Thermoelectric Materials and Devices - Hierarchical Nanostructures for Energy Devices - page 111

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Figure 6.2 (a) Band diagrams of metal, semiconductor and insulator. Electrical

conductivity increases as electron density increases. Seebeck coecient
increases when E ave E f increases. 22,23 (b) Relationship between Seebeck
coecient and electrical conductivity, given as carrier concentration.
Reprinted by permission from Ref. 23. Copyright r 2008 Nature
Publishing Group.

between the power factor (which is defined as S 2 s) and carrier concentration
in a typical bulk semiconductor. As the carrier concentration increases, the
electrical conductivity generally increases. On the other hand, the Seebeck
coecient decreases as the carrier concentration increases. As one can see in
Figure 6.2(b), there is an optimum carrier concentration that maximizes the
power factor.
The thermal conductivity consists of two contributions from electrons, i.e.,
electronic thermal conductivity (k e ) and from phonons or lattice vibrations,
i.e., lattice thermal conductivity (k l ): 24

.

k ¼ k e þ k l (6.5)

The lattice contribution of thermal conductivity is more or less independent
of the carrier concentration. The electron contribution is typically negligibly
small at low carrier concentrations, but increases as the carrier concen-
tration increases, although it is known that typically the lattice thermal
conductivity dominates over the electronic thermal conductivity in semi-
conductors. 25 Thus, the total thermal conductivity increases as the carrier
concentration increases. Therefore, there exists an optimum carrier con-
centration that maximizes ZT in bulk materials.

6.2.2 Power Factor Enhancement
From the 1950s to 1960s, the only way to control the power factor was
doping. 1,8 As one can see in Figure 6.2(b), there is an optimum ZT value
because the Seebeck coecient and electrical conductivity have different
trends with carrier concentration, so it is important to control the carrier
concentration close to the optimal value, which is a function of temperature,
and varies among different materials.