Comprehensive Model for On-Chip Power Grid Transient Analysis and Power Grid-Induced Noise Prediction

A comprehensive modeling methodology is presented for the switching analysis of the on-chip power grid. Contrary to commonly used techniques, an electromagnetic model is used for the discretization of the volume occupied by the grid. Thus, the tedious and error-prone extraction of a distributed RLC model for the power grid is avoided. In addition, the generated discrete model allows for power grid induced coupling to be taken into account in the transient simulation. The electromagnetic model for the power grid is complemented by a distributed RC model for the semiconductor substrate and RLCG models for the interconnects. Thus, a comprehensive model results for the quantification of on-chip interconnect and power grid noise effects during switching. Transient simulations using this model are carried out using a hybrid time-domain integration scheme which combines a SPICE-like engine for the analysis of the RLCG netlists and the nonlinear drivers, and a numerical integration algorithm for the discrete electromagnetic model for the power grid