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Title: Full wave electromagnetic analysis of vias and interconnect structures
Other Titles: Dao kong he hu lian jie gou de dian ci chang quan bo fen xi
Authors: Lai, Kin Lun (黎健倫)
Department: Dept. of Electronic Engineering
Degree: Master of Philosophy
Issue Date: 2004
Publisher: City University of Hong Kong
Subjects: Electromagnetism -- Mathematical models
Microelectronic packaging -- Mathematical models
Notes: CityU Call Number: TK7874.L24 2004
Includes bibliographical references
Thesis (M.Phil.)--City University of Hong Kong, 2004
iii, [98] leaves : ill. ; 30 cm.
Type: Thesis
Abstract: The electronic packaging devices for high-speed digital circuits becomes more complicated with increasing functionalities. It leads to the fact that the complexity of the packages grows tremendously. It is useful to implement a computational analysis for these packaging technologies. Many commercial software toolkits are developed to solve for these problems. However, results are not perfect and computational time is slow. A lot of achievements obtained accurate results in this kind of aspect. But the computational speed is still not acceptable. We are going to present faster and robust approaches to speed up the process. In the first part of my study, we focus on the critical concern about the difficulties in evaluating the surface electric fields of spatial domain Green’s functions for multi-layered medium, where the source and observation points are located on the interface between two different dielectric substrates. We adopt a Green’s function calculation method and apply to the interconnect structures with multi-via coupling problems. In the past, there are many fast calculation approaches for particular range of variations. We present two complementary and robust methods that solve for the multi-layered medium Green’s functions with lossless or lossy dielectric materials over a wide range of frequencies and layer thickness. The first approach involves the use of Fast Fourier Transform (FFT) based on the half-space extraction approach, which is able to compute different source-to-field distances simultaneously. It is used for solving moderate layer thickness of total dielectric substrates, with d>0.05λo. For thin layer thickness, 0<d≤0.05λo, another approach involves the vertical branch cut contribution with the addition of surface wave pole extraction is adopted. We compute for 200 different ρ from 0.01 to 10 wavelengths and the CPU time is less than 30 seconds at each frequency for both methods. The accuracy of this technique is verified by comparing the Sommerfeld integration. For the second part of the work, a full-wave modeling of multi-layered interconnect problem with multi-via structures on the actual layout of the printed circuit boards (PCBs). The microstrip problem is decomposed into exterior problem and interior problem, where the exterior problem is realized by the actual geometrical configuration of the exterior structure with dielectrics between the traces and reference ground plane. By means of the RWG basis functions and the Galerkin’s testing technique, the combined EFIE-MPIE formulations are expressed and solved by MoM matrix using our Green’s function calculation methods. The interior problem for thousands of cylindrical vias between planar waveguides is formulated using Foldy-Lax multiple scattering equation. A sparse-matrix canonical-grid (SMCG) method with a pre-conditioned scheme is adopted as the fast matrix solver. For exterior problem, the computation time required for solving the scattering matrix for a given geometry of 200 unknowns takes about 3.2 minutes for each frequency using Matlab 6.1. Numerical simulations are illustrated for physical problems such as differential signaling and comparison with commercial modeling tool such as HFSS and IE3D. By using our analysis, it is reasonable to simulate large-scale interconnect packages with a much shorter computational time and a more accurate result.
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