8.14 Coupled Heat and Charge Transport
255
Fig. 8.31 Schematic
Peltier cooler. The heat
sinks (grey) and the cold
junction (black) on the left
are metals that make ohmic
contacts with the
semiconductors. The
current flow is such that
electrons move through the
n-type semiconductor from
right to left
p-type
heat
sink
T
n-type
heat
sink
j
j
P =
j · j
σ
+ S j ·∇T − ∇ · q + κ .
(8.79)
The first term is Joule heating, the second term is Thomson heating. The third exists only when carriers
are generated or when they recombine. The fourth term is the heat conduction. In the Thomson term
S j ·∇T heat is generated in an n-type semiconductor if j and ∇T are in the same direction. This means
that electrons that move from the hotter to the colder part transfer energy to the lattice. The effect
can be used to construct a thermoelectric cooler, as shown in Fig. 8.31, that generates a temperature
difference due to a current flow. For optimal performance σ should be large to prevent excess Joule
heating and κ should be small such that the generated temperature difference is not rapidly equalized.