Uncertainty analysis for common Seebeck and electrical resistivity measurement systems
This work establishes the level of uncertainty for electrical measurements commonly made on thermoelectric samples. The analysis targets measurement systems based on the four probe method. Sources of uncertainty for both electrical resistivity and Seebeck coefficient were identified and evaluated. Included are reasonable estimates on the magnitude of each source, and cumulative propagation of error. Uncertainty for the Seebeck coefficient includes the cold-finger effect which has been quantified with thermal finite element analysis. The cold-finger effect, which is a result of parasitic heat transfer down the thermocouple probes, leads to an asymmetric over-estimation of the Seebeck coefficient. A silicon germanium thermoelectric sample has been characterized to provide an understanding of the total measurement uncertainty. The electrical resistivity was determined to contain uncertainty of +/- 7.0% across any measurement temperature. The Seebeck coefficient of the system is +1.0%/-13.1% at high temperature and +/- 1.0% near room temperature. The power factor has a combined uncertainty of +7.3%/-27.0% at high temperature and +/- 7.5% near room temperature. These ranges are calculated to be typical values for a general four probe Seebeck and resistivity measurement configuration.