Algorithms in FastImp: a fast and wide-band impedance extraction program for complicated 3-D geometries

In this paper, we describe the algorithms used in FastImp, a program for accurate analysis of wide-band electromagnetic effects in very complicated geometries of conductors. The program is based on a recently developed surface integral formulation and a precorrected fast Fourier transform (FFT) accelerated iterative method, but includes a new piecewise quadrature panel integration scheme, a new scaling and preconditioning technique as well as a generalized grid interpolation and projection strategy. Computational results are given on a variety of integrated circuit interconnect structures to demonstrate that FastImp is robust and can accurately analyze very complicated geometries of conductors.

[1]  Kapur,et al.  IES/sup 3/: a fast integral equation solver for efficient 3-dimensional extraction , 1997, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[2]  L. N. Medgyesi-Mitschang,et al.  Generalized method of moments for three-dimensional penetrable scatterers , 1994 .

[3]  Albert E. Ruehli,et al.  Three-dimensional interconnect analysis using partial element equivalent circuits , 1992 .

[4]  X. Wang,et al.  Fast fluid analysis for multibody micromachined devices , 2001 .

[5]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[6]  Eli Chiprout,et al.  Efficient full-wave electromagnetic analysis via model-order reduction of fast integral transforms , 1996, DAC '96.

[7]  Weng Cho Chew,et al.  A surface integral equation method for solving complicated electrically small structures , 2003, Electrical Performance of Electrical Packaging (IEEE Cat. No. 03TH8710).

[8]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[9]  S. Ramo,et al.  Fields and Waves in Communication Electronics , 1966 .

[10]  Aosheng Rong,et al.  Comprehensive broadband electromagnetic modeling of on-chip interconnects with a surface discretization-based generalized PEEC model , 2003, Electrical Performance of Electrical Packaging (IEEE Cat. No. 03TH8710).

[11]  Roger F. Harrington,et al.  An E-Field solution for a conducting surface small or comparable to the wavelength , 1984 .

[12]  Jacob K. White,et al.  Fast methods for simulation of biomolecule electrostatics , 2002, ICCAD 2002.

[13]  R. Kress,et al.  Integral equation methods in scattering theory , 1983 .

[14]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[15]  Jianming Jin,et al.  Efficient electromagnetic modeling of microstrip structures in multilayer media , 1999 .

[16]  David C. Chang,et al.  Electromagnetic modeling of passive circuit elements in MMIC , 1992 .

[17]  Branko M. Kolundzija,et al.  Electromagnetic modeling of composite metallic and dielectric structures , 1999 .

[18]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[19]  C. Tai,et al.  Dyadic green functions in electromagnetic theory , 1994 .

[20]  T. Sarkar,et al.  Comments on "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies" , 1986 .

[21]  Junfeng Wang,et al.  A new surface integral formation of EMQS impedance extraction for 3-D structures , 1999 .

[22]  Christian Lage,et al.  A system for full-chip and critical net parasitic extraction for ULSI interconnects using a fast 3-D field solver , 2000, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[23]  L. Greengard.  The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[24]  R. Harrington.  Time-Harmonic Electromagnetic Fields , 1961 .

[25]  Joel R. Phillips,et al.  Rapid solution of potential integral equations in complicated 3-dimensional geometries , 1997 .

[26]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[27]  Albert E. Ruehli,et al.  Enhanced skin effect for partial-element equivalent-circuit (PEEC) models , 2000 .

[28]  Jiming Song,et al.  Fast Illinois solver code (FISC) , 1998 .

[29]  Andrew F. Peterson,et al.  The “Interior Resonance” Problem Associated with Surface Integral Equations of Electromagnetics: Numerical Consequences and a Survey of Remedies , 1990 .

[30]  Te-kao Wu,et al.  Scattering from arbitrarily‐shaped lossy dielectric bodies of revolution , 1977 .

[31]  A. Brandt,et al.  Multilevel matrix multiplication and fast solution of integral equations , 1990 .

[32]  W. M. Rucker,et al.  Various BEM formulations for calculating eddy currents in terms of field variables , 1995 .

[33]  D. R. Wilton,et al.  E-Field, H-Field, and Combined Field Solution for Arbitrarily Shaped Three-Dimensional Dielectric Bodies , 1990 .

[34]  Vikram Jandhyala,et al.  Integral equation based time domain coupled EM-circuit simulation for packaged conductors and dielectrics , 2003, Electrical Performance of Electrical Packaging (IEEE Cat. No. 03TH8710).

[35]  Hermann A. Haus,et al.  Electromagnetic Fields And Energy , 1989 .

[36]  J. Kong,et al.  A hybrid method for the calculation of the resistance and inductance of transmission lines with arbitrary cross sections , 1991 .

[37]  Jacob K. White,et al.  A precorrected-FFT method for electrostatic analysis of complicated 3-D structures , 1997, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[38]  Jacob K. White,et al.  Automatic generation of accurate circuit models of 3-D interconnect , 1998 .

[39]  J. Mosig.  Arbitrarily shaped microstrip structures and their analysis with a mixed potential integral equation , 1988 .

[40]  Mattan Kamon,et al.  FASTHENRY: a multipole-accelerated 3-D inductance extraction program , 1994 .

[41]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[42]  Dean P. Neikirk,et al.  Interconnect series impedance determination using a surface ribbon method , 1994, Proceedings of 1994 IEEE Electrical Performance of Electronic Packaging.

[43]  F. Arndt,et al.  Efficient MPIE approach for the analysis of three-dimensional microstrip structures in layered media , 1997 .

[44]  M. Bleszynski,et al.  AIM: Adaptive integral method for solving large‐scale electromagnetic scattering and radiation problems , 1996 .

[45]  Jacob K. White,et al.  FastCap: a multipole accelerated 3-D capacitance extraction program , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[46]  Alberto L. Sangiovanni-Vincentelli,et al.  Using conduction modes basis functions for efficient electromagnetic anaysis of on-chip and off-chip interconnect , 2001, DAC '01.

[47]  R. Harrington.  Boundary integral formulations for homogeneous material bodies , 1989 .

[48]  Yehia Massoud,et al.  Simulation algorithms for inductive effects , 1999 .

[49]  Koji Fujiwara,et al.  Comparison of various methods for 3-D eddy current analysis , 1988 .

[50]  J. Hess,et al.  Calculation of potential flow about arbitrary bodies , 1967 .