Effect of Quantum-Well Structures on the Thermoelectric Figure of Merit in the Si/Si 1-x Ge x System
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ABSTRACT The Si/Sii_- Ge, quantum well system is attractive for high temperature thermoelectric applications and for demonstration of proof-of-principle for enhanced thermoelectric figure of merit Z, since the interfaces and carrier densities can be well controlled in this system. We report theoretical calculations for Z in this system, based on which Si/Si_.0Ge. quantumwell structures were grown by molecular-beam epitaxy. Thermoelectric and other transport measurements were made, indicating that an increase in Z over bulk values is possible through quantum confinement effects in the Si/Si 1_.Ge. quantum-well structures. INTRODUCTION Recently, it has been shown theoretically [1] that it may be possible to increase the thermoelectric figure of merit (Z), defined by [2]
z
S2 ,
(1)
K
where S is the thermoelectric power (Seebeck Coefficient), a is the electrical conductivity and K is the thermal conductivity, of certain materials by preparing them in the form of two-dimensional quantum-well structures. This has already been demonstrated experimentally [3] using PbTe/Pbi_,Eu.Te multiple-quantum-well structures grown by molecularbeam epitaxy. In bulk form, Si-_-Ge. is a promising thermoelectric material for high temperature applications [4, 5, 6], and has been used in radio-isotope thermoelectric generators (RTGs) on satellites and spacecraft for compositions of about SiO.yGeo. 3 operating at - 1000 K [7]. Because of the large amount of expertise and information available on this system regarding the materials science of fabricating Sii_ 3 Ge1 /Si quantum wells, it is an interesting system for the demonstration of both proof-of-principle and high performance thermoelectric devices operating at high temperatures. THEORETICAL MODELING For a material to be a good thermoelectric cooler, it must have a high thermoelectric figure of merit, Z. In order to achieve a high Z, one requires a high thermoelectric power S, a high electrical conductivity ar, and a low thermal conductivity x. In general, it is difficult to increase Z because a modification to any one of the three parameters S, a, or ic,adversely affects the other transport coefficients, so that the resulting Z does not vary significantly. Currently, the materials with the highest Z are Bi 2 Tes alloys such as Bi0. 5Sb1 .5Te3 , with ZTz_ 1.0 at T= 300 K [8]. 261 Mat. Res. Soc. Symp. Proc. Vol. 452 01997 Materials Research Society
The effect on Z of using materials in two-dimensional (2D) structures, such as 2D multiple-quantum-well (MQW) structures, has been studied earlier [1] and it was shown theoretically that this approach could yield a significant increase in Z over the bulk value as the quantum-well width is decreased. The proposed increase in the power factor S2a arises mainly from the enhancement of the density of electron states per unit volume (near the Fermi level) that occurs for small quantum well widths. Further increase in Z is possible through the reduction of thermal conductivity, K, resulting from enhanced phonon scattering at the interfaces betw
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