Analytical Model for Thermal Warpage History of Laminated PBGAs

Thermally induced warpage can lead to deformed or bridged solder joints during reflow of large laminate-based area-array components like high I/O PBGAs. This study presents a simple, rapid-assessment modeling capability to assess the warpage risk of such components, based on their architecture information. A piece-wise, classical laminated plate model is used in this study for estimation of the thermally induced warpage. This model uses temperature-dependent elastic properties to account for the large change in material behavior as the reflow temperature exceeds the glass-transition temperatures of the various polymers (substrate, die attach and epoxy molding compound). The laminated plate modeling strategy provides the capability to handle complex component architectures and temperature gradients in the thickness direction. The piecewise modeling strategy allows the model to account for the changes in the stack-up as we move from under the die footprint to the region outside the footprint. Several test cases are examined during the model development. Results are compared to detailed finite element models, as well as to other analytical methods like finite-length plate models. The model is found to be very sensitive to the thermo-mechanical properties of common epoxy molding compounds (EMCs) above their glass transition temperature. Since the model approximates a complex viscoplastic problem with an equivalent temperature-dependent elastic formulation, part of the focus is on developing equivalent temperature-dependent material properties to calibrate the model. The goal in this approximation is to find a suitably smooth transition between the material properties below and above T_g, based on the discrete properties typically found in data sheets. The trends predicted by this simplified model are also found to agree well with shadow moire measurements of warpage in actual components during large temperature excursions.