Title :
A new efficient method for modeling dense via arrays with 1D discretization in 2D method of moment and group T matrix
Author :
Xin Chang ; Leung Tsang
Author_Institution :
Dept. of Electr. Eng., Univ. of Washington, Seattle, WA, USA
Abstract :
In this paper, a new efficient methodology is used to model dense via arrays in 3D integrated circuit and package system, which also can include the layout of multiple vias sharing the same antipad. In order to accurately calculate all the effects of high order waveguide modes and azimuthal modes for complete signal integrity analysis of multiple closely spaced vias, we make use of transformation that converts the surface integration of magnetic surface currents into 1-dimensional line integration of surface charges on the vias and on the ground plane. We also use group T matrix to represent a group of vias to account for the scattering among different groups of vias. Numerical results illustrate physics that, after including high order mode effects using 1D line integration and group T matrix, the new method has great accuracy and efficiency for modeling multiple closely spaced vertical vias.
Keywords :
integrated circuit layout; integrated circuit modelling; integrated circuit packaging; matrix algebra; method of moments; surface charging; three-dimensional integrated circuits; waveguides; 1D discretization; 1D line integration; 2D method of moment; 3D integrated circuit; azimuthal modes; dense via array modelling; ground plane; group T matrix; high order waveguide modes; integrated circuit package system; magnetic surface current surface integration; multiple closely spaced vias; one-dimensional line integration; signal integrity analysis; surface charges; Equations; Insertion loss; Mathematical model; Moment methods; Scattering; Surface waves; Transmission line matrix methods; Foldy-Lax equations; T-matrix; multiple scattering; signal integrity; vias;
Conference_Titel :
Electrical Performance of Electronic Packaging and Systems (EPEPS), 2012 IEEE 21st Conference on
Conference_Location :
Tempe, AZ
Print_ISBN :
978-1-4673-2539-4
Electronic_ISBN :
978-1-4673-2537-0
DOI :
10.1109/EPEPS.2012.6457868