Efficient 3-D extraction of interconnect capacitance considering floating metal fills with boundary element method

Inserting dummy (area fill) metals is necessary to reduce the pattern-dependent variation of dielectric thickness in the chemical-mechanical polishing (CMP) process. Such floating dummy metals affect interconnect capacitance and, therefore, signal delay and crosstalk significantly. To take the floating dummies into account, an efficient method for three-dimensional (3-D) capacitance extraction based on boundary element method is proposed. By introducing a floating condition into the direct boundary integral equation (BIE) and adopting an efficient preconditioning technique, and the quasi-multiple medium (QMM) acceleration, the method achieves very high computational speed. For some typical structures of area fill, the presented algorithm has shown over 1000× speedup over the industry-standard Raphael while preserving high accuracy. Compared with the recently proposed PASCAL in the work of Park et al. (2000), the proposed method also has about ten times speedup. Since the dummies are not regarded as normal electrodes in capacitance extraction, the proposed method is much more efficient than the conventional method, especially in cases with a large number of floating dummies.