| Substrate noise coupling continues to be one of the bottleneck challenges in mixed-signal integrated circuit design and system-on-chip (SOC) integration. Proper substrate modeling is required to include the substrate noise coupling effects in the design process. Conventional 3-D mesh- or boundary-based substrate modeling methods are computationally expensive and typically limited to analysis of simple configurations. This research work presents a synthesized compact modeling (SCM) approach for substrate coupling analysis.; This work first analyzes the complexity of substrate network topologies. A hybrid topology is proposed, combining a locally fully-connected near-field model with a far-field model, to reduce the substrate network complexity in conventional topologies. The SCM is formulated using a scalable Z matrix approach for heavily doped substrates with a lightly doped epitaxial layer and using a nodal lumped resistance approach for lightly doped substrates. The SCM models require a set of process-dependent fitting coefficients and incorporate geometrical parameters of the substrate ports in a compact form that includes size, perimeter, and separation defined using the geometric mean distance to accommodate both far-field and near-field effects. The SCM approach is verified based on measurement data from two test chips, one in a custom lightly doped process and the other one using a 0.18-mum BiCMOS lightly doped foundry process. The model accuracy is shown to be within 15% compared to measured data extracted from the test patterns. The SCM is exploited under an automated CAD framework with application examples to show substrate model generation efficiency and accuracy at different levels of complexity, including a full chip substrate noise distribution analysis for a 2 mm by 2 mm chip with 319 substrate contacts.; Finally, this work presents results of substrate modeling in the high frequency region. It is shown that the substrate cannot be treated as purely resistive for frequencies above 1-2 GHz for heavily doped substrate processes and for frequencies above 10 GHz for lightly doped substrate processes. A CAD-oriented modeling approach is proposed to synthesize the broadband equivalent circuit model consisting solely of ideal lumped elements for the frequency-dependent behavior of substrate coupling. |
