Chemistry Reference
In-Depth Information
As shown in Figure 6.1(a), there had been no significant improvement in
ZT for a long time until the last few decades. Improving ZT is challenging,
because the individual properties in the definition of ZT are mutually cou-
pled, so that it is hard to enhance one property without affecting the others
unfavourably. In 1993, however, Hicks and Dresselhaus reported the possi-
bility of enhancing the thermoelectric effect by using low-dimensional ma-
terials.
14,15
Since then, a great number of studies have been reported for the
enhancement of ZT using nanoscale materials and nanostructures.
16-21
Consequently, as shown in Figure 6.1(a), ZT has been enhanced consider-
ably since around the 2000s. The main breakthrough was that the three
parameters in ZT are somewhat decoupled now by several methods proposed
during the last decade or so. We will discuss these methods of enhancing
ZT in the following sections.
Figure 6.1(b)
11
shows the relationship between ZT and the energy con-
version eciency. As the figure shows, ZT is a representative parameter that
determines the conversion eciency. The eciency converges to the Carnot
eciency when ZT becomes infinity.
11
d
n
3
r
4
n
g
|
7
6.2
Schemes for Enhancing Thermoelectric
Properties
6.2.1 Three Coupled Parameters in the Thermoelectric
Figure of Merit
Before describing the enhancement of ZT by using nanostructures, we will
explain why improving ZT can be a dicult task. The electrical conductivity,
s, is given as
.
s
¼
nqm
(6.3)
where n, q and m are carrier concentration, electron charge unit and carrier
mobility, respectively. According to this relation, electrical conductivity is
proportional to carrier concentration. Electron mobility changes only
slightly with carrier concentration in most semiconductors. Therefore elec-
trical conductivity generally increases with carrier concentration. However,
the Seebeck coecient generally follows the rule given by
22
S
1
qT
ð
E
ave
E
F
Þ
(6
:
4)
where E
ave
and E
F
are the average energy of free charge carriers and Fermi
energy, respectively. Figure 6.2(a) illustrates the band structures and electron
densities in metals, semiconductors and insulators. The electrical conduct-
ivity is proportional to the carrier concentration (orange area) and decreases
exponentially as the Fermi energy moves away from the band edge. At the
same time, the Seebeck coecient increases because E
ave
E
F
increases (eqn
(6.4)). Thus, the Seebeck coecient and electrical conductivity have opposite
tendencies with carrier concentration.
23
Figure 6.2(b) shows the relationship
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