Impedance spectroscopy models for the complete characterization of thermoelectric materials

Abstract

This paper analyses the use of impedance spectroscopy as a characterization tool applied to thermoelectric materials. The impedance function of the thermoelectric system under adiabatic conditions and Peltier mode operation is calculated by solving the heat equation in the frequency domain. The analysis, focused on the complex plane, provides the required equivalent circuit elements to interpret the impedance measurements. Using this approach, all the relevant thermoelectric parameters and thermal properties can be potentially extracted at a given temperature from the impedance spectra, i.e., the Seebeck coefficient, electrical resistivity, thermal conductivity, figure of merit (zT), specific heat, and thermal diffusivity. This can be done without the need of measuring temperature differences. To validate the models described, impedance measurements have been carried out in single thermoelectric elements and modules, showing an excellent agreement with the theory. The simple nature of the measurements in conjunction with the advantage of obtaining all the important thermoelectric parameters opens up the possibility of establishing impedance spectroscopy as a very useful characterization method for the thermoelectric field.

Thermal dynamics of thermoelectric phenomena from frequency resolved methods

“…The fitting parameters obtained appear in Table I. As previously reported, 9 all the thermal properties of the element can be obtained if the S value is known (see Table I). …”

“…By using impedance spectroscopy, which employs ac current excitation waves, we can extract very useful information about the dynamics of these fundamental TE processes, which provides a unique detailed knowledge of the system operation. This detailed analysis, in despite of the fact that previous work has been reported in the application of frequency resolved methods in the TE field, [7][8][9] has not been developed so far. Moreover, the transient behavior of thermoelectric elements and devices is less investigated in comparison to steady state phenomena and operation of devices in this regime has been claimed to enhance their performance, 10,11 therefore there is a need of fundamental studies in this field.…”

“…A constant current of 100 mA was applied to the element before measuring the impedance in order to settle the electrical contacts. 9 A commercial TE module (European Thermodynamics Ltd.) formed by 252 thermoelements (1 mm x 1 mm x 1.5 mm) was also measured by directly contacting to the equipment leads. Both samples were suspended in air to provide adiabatic conditions.…”

“…The impedance response of a p-type Bi 2 Te 3 element (European Thermodynamics Ltd.) with a cross-sectional area of 1.4 x 1.4 mm 2 and a length of 1.6 mm was measured similarly to a previously reported procedure. 9 A layer of Ag paint was spread on the top and bottom sides of the element. The sample was sandwiched by two short stainless steel probes with sharp tips that were connected to the input leads of the equipment.…”

“…Our previous work 9 analyzed the impedance response in a single TE material and the case of a TE device by solving the heat equation in the frequency domain. It also provided experimental validation of the theoretical models.…”