Simple and Accurate Models for Capacitance Increment due to Metal Fill Insertion

Inserting metal fill to improve inter-level dielectric thickness planarity is an essential part of the modern design process. However, the inserted fill shapes impact the performance of signal interconnect by increasing capacitance. In this paper, we analyze and model the impact of the metal dummy on the signal capacitance with various parameters including their electrical characteristic, signal dimensions, and dummy shape and dimensions. Fill has differing impact on interconnects depending on whether the signal of interest is in the same layer as the fill or not. In particular intra-layer dummy has its greatest impact on coupling capacitance while inter-layer dummy has more impact on the ground capacitance component. Based on an analysis of fill impact on capacitance, we propose simple capacitance increment models (Cc for intra-layer dummy and Cg for inter-layer dummy). To consider the realistic case with both signals and metal fill in adjacent layers, we apply a weighting function approach in the ground capacitance model. We verify this model using simple test patterns and benchmark circuits and find that the models match well with field solver results (1.2% average error with much faster runtime than commercial extraction tools, the runtime overhead reduced by ~75% for all benchmark circuits).