A STOCHASTIC ALGORITHM FOR THE EXTRACTION OF PARTIAL INDUCTANCES IN IC INTERCONNECT STRUCTURES
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A STOCHASTIC ALGORITHM FOR THE EXTRACTION OF PARTIAL INDUCTANCES IN IC INTERCONNECT STRUCTURESAbstract
With recent increases in operating frequencies, the modeling and extraction of on-chip inductance is becoming an increasingly significant consideration. The inductance models include the “loop inductance” models and the “partial inductance” models. In this paper, we develop a stochastic solution methodology for the extraction of partial inductances in IC interconnect structures. An important advantage of this approach is that it requires no discretization meshing of either the volume or the surface of the problem domain. As a result, it has very low memory requirements compared to the more conventional deterministic techniques. Another advantage of this approach is that it is inherently parallelizable and a linear increase in speed is expected with the increase in the number of processors. Excellent agreement has been obtained with analytical benchmark solutions.
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References
B. Krauter and S. Mehrotra, “Layout based
frequency depended inductance and
resistance extraction for on-chip
interconnect timing analysis,” Proceedings
Design Automation Conference, pp. 303-
, June, 1998.
K. Gala, D. Blauuw, V. Zolotov, P. Vaidya
and A. Joshi, “Inductance model and
analysis methodology for high-speed onchip interconnect”, IEEE Transactions on
Very Large-Scale Integration Systems, Vol.
, No. 6, pp. 730-745, December 2002.
A. E. Ruehli, “Inductance calculations in a
complex integrated circuit environment,”
IBM Journal of Research and Development,
pp. 470-481, September 1972.
C. Hoer and C. Love, “Exact inductance
equations for rectangular conductors with
applications to more complicated
geometries,” Journal of Research of the
National Bureau of Standards, Vol. 69C,
No. 2, pp. 127-137, April, 1965.
See, for example, K. K. Sabelfeld, Monte
Carlo Methods in Boundary Value
Problems, Springer Verlag, 1991.
K. Chatterjee, P. Matos and B. Hawkins, “A
novel stochastic algorithm for the extraction
of frequency-independent partial
inductances in digital IC interconnect
structures and a frequency-dependent
generalization,” 20th Annual Review of the
Applied Computational Electromagnetics
Society, Syracuse, NY, April 19-23, 2004.
J. D. Jackson, Classical Electrodynamics,
Third Edition, pp. 215-216, John Wiley &
Sons, New York, NY, 1999.
S. Ramo, J. R. Whinnery and T. van Duzer,
Fields and Waves in Communication
Electronics, Third Edition, pp. 180-181,
John Wiley & Sons, New York, NY, 1993.
R. Haberman, Elementary Applied Partial
Differential Equations, Third Edition, pp.
-413, Prentice Hall, Upper Saddle River,
NJ, 1998.
Ilya M. Sobol, A Primer for the Monte Carlo
Method, CRC Press, Boca Raton, 1994.
R. Courant and F. John, Introduction to
Calculus and Analysis, Volume 1, Springer,
J. Banks and J. Carson, Discrete Event
System Simulation, Prentice Hall, pp. 257-
, 1984.
K. Chatterjee, Development of a Floating
Random-Walk Algorithm for Solving
Maxwell’s Equations in Complex ICInterconnect Structures, Rensselaer
Polytechnic Institute, May 2002, UMI
Dissertation Services, 300 North Zeeb Road,
P.O. Box 1346, Ann Arbor, Michigan
-1346, USA, UMI Number: 3045374,
Web Address: www.il.proquest.com.
K. Chatterjee, R.B. Iverson and Y.L. Le
Coz, “Development of a Random-Walk
Algorithm for IC-Interconnect Analysis: 2D
TE Benchmarks, Materially Heterogeneous
Domains,” VLSI Multilevel Interconnection
Conference, Santa Clara, CA, pp. 374-379,
June 2000.
J. M. Hammersley, D. C. Handscomb,
Monte Carlo Methods, John Wiley & Sons,
New York, NY, 1964, pp. 50-54.


