With device feature size continuing to decrease and 3D IC integration continuing to mature, high-density, high-speed/high-frequency IC functionality integration is making significant strides forward. The opportunities made available by such integration cannot be fully exploited without addressing effectively the reliability challenges resulting from such integration. More specifically, in addition to the reduced device reliability and increased device parameter uncertainty associated with the sub-45 nm technology nodes, the electromagnetic interference (EMI) between densely integrated components and circuits stands out as a major hurdle in robust mixed-signal IC design. While integration complexity is one of the major obstacles in the use of electromagnetic computer-aided design (EM-CAD) tools for comprehending EMI in the development of rules and guidelines for noise-aware, functional integration of such systems, the uncertainty in layout and operating conditions after integration looms as another hindrance of reliable functionality.

This paper presents a methodology for the efficient modeling of substrate noise coupling. A closed-form Green's function for nonuniformly doped substrates is employed with the correct singular characteristics. A novel global surface impedance matrix scheme is introduced to efficiently model nonuniformly doped wells, channel stop implants, and buried layers. Layout, device, and netlist extractors are developed so as to integrate our boundary element method (BEM) solver with commercial layout and circuit simulation tools.

We present a comprehensive methodology for the electrodynamic modeling of substrate noise coupling. A new and efficient method is introduced for the calculation of the Green's function that can accommodate arbitrary substrate doping profiles and thus facilitate substrate noise analysis using boundary element methods. In addition to a discussion of the application of the method and its validation in the context of substrate transfer resistance extraction, preliminary results from its application to frequency-dependent substrate noise modeling are presented also.

The rapid growth of the electrical modeling and analysis of the interconnect structure, both at the electronic chip and package level, can be attributed to the increasing importance of the electromagnetic properties of the interconnect circuit on the overall electrical performance of state-of-the-art very large scale integration (VLSI) systems. With switching speeds well below 1 ns in today's gigahertz processors, and VLSI circuit complexity exceeding the 100 million transistors per chip mark, power and signal distribution is characterized by multigigahertz bandwidth pulses propagating through a tightly coupled three-dimensional wiring structure that exhibits resonant behavior at the upper part of the spectrum. Consequently, in addition to the inductive and capacitive coupling, present between adjacent wires across the entire frequency bandwidth, distributed electromagnetic effects, manifested as interconnect-induced delay, reflection, radiation, and long-range nonlocal coupling, become prominent at high frequencies, with a decisive impact of overall system performance. The electromagnetic nature of such high-frequency effects, combined with the geometric complexity of the interconnect structure, make the electrical design of today's performance-driven systems extremely challenging. Its success is heavily dependent on the availability of sophisticated electromagnetic modeling methodologies and computer-aided design tools. This paper presents an overview of the different approaches employed today for the development of an electromagnetic modeling and simulation framework that can effectively tackle the complexity of the interconnect circuit and facilitate its design. In addition to identifying the current state of the art, an assessment is given of the challenges that lie ahead in the signal integrity-driven electrical design of tomorrow's performance- and/or portability-driven, multifunctional ULSI systems.

A methodology is presented for the simulation of electromagnetic noise interactions in packaged low-power electronics using circuit-based models. The availability of such a methodology provides for a unified approach to the modeling of crosstalk, simultaneous switching noise, as well as all other types of noise interactions that impact signal integrity and component/system internal and external electromagnetic compatibility, using a simulation environment that is very compatible with existing circuit simulators such as SPICE. Illustrative examples from noise interactions in mixed-signal analog/digital circuits are used to demonstrate the unique capabilities of the proposed electromagnetic modeling methodology.

A mathematical model for lossy, multiconductor transmission lines is introduced to facilitate the efficient application of Krylov subspace order-reduction techniques to the analysis of linear networks with transmission line systems. The model is based on the use of Chebyshev polynomial expansions for the approximation of the spatial variation of the transmission-line voltages and currents. The exponential convergence of Chebyshev expansions, combined with a simple collocation procedure, leads to a low-order matrix representation of the transmission line equations with matrix coefficients that are first polynomials in the Laplace variable s, and in which terminal transmission-line voltages and currents appear explicitly. Thus, the resulting low-order model is compatible with both Krylov subspace order-reduction methods (such as the Lanczos and the Arnoldi processes) and the modified nodal analysis formalism. The accuracy and efficiency of the proposed model, as well as its compatibility with Krylov subspace order reduction, are demonstrated through its application to the numerical simulation of several interconnect circuits.

Although numerous methods have been proposed for interconnect simulation, no single model exists for all kind of transmission line problems. This paper presents a new, single, general dispersive coupled uniform/nonuniform transmission line model which can be used for interconnect simulation in SPICE. The mathematical model is based on the use of Chebyshev polynomials for the representation of the spatial variation of the transmission-line voltages and currents. A simple collocation procedure is used to obtain a matrix representation of the transmission line equations with matrix coefficients that are first polynomials in s, and in which terminal transmission-line voltages and currents appear explicitly. Thus, the model is compatible with both the SPICE's numerical integration algorithm and the modified nodal analysis formalism.

The authors explore the use of S-parameter-based network techniques for the analysis of coupled, multiconductor, high-speed analog and digital integrated circuit interconnects. S-parameter-based computer-aided design (CAD) techniques, widely used in microwave network analysis, provide a powerful framework for the analysis of analog and digital integrated circuit interconnect systems. The specific additions to the existing S-parameter network analysis framework developed provide for multiport interconnect capabilities and for the use of multiconductor S-parameters derived from three categories of input parameters: (1) lossy quasi-static R,L,C and G; (2) lossy frequency-dependent (dispersive) R,L,C,G; and (3) the propagation constants, characteristic impedance, and conductor eigencurrents, derived from full-wave electromagnetic analysis. Results are compared with computed simulations and experimental measurements.>

The authors present techniques for the analysis of signal propagation in the interconnections used in VLSI systems. The propagation is modelled by coupled transmission lines which include losses. For conductors whose thickness is small compared to the skin depth over the principal spectrum of the pulse being propagated, the losses can be treated as frequency-independent; otherwise, the losses must be calculated as a function of frequency. It was observed that the inductance may be approximately treated as constant, but the resistance variations in frequency may be significant. A semi-analytical method for computing the transients in lossy lines serves as the basis for the simulation of nonuniform lines.>