Learning the Stress-Strain Relationships of Ultra-Thin Package Materials using a Bayesian Approach

Package warpage simulations carried out using finite element analysis typically require several assumptions to be made for simplicity and computational efficiency. These assumptions usually include the linear elasticity of the materials and negligible impact of process dependence on warpage (allowing the loading condition to be a single-step temperature ramp down from the stress-free temperature). For standard packages, these assumptions still yield acceptable results. However, for ultra-thin packages with the higher incoming bare substrate warpage and more complex warpage profiles, more sophisticated models and simulation frameworks are required for accurate warpage predictions. In this work, we use an interesting mix of techniques such as finite element analysis, neural networks, and Markov Chain Monte Carlo to first generate an efficient model for warpage and then learn the stress-strain relationship of the adhesive given an experimental warpage profile. Learning whether the adhesive material undergoes yield and plastic deformation is beneficial to package designers because the resulting poor stiffener attachment and poor warpage control can be avoided.