When we are discussing the
thermoelectric generator, we need to take into account the application of the Seebeck
effect to the electrical generation. As has previously been shown in fig. 1,
the carriers in both p-type and n-type material are moving from the hot side to
the cooler side. In the determination of the thermoelectric performance, we
assume that the heat transfer occurs only between the two branches, excluding
the heat transfer by radiation. The efficiency of the thermoelectric generator
is given by the ratio between electrical energy provided to the load and the
total heat flow from the hot junction 16. The equation can be written as:

(6)

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The
performance of the thermoelectric material, the p-type and n-type
semiconductor, can be expressed by a dimensionless figure of merit or ZT, with
the equation:

(10)

Where
? is the Seebeck coefficient of the material, ? is the electrical resistivity
of the material, ? is the thermal conductivity of the material, and T is the
working temperature. We call the value of ?2/? as the power factor.
The relation between efficiency and the figure of merit can be written by the
following equation:

(11)

When we are discussing
about power generation that has thermal process in the system, the maximum
efficiency will have the value of Carnot cycle, which is equal to the first
part of the equation. The second part of the equation shows the relation
between efficiency and ZT, where the higher ZT leads the efficiency closer
towards the efficiency of the Carnot cycle 3. In the determination of the
total efficiency, it is also important to include geometric parameters such as
length and area which is excluded from the equation 3,16-19.

From
the equation of the ZT above, we can see that it is related to several
parameters. It is important in the research of thermoelectric to find the
suitable material because some of the parameters mentioned before has an inverse
relationship with the other, when one parameter goes up, the other goes down.
In the figure below we can see the relation of those parameters with the carrier
concentration of the materials:

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