Thermal Stresses in a Bi-Layer Assembly in Electronics Packaging

Bi-material interfaces have practical applications in semiconductor packaged devices as a typical semiconductor package is a layered assembly consisting of various materials having different coefficients of thermal expansion (CTEs). CTE mismatch-induced thermal stresses during heating, cooling, or temperature cycling cause failures of semiconductor devices in manufacturing and operation conditions. It is well known that the laminates develop free-edge stresses that are major causes of interface delamination or cracking. Timoshenko first developed analytical solutions for axial stress and curvature radius using classical bending theory. However, stresses at the end of a bi-material interface are neglected. Suhir developed analytical solutions for peeling and shear stresses near the edges, but the stresses are considered bound with certain values. When bi-materials are both considered linear elastic, the peeling stress is singular at the free edges. In this paper, finite element analysis is performed to investigate the stress and deformation of a bi-layer strip assembly. The axial stress that acts in the longitudinal direction of the assembly can be accurately predicted by Timoshenko’s theory. The curvature of the assembly, or warpage using the terminology in electronics packaging, can also be predicted accurately using Timoshenko’s equation. However, the peeling stress at the free edge appears to be mesh-dependent, indicating an infinite stress value. Despite the free surface at the free edge, shear stress is also mesh-dependent. The fracture mechanics approach is often used to take singular behaviors into consideration for the extraction of meaningful fracture parameters. However, only the standard type of crack or interface crack is considered in the context of classical fracture mechanics. To tackle this issue, the finite element mesh should keep the fixed size and shape at the location of interest where the singular point exists. This approach provides a simple way for relative stress comparison in different designs, although the absolute value of stress components has no actual meaning. In this paper, we also find that the peeling stress is in tension during cooling but in compression during heating, regardless of the material properties.