Use of Quantum-Well Superlattices to Increase the Thermoelectric Figure of Merit: Transport and Optical Studies
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Abstract The thermoelectric figure of merit (ZT) of a material is a measure the usefulness of the material in a thermoelectric device. Presently, the materials with the highest ZT are Bi 2 Te3 alloys, with ZT _ 1. There has been little improvement in ZT for over 30 years. So far, all the materials used in thermoelectric applications have been in bulk form. Recently, however, calculations have shown that it may be possible to increase ZT of some materials through the use of quantum-well superlattices. We have made preliminary measurements on the Bi/PbTe superlattice system using transport and optical techniques to determine whether it is possible to achieve such an increase in ZT.
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] ZT -
S
2
oT
K
(1)
where S is the thermopower (Seebeck coefficient), o is the electrical conductivity and r. is the thermal conductivity. Currently, the materials with the highest ZT are Bi 2 Te3 alloys, 1.0 at 300 K [2]. Only small increases in ZT have been such as Bio.sSb 1 .sTe3 , with ZT 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 earlier papers, we considered theoretically the effect on ZT of using certain materials in a two-dimensional (2D) quantum-well superlattice. First, we considered the effect on ZT of using a one-band material such as Bi 2 Te3 in a 2D quantum well [3]. Our calculations showed that this approach could yield a significant increase in ZT, with ZT increasing as
the width of the quantum well is reduced. This increase is due to the 2D nature of the density of states of the electrons in the quantum well. Second, we considered the case of using a 1035 Mat. Res. Soc. Symp. Proc. Vol. 358 ©1995 Materials Research Society
(a)•,)
10.0 6.0
8.0
6.0
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a.-c,4.0 2.0 0.0
2.0 0.0
0.0
20.0
40.0 60.0 a(A)
80.0 100.0
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a (A)
Figure 1: Plot of ZT vs layer thickness for (a) a quantum well of Bi 2 Te3 and (b) a quantumwell of Bi. 2-band material such as a semimetal or a semiconductor in a quantum-wel structure [4]. In general, 2-band materials (in which both electrons and holes contribute significantly to the transport) do not give a high ZT because of their low Seebeck coefficient. This is because the Seebeck coefficient of the electrons is negative and that of the holes is positive, so these cancel out in the overall Seebeck coefficient and the resulting ZT is low. Bi is a semimetal and as a result of the contribution of both electrons and holes, it has a low ZT. However, if is were somehow possible to remove the holes from the system to make Bi a one-band system, Bi would have a high ZT [5]. By preparing a two-band material in the form of a quantum-well superlattice, it is possible to separate the two bands (by decreasing the well thickness), and to create an effectively one-band material [6]. Thu
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