⬇ Download Markdown  ·  ⬇ Download LaTeX  ·  ⬇ original  ·  view original

VoxCap: An FFT-Accelerated Capacitance Extractor for Voxelized

Structures

Abdulkadir C. Yucel*1 , Gokhan Karaova2 , Hakan Bagci3 , and Jacob K. White4 1 School of Electrical and Electronic Engineering, Nanyang Technological University Singapore 639798, Singapore 2 Department of Electrical and Electronics Engineering Middle East Technical University, Ankara 06800, Turkey 3 Computer, Electrical, and Mathematical Science and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal, 23955-6900, Saudi Arabia 4 Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology, Cambridge 02139, United States Capacitance extractors are of great importance for designers to obtain accurate equivalent circuit models of interconnects on chips, boards, or packages. Among a plethora of ca- pacitance extractors developed so far, those that are accelerated by fast multipole method

(FMM) (Nabors and White, IEEE Trans. Comput.-Aided Design Integr. Circuits Syst.,

(FMM) (Nabors and White, IEEE Trans. Comput.-Aided Design Integr. Circuits Syst.,
10(11), 1991, pp. 1447-1459) and precorrected-fast Fourier transform (FFT) (Phillips and
White, IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., 16(10), 1997, pp. 1059-
1072) have sustained their popularity over more than a decade. It has been shown that the is
more memory and CPU efficient than the FMM accelerated one for the electrostatic analysis
of three dimensional (3D) complex and dense interconnect structures discretized by unstruc-
tured meshes. However, many of virtual fabrication environments make use of voxelized
geometries since their use in unit process steps of the iterative design explorations is signifi-
cantly easier. In the case of a voxelized geometry, projection and interpolation operations of
the precorrected-FFT accelerated extractor becomes redundant (voxels naturally reside on
a 3D uniform grid). To this end, a efficient and accurate capacitance extractor capable of
working directly with voxelized geometries would be highly useful in design processes. Ad-
ditionally, such extractor would be straightforward to use in conjunction with the VoxHenry
inductance extractor (Yucel et.al, Progress In Electromagnetics Research Symposium, 2017)
to build simulators for electro-magneto-quasi-static and full-wave analyses of complex and
dense interconnect structures.
In this work, an FFT-accelerated capacitance extractor for voxelized structures, called Vox-
Cap, is proposed for this purpose. The VoxCap solves a first kind integral equation in charge
density induced on conductor-dielectric and dielectric-dielectric interfaces. The charge den-
sity is expanded using pulse basis functions; inserting this expansion into the integral equa-
tion and applying Galerkin testing to the resulting equation yield a matrix system in un-
known expansion coefficients. This matrix system is solved iteratively, where FFTs are used
to accelerate the matrix-vector multiplications. The accuracy and efficiency of the proposed
VoxCap will be demonstrated through its application to the capacitance extraction of various
voxelized structures including concentric spheres, parallel buses, parallel plates, comb drive,
SRAM, and vowen bus structures. In the talk, several preconditioning strategies to ensure
the rapid convergence of the matrix system’s iterative solution will be discussed.