Statistical circuit simulations - from ‘atomistic’ compact models to statistical standard cell characterisation

This thesis describes the development and application of statistical circuit simulation methodologies to analyse digital circuits subject to intrinsic parameter fluctuations. The specific nature of intrinsic parameter fluctuations are discussed, and we explain the crucial importance to the semiconductor industry of developing design tools which accurately account for their effects. Current work in the area is reviewed, and three important factors are made clear: any statistical circuit simulation methodology must be based on physically correct, predictive models of device variability; the statistical compact models describing device operation must be characterised for accurate transient analysis of circuits; analysis must be carried out on realistic circuit components. Improving on previous efforts in the field, we posit a statistical circuit simulation methodology which accounts for all three of these factors. The established 3-D Glasgow atomistic simulator is employed to predict electrical characteristics for devices aimed at digital circuit applications, with gate lengths from 35 nm to 13 nm. Using these electrical characteristics, extraction of BSIM4 compact models is carried out and their accuracy in performing transient analysis using SPICE is validated against well characterised mixed-mode TCAD simulation results for 35 nm devices. Static d.c. simulations are performed to test the methodology, and a useful analytic model to predict hard logic fault limitations on CMOS supply voltage scaling is derived as part of this work. Using our toolset, the effect of statistical variability introduced by random discrete dopants on the dynamic behaviour of inverters is studied in detail. As devices scaled, dynamic noise margin variation of an inverter is increased and higher output load or input slew rate improves the noise margins and its variation. Intrinsic delay variation based on CV/I delay metric is also compared using ION and IEFF definitions where the best estimate is obtained when considering ION and input transition time variations. Critical delay distribution of a path is also investigated where it is shown non-Gaussian. Finally, the impact of the cell input slew rate definition on the accuracy of the inverter cell timing characterisation in NLDM format is investigated

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

Cell Library Creation using ALF

The design of Integrated Circuit (ASICs and SoCs) typically relies on the availability of a library consisting of predefined components called technology cells. Silicon vendors use proprietary formats to describe technology cells and macro modules in conjunction with numerous translators to feed technology library data to Electronic Design Automation (EDA) tools. Multiple grammar formats are used to represent various aspects of the cells in the same technology library, such as behavior for simulation, timing parameters for synthesis, physical data for layout, noise parameters for signal integrity checks, etc. In addition, most of these formats are highly tool-oriented and are not grammatically consistent. In this paper we will discuss the newly adopted IEEE 1603-2003 Advanced Library Format (ALF) standard which eliminates such drawbacks. This standard defines a grammar for accurate and comprehensive modeling of technology libraries and macro modules in order to bridge the growing gap between new design rules and the analysis required for complex high-end IC implementations

Novel Multicarrier Memory Channel Architecture Using Microwave Interconnects: Alleviating the Memory Wall

abstract: The increase in computing power has simultaneously increased the demand for input/output (I/O) bandwidth. Unfortunately, the speed of I/O and memory interconnects have not kept pace. Thus, processor-based systems are I/O and interconnect limited. The memory aggregated bandwidth is not scaling fast enough to keep up with increasing bandwidth demands. The term "memory wall" has been coined to describe this phenomenon. A new memory bus concept that has the potential to push double data rate (DDR) memory speed to 30 Gbit/s is presented. We propose to map the conventional DDR bus to a microwave link using a multicarrier frequency division multiplexing scheme. The memory bus is formed using a microwave signal carried within a waveguide. We call this approach multicarrier memory channel architecture (MCMCA). In MCMCA, each memory signal is modulated onto an RF carrier using 64-QAM format or higher. The carriers are then routed using substrate integrated waveguide (SIW) interconnects. At the receiver, the memory signals are demodulated and then delivered to SDRAM devices. We pioneered the usage of SIW as memory channel interconnects and demonstrated that it alleviates the memory bandwidth bottleneck. We demonstrated SIW performance superiority over conventional transmission line in immunity to cross-talk and electromagnetic interference. We developed a methodology based on design of experiment (DOE) and response surface method techniques that optimizes the design of SIW interconnects and minimizes its performance fluctuations under material and manufacturing variations. Along with using SIW, we implemented a multicarrier architecture which enabled the aggregated DDR bandwidth to reach 30 Gbit/s. We developed an end-to-end system model in Simulink and demonstrated the MCMCA performance for ultra-high throughput memory channel. Experimental characterization of the new channel shows that by using judicious frequency division multiplexing, as few as one SIW interconnect is sufficient to transmit the 64 DDR bits. Overall aggregated bus data rate achieves 240 GBytes/s data transfer with EVM not exceeding 2.26% and phase error of 1.07 degree or less.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Limits on Fundamental Limits to Computation

An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the last fifty years. Such Moore scaling now requires increasingly heroic efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and enrich our understanding of integrated-circuit scaling, we review fundamental limits to computation: in manufacturing, energy, physical space, design and verification effort, and algorithms. To outline what is achievable in principle and in practice, we recall how some limits were circumvented, compare loose and tight limits. We also point out that engineering difficulties encountered by emerging technologies may indicate yet-unknown limits.Comment: 15 pages, 4 figures, 1 tabl

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

Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

Thermal-Aware Networked Many-Core Systems

Advancements in IC processing technology has led to the innovation and growth happening in the consumer electronics sector and the evolution of the IT infrastructure supporting this exponential growth. One of the most difficult obstacles to this growth is the removal of large amount of heatgenerated by the processing and communicating nodes on the system. The scaling down of technology and the increase in power density is posing a direct and consequential effect on the rise in temperature. This has resulted in the increase in cooling budgets, and affects both the life-time reliability and performance of the system. Hence, reducing on-chip temperatures has become a major design concern for modern microprocessors. This dissertation addresses the thermal challenges at different levels for both 2D planer and 3D stacked systems. It proposes a self-timed thermal monitoring strategy based on the liberal use of on-chip thermal sensors. This makes use of noise variation tolerant and leakage current based thermal sensing for monitoring purposes. In order to study thermal management issues from early design stages, accurate thermal modeling and analysis at design time is essential. In this regard, spatial temperature profile of the global Cu nanowire for on-chip interconnects has been analyzed. It presents a 3D thermal model of a multicore system in order to investigate the effects of hotspots and the placement of silicon die layers, on the thermal performance of a modern ip-chip package. For a 3D stacked system, the primary design goal is to maximise the performance within the given power and thermal envelopes. Hence, a thermally efficient routing strategy for 3D NoC-Bus hybrid architectures has been proposed to mitigate on-chip temperatures by herding most of the switching activity to the die which is closer to heat sink. Finally, an exploration of various thermal-aware placement approaches for both the 2D and 3D stacked systems has been presented. Various thermal models have been developed and thermal control metrics have been extracted. An efficient thermal-aware application mapping algorithm for a 2D NoC has been presented. It has been shown that the proposed mapping algorithm reduces the effective area reeling under high temperatures when compared to the state of the art.Siirretty Doriast

Limitations and opportunities for wire length prediction in gigascale integration

Wires have become a major source of bottleneck in current VLSI designs, and wire length prediction is therefore essential to overcome these bottlenecks. Wire length prediction is broadly classified into two types: macroscopic prediction, which is the prediction of wire length distribution, and microscopic prediction, which is the prediction of individual wire lengths. The objective of this thesis is to develop a clear understanding of limitations to both macroscopic and microscopic a priori, post-placement, pre-routing wire length predictions, and thereby develop better wire length prediction models. Investigations carried out to understand the limitations to macroscopic prediction reveal that, in a given design (i) the variability of the wire length distribution increases with length and (ii) the use of Rent s rule with a constant Rent s exponent p, to calculate the terminal count of a given block size, limits the accuracy of the results from a macroscopic model. Therefore, a new model for the parameter p is developed to more accurately reflect the terminal count of a given block size in placement, and using this, a new more accurate macroscopic model is developed. In addition, a model to predict the variability is also incorporated into the macroscopic model. Studies to understand limitations to microscopic prediction reveal that (i) only a fraction of the wires in a given design are predictable, and these are mostly from shorter nets with smaller degrees and (ii) the current microscopic prediction models are built based on the assumption that a single metric could be used to accurately predict the individual length of all the wires in a design. In this thesis, an alternative microscopic model is developed for the predicting the shorter wires based on a hypothesis that there are multiple metrics that influence the length of the wires. Three different metrics are developed and fitted into a heuristic classification tree framework to provide a unified and more accurate microscopic model.Ph.D.Committee Chair: Dr. Jeff Davis; Committee Member: Dr. James D. Meindl; Committee Member: Dr. Paul Kohl; Committee Member: Dr. Scott Wills; Committee Member: Dr. Sung Kyu Li