Quantitative comparison of heat flow, guarded-heater and AC Harman methods for thermoelectric module efficiency

Technical Summary: Quantitative Comparison of Heat Flow, Guarded-Heater, and AC Harman Methods for Thermoelectric Module Efficiency

Problem Statement
The evaluation of thermoelectric conversion efficiency ($\eta$) faces significant challenges due to the absence of internationally standardized measurement protocols. Current uncertainty in measuring thermoelectric properties is approximately 20%, highlighting a lack of consensus on evaluation methods and sample modules. While the heat flow method (HFM) and guarded heater method (GHM) are established steady-state techniques for determining input heat flow ($Q_{in}$), the AC Harman method—a transient technique widely used for rapid estimation of the dimensionless figure of merit ($ZT$)—lacks systematic quantitative comparison against steady-state methods at the module level. Specifically, the extent to which differences in measurement principles and thermal boundary conditions lead to discrepancies in evaluated conversion efficiency remains unclear.

Methodology
The study benchmarked three module-level efficiency measurement techniques using commercial $Bi_2Te_3$-based thermoelectric modules with two distinct substrate types: a "skeleton" type with a thin polyimide substrate and a "rigid" type with a thick alumina substrate.

1. Experimental Setup:

   • Heat Flow Method (HFM): Utilized a calibrated Cu-block heat flow meter to measure heat flow from the cold side ($Q_{flow}$). Input heat was calculated as $Q_{in} = Q_{flow} + P_{out}$.
   • Guarded Heater Method (GHM): Determined input heat flux based on the electrical power supplied to a heater ($P_{heater}$), assuming all input heat conducts through the module ($Q_{in} = P_{heater}$).
   • AC Harman Method: Employed a heater block beneath the module with one side exposed to the environment (vacuum). It measured DC and AC resistances to calculate $ZT$ via the formula $ZT = (R_{DC} - R_{AC})/R_{AC}$, subsequently estimating maximum efficiency ($\eta_{max}$) using the Carnot efficiency and the derived $ZT$.
   • Conditions: Measurements were conducted in a vacuum ($P \le 10^{-1}$ Pa) to minimize convective losses, with temperature differences ($\Delta T$) up to 70 K.

2. Numerical Simulation:

   • Finite Element Method (FEM) simulations were performed using COMSOL Multiphysics to analyze temperature distributions.
   • The models coupled the Heat Transfer in Solids interface with Surface-to-Surface Radiation to account for radiative heat dissipation from exposed surfaces and substrates.
   • Simulations specifically investigated the impact of boundary conditions and radiative losses on the effective temperature difference ($\Delta T$) within the module under Harman configuration.

Key Results

• Agreement between Steady-State Methods: The conversion efficiencies obtained via HFM and GHM showed good agreement within experimental uncertainty for temperature differences up to 70 K. The uncertainty for HFM was estimated at ~12%, while GHM was significantly lower at ~1%.
• AC Harman Underestimation: The AC Harman method consistently underestimated the conversion efficiency compared to HFM and GHM.
  • For the skeleton-type module (polyimide substrate), the discrepancy was approximately 16%.
  • For the rigid-type module (alumina substrate), the discrepancy increased to approximately 30% at $\Delta T = 64$ K.
• Root Cause Analysis: FEM simulations revealed that in the AC Harman configuration, the module's low-temperature side is exposed, leading to uncontrolled radiative heat dissipation. This radiation, combined with boundary-condition effects, significantly reduces the effective temperature difference developed across the thermoelectric legs compared to the steady-state methods where the cold side is actively cooled.
• Substrate Influence: The magnitude of the underestimation was strongly influenced by the substrate material. The thinner polyimide substrate facilitated greater heat dissipation, while the thicker alumina substrate retained more heat, yet both exhibited significant radiative losses that the standard AC Harman calculation failed to account for.

Significance and Claims
The authors claim that their results provide a quantitative benchmark of major measurement techniques, clarifying best practices for module-level thermoelectric metrology. The study demonstrates that:

1. Limitations of AC Harman: The AC Harman method is not suitable for quantitative conversion-efficiency evaluation under non-ideal thermal environments without correction, as radiative and substrate-related heat losses significantly distort the effective temperature gradient.
2. Necessity of Corrections: Accurate efficiency assessment requires accounting for radiative heat dissipation and substrate properties, particularly when using the AC Harman method at higher temperature differences.
3. Standardization Support: By employing identical modules, systematic boundary condition control, and coupled numerical-experimental validation, the study contributes to the development of practical measurement protocols and selection guidelines. This work supports future efforts toward internationally standardized thermoelectric module metrology, distinguishing between rapid performance screening (where AC Harman remains viable with appropriate modeling) and precise efficiency determination (where steady-state methods are superior).