Predicted Thermal Stress in a Multileg Thermoelectric Module (TEM) Design

A physically meaningful analytical (mathematical) model is developed for the prediction of the interfacial shearing thermal stress in an assembly comprised of two identical components, which are subjected to different temperatures. The bonding system is comprised of a plurality of identical columnlike supports located at equal distances (spaces) from each other. The model is developed in application to a thermoelectric module (TEM) design where bonding is provided by multiple thermoelectric material supports (legs). We show that thinner (dimension in the horizontal direction) and longer (dimension in the vertical direction) TEM legs could result in a significant stress relief, and that such a relief could be achieved even if shorter legs are employed, as long as they are thin and the spacing between them is significant. It is imperative, of course, that if thin legs are employed for lower stresses, there is still enough interfacial “real estate,” so that the adhesive strength of the assembly is not compromised. On the other hand, owing to a lower stress level in an assembly with thin legs and large spacing, assurance of its interfacial strength is less of a challenge than for a conventional assembly with stiff, thick, and closely positioned legs. We show also that the thermal stresses not only in conventional TEM designs (using $Be2Te3$ as the thermoelectric material, and Sn-Sb solder), but also in the future high-power (and high operating temperatures) TEM design (using Si or SiGe as the thermoelectric material and Gold100 as the appropriate solder), might be low enough, so that the short- and long-term reliability of the TEM structure could still be assured. We have found, however, that thin-and-long legs should be considered for lower stresses, but not to an extent that appreciable bending deformations of the legs become possible. Future work will include, but might not be limited to, the finite-element computations and to experimental evaluations (e.g., shear-off testing) of the stress-at-failure for the TEMs of interest.