Predictive model for optimized design parameters in flip-chip packages and assemblies

An analytical model is developed to predict the out-of-plane deformation and thermal stresses in multilayered thin stacks subjected to temperature. Coefficient of thermal expansion mismatches among the components (chip, substrate, underfill, flip-chip interconnect or C4s) are the driving force for both first and second levels interconnect reliability concerns. Die cracking and underfill delamination are the concerns for the first level interconnects while the ball grid array solder failure is the primary concern for the second level interconnects. Inadvertently, many researchers use the so-called rule of mixture in its effective moduli for the flip chip solder (C4)/underfill layer. In this study, a proper formula for effective moduli of solder (C4)/underfill layer, is presented. The classical lamination theory is used to Predict the out-of-plane displacement of the chip substrate structure under temperature variation (AT). The warpage and stresses resulting from the analytical formulation are compared with the 3-D finite element analysis. The study helps to design more reliable components or assemblies with the design parameters being optimized in the early stage of the development using closed form analytical solutions.