Analytical estimate for cure-induced stresses and warpage in flat packages

Warpage of flat packages is partly due to chemical shrinkage of the molding compound during cure and partly due to differences in thermal contraction in the subsequent cooling stage. The latter effect is relatively easy to incorporate in numerical simulations but the cure-induced shrinkage effect is not and is therefore often neglected in warpage simulations. Recent validation studies however showed that it is essential that both effects are taken into account. In this paper we develop explicit analytical expressions for the cure-induced residual stresses and warpage of a simple bilayer construction. We do this by assuming that curing always takes place above the molding compounds glass transition temperature such that the material is in its rubbery state and that viscoelastic effects are absent. The analytical warpage model was shown to give results comparable to numerical calculations using a fully cure dependent viscoelastic material model. Furthermore, for the first time accurate analytical expression for the Stress Free Temperature and Stress Free Strain are obtained. With these expressions the effect of cure shrinkage on residual stresses can easily be incorporated in existing (numerical) stress analyses without the need of using extensive cure dependent viscoelastic material models.