Analytical Solutions for PCB Assembly Subjected to Mismatched Thermal Expansion

Thermal stress due to mismatched thermal expansion is a problem that has challenged the electronics packaging industry for decades. Analytical solutions are available in the literature for a tri-material in which the sandwiched layer is an adhesive, but the solutions may not be suitable for a sandwiched layer consisting of discrete elements such as solder joints which experience significant bending. In this paper, closed-form analytical solutions have been developed for both continuous and discrete sandwiched layers by modelling the interconnects as a slab of spring elements capable of transferring axial, shear, and bending load. The analytical solutions have been successfully validated with finite element analysis.