Fast Capacitance Extraction in Multilayer, Conformal and Embedded Dielectric using Hybrid Boundary Element Method

In modern VLSI circuits, metal conductors are separated by multiple planar, conformal or embedded dielectric media. Previous algorithms based on Boundary Element Method (BEM) are inefficient to extract interconnect capacitance due to the complex dielectric structures. In this paper, we present a new algorithm that combines multilayer Green's function with the equivalent charge method to efficiently deal with the complex dielectrics. The multilayer Green's function is efficient to model layered dielectric media, while the equivalent charge method is powerful to model non-planar complex dielectric. Our method can also model ground plane and reflective boundary wall. From experimental results, the new method is significantly faster than previous methods in realistic conditions, i.e., 70X speedup and 99% memory saving compared with FastCap and 2X speedup and 80% memory saving compared with PHiCap for complex dielectric structure with similar accuracy.

[1]  Jacob K. White,et al.  Algorithms in FastImp: a fast and wideband impedance extraction program for complicated 3-D geometries , 2003, Proceedings 2003. Design Automation Conference (IEEE Cat. No.03CH37451).

[2]  K. Michalski,et al.  Multilayered media Green's functions in integral equation formulations , 1997 .

[3]  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..

[4]  Weiping Shi,et al.  A fast hierarchical algorithm for three-dimensional capacitanceextraction , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[5]  Lawrence T. Pileggi,et al.  Electromagnetic parasitic extraction via a multipole method with hierarchical refinement , 1999, 1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051).

[6]  Tapan K. Sarkar,et al.  The Electrostatic Field of Conducting Bodies in Multiple Dielectric Media , 1984 .

[7]  Jacob K. White,et al.  A multiscale method for fast capacitance extraction , 1999, DAC '99.

[8]  Jacob K. White,et al.  Multipole-accelerated 3-D capacitance extraction algorithms for structures with conformal dielectrics , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

[9]  Junfa Mao,et al.  Parameter extraction for on-chip interconnects by double-image Green's function method combined with hierarchical algorithm , 2005, IEEE Transactions on Microwave Theory and Techniques.

[10]  T. Sarkar,et al.  Multiconductor Transmission Lines In Multilayered Dielectric Media , 1984 .

[11]  Weiping Shi,et al.  Sparse transformations and preconditioners for hierarchical 3-D capacitance extraction with multiple dielectrics , 2004, Proceedings. 41st Design Automation Conference, 2004..

[12]  Raymond Crampagne,et al.  A Simple Method for Determining the Green's Function for a Large Class of MIC Lines Having Multilayered Dielectric Structures , 1978 .