Machine Learning Approach to Improve Accuracy of Warpage Simulations

Warpage control of electronic packages has become a critical challenge given the requirement of thinner packaging solutions for the future. While modeling warpage using finite element models is a good way to predict stresses and warpage, the analysis results are only as good as the assumed model inputs such as material properties. This is especially true with warpage simulations and the anisotropic and temperature-dependent material properties of the electronic substrate. With the varying metal line patterns and densities across the substrate, the substrate material properties can be spatially varying in ultra-thin packages resulting in complex warpage profiles. To aid in better design for reliability of future ultra-thin packages, we propose here the use of the Markov Chain Monte Carlo (MCMC) approach (Bayesian inference) combined with finite element simulations to identify the sensitive material parameters that most affect warpage and learn the localized material properties based on warpage contours that have been measured using digital image correlation (DIC). The proposed technique can enable us to design better packages with locally tailored material properties (by tuning metal layer densities, for example) to enable us to stay within an acceptable warpage threshold.