A theoretical solution for thermal warpage of flip-chip packages

The control of thermally induced warpage on electronic packages is an important issue during their fabrication process and assembly. Apart from a commonly used finite-element method and experimental methods for thermally induced warpage analysis of the packages, it still needs a fundamental theory to provide an insight of mechanics to assist and further check the finite-element and experiment-obtained results, especially for critical parameter identification. This article aims to take a close look into the well-known, closed-form Suhir theory for calculating thermally induced deformation of die-substrate assembly and correlate it with a finite-element analysis and further to propose a new Suhir-solution-based theory for predicting the thermal deformation of flip-chip packages. Through this article, the shear-effect region has been found, and its effect on curvature distribution over entire package length and corresponding warpage has been examined in terms of elastic modulus and thickness of underfills. The other parameters such as extended substrate and fillets of underfill are also studied. The limitation and feasibility of the theoretical solution to thermal deformation (warpage) prediction of flip-chip packages are discussed in detail by comparing with the finite-element and moiré experimental results in this article.