Single Pin Redundancy for Robust Power Grid Delivery

C4 bumps are susceptible to electromigration failure due to large power-supply currents. Electromigration failure is exacerbated by manufacturing variability, which increases bump resistance and consequently the current draw in neighboring bumps. A typical solution entails adding redundant bumps while guard-banding the maximum current per bump. Instead, we propose a mixed-integer linear program for redundant bump placement that minimizes the total bump count, while ensuring power supply integrity in the presence of a single-bump failure (SBF). Our experiments show a power grid can be made resilient to SBF by adding 32% more bumps, compared to 77% used in a greedy approach.