Carrier concentration optimization in semiconductor thermoelements

One of the problems in the application of semiconductors to thermoelectric generation of power is the determination of the optimum carrier concentration in order to achieve maximum efficiency. Up to the present time, this problem has been approached by determining the cartier concentration which maximizes the conventional figure of merit ; however, this approach is unsatisfactory. The criterion of using the conventional figure of merit as quantity to be maximized in order to achieve maximum efficiency is only valid for materials with temperature independent parameters. An analysis of the performance of thermoelectric generators has shown that a quantity similar in form to the conventional figure of merit but using temperature averaged parameters plays the role of figure of merit in the case of materials with temperature dependent parameters. This paper considers the problem of carrier concentration optimization giving attention to the temperature dependence of the material parameters. The equations to be satisfied by the optimum constant and optimum variable cartier concentrations, in order to obtain maximum "average parameters" figure of merit, are derived. The equations are solved for a non-degenerate extrinsic semiconductor. A comparison is made between the maximum "average parameters figures of merit" which can be obtained using optimum constant and optimum variable carrier concentrations; and the results interpreted in terms of available materials. A method is presented for the calculation of the optimum constant carrier concentration in a material when the thermoelectric parameters are known as functions of temperature.