Modeling of semiconductor substrate on on-chip power grid switching

A methodology is proposed and demonstrated for the modeling of the semiconductor substrate on on-chip power grid switching. A comprehensive electromagnetic model for the power grid, founded on the finite-difference approximation of Maxwell´s curl equations, is combined with properly constructed, frequency-dependent equivalent surface impedance models for the doped semiconductor substrate to capture the impact of substrate loss on the grid response during switching. Numerical studies are utilized to illustrate the capabilities of the developed on-chip power grid solver.