Scaling framework for measurement-induced deviation of the dimensionless figure of merit via time-domain impedance spectroscopy

Abstract In this study, a scaling framework for quantifying the measurement-induced deviation in the measured dimensionless figure of merit, ZT , during the transition from the high-vacuum limit to ambient-air conditions was experimentally validated using time-domain impedance spectroscopy (TDIS). Although z T is generally considered an intrinsic material parameter under ideal measurement conditions, experimentally measured values can be affected by heat leakage, particularly through convective heat transfer between the sample surface and surrounding air. By systematically varying the pressure P , the measured z T value, denoted as z T eff ( P ) , was shown to deviate from the intrinsic z T in a reproducible manner. To quantify this deviation, a dimensionless parameter, Λ ( P ) , was introduced and defined as the ratio of the sample length to the thermal decay length. Experimental results, supported by one-dimensional modeling and three-dimensional simulations using COMSOL Multiphysics, exhibited a common trend when z T eff ( P ) / z T was plotted against Λ ( P ) , demonstrating that Λ ( P ) governs the measurement-induced deviation. In particular, Λ ( P ) < 0.1 ensures that z T eff ( P ) closely approaches the intrinsic