Direct Energy, 2018a

184 8.6 Thermoelectric Eects
In this expression, n is the concentration of valence electrons in units
electrons
m , and it was introduced in Sec. 5.2. The magnitude of the charge
3
of an electron is q =1.6 · 10 −19 C. Mobility of electrons, μ n , is the ease
with which charge carriers drift in a material, and it has units
V·s m2 . By
denition, mobility is the ratio of the average drift velocity of electrons to
the applied electric eld in m V [9, p. 84].
μ n =
−avg drift velocity of electrons
∣ −→ E ∣
(8.31)
For semiconductors, both electrons and holes act as charge carriers, and
both contribute to the conductivity,
σ = q (nμ n + pμ p ) (8.32)
where μ p is the mobility of the holes, and p is the concentration of holes.
To understand which materials have large electrical conductivities, and
hence make good thermoelectric devices, we need to consider the charge
concentrations n and p. Conductors and semiconductors have charges that
can move through the material while insulators do not. Thus conductors
and semiconductors have large electrical conductivity and are used
to make thermoelectric devices. Furthermore, a doped semiconductor has
more charge carriers than an undoped, also called intrinsic, semiconductor.
Thus, doped semiconductors usually have higher electrical conductivity
than undoped semiconductors of the same material [110].
Electrical conductivity σ is proportional to the electron and hole mobilities,
μ n and μ p , and the mobilities are a strong function of temperature
[9]. For this reason, the electrical conductivity is a function of temperature.
At low temperature, mobilities are limited by impurity scattering
while at high temperatures, they are limited by phonon scattering. At
some intermediate temperature, mobility and conductivity are maximum,
and this peak occurs at dierent temperatures for dierent materials. Mobility
also depends on whether a material is crystalline or amorphous and
on the degree of crystallinity. Mobility and electrical conductivity are both
typically higher in crystals than glasses because charges are more likely to
get scattered in amorphous materials.
8.6.3 Thermal Conductivity
Thermal conductivity κ is a measure of the ability of heat to ow through a
material, and it has units
m·K W [109, p. 793]. Example thermal conductivity