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The thermoelectric powers, or Seebeck coefficients for electrons and holes
depict the ratio between a temperature gradient and the resulting driving
forces on the carriers as presented in Section 3.5.12. They show
dependencies on both temperature and carrier concentration.
A comparison between measurement data for n-type lead telluride
[228] and the theoretical models of the Seebeck coefficient
is illustrated in Fig. 5.5. Values for the effective densities of
states
and
incorporated in the theoretical models are given in
Section 5.3.2.
In contrast to silicon, additional gain on the thermoelectric power by phonon-drag is limited to very low temperatures. Thus, good agreement between theoretical and measured data is achieved. At high temperatures, the measured values drop to lower values due to the additionally available free holes in the intrinsic range, as indicated in Figures 5.5 and 5.6.
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Measurement data illustrated by circles in Fig. 5.6 have been
taken from [229]. Different concentrations of free carriers have
been obtained by deviation from the stoichiometric equilibrium between Pb and
Te. The good agreement between theoretical curves and measurement data in the
low temperature range indicates that additional phonon-drag is absent in the
indicated temperature range. For temperatures above
, carriers
start to populate the second valence band, thus the averaged effective mass of
both valleys must be taken into account [230]. On the transition to the intrinsic range, precipitation of
tellurium reduces the thermoelectric powers with increasing temperatures due to the shifted
ratio of Pb and Te. With further increasing temperatures, the total
thermoelectric powers even change their signs due to the additional contribution
of electrons. A comparable behavior is reported for silicon in
[97].
Considerably larger values for thermoelectric powers have been measured for
sintered samples, where a strong dependence on the grain size has been reported
[128,228]. Values for thermoelectric powers double
if the grain size is reduced from
down to
.
Further investigations of several alloys can be found in
[218,231].
M. Wagner: Simulation of Thermoelectric Devices