Use of Quantum-Well Superlattices to Obtain a High Figure of Merit from Nonconventional Thermoelectric Materials
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Abstract Currently, the materials with the highest thermoelectric figure of merit (ZT) are one-band materials. The presence of both electrons and holes lowers ZT, so two-band materials such as semimetals are not useful thermoelectric materials. However, by preparing these materials in the form of two-dimensional quantum-well superlattices, it is possible to separate the two bands and transform the material to an effectively one-carrier system. We have investigated theoretically the effect of such an approach and our results indicate that a significant increase in ZT may be achieved. We have also evaluated the possibility of using intercalation as a means to achieve an increase in ZT. Our results allow the possibility of using new types of materials as thermoelectric refrigeration elements.
1
Introduction
For a material to be a good thermoelectric cooler, it must have a high thermoelectric figure of merit ZT. The figure of merit is defined by [1] SaT ZT-
,
(1)
where S is the thermopower (Seebeck coefficient), oais the electrical conductivity and r is the thermal conductivity. Currently, the materials with the highest ZT are Bi 2Te3 alloys such as Bi0..5Sb. 5Te3 , with ZT c_ 1.0 at 300 K [2]. Only small increases in ZT have been achieved in the last two decades, so it is now felt that the Bi 2 Te3 compounds may be nearing the limit of their potential performance [2].
2
Quantum-well superlattices
In an earlier paper [3], we considered the effect on ZT of using a one-band thermoelectric material such as Bi 2 Te3 in a two-dimensional (2D) quantum-well superlattice. Our calculations showed that this approach could yield a significant increase in ZT. In those earlier calculations, we assumed a one-band model since one-carrier systems give the best ZT for bulk materials [1]. However, it is now well-established that by preparing a twoband material in the form of a quantum-well superlattice, it is possible to separate the
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Mat. Res. Soc. Symp. Proc. Vol. 326. 01994 Materials Research Society
two bands (by decreasing the well thickness) and to create an effectively one-band material [4]. This semimetal-semiconductor transition has been demonstrated with HgTe/CdTe superlattices [5]. Thus, some semimetals which do not have a high ZT may be good thermoelectric materials in the form of 2D quantum-well superlattices. Gallo et al. [6] have shown that Bi, a semimetal with a low ZT, could have a ZT of nearly 2 if it were somehow possible to remove the holes from the system. In this paper, calculations have been performed to investigate the effect on ZT of preparing a two-band material in the form of a 2D quantum well. The methods used in Ref. [3] were extended to a two-band system in order to derive an expression for the figure of merit of a two-band material in a 2D quantum well. Briefly, expressions for S, a and r, were derived for 2D transport in a two-band system using the standard expressions for degenerate semiconductors in Ref. [7]. Z 2 DT was found using Eq.
(1). The calculations are for a general, anisotropi
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