| We have developed a computationally efficient, nonlinear transient simulator streamlined for the charging and switching analysis of the on-chip power grid with electromagnetic accuracy. The proposed simulator couples a rigorous electromagnetic field solver for the modeling of the three-dimensional physical structure of the power grid, with a SPICE engine for the simulation of all electronics and lumped circuit elements attached to the grid. Compared to earlier versions of such hybrid field-circuit solvers, the use of an unconditionally stable Crank-Nicolson (CN) scheme for the numerical integration of the EM fields in the power grid model allows us to improve the speed of the numerical integration by one to two orders of magnitude, particularly through an adaptive time stepping to exploit the disparate time scales associated with the charging of the grid and the subsequent fast switching events.;The second contribution concerns the demonstration of scalability of the CN-based transient simulator by the use of a metallization layer-centric domain decomposition of the power grid. The domain decomposition approach used relies on the iterative exchange of field information between adjacent subdomains over an overlap region. For the case of on-chip power grid structures, it is shown that at most two iterations are needed for convergence. Hence, the scheme is computationally very efficient for the handling of large portions of the on-chip power grid. |
