Rapid Inverse Modeling of Integrated Circuit Layout in Both Frequency and Time Domain
In this paper, starting from full-wave Maxwell’s equations where E and H are coupled, we derive a closed-form model of the inverse of the Maxwell’s system of equations in the physical layout of an integrated circuit, package, and board. In this model, we decompose the inverse rigorously into R-, C-, L- and full-wave components, with neither numerical computation nor approximation, and for an arbitrary physical layout. As a result, each component can be found independently, and then superposed to obtain the total response of a layout to any circuit stimuli. The time marching and point-by-point frequency sweeping are also avoided for the RC-component as its time and frequency dependence is analytically revealed in the proposed model. Moreover, the full-wave component is efficiently represented by a small number of high-frequency modes of the curl-curl operator, which are analytically derived. Using the proposed model, not only many accuracy issues related to existing layout modeling can be addressed, but also we drastically speed up layout modeling and simulation, and provide circuit designers with an effective model for layout automation. In addition, we develop fast and large-scale algorithms to find each component of the inverse in optimal (linear) complexity, where many steps are made analytical, thus further saving CPU run time. The proposed work has been applied to large-scale layout extraction and analysis. Superior performance has been demonstrated in accuracy, efficiency, and capacity.