Delay Extraction Based Equivalent Elmore Model For RLC On-Chip Interconnects

As feature sizes for VLSI technology is shrinking, associated with higher operating frequency, signal integrity analysis of on-chip interconnects has become a real challenge for circuit designers. For this purpose, computer-aided-design (CAD) tools are necessary to simulate signal propagation of on-chip interconnects which has been an active area for research. Although SPICE models exist which can accurately predict signal degradation of interconnects, they are computationally expensive. As a result, more effective and analytic models for interconnects are required to capture the response at the output of high speed VLSI circuits. This thesis contributes to the development of efficient and closed form solution models for signal integrity analysis of on-chip interconnects. The proposed model uses a delay extraction algorithm to improve the accuracy of two-pole Elmore based models used in the analysis of on-chip distributed RLC interconnects. In the proposed scheme, the time of fight signal delay is extracted without increasing the number of poles or affecting the stability of the transfer function. This algorithm is used for both unit step and ramp inputs. From the delay rational approximation of the transfer function, analytic fitted expressions are obtained for the 50% delay and rise time for unit step input. The proposed algorithm is tested on point to point interconnections and tree structure networks. Numerical examples illustrate improved 50% delay and rise time estimates when compared to traditional Elmore based two-pole models

Modeling and Analysis of Noise and Interconnects for On-Chip Communication Link Design

This thesis considers modeling and analysis of noise and interconnects in onchip communication. Besides transistor count and speed, the capabilities of a modern design are often limited by on-chip communication links. These links typically consist of multiple interconnects that run parallel to each other for long distances between functional or memory blocks. Due to the scaling of technology, the interconnects have considerable electrical parasitics that affect their performance, power dissipation and signal integrity. Furthermore, because of electromagnetic coupling, the interconnects in the link need to be considered as an interacting group instead of as isolated signal paths. There is a need for accurate and computationally effective models in the early stages of the chip design process to assess or optimize issues affecting these interconnects. For this purpose, a set of analytical models is developed for on-chip data links in this thesis. First, a model is proposed for modeling crosstalk and intersymbol interference. The model takes into account the effects of inductance, initial states and bit sequences. Intersymbol interference is shown to affect crosstalk voltage and propagation delay depending on bus throughput and the amount of inductance. Next, a model is proposed for the switching current of a coupled bus. The model is combined with an existing model to evaluate power supply noise. The model is then applied to reduce both functional crosstalk and power supply noise caused by a bus as a trade-off with time. The proposed reduction method is shown to be effective in reducing long-range crosstalk noise. The effects of process variation on encoded signaling are then modeled. In encoded signaling, the input signals to a bus are encoded using additional signaling circuitry. The proposed model includes variation in both the signaling circuitry and in the wires to calculate the total delay variation of a bus. The model is applied to study level-encoded dual-rail and 1-of-4 signaling. In addition to regular voltage-mode and encoded voltage-mode signaling, current-mode signaling is a promising technique for global communication. A model for energy dissipation in RLC current-mode signaling is proposed in the thesis. The energy is derived separately for the driver, wire and receiver termination.Siirretty Doriast

Investigation of Interconnect and Device Designs for Emerging Post-MOSFET and Beyond Silicon Technologies

Title from PDF of title page viewed May 31, 2017Dissertation advisor: Masud H. ChowdhuryVitaIncludes bibliographical references (pages 94-108)Thesis (Ph.D.)--School of Computing and Engineering and Department of Physics and Astronomy. University of Missouri--Kansas City, 2016The integrated circuit industry has been pursuing Moore’s curve down to deep nanoscale dimensions that would lead to the anticipated delivery of 100 billion transistors on a 300 mm² die operating below 1V supply in the next 5-10 years. However, the grand challenge is to reliably and efficiently take the full advantage of the unprecedented computing power offered by the billions of nanoscale transistors on a single chip. To mitigate this challenge, the limitations of both the interconnecting wires and semiconductor devices in integrated circuits have to be addressed. At the interconnect level, the major challenge in current high density integrated circuit is the electromagnetic and electrostatic impacts in the signal carrying lines. Addressing these problems require better analysis of interconnect resistance, inductance, and capacitance. Therefore, this dissertation has proposed a new delay model and analyzed the time-domain output response of complex poles, real poles, and double poles for resistance-inductance capacitance interconnect network based on a second order approximate transfer function. Both analytical models and simulation results show that the real poles model is much faster than the complex poles model, and achieves significantly higher accuracy in order to characterize the overshoot and undershoot of the output responses. On the other hand, the semiconductor industry is anticipating that within a decade silicon devices will be unable to meet the demands at nanoscale due to dimension and material scaling. Recently, molybdenum disulfide (MoS₂) has emerged as a new super material to replace silicon in future semiconductor devices. Besides, conventional field effect transistor technology is also reaching its thermodynamic limit. Breaking this thermal and physical limit requires adoption of new devices based on tunneling mechanism. Keeping the above mentioned trends, this dissertation also proposed a multilayer MoS₂ channel-based tunneling transistor and identifies the fundamental parameters and design specifications that need to be optimized in order to achieve higher ON-currents. A simple analytical model of the proposed device is derived by solving the time-independent Schrodinger equation. It is analytically proven that the proposed device can offer an ON-current of 80 A/m, a subthreshold swing (S) of 9.12 mV/decade, and a / ratio of 10¹².Introduction -- Previous models on interconnect designs -- Proposed delay model for interconnect design -- Investigation of tunneling for field effect transistor -- Study of molybdenum disulfide for FET applications -- Proposed molybdenum disulfide based tunnel transistor -- Conclusion -- Appendix A. Derivation of time delay model -- Appendix B. Derivation of tunneling current model Appendix C. Derivation of subthreshold swing mode

Analytic Delay Model of RLC Interconnects using Numerical Inversion of the Laplace Transform

Signal integrity analysis for on-chip interconnect becomes increasingly important in high-speed designs. SPICE, a conventional circuit simulator, can provide accurate prediction for interconnects, however, using SPICE is extremely computationally expensive. On the other hand, explicit moment matching technique can produce unstable poles for highly accurate approximations and implicit moment matching technique can obtain more accurate approximations at the expense of computational complexity. This thesis presents an analytic model to efficiently estimate the signal delays of RLC on-chip interconnects. It uses the numerical inversion of Laplace transform (NILT) to obtain time function, suitable for transient analysis. Since the integration formula of the NILT is numerically stable for higher order approximations, the developed algorithm provides a mechanism to increase the accuracy for delay estimation. Numerical examples are implemented and compared with HSPICE, two-pole model and Passive Reduced-Order Interconnect Macromodeling Algorithm (PRIMA) to illustrate the efficiency and validity of the proposed work

Transient simulation of complex electronic circuits and systems operating at ultra high frequencies

The electronics industry worldwide faces increasingly difficult challenges in a bid to produce ultra-fast, reliable and inexpensive electronic devices. Electronic manufacturers rely on the Electronic Design Automation (EDA) industry to produce consistent Computer A id e d Design (CAD) simulation tools that w ill enable the design of new high-performance integrated circuits (IC), the key component of a modem electronic device. However, the continuing trend towards increasing operational frequencies and shrinking device sizes raises the question of the capability of existing circuit simulators to accurately and efficiently estimate circuit behaviour. The principle objective of this thesis is to advance the state-of-art in the transient simulation of complex electronic circuits and systems operating at ultra high frequencies. Given a set of excitations and initial conditions, the research problem involves the determination of the transient response o f a high-frequency complex electronic system consisting of linear (interconnects) and non-linear (discrete elements) parts with greatly improved efficien cy compared to existing methods and with the potential for very high accuracy in a way that permits an effective trade-off between accuracy and computational complexity. High-frequency interconnect effects are a major cause of the signal degradation encountered b y a signal propagating through linear interconnect networks in the modem IC. Therefore, the development of an interconnect model that can accurately and efficiently take into account frequency-dependent parameters of modem non-uniform interconnect is of paramount importance for state-of-art circuit simulators. Analytical models and models based on a set of tabulated data are investigated in this thesis. Two novel, h igh ly accurate and efficient interconnect simulation techniques are developed. These techniques combine model order reduction methods with either an analytical resonant model or an interconnect model generated from frequency-dependent sparameters derived from measurements or rigorous full-wave simulation. The latter part o f the thesis is concerned with envelope simulation. The complex mixture of profoundly different analog/digital parts in a modern IC gives rise to multitime signals, where a fast changing signal arising from the digital section is modulated by a slower-changing envelope signal related to the analog part. A transient analysis of such a circuit is in general very time-consuming. Therefore, specialised methods that take into account the multi-time nature o f the signal are required. To address this issue, a novel envelope simulation technique is developed. This technique combines a wavelet-based collocation method with a multi-time approach to result in a novel simulation technique that enables the desired trade-off between the required accuracy and computational efficiency in a simple and intuitive way. Furthermore, this new technique has the potential to greatly reduce the overall design cycle

Addressing Computational Complexity of Electromagnetic Systems Using Parameterized Model Order Reduction

As operating frequencies increase, full wave numerical techniques such as the finite element method (FEM) become necessary for the analysis of high-frequency and microwave circuit structures. However, the FEM formulation of microwave circuits often results in very large systems of equations which are computationally expensive to solve. The objective of this thesis is to develop new parameterized model order eduction (MOR) techniques to minimize the computational complexity of microwave circuits. MOR techniques provide a mechanism to generate reduced order models from the detailed description of the original FEM formulation. The following contributions are made in this thesis: 1. The first project deals with developing a parameterized model order reduction to solve eigenvalue equations of electromagnetic structures that are discretized by using FEM. The proposed algorithm uses a multidimensional subspace method based on modified perturbation theory and singular-value decomposition to perform reduction directly on the finite element eigenvalue equations. This procedure generates parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction when design parameters are changed. This provides significant computational savings when compared to previous eigenvalue MOR techniques, since a new reduced order model is not required each time a design parameter is changed. 2. Implicit moment match techniques such as the Arnoldi algorithm are often used to improve the accuracy of the reduced order model. However, the traditional Arnoldi algorithm is only applicable to first order linear systems and can not directly include arbitrary functions of frequency due to material and boundary conditions. In this work, an efficient algorithm to create parametric reduced order models of distributed electromagnetic systems that have arbitrary functions of frequency (due to material properties, boundary conditions, and delay elements) and design parameters. The proposed method is based on a multi-order Arnoldi algorithm used to implicitly calculate the moments with respect to frequency and design parameters, as well as the cross-moments. This procedure generates parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction when design parameters are changed and provides more accurate reduced order systems when compared with traditional approaches such as Modified Gram Schmidt. 3. This project develops an efficient technique to calculate sensitivities of microwave structures with respect to network design parameters. The proposed algorithm uses a parametric reduced order model to solve the original network and an adjoint variable method to calculate sensitivities. Important features of the proposed method are 1) that the solution of the original network as well as sensitivities with respect to any parameter is obtained from the solution of the reduced order model, and 2) a new reduced order model is not required each time design parameters are varied

Modeling for the Computer-Aided Design of Long Interconnects

L'abstract è presente nell'allegato / the abstract is in the attachmen