Effects of heat spreading resistance on configuration optimization and cooling performance of two-stage thermoelectric coolers

Two-stage thermoelectric coolers (TECs) are promising for applications requiring large temperature lifts. However, the heat spreading resistance (HSR) arising from dimensional mismatch is often neglected in conventional theoretical models, limiting the accuracy of performance analysis for two-stage TECs. This study develops an analytical model to investigate the effects of HSR and the Thomson effect on the cooling performance and configuration optimization of two-stage TECs. The HSR associated with dimensional mismatch between thermoelectric legs and ceramic substrates, as well as between adjacent-stage substrates, is quantified using correction factors to account for three-dimensional thermal effects. The influences of HSR and the Thomson effect are analyzed, and key parameters, including the fill factor, stage leg-number ratio, and operating current, are optimized. The results demonstrate that the Thomson effect improves the cooling capacity of Bi 2 Te 3 -based TECs, whereas HSR significantly reduces the cooling performance, particularly for TECs with lower ceramic substrate thermal conductivity and smaller fill factor. Furthermore, the volumetric cooling capacity is found to be an effective criterion for determining the stage leg-number ratio. The proposed model provides insights into the thermal mechanisms governing two-stage TEC performance and offers a practical tool for their performance evaluation and configuration optimization.