I. Introduction
Over the last decade, the semiconductor industries have advanced to meet more parasitic noises in integrated circuits (IC), packages, and printed circuit boards (PCB). The field on signal integrity (SI) and power integrity (PI) has been enormously studied and broadly adopted for high-speed link designs. Via structures are necessary in multilayer printed circuit boards (PCB) to connect each single trace in different layers. However, as the data rate of high speed IO is increasing and doubling, the discontinuities of vias become more and more significant. Via design with optimization has been a critical topic in recent years.