Assembly Bonded at the Ends: Could Thinner and Longer Legs Result in a Lower Thermal Stress in a Thermoelectric Module Design?

An analytical (mathematical) thermal stress model has been developed for an electronic assembly comprised of identical components bonded at their end portions and subjected to different temperatures. The model is used to assess the effect of the size (dimension in the x-direction) and compliance of the bonded regions (legs) on the maximum interfacial shearing stress that is supposedly responsible for the mechanical robustness of the assembly. The numerical example is carried out for a simplified two-legged Bismuth-Telluride-Alloy (BTA)-based thermoelectric module (TEM) design. It has been determined that thinner (dimension in the horizontal, x-direction) and longer (dimension in the vertical, y-direction) bonds (legs) could result in a considerable relief in the interfacial stress. In the numerical example carried out for a 10 mm long (dimension in the x-direction) TEM assembly with two peripheral 1 mm thick (dimension in the x-direction) legs, the predicted maximum interfacial shearing stress is only about 40% of the maximum stress in the corresponding homogeneously bonded assembly, when the bond occupies the entire interface between the assembly components. It has been determined also that if thick-and-short legs are employed, the maximum interfacial shearing stress might not be very much different from the stress in a homogeneously bonded assembly, so that there is no need, as far as physical design and robustness of the assembly is concerned, to use a homogeneous bond or a multileg system. The application of such a system might be needed, however, for the satisfactory functional (thermo-electrical) performance of the device. In any event, it is imperative that sufficient bonding strength is assured in the assembly. If very thin legs are considered for lower stresses, the minimum acceptable size (real estate) of the interfaces (in the horizontal plane) should be experimentally determined (say, by shear-off testing) so that this strength is not compromised. On the other hand, owing to a lower stress level in an assembly with thin-and-long legs, assurance of its interfacial strength is less of a challenge than for an assembly with a homogeneous bond or with stiff thick-and-short legs. The obtained results could be used particularly for considering, based on the suggested predictive model, an alternative to the existing TEM designs, which are characterized by multiple big (thick-and-long) legs. In our novel design, fewer small (thin-and-short) legs could be employed, so that the size and thickness of the TEM is reduced for the acceptable stress level.