Inverse Design for Low Warpage Ultra-Thin Packages Using Constrained Particle Swarm Optimization

Warpage of electronic packages is the result of mismatch in the coefficient of thermal expansion (CTE) between the silicon die (CTE = 2.6ppm/°C) and the substrate (CTE = 15-25 ppm/°C). In ultra-thin packages, the reduced thicknesses can result in even higher package warpage due to the reduced flexural rigidity. Current approaches to minimize warpage include selecting constituent materials in the substrate with lower CTE as well as carrying out copper balancing of metal layers which are equidistant but on opposite sides of the core. In this work, we aim to optimize the metal density of the substrate layers by using an inverse design framework using Particle Swarm Optimization (PSO) with carefully selected constraints to minimize the rework required on the electrical tracing artwork. Results show that the inverse design framework is able to arrive at a 20% reduced warpage by changing local metal densities by just up to 5%. This is a significant reduction in warpage that is achievable by incorporating minor changes to the electrical artwork of the substrate. In future, this methodology can be applied to not only minimize warpage on ultra-thin packages but also enable even thinner ultra-thin package designs to be realized.