Modeling the effects of non-linear materials in de-coupling components of digital systems

This paper describes a physics-based numerical approach to building circuit models for electronic components that are made using nonlinear dielectrics. The resulting models are intended for use in time-domain circuit simulators to assess the effects of material nonlinearity on the electrical performance of such components as discrete, on-substrate and on-chip de-coupling capacitors. A 3D electrostatic field solver is modified to take into account the nonlinear field dependence of the dielectric material and is employed to calculate the Q-V curve for any capacitive structure. Subsequently, a time integration method (similar to that used in SPICE) is utilized to devise an appropriate time-stepping algorithm for the current-charge relationship of a nonlinear capacitor that can be used to simulate the time-domain electrical characteristics of such passive components. Sample results are also provided to illustrate the methodology