Rigorous Electromagnetic Modeling of Conductor and Substrate Losses for High -Speed Interconnect Structures
Coperich, Karen Marie
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https://hdl.handle.net/2142/80707
Description
Title
Rigorous Electromagnetic Modeling of Conductor and Substrate Losses for High -Speed Interconnect Structures
Author(s)
Coperich, Karen Marie
Issue Date
2001
Doctoral Committee Chair(s)
Cangellaris, Andreas C.
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
This dissertation focuses on the electromagnetic modeling of planar layered interconnect structures. This broad class of transmission lines includes structures ranging from on-chip interconnects, thin film, and ceramic multichip modules to printed circuit boards. While similar, these wiring architectures vary in feature size and length, electrical material parameters, and bandwidth of operation. The electromagnetic analysis relies upon a pair of two-dimensional techniques. The analysis procedure begins with the introduction of the global surface impedance model that enables the representation of the frequency-dependent current distribution inside the conductor cross section in terms of a mathematically equivalent surface impedance relationship. In order to minimize the computational cost associated with the rigorous modeling of the skin effect, model order reduction techniques based on Krylov projections and balanced realizations are used to reduce the global surface impedance model. The reduced model is then used in an integral equation statement of the magneto-quasi-static problem in the lossy-layered background medium, the properties of which are captured by a specially developed closed-form Green's function. The numerical solution of the resulting integral statement leads to the extraction of the frequency dependent per-unit-length resistance and inductance matrices of multiline interconnect configurations embedded or shielded by lossy materials such as silicon or copper. To utilize this broadband model in time-domain analysis, a closed form rational function approximation is systematically generated. A stand-alone dispersive multiconductor transmission line simulator was devised as an alternative to time domain simulations within SPICE, both of which use the equivalent closed-form representation. Each algorithm discussed possesses unique and beneficial properties that are necessary to cumulatively predict signal integrity performance criteria with sufficient accuracy and efficiency for the specific interconnect technology of interest.
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