Research On Fast Extraction For 3-D Frequency-dependent Inductance And Resistance Of VLSI Interconnects

Recently, the applications of SOC ( System on a Chip ), RF ( Radio Frequency) circuit and wireless communication technology push the development of digitaland A/D integrated circuits with frequency above several GHz. In these chips withhigh integrated density and high working frequency, The interconnect frequency-dependent inductance and resistance have an essential effect on the signal delay andcrosstalk. Therefore, it is important for designing high-performance chip to extract 3-Dfrequency-dependent inductance and resistance fast and accurately.Based on volume element model, FastHenry can compute 3-D complex structurewith high accuracy. But its time and memory requirement is too prohibitive to deal withpractical chips with large scale. The work of this dissertation focuses on the researchof fast algorithm of fast algorithm of 3-D interconnects inductance and resistance ex-traction through reasonable simplification and improvement for volume model. Thefollowing achievements are obtained:1. We improve the average formula by Ruehli which can only be applied to computeinductance in low frequency, and propose a series of weighted average formulaewhich can be used to compute 3-D interconnect inductance and resistance in lowand high frequency. Compared with FastHenry, it only need to set conductor voltonce and solve one large and dense equation. Therefore, its computing speedincreased 4-5 times, while computing result are still very accuracy.2. Through an example, We point out that the admittance matrix Y ( the inverse ofimpedance matrix Z ) has locality similar with K matrix ( the inverse of induc-tance L ), and propose a method to extract interconnect inductance and resistancebased on Y element. Compared with other methods based K element, our methoddoes not only increase the computation speed because of reducing the times ofmatrix inversion, but also can extract interconnect resistance at high frequency.In order to deal with 3-D complex structure and increase speed more, five im-provements are implemented: a window selection algorithm for 3-D complexstructure;a simplified multipole accelerate method;grouping inversion of ad-mittance matrix;reusing of filament impedance;reusing of window impedancematrix. The numerical results of some examples display that our method canincrease the speed more than 100 times compared with FastHenry.3. Through numerical experiments, we indicate that the filaments current can beignored as zero when conductor is set open. Based on this observation, we candeduce that the mutual inductrance between two conductors are only in?uencedby themselves. Therefore, We can proposed a fast inductance extraction algo-rithm based open-circuit. The numerical results of some examples display thatthis method can increase the speed hundreds of times compared with FastHenry.