| Improved verification of mixed-signal designs requires substrate noise coupling simulation tools. Due to the complexity of substrate structures, fast robust tools are still a subject of active research. This dissertation presents a methodology for the efficient modeling of substrate noise coupling. A closed-form Green's function for nonuniformly doped substrates is employed. A CG-FFT (conjugate-gradient fast Fourier transform) based solver provides state-of-the-art computational efficiency of O(Nlog N) time consumption and O(N) memory consumption. A novel, global surface impedance matrix scheme is introduced to efficiently model nonuniformly doped regions of finite extent.; In addition, the need for the extension of this methodology to the frequency-dependent case, where electromagnetic effects such as displacement current and skin effect cannot be assumed negligible, has been argued and demonstrated in this dissertation. |
