Boundary Integral Equation Model For Extracting Parasitic Inductance And Resistance Of Interconnects In VLSI

With the increase in VLSI circuit density, complexity and levels ofintegration in deep sub-micron design as well as the working frequencies ofthe circuits reaching a couple of GHz, inductive effects on circuitperformance are gradually emerging. Therefore, to extract thefrequency-dependent parasitic inductance and resistance in addition tothe capacitance of the interconnects has already become anindispensable step in the high performance VLSI circuit design. Presently, only a few of the proposed models can take into accountthe eddy current effect, most of which have not yet shaped intopractical software because of their computing complexity. This paper is to put forward a new boundary integral equation model forextracting frequency-dependent parasitic inductance and resistance with the3-D eddy current effect considered. The new model has the followingtraits:1. The model employs the imaginary magnetic current density and magnetic charge density distributed over the interfaces of different regions, and the scalar potential on these interfaces as unknowns;2. As a boundary element model, it assigns only 4 unknowns for each boundary element. This endues it with a potential speed advantage in numerical computing;3. This model can be used to calculate mutual impedance between two perpendicular conductors by discarding the assumption that the current flows only along the axis direction of the conductors. Furthermore, it is applicable to general complex 3-D structures without making any assumption about the geometry of the interconnects. ? II ?Abstract The validity and feasibility of the new model is verified by the numericalresults from several simple examples.