Optimization of thermoelectric efficiency in graded materials

In order to achieve high thermoelectric conversion efficiency, it is necessary to make use of materials with a maximal figure of merit Z = S²×σ/k (S is the Seebeck coefficient, σ and k are the electrical and thermal conductivity, respectively) over a wide temperature range. A^IVB^VI(chalcogenides of group IV elements) semiconductors are well known materials that have found widespread applications in thermoelectric energy converters. The thermoelectric properties of semiconductors may be improved by designing crystals with a gradient of charge carrier concentration that is commensurate with the temperature gradient that prevails along the axis in an actual thermoelectric device. Recently graded n-type PbTe-based single crystals doped with indium have been shown to display promising thermoelectric properties. The thermoelectric efficiency of graded materials is usually not a direct measurable quantity. It seemed of interest to develop a theoretical model that would allow deriving this property. The present communication is concerned with the development of a simulation model for estimating the characteristics of a thermoelectric leg and based on determining the temperature profile along its length. The temperature distribution along a leg was calculated from the heat flux equation under steady state conditions for the 50-500°C temperature range. In the calculation, account was taken of the temperature dependence of S, σ and k, respectively, for graded n-type PbTe crystals doped with indium. A comparison to iodine-doped homogeneous PbTe crystals is presented as well. These calculations allow determining the dopant concentration profile along the thermoelectric leg that provides optimal efficiency. The results suggest the possibility, in principle, of achieving conversion efficiency higher than 12% by using graded n-type PbTe crystals doped with indium in the 50-600°C temperature range.