Abstract
As electronic packages get thinner, controlling the warpage of these parts becomes more challenging. Highly warped packages can encounter yield losses due to bump bridging and solder extrusion. Modeling the warpage using finite element analysis (FEA) is a good way to predict warpage during the design stage. However, a good FEA model requires accurate material property inputs for the simulation results to be useful. Electronic substrates with their anisotropic metal lines and temperature-dependent core and Ajinomoto Build-up Film (ABF) are quite cumbersome to characterize and tedious to simulate analytically or computationally accurately. In addition, at the design stage, substrate samples are not available for characterization and metal pattern designs are not available to simulate. In this work, the objective is to develop a physics-informed machine learning based inverse design framework for optimizing the metal layers in the substrate for achieving low warpage of the ultrathin package. The proposed framework consists of three phases. In Phase A, we derive the dataset with which to build the surrogate model using a purely physics-based approach by using two FEA models. One model was used to derive the coefficient of thermal expansion (CTE) of the subsection from the metal density of each of the layers and the other was used to determine the warpage using the CTE values as the input. In Phase B, we construct the surrogate model using tensor train decomposition (TTD) and artificial neural network (ANN). TTD is an important feature of this framework because we are building a surrogate model for the entire warpage contour (75 × 55) which is a large dataset for optimization. Finally in Phase C, we run global optimization of the surrogate model using Cross Entropy (CE) technique. The novelty of this inverse design framework is that we are enabling the optimization of a large design space of 72 × 1 metal densities for low warpage on the entire surface profile of the substrate in an efficient timeframe (< 4% error in warpage). This is a huge problem that is not feasible to solve using FEA and CE optimization alone due to the time and human resources that would be required (estimated to be ~17 days). With the proposed framework setup in this thesis, the optimized solution is obtainable in less than 1 day.