Toward a more robust and accurate CEM fast integral equation solver for IC applications

IEEE Transactions on Advanced Packaging

Volumn 28, Issue 3, 2005, Pages 449-464

  Chew, Weng Cho ^a   Jiang, Li Jun ^b   Chu, Yun Hui ^c   Wang, Gong Li ^a   Chiang, I Ting ^a   Pan, Yuancheng Christopher ^d   Zhao, Jun Sheng ^e  

^a University of Illinois at Urbana Champaign   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

^c AGILENT TECHNOLOGIES   (United States)

^d INTEL CORPORATION   (United States)

^e Madmax Optics   (United States)

Author keywords

Fast real time convolution; Integral equation; Lithography; Method of moments (MoM); Multilevel fast multipole algorithm (MLFMA)

Indexed keywords

ALGORITHMS; CONVOLUTION; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; LITHOGRAPHY; METHOD OF MOMENTS;

FAST REAL TIME CONVOLUTION; MULTILEVEL FAST MULTIPOLE ALGORITHM (MLFMA);

INTEGRATED CIRCUITS;

EID: 24644488919     PISSN: 15213323     EISSN: None     Source Type: Journal    
DOI: 10.1109/TADVP.2005.848665     Document Type: Review

References (82)

1. International Roadmap Committee and ITWGs, "International Roadmap for Semiconductors," SIA, design update. Tech. Rep. http://public. itrs.net/, 2000.
2. M. Kamon, S. McCormick, and K. Shepard, "Interconnect parasitic extraction in the digital IC design methodology," in IEEE/ACM Int. Conf. Computer-Aided Design, Nov. 1999, pp. 223-230.
3. A. E. Ruehli, "Equivalent circuit models for three-dimensional multiconductor systems," IEEE Trans. Microw. Theory Tech., vol. MTT-22, no. 3, pp. 216-221, Mar. 1974.
4. E. Chiprout, H. Heeb, M. S. Nakhla, and A. E. Ruehli, "Simulating 3-D retarded interconnect models using complex frequency hopping (CFH)," in Proc. IEEE/ACM Int. Conf. Computer-Aided Design, Santa Clara, CA, Nov. 1993, pp. 66-72.
5. J. R. Phillips, E. Chiprout, and D. D. Ling, "Efficient full-wave electromagnetic analysis via model-order reduction of fast integral transforms," in Proc. 33rd Design Automation Conf., Las Vegas, NV, Jun. 1990.
6. M. Kamon, N. Marques, L. M. Silveira, and J. White, "Automatic generation of accurate circuit models of 3-D interconnect," IEEE Trans. Compon., Packag., Manuf. Technol. B, vol. 21, no. 3, pp. 225-240, Aug. 1998.
7. L. T. Pillage and R. A. Rohrer, "Asymptotic waveform evaluation for timing analysis," IEEE Trans. Computer-Aided Design, vol. 9, no. 4, pp. 352-366, Apr. 1990.
8. C. L. Ratzalaff and L. T. Pillage, "RICE: rapid interconnect circuit evaluation using AWE," IEEE Trans. Computer-Aided Design, vol. 13, no. 6, pp. 763-776, Jun. 1994.
9. G. A. Baker Jr., Essentials of Padé Approximants, 1st ed. New York: Academic, 1975.
10. P. Feldmann and R. W. Freund, "Reduced-order modeling of large linear subcircuits via a block lanczos algorithm," in Proc. 32nd ACM/IEEE Design Automation Conf., San Francisco, CA, Jun. 1995, pp. 474-479.
11. L. M. Silveria, M. Kamon, and J. K. White, "Efficient reduced-order modeling of frequency-dependent coupling inductances associated with 3-D interconnects structures," in Proc. 32nd ACM/IEEE Design Automation Conf., San Francisco, CA, Jun. 1995, pp. 376-380.
12. A. Odabasioglu, M. Celik, and L. Pileggi, "PRIMA: passive reduced-order interconnect macromodeling algorithm," IEEE Trans. Computer-Aided Design, vol. 17, no. 8, pp. 645-654, Aug. 1998.
13. Z. Chen and A. Ruehli, "Time-domain scattering method using triangle impulse responses for modeling electronic packaging components," in Proc. 10th Topical Meeting Electrical Performance Electronic Packaging, Oct. 2001, pp. 51-54.
14. M. Kamon, N. Marques, Y. Massoud, L. Silveira, and J. White, "Interconnect analysis: from 3-d structures to circuit models," in Proc. 36th Design Automation Conf., New Orleans, LA, Jun. 1999, pp. 910-914.
15. M. Kamon, M. J. Tsuk, and J. White, "Fasthenry: a multipole-accelerated 3-D inductance extraction program," IEEE Trans. Microw. Theory Tech., vol. 42, no. 9, pp. 1750-1758, Sep. 1994.
16. N. Marques, M. Kamon, J. White, and L. M. Silveira, "An efficient algorithm for fast parasitic extraction and passive order reduction of 3d interconnect models," in Proc. DATE, Design Automation and Test in Europe, Feb. 1998, pp. 538-543.
17. J.-R. Li, F. Wang, and J. White, "An efficient Lyapunov equation-based approach for generating reduced-order models of interconnect," in Proc. 6th Design Automation Conf., New Orleans, LA, Jun. 1999, pp. 1-6.
18. B.-T. Lee, E. Tuncer, and D. P. Neikirk, "3-D series impedance determination using a surface ribbon method," in Proc. 4th Topical Meeting Electrical Performance Electronic Packaging, Portland, OR, Oct. 1995, pp. 220-222.
19. J. Wang, J. Tausch, and J. White, "A wide frequency range surface integral formulation for 3-D inductance and resistance extraction," in Int. Conf. Modeling Simulation Microsystems, Semiconductors, Sensors, Actuators, San Juan, Puerto Rico, Apr. 1999, pp. 168-171.
20. S. Kapur and D. E. Long, "IES3: a fast integral equation solver for efficient 3-dimensional extraction," in Proc. Int. Conf. Computer-Aided Design, 1997, pp. 448-455.
21. D. A. White and M. Stowell, "Full-wave simulation of electromagnetic coupling effects in RF and mixed-signal IC's using a time-domain finite-element method," IEEE Trans. Microw. Theory Tech., vol. 52, no. 5, pp. 1404-1413, May 2004.
22. N. Verghese, J. Schmerbeck, and D. Allstot, Simulation Techniques and Solutions for Mixed-Signal Coupling in Integrated Circuits. Norwell, MA: Kluwer, 1995.
23. B. Stanisic, N. Verghese, R. Rutenbar, L. R. Carley, and D. J. Allstot, "Addressing substrate coupling in mixed-mode ICs: simulation and power distribution synthesis," IEEE J. Solid-State Circuits, vol. 29, no. 3, pp. 226-237, Mar. 1994.
24. L. M. Silveira and N. Vargas, "Multilevel finite difference methods for the characterization of substrate coupling in deep sub-micron designs," in Integrated Circuits and Systems Symp., vol. 7, Sep. 1999, pp. 26-30.
25. R. Garhpurey and R. G. Meyer, "Modeling and analysis of substrate coupling in integrated circuits," IEEE J. Solid-State Circuits, vol. 31, no. 3, pp. 344-353, Mar. 1996.
26. J. P. Costa, M. Chou, and L. M. Silveira, "Efficient techniques for accurate modeling and simulation of substrate coupling in mixed-signal ICs," IEEE Trans. Computer-Aided Design, vol. 18, no. 5, pp. 597-607, May 1999.
27. S.-Q. Li, Y. Yu, C. H. Chan, K. F. Chan, and L. Tsang, "A sparse-matrix/canonical grid method for analyzing densely packed interconnects," IEEE Trans. Microw. Theory Tech., vol. 49, no. 7, pp. 1221-1228, Jul. 2001.
28. J. M. Jian and J. L. Volakis, "A biconjugate gradient solution for scattering by planar plates," Electromagnetics, vol. 12, pp. 105-119, 1992.
29. Y. Zhuang, K. Wu, C. Wu, and J. Litva, "A combined full-wave CG-FFT method for rigorous analysis of large microstrip antenna array," IEEE Trans. Antennas Propag., vol. 44, no. 1, pp. 102-109, Jan. 1996.
30. P. A. Macdonald and T. Itoh, "Fast simulation of microstrip structures using the fast multipole method," Int. J. Numer. Modeling, vol. 9, pp. 345-357, 1996.
31. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, "A fast integral-equation solver for electromagnetic scattering problems," in IEEE AP-S Int. Symp. Dig., vol. 1, Seattle, WA, Jun. 1994, pp. 416-419.
32. F. Ling, C.-F. Wang, and J.-M. Jin, "An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex-image method," IEEE Trans. Microw. Theory Tech., vol. 48, no. 5, pp. 832-839, May 2000.
33. J. Jere and Y. L. Le Coz, "An improved floating-random-walk algorithm for solving the multi-dielectric Dirichlet problem," IEEE Trans. Microw. Theory Tech., vol. 41, no. 2, pp. 325-329, Feb. 1993.
34. Y. L. Le Coz and R. B. Iverson, "A stochastic algorithm for high-speed capacitance extraction in integrated circuits," Solid-State Electron., vol. 35, pp. 1005-1012, 1992.
35. G. M. Royer, "A Monte Carlo procedure for potential theory of problems," IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 10, pp. 813-818, Oct. 1971.
36. A. Haji-Sheikh and E. M. Sparrow, "The floating random walk and its application to Monte Carlo solutions of heat equations," J. SIAM Appl. Math., vol. 14, no. 2, pp. 370-389, Mar. 1966.
37. A. Haji-Sheikh and E. M. Sparrow, "The solution of heat condition problems by probability methods," J. Heat Transfer, Trans. ASME, ser. C, vol. 89, no. 2, pp. 121-131, May 1967.
38. M. D. R. Beasley, J. H. Pickles, G. d'Amico, L. Beretta, M. Fanelli, G. Giuseppetti, A. di. Monaco, G. Gallet, J. P. Gregoire, and M. Morin, "Comparative study of three methods for computing electric fields," Proc. Inst. Elec. Eng., vol. 126, no. 1, pp. 126-134, Jan. 1979.
39. W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Norwood, MA: Axtech House, 2001.
40. C. C. Lu and W. C. Chew, "A multilevel algorithm for solving a boundary integral equation of wave scattering," Micro. Opt. Tech. Lett., vol. 7, no. 10, pp. 466-470, Jul. 1994.
41. J. M. Song and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Micro. Opt. Tech. Lett., vol. 10, no. 1, pp. 14-19, Sep. 1995.
42. A. A. Ergin, B. Shanker, and E. Michielssen, "Fast evaluation of transient wave fields using diagonal translation operators," J. Comp. Phys., vol. 146, pp. 157-180, 1998.
43. A. A. Ergin, B. Shanker, and E. Michielssen, "The plane wave time domain algorithm for the fast analysis of transient wave phenomena," IEEE Antennas Propag. Mag., vol. 41, no. 4, pp. 39-52, Aug. 1999.
44. J. S. Zhao and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," IEEE Trans. Antennas Propag., vol. 48, pp. 1635-1645, Oct. 2000.
45. R. F. Harrington, Field Computation by Moment Method. New York: Macmillan, 1968. Reprinted: Krieger Publ., Malabar, FL, 1982.
46. D. R. Wilton and A. Glisson, "On improving the electric field integral equation at low frequencies," in URSI Radio Science Meeting Dig., Jun. 1981, p. 24.
47. E. Arvas, R. F. Harrington, and J. R. Mautz, "Radiation and scattering from electrically small conducting bodies of arbitrary shape," IEEE Trans. Antennas Propag., vol. 34, no. 1, pp. 66-77, Jan. 1986.
48. S. Velamparambil, W. C. Chew, and J. M. Song, "10 Million unknowns: is it that big?," IEEE Antennas Propag. Mag., vol. 45, no. 2, pp. 43-58, Apr. 2003.
49. M. L. Hastriter, "A study of MLFMA for large-scale scattering problems," Ph.D. dissertation, Dept. Electrical and Computer Engineering, Univ. Illinois, Urbana, IL, Jun. 2003.
50. L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," J. Comp. Phys., vol. 73, pp. 325-348, 1987.
51. W. T. Rankin and J. A. Board, "A portable distributed implementation of the parallel multipole tree algorithm," in IEEE Int. Symp. High Perf. Distr. Comput., Aug. 1995, pp. 17-22.
52. L. Ying, G. Biros, D. Zorin, and H. Langston, "A new parallel kernel-independent fast multipole method," in The SCXY Conf. Series, Nov. 2003, pp. 1-16.
53. Y. H. Chu and W. C. Chew, "Large Scale Computation of Electrically Small Structures Using Surface Integral Equation Method," Micro. Opt. Tech. Lett., submitted for publication.
54. J. E. Schutt-Ainé, "High-frequency characterization of twisted-pair cables," IEEE Trans. Comm., vol. 49, no. 4, pp. 598-601, Apr. 2001.
55. V. Rokhlin, "Rapid solution of integral equations of scattering theory in two dimensions," J. Comput. Phys., vol. 86, pp. 414-439, 1990.
56. A. Brandt, "Multilevel computations of integral transforms and particle interactions with oscillatory kernels," Comp. Phys. Comm., vol. 65, pp. 24-38, 1991.
57. R. Coifman, V. Rokhlin, and S. Wandzura, "The fast multipole method: a pedestrian prescription," IEEE Antennas Propag. Mag., vol. 35, no. 3, pp. 7-12, Jun. 1993.
58. E. Darve, "The fast multipole method: numerical implementation," J. Comput Phys., vol. 160, no. 1, pp. 195-240, 2000.
59. B. Hu and W. C. Chew, "Fast inhomogeneous plane wave algorithm for multi-layered medium problems," in Proc. IEEE AP-S Int. Symp. Dig., vol. 2, Salt Lake City, UT, Jul. 2000, pp. 606-609.
60. B. Hu and W. C. Chew, "Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium," IEEE Trans. Geosci. Remote Sens., vol. 39, no. 5, pp. 1028-1038, May 2001.
61. D. T. Borup, D. M. Sullivan, and O. P. Ghandi, "Comparison of the FFT conjugate gradient method and the finite difference time-domain method for the 2D absorption problem," IEEE Trans. Microw. Theory Tech., vol. MTT-35, no. 4, pp. 383-395, Apr. 1987.
62. P. Zwamborn and P. M. van den Berg, "The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems," IEEE Trans. Microw. Theory Tech., vol. 40, no. 9, pp. 1757-1766, Sep. 1992.
63. H. Gan and W. C. Chew, "A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems," J. Electromag. Waves Appl., vol. 9, no. 10, pp. 1339-1357, 1995.
64. J. R. Phillips and J. K. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Trans. Computer-Aided Design, vol. 16, no. 10, pp. 1059-1072, Oct. 1997.
65. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, "AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Sci., vol. 31, no. 5, pp. 1225-51, 1996.
66. L. J. Jiang and W. C. Chew, "A new capacitance extraction method," J. Electromagnetic Waves Applications, vol. 18, no. 3, pp. 287-299, Jan. 2004.
67. A. A. Appel, "An efficient program for many-body simulation," SIAM J. Sci. Stat. Comput., vol. 6, no. 1, pp. 85-103, 1985.
68. Y. C. Pan and W. C. Chew, "A fast multipole method for embedded structure in a stratified medium," Progress in Electromagnetics Research, Pier, vol. 44, pp. 1-38, 2004.
69. W. C. Chew, Waves and Fields in Inhomogeneous Media. New York: Van Nostrand, 1990. Second printing, Piscataway, NJ: IEEE Press, 1995.
70. L. J. Jiang, W. C. Chew, and Y. C. Pan, "DCIM - accelerated SMFMA for capacitance extraction," in Proc. IEEE AP-S Int. Symp. Dig., vol. 1, Columbus, OH, Jun. 2003, pp. 47-50.
71. Y. H. Zhang, T. J. Cui, W. C. Chew, and J. S. Zhao, "Magnetic field integral equation at very low frequencies," IEEE Trans. Antennas Propag., vol. 54, no. 8, pp. 1864-1871, Aug. 2003.
72. J. S. Zhan and W. C. Chew, "Three dimensional multilevel fast multipole method algorithm from static to electrodynamic," Microw. Opt. Tech. Lett., vol. 26, no. 1, pp. 43-48, Jul. 2000.
73. L. J. Jiang and W. C. Chew, "Low frequency inhomogeneous plane wave algorithm - LF-FIPWA," Microwave Opt. Tech. Lett., vol. 40, no. 2, Jan. 2004.
74. L. Greeagard, J. F. Huang, V. Rokhlin, and S. Wandzura, "Accelerating fast multipole methods for the Helmholtz equation at low frequencies," IEEE Comput. Sci. Eng. Mag., vol. 5, pp. 32-38, Jul-Sep. 1998.
75. P. J. Restle, A. E. Ruehli, S. G. Walker, and G. Papadopoulos, "Full-wave PEEC time-domain method for the modeling of on-chip interconnects," IEEE Trans. Computer-Aided Design, vol. 20, no. 7, pp. 877-887, Jul. 2001.
76. A. Ruehli, J. Esch, J. S. Zhao, and W. C. Chew, "Solution of large differential signal problem using two different integral equation based methods," in Proc. IEEE EMC Int. Symp., vol. 2, Montreal, QC, Canada, Aug. 2001, pp. 815-820.
77. L. W. Liebmann, "Layout impact of resolution enhancement techniques: impediment or opportunity," in Proc. Int. Symp. Physical Design, Monterey, CA, Apr. 2003, pp. 110-117.
78. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithography, Microfabrication, and Microsystems, vol. 1, no. 1, p. 13, 2002.
79. I. T. Chiang and W. C. Chew, "Fast real-time convolution algorithm for transients of nonlinearly-terminated microwave multiport circuits," Microw. Opt. Tech. Lett., vol. 39, no. 4, pp. 280-282, Nov. 2003.
80. E. Hairer, C. Lubich, andM. Schliche, "Fast numerical solution of nonlinear Volterra convolution equations," SIAM J. Sci. Stat. Comput., vol. 6, no. 3, pp. 532-541, 1985.
81. I. T. Chiang and W. C. Chew, "Fast real-time convolution algorithm for microwave multiport networks with nonlinear terminations," IEEE Trans. Circuits Syst., vol. 52, no. 7, pp. 370-375, Jul. 2005.
82. J. S. Zhao and W. C. Chew, "Low-frequency MLFMA algorithm for simulation of some complex structures," in Proc. Int. Conf. Electromagnetics Advanced Applications, Torino, Italy, Sep. 10-14, 2001, pp. 117-120.