Materials 2014, 7

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Z should be defined for a pair of thermoelements, since the Peltier and Seebeck effects are manifest for

thermocouples rather than single materials, but it is convenient to select materials on the basis of the

maximization of Z for each branch. It is only when the two branches have widely different properties

that this strategy must be modified as, for example, when one branch is a superconductor [3,4].

From the outset it was realized that there was the need to optimize [1,2] the charge carrier

concentration, by doping with donor or acceptor impurities. When there is only one type of carrier,

electrons or positive holes, the Seebeck coefficient at a given temperature falls as the electrical

conductivity increases. The Seebeck coefficient and the electrical conductivity are combined in a

quantity, α

σ, known as the power factor. One aims to make this parameter as large as possible, though

it must be remembered that a large electrical conductivity also implies a large electronic component of

the thermal conductivity. Most of the early improvements came about through a reduction in the lattice

component of the thermal conductivity, λ

. This was achieved through the use of solid solutions [5] of

bismuth telluride with the isomorphous compounds antimony telluride and bismuth selenide. The

enhanced scattering of phonons in these solid solutions is not usually accompanied by a reduction in

the mobility of the charge carriers. This is somewhat surprising since the charge carriers usually

possess the larger mean free path.

In recent years, further reductions in the lattice conductivity have been obtained by the adoption of

nanostructures. Although the original aim seems to have been the improvement of the power factor

through quantum confinement effects [6], in actual fact it appears that the main advantage has stemmed

from phonon scattering on the boundaries of nano-sized grains [7,8]. In other words, nano-structuring

usually seems to affect the lattice conductivity rather than the electronic transport properties.

It is important to realize that the same figure of merit applies for thermoelectric generation [2],

using the Seebeck effect, as for refrigeration using the Peltier effect. Thus, at any given temperature,

the best refrigeration material will also be the best material for generation. In so far as bismuth

telluride alloys are the best materials at room temperature, they must also be the best generator

materials, at least close to this temperature.

One must remember that the electrical and thermal conductivities of bismuth telluride are

anisotropic [9] although the Seebeck coefficient does not depend on orientation in the extrinsic or

one-carrier regime. The lattice conductivity is about twice as large along the cleavage planes as it is in

the perpendicular direction [10]. The anisotropy of the hole mobility is almost the same as that of the

lattice conductivity so that, although the electrical and thermal conductivities in aligned crystals are

different from those in randomly oriented polycrystalline material, the figure of merit is virtually

isotropic for p-type bismuth telluride. On the other hand, the electron mobility is more strongly

anisotropic than the lattice conductivity and this means that the figure of merit is significantly less for

non-aligned n-type samples [11] than it is for properly oriented material. This is unfortunate since

there are practical advantages in making material in polycrystalline form using a sintering process

rather than a melt-growth process. For example, the concept of a bulk nanostructure is probably most

easily realized using sintered material. Unless some measure of orientation can be achieved during

sintering, the advantage of a reduction in the lattice conductivity due to nanostructuring may be

outweighed by a fall in the power factor, α

σ.