Efficient computation of localized fields for through silicon via modeling up to 500 GHz

Journal
IEEE transactions on components, packaging and manufacturing technology  
Volume
5
Issue
12
Start Page
1793
End Page
1801
Article Number
7329973
Citation
IEEE Transactions on Components, Packaging and Manufacturing Technology 12 (5): 7329973, 1793-1801 (2015-12-01)
Publisher DOI
10.1109/TCPMT.2015.2490601
Scopus ID
2-s2.0-84947969554
Publisher
IEEE
This paper presents methods for the modeling of the localized (near) fields of vertical interconnects in silicon interposers and the applications of these methods for the efficient computation of the electromagnetic properties of through silicon via structures. The localized fields are due to the mode conversions of the coaxial-to-radial waveguide junctions present in these structures. Because exact analytical techniques exist only for the homogeneously filled junction, an efficient numerical technique is proposed in this paper for the modeling of the inhomogeneous cases. This technique provides accurate results in the form of network parameters with three ports, which can be applied, e.g., in the framework of the physics-based via models. The finite-difference frequency domain method for the case of rotational symmetry is adapted to variable grid distances along the axial and radial coordinates, and interface conditions for the inhomogeneous filling of silicon and electrically isolating silicon dioxide are implemented. The method is validated with full-wave results from finite-element simulations and with the results from the published analytical methods that are adapted to the layered structures. The main focus is in the modeling for signal integrity analysis from the frequencies where the skin effect is well developed at about 100 MHz up to 100 GHz. Nevertheless, good agreement with the results from finite-element simulations up to 500 GHz is obtained for several relevant example structures, and a speedup of at least two orders compared with the finite-element simulations is achieved.
Subjects
3-D integration
Finite-difference frequency domain (FDFD)
Inhomogeneous substrate
Physics-based via (PBV) model
Radial waveguide
Rotational symmetry
Signal integrity (SI)
Through silicon via (TSV)
DDC Class
600: Technik