Hierarchical Modeling and Computationally-Efficient Transient Simulation of On-Chip Power Grid

We report on an unconditionally-stable, Crank-Nicolson numerical integration scheme for the computationally-efficient, transient electromagnetic analysis of the on-chip power grid during switching. Compared to the conditionally-stable finite-difference time-domain approach, this scheme provides for two orders of magnitude reduction in the time required for the numerical simulation. The resulting transient electromagnetic field solver is interfaced with a SPICE simulation engine. Its use is demonstrated through the transient, nonlinear switching analysis of a portion of an on-chip power grid used in the 90-nm CPU process.