Analytical model for thermally-induced warpage of POP

The thermally-induced deformations of package-on- package (POP) are investigated theoretically, numerically and experimentally in this paper. An analytical model of POP is newly proposed for prediction of the warpage of POP, which can be achieved by solving a few linear multiple polynomial equations rather than building a complex model in ANSYS, and leads to satisfying results. All the parameters needed for the analytical model are temperature-dependant material properties, and geometrical parameters. Measurements of the the warpage of POP under various temperature loads are made with a Profilometer Altisurf 500. Moreover, a 3-D linear finite element model was built. Both measurements and simulation validate our analytical model. The results from the experiments are presented and compared in detail with those from the 3-D linear finite element and theoretical analysis. The good agreements in the experimental and modelling results reveal the validation of 3-D linear finite element model in mechanics sense and the effectiveness of the numerical and theoretical models in physics predictions. The interest lies in a very easy use of this theoretical model to quickly obtain the warpage information for deciding whether the design is suitable and/or comparing the different POP circuits design.