Page 268 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Electron-Phonon
q
where is the fundamental charge, N
is the conduction band effective
C
density of states, N is the valence band effective density of states, n is
V e
the electron concentration, n is the hole concentration, s and s are
h e h
corrections due to enhanced electron and hole carrier scattering, and φ
e
and φ are corrections that take into account the phonon drag on the
h
electrons and holes.
Peltier At a material junction we observe a further thermoelectric effect that is
Heating and reversible. Depending on the direction of current flowing through the
Cooling
junction, heat is either generated or absorbed according to
∆J = Π J (7.72)
q AB e
The Peltier coefficient Π between materials and defines both the
B
A
AB
sign and quantity of heat current transported per unit carrier current, and
is obtained from (6.41b) for isothermal conditions
η η
n
∇
∇
j = – ( Tε σ ) ----- – ( Tε σ ) ------ p (7.73a)
q n n p p
q q
n p
η
∇
i = ( – σ ) ----- n (7.73b)
n n
q n
η
∇
i = ( – σ ) ------ p (7.73c)
p p
q p
When we combine the equations in favour of the heat and carrier current
densities, we obtain
j = ( Tε )i + ( Tε )i p (7.74)
n
n
p
q
In an uniformly doped region, (7.74) reduces to
j = ( Tε)i = Πi (7.75)
q
where Π = Tε is the absolute thermoelectric power of the material.
Usually we only deal with differences between two materials adjoining at

Semiconductors for Micro and Nanosystem Technology 265