Thermoelectric Materials and Devices - Hierarchical Nanostructures for Energy Devices - page 117

d n 3 r 4 n g | 7

Figure 6.7 (a) Thermal conductivity of an Si x Ge 1-x alloy. Thermal conductivity

dramatically decreases when Si and Ge form an alloy. Reprinted with
permission from Ref. 38. Copyright r 1967 Elsevier. (b) Schematic of
alloy scattering. Atomic substitutions scatter short-wavelength

phonons. 37

6.2.4 Thermal Conductivity Reduction by Nanostructures
The earlier experimental demonstration of nanostructured materials for
thermoelectrics exhibited both reduced thermal conductivity and reduced
power factor. 16 The increased surface-to-volume ratio by nanostructures in-
creases the phonon scattering at the interfaces, but it also increases the
electron scattering at the same time. However, it is still possible to reduce
the lattice thermal conductivity without affecting the electral transport too
much, if one could find a material such that the electron mean free path is
shorter than the phonon mean free path. 6 In general, the phonon mean free
path is generally on the order of

.

B 100 nm, but the electron mean free path

10 nm. 37,44 Therefore, if the system dimensions are
maintained in between the electron and the phonon mean free paths,
phonons can be effectively scattered to reduce the thermal conductivity,
while the transport of electrons is not significantly affected.
The phonon (lattice) thermal conductivity is written as 2
k p ¼ 1

is on the order of B

3 C ð o Þ v p ð o Þ l ð o Þ do

(6 : 10)

where C, v p and l are the specific heat, phonon group velocity and mean free
path, respectively, all of which are functions of the phonon frequency, o. The
effective mean free path is determined by various scattering mechanisms
and is written as 45,46
l 1

eff ¼ l 1

þ l U þ l N þ l 1 þ l D þ l 1

(6 : 11)

B A e ph