Theoretical model for micro-thermoelectric coolers: influence of coupled interfacial and Thomson effects on cooling performance

Micro-thermoelectric coolers (M-TECs) exhibit considerable promise in thermal management for high-performance electronic integrated devices, especially for precise and localized cooling solutions. However, assessing the cooling performance of M-TECs at the micro-device level is challenging due to the combined influence of interfacial and Thomson effects. This paper presents a theoretical model for M-TECs that accounts for both of these coupled effects. Utilizing the eigenfunction expansion method, analytical solutions for temperature distributions are derived, and the influence of operating current, fill factor, and thermoelectric arm height on M-TEC performance is investigated. Numerical results reveal that electron temperature fluctuation is more pronounced adjacent to boundaries compared to phonon temperature, particularly when thermoelectric arm height is comparable to the carrier cooling length. The Thomson effect notably enhances the cooling performance of Bi2Te3-based M-TECs. Neglecting the Thomson effect at a set cooling temperature results in a roughly 20 % reduction in predicted cooling capacity, and leads to an increase of 2.5 K in the minimum achievable cooling temperature for a specified capacity when the thermoelectric arm height is 4 μm. The presented theoretical model is a key tool for accurate estimation of cooling performance and configuration optimization of M-TECs.