Thermal-Conductivity Measurement of Thermoelectric Materials Using $3{{\upomega }}$ Method

Abstract

In this work, a measurement system for high-temperature thermal-conductivity measurements has been designed, constructed, and characterized. The system is based on the $3{\upomega }$ method which is an ac technique suitable for both bulk and thin-film samples. The thermal-conductivity measurements were performed in a horizontal three-zone tube furnace whose sample space can be evacuated to vacuum or alternatively a protective argon gas environment can be applied to prevent undesired oxidation and contamination of the sample material. The system was tested with several dielectric, semiconductor, and metal bulk samples from room temperature up to 725 K. The test materials were chosen so that the thermal-conductivity values covered a wide range from $0.37\,\hbox {W}\!\cdot \! \hbox {m}^{-1}\!\cdot \! \hbox {K}^{-1}$ to $150\,\hbox {W}\!\cdot \! \hbox {m}^{-1}\!\cdot \!\hbox {K}^{-1}$. An uncertainty analysis for the thermal-conductivity measurements was carried out. The measurement accuracy is mainly limited by the determination of the third harmonic of the voltage over the resistive metal heater strip that is used for heating the sample. A typical relative measurement uncertainty in the thermal-conductivity measurements was between 5 % and 8 % ($k=2$). An extension of the $3{\upomega }$ method was also implemented in which the metal heater strip is first deposited on a transferable Kapton foil. Utilizing such a prefabricated sensor allows for faster measurements of the samples as there is no need to deposit a heater strip on each new sample.