gratefully acknowledge support by the US [22] S. Cho, A. DiVenere, G.K. Wong, J.B. Ketterson. In: 16th Navy under Contract N N00167-98-K-0024 (MIT), and Int. Conf. on Thermoelectrics: Proceedings, ICT97; Dresden, ONR under MURI (UCLA). Support from the Honda Germany / Ed. by Armin Heinrich, Joachim Schumann. InstiCorporation for temperature dependent studies is gratefully tute of Electrical and Electronics Engineers, Inc., Piscataway acknowledged.

(1997). P. 188.

[23] Z. Zhang, J.Y. Ying, M.S. Dresselhaus. J. Materials Research 13, 1745 (1998).

References [24] Z. Zhang, X. Sun, M.S. Dresselhaus, J.Y. Ying, J. Heremans, Appl. Phys. Lett. 73, 1589 (1998).

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haus, J.Y. Ying, D.T. Morelli. Phys. Rev. B58, 0000 (1998).

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