Thermoelectric Materials and Devices - Hierarchical Nanostructures for Energy Devices - page 112

6.2.2.1 Quantum Confinement Effect
As we discussed in the previous section, the three parameters, particularly
the power factor, determining ZT are interdependent. To uncouple the three
parameters, it has been proposed 14,15 that as a dimensionality of a material
changes, so does the electron density of states, which offers excellent po-
tential for increasing the Seebeck coecient without affecting the electrical
conductivity too much (see Figure 6.3). This is due to the confinement of
electron waves in the direction of reduced dimensionality. Thus, the electron
states become discrete in that direction. 3 The Seebeck coecient can be
approximated as 26

d n 3 r 4 n g | 7

S ¼ p 2
3

k B
q k B T

d ln s ðÞ ½ ð Þ

dE

E ¼ E F

(6 : 6)

¼ p 2
3

k B
q k B T

1
n

dn ð E Þ
dE

þ 1
m

dm ð E Þ
dE

E ¼ E F

.

Figure 6.3 (a) Electronic density of states for (left to right) a bulk 3D crystalline

semiconductor, a 2D quantum well, a 1D nanowire or nanotube and a 0D
quantum dot. Reprinted with permission from Ref. 3. Copyright r 2007
WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (b) Power factor of the
InAs nanowire at various temperatures versus gate voltage. Inset shows
SEM image of experimental setup of the demonstration of the quantum
confinement effect in an InAs nanowire. Reprinted with permission from
Ref. 27. Copyright r 2013 American Chemical Society.