Uncertainty analysis for common Seebeck and electrical resistivity measurement systems

Abstract

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.

Enhanced stability and thermoelectric figure-of-merit in copper selenide by lithium doping

“…The unusual departure from the typical trend of acoustic-phonon scattering is associated with the steep increase in thermopower measurements at high temperature above 750 K (Fig.2b). We tentatively attribute this anomalous behavior to uncertainties in the ZEM measurement method, where thermopower is often overestimated at high temperatures due to cold-finger effects [26][27][28][29] (overestimation could be as large as >10% [26,29,30]) and the high temperature reactivity of Type S thermocouples with chalcogenides [28]. We use a measurement method where such artifacts are avoided (see Methods).…”

Si/Ge–WSi 2 composites: Processing and thermoelectric properties

“…The error bars shown on the plots represent typical uncertainty for all samples and are only shown on selected curves to retain readability. The uncertainty calculation was discussed in a previous publication [14]. The bars include a range of measurement uncertainty sources rather than simply statistical error, and the asymmetry in the Seebeck error bars at high temperatures are due to the cold-finger effect.…”

“…The uncertainty analysis includes statistical, geometric, instrument, and thermal contact resistance sources; details of the uncertainty analysis can be found in Ref. [14]. Specimens were subjected to a thermal gradient up to 0.5°C/mm by a platinum wire heater mounted in the lower support arm.…”

Thermoelectric characteristics of textured KSr2Nb5O15 ceramics

“…SN and KN reacted to form the final KSN phase during reactive sintering. In this study, a fixed sintering temperature-time profile (e.g., 1400°C for 1 h) and excess Nb 2 O 5 content (e.g., 1.5 wt.%) were applied to produce highly textured KSN ceramics, based on our earlier studies [12][13][14][15]. Those studies were primarily carried out to investigate phase formation, fabrication conditions for highly textured KSN ceramics in [001] or the c direction, texture characterization and finally measurements of the dielectric and ferroelectric properties.…”

“…The uncertainty on resistivity was found to be ±7% and Seebeck uncertainty was ±1% near room temperature and +1%/−13% at high temperature. Details were explained elsewhere [12]. SN and KN reacted to form the final KSN phase during reactive sintering.…”