Sensitivity analysis of via impedance using polynomial chaos expansion

This work addresses the sensitivity of the characteristic via impedance used in high-speed digital systems with respect to variations of geometrical parameters. For modeling of the electromagnetic characteristics of a signal via surrounded by ground vias the physics-based via (PBV) model is used, which provides an equivalent circuit representation for a via interconnect. This circuit is augmented element-wise using polynomial chaos expansion (PCE) to include variability in form of stochastic parameters. This representation is used to derive a stochastic characteristic via impedance. The proposed method is validated with Monte-Carlo (MC) simulations and is proven to be more efficient. Finally, the sensitivity of a via on a printed circuit board (PCB) and a via on a glass interposer with respect to variations of geometrical parameters are analyzed.