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Thermoelectrics is an old field. In 1823, Thomas Seebeck discovered that a voltage drop appears across a sample that has a temperature gradient. This phenomenon provided the basis for thermocouples used for measuring temperature and for thermoelectric power generators. In 1838, Heinrich Lenz placed a drop of water on the junction of metal wires made of bismuth and antimony. Passing an electric current through the junction in one direction caused the water to freeze, and reversing the current caused the ice to quickly melt; thus thermoelectric refrigeration was demonstrated (figure 1).

It is shown that the magnitude of the Seebeck coefficient of a semiconductor has a maximum value that is close to one-half the energy gap divided by eT. An expression for the position of the Fermi level at which the Seebeck coefficient has a maximum or minimum value is derived, with account taken of the mobility and effective mass ratios. It is concluded that measurement of the Seebeck coefficient as a function of temperature on any novel semiconductor is one of the simplest ways of estimating its band gap.

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