A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

We present an algorithm for two- and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algorithm decreases with better resolution of the input image. Those features render the presented algorithm well suited for fast prototyping while using the most realistic IC geometry data.

[1]  G. Amdhal,et al.  Validity of the single processor approach to achieving large scale computing capabilities , 1967, AFIPS '67 (Spring).

[2]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[3]  R. B. Iverson,et al.  A stochastic algorithm for high speed capacitance extraction in integrated circuits , 1992 .

[4]  S. Yoo,et al.  An effective image segmentation technique for the SEM image , 2008, 2008 IEEE International Conference on Industrial Technology.

[5]  Lorenz Holzer,et al.  Review of FIB tomography , 2012 .

[6]  Karl K. Sabelfeld.  Monte Carlo Methods in Boundary Value Problems. , 1991 .

[7]  J. Baerentzen,et al.  On the Implementation of Fast Marching Methods for 3d Lattices , .

[8]  Weiping Shi,et al.  A New Methodology for Interconnect Parasitics Extraction Considering Photo-Lithography Effects , 2007, 2007 Asia and South Pacific Design Automation Conference.

[9]  Erich Hartmann.  Numerical parameterization of curves and surfaces , 2000, Comput. Aided Geom. Des..

[10]  Chi-Yuan Lo,et al.  Parasitic extraction: current state of the art and future trends , 2001 .

[11]  Y. L. Le Coz,et al.  Performance of random-walk capacitance extractors for IC interconnects: A numerical study , 1998 .

[12]  E. Ramsay,et al.  Three-dimensional imaging of a silicon flip chip using the two-photon optical-beam induced current effect , 2002 .

[13]  Alok Aggarwal,et al.  Fast algorithms for computing the largest empty rectangle , 1987, SCG '87.

[14]  P. Maffezzoni,et al.  A statistical algorithm for 3D capacitance extraction , 2000 .

[15]  Zhi Liu,et al.  Fast floating random walk algorithm formulti-dielectric capacitance extraction with numerical characterization of Green's functions , 2012, 17th Asia and South Pacific Design Automation Conference.

[16]  R. B. Iverson,et al.  A floating random-walk algorithm for extracting electrical capacitance , 2001 .

[17]  Aly A. Farag,et al.  MultiStencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Zeyi Wang,et al.  CAPACITANCE EXTRACTION , 2004 .

[19]  Nikolai A. Simonov,et al.  Monte Carlo Methods for Calculating Some Physical Properties of Large Molecules , 2004, SIAM J. Sci. Comput..

[20]  T El-Moselhy,et al.  A Markov Chain Based Hierarchical Algorithm for Fabric-Aware Capacitance Extraction , 2010, IEEE Transactions on Advanced Packaging.

[21]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Zhi Liu,et al.  RWCap: A Floating Random Walk Solver for 3-D Capacitance Extraction of Very-Large-Scale Integration Interconnects , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.