Role of out-of-plane coefficient of thermal expansion in electronic packaging modeling

Components in electronic packaging structures are of different dimensions a nd are made of dissimilar materials that typically have time, temperature, and direction-dependent thermo-mechanical properties. Due to the complexity in geometry, material behavior, and thermal loading patterns, finite-eleme nt analysis (FEA) is often used to study the thermo-mechanical behavior of electronic packaging structures. For computational reasons, researchers oft en use two-dimensional (2D) models instead of three-dimensional (3D) models . Although 2D models are computationally efficient, they could provide misl eading results, particularly under thermal loading. The focus of this paper is to compare the results from various 2D, 3D, and generalized plane-defor mation strip models and recommend a suitable modeling procedure. Particular emphasis is placed to understand how the third-direction coefficient of th ermal expansion (CTE) influences the warpage and the stress results predict ed by 2D models under thermal loading. It is seen that the generalized plan e-deformation strip models are the best compromise between the 2D and 3D mo dels. Suitable analytical formulations have also been developed to corrobor ate the findings from the study.