Thermoelectric, Photovoltaic, and Magnetotransport Properties

Seebeck experimented with a number of metals including antimony, iron, zinc, silver, gold, lead, mercury, copper, platinum, and bismuth. Later, the observation was made that the electromotive force (EMF) generated is proportional to the temperature difference between the junctions. Today, TE couples are often made from semiconductor alloys of bismuth antimony telluride, Bi Sb2- cTe3 (x 0.5), that have been suitably doped to possess distinct n- or p-type characteristics. A practical TE cooler consists of one or more couples that are connected electrically in series and thermally in parallel. 

Peltier coefficient, II, is the ratio of the rate at which heat flows across a material to the electrical current flow and is, therefore, a nonsymmetrical second-rank tensor that relates a scalar with another second-rank tensor  

In practice, one rarely measures the absolute thermopower of a single material. This is because electrodes attached to a voltmeter must be placed onto the material in order to measure the TE voltage. The temperature gradient then also typically induces a TE voltage across one leg of the measurement electrodes therefore, the measured thermopower is a contribution from the thermopower of the material of interest and the material of the measurement electrodes. This arrangement of two materials is usually called a thermocouple. By using superconducting leads, which have zero thermopower, it is possible to get a direct measurement of the absolute thermopower of the material of interest, since it is the thermopower of the entire thermocouple as well. 

Couples comprised of two different pure metals have low Seebeck coefficients since the absolute thermopowers of pure metals are in the microvolt per degree Celsius range (superconductors have zero absolute thermopowers). The difference between the absolute thermopowers of each metal in a couple yields the observed TE power of the couple. However, in metals (with half-filled bands) the electrons and holes have a cancelling effect the TE voltage produced is small. This makes them unsuitable for use in most TE apphcations with the exception of thermocouples that are used for temperature measurements. Semiconductors, by contrast, can be doped with an excess of electrons 

Materials under consideration for use in TE devices may be rated based on their TE power figure of merit, which is given by the expression  

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