Efficient sensitivity-based capacitance modeling for systematic and random geometric variations

This paper presents a highly efficient sensitivity-based method for capacitance extraction, which models both systematic and random geometric variations. This method is applicable for BEM-based Layout Parasitic Extraction (LPE) tools. It is shown that, with only one system solve, the nominal parasitic capacitances as well as its relative standard deviations caused by both systematic and random geometric variations can be obtained. The additional calculation for both variations can be done at a very modest computational time, which is negligible compared to that of the standard capacitance extraction without considering any variation. Specifically, using the proposed method, experiments and a case study have been analyzed to show the impact of the random variation on the capacitance for a real design.