Finite element analysis of a multistage Bi₂Te₃ thermoelectric cooler module for deep sub-ambient cooling applications

Multistage thermoelectric coolers (TECs) provide large temperature differentials with precise, refrigerant-free thermal control, yet conventional analytical models cannot capture the spatial non-uniformities and inter-stage thermal–electrical coupling that govern their real behaviour. In this study, a fully coupled three-dimensional finite-element model is developed in COMSOL Multiphysics for the commercial MS2–010–06–06–11–11–11-W2 module, using temperature-dependent Bi₂Te₃ properties and realistic boundary conditions. The model resolves the temperature and current-density fields across the two physical stages (10×10 mm and 8×8 mm footprints) and quantifies Qc, Qh and COP as continuous maps of both current and voltage. The module attains ΔTmax = 94 °C at zero heat load and Qcmax = 0.30 W at ΔT = 0 °C, at Imax = 1.2 A, Vmax = 0.8 V and an internal resistance of 0.63 Ω, reaching approximately −67 °C under efficient hot-side heat rejection. A grid-independence study (ΔT variation below 1%) confirms numerical accuracy, and the model is validated against the manufacturer datasheet and published Bi₂Te₃ data. The results provide quantitative design guidance for deep sub-ambient and precision cooling applications such as CMOS sensor stabilization and microelectronic thermal management.