Scaling dynamics of electrothermal coupling in thermoelectric materials probed by time-domain impedance spectroscopy

Abstract

The time-dependent resistance R(t) in time-domain impedance spectroscopy (TDIS) is derived from the frequency-dependent impedance Z(ω) using the inverse Laplace transform within a unified electrothermal framework that incorporates the thermoelectric element, electrodes, and lead wires that act as heat-leakage paths. A normalized response function Ψ(tΩ) is introduced to separate transient dynamics from the steady-state amplitude. This function reveals a continuous transition characterized by Ψ(tΩ<1)∝tΩn (where 1/2≤n≤1), reflecting the crossover from diffusion-dominated transport to boundary-dominated behavior. The transient response is determined by a small set of dimensionless parameters that describe both the intrinsic thermoelectric properties and the measurement configuration. Notably, both the normalized time constant τΩ and the effective scaling behavior are governed primarily by the electrode-to-thermoelectric heat-capacity ratio, demonstrating that the electrode heat capacity plays a dominant role in the electrothermal response. Measurements on a thermoelectric element and a module confirm the predicted scaling behavior and power-law response. These results establish TDIS as a probe of electrothermal dynamics and provide practical guidelines for optimizing TDIS measurements through control of electrode heat capacity.