A More Comprehensive Solution for Tri-Material Layers Subjected to Thermal Stress

Thermal stress due to mismatched coefficients of thermal expansion is a problem that has challenged the electronics packaging industry for decades. Analytical solutions are available in the literatures for a tri-material in which the sandwiched layer is a continuous layer. This author has earlier presented a solution for the sandwiched layer constituted of discrete interconnects; however, the solution ignores the shear deformation of the substrate layers. This paper removes the above assumptions and provides closed-form solutions for the shear, bending, and axial stresses in the sandwiched layer, as well as the in-plane stress in the substrate layers. The solutions are applicable to printed circuit board (PCB) assemblies constituting of an integrated circuit (IC) component, solder joints, and the PCB or to an IC component of tri-material layer structure. The solutions have been successfully validated with finite element analysis. Design analyses based on the analytical solutions have been performed for the shear and peeling stresses in the interconnects, the tensile fracture of IC chips due to in-plane stress, and the warpage of the IC component.