Application of Lamination Theory to Study Warpage Across PWB and PWBA During Convective Reflow Process
Out-of-plane displacement (warpage) has been a major reliability concern for board-level electronic packaging. Printed wiring board (PWB) and component warpage results principally from coefficient of thermal expansion (CTE) mismatch among the materials that make up the PWB assembly (PWBA). Warpage occurring during surface-mount assembly processes and normal operations may lead to severe solder bump failures. In this paper, the classical laminated plate theory was applied to study the warpage behavior of PWBs and PWBAs during the thermal reflow process. The rule of mixtures was used to estimate the effective material properties of PWBA composites. Closed form solutions of the differential equations for the PWB and PWBA deformation were generated from the classical lamination theory to evaluate the sample warpage. The board support conditions and thermal gradients through the assembly thickness were considered in the theoretical model. The calculated warpage results were compared with experimental results using the projection moire measurement system in a simulated convective reflow process to evaluate the accuracy of the model. Finite element modeling was applied to estimate the sample warpage values under the same thermal loading and boundary constraints. The warpage values obtained from the theoretical models show high sensitivity to the thermal loads, through-the-thickness temperature gradients of the test samples, and CTE values of the composite materials. The relative warpage results obtained from the theoretical models and numerical models agreed well with the experimental measurement results during the thermal reflow process.