A Thermomechanical Model for Warpage Prediction of Microelectronic Packages

The thermomechanical warpage or vertical deflection of microelectronic packages due to temperature change is caused by the mismatch in the coefficients of thermal expansion between vertically asymmetric layers of materials. The structure of many microelectronic packages may be characterized as a multi-layered plate consisting of two regions, that of a die area and a mold area. Physical observation of various packages demonstrates that these two regions cause the package to exhibit dual curvatures, which are approximated using closed form sets of algebraic equations. The resulting technique, termed the dual-curvature approach, predicts the thermomechanical warpage of packages composed of temperature-dependent materials and may be extended for application to packages having a diverse range of geometries. The accuracy of the dual-curvature approach is assessed for square, single-die packages by means of threedimensional, finite element simulations at nine in-plane locations. It is shown that the dual-curvature approach significantly improves the thermomechanical warpage prediction of microelectronic packages relative to earlier analytical models.