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

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

Interconnect Challenges and Carbon Nanotube as Interconnect in Nano VLSI Circuits

This chapter discusses about the behavior of Carbon Nanotube (CNT) different structures which can be used as interconnect in Very Large Scale (VLSI) circuits in nanoscale regime. Also interconnect challenges in VLSI circuits which lead to use CNT as interconnect instead of Cu, is reviewed. CNTs are classified into three main types including Single-walled Carbon Nanotube (SWCNT), CNT Bundle, and Multi-walled Carbon Nanotube (MWCNT). Because of extremely high quantum resistance of a SWCNT which is about 6.45 kΩ, rope or bundle of CNTs are used which consist of parallel CNTs in order to overcome the high delay time due to the high intrinsic (quantum) resistance. Also MWCNTs which consist of parallel shells, present much less delay time with respect to SWCNTs, for the application as interconnects. In this chapter, first a short discussion about interconnect challenges in VLSI circuits is presented. Then the repeater insertion technique for the delay reduction in the global interconnects will be studied. After that, the parameters and circuit model of a CNT will be discussed. Then a brief review about the different structures of CNT interconnects including CNT bundle and MWCNT will be presented. At the continuation, the time domain behavior of a CNT bundle interconnect in a driver-CNT bundle-load configuration will be discussed and analyzed. In this analysis, CNT bundle is modeled as a transmission line circuit model. At the end, a brief study of stability analysis in CNT interconnects will be presented

HIGH PERFORMANCE CLOCK DISTRIBUTION FOR HIGH-SPEED VLSI SYSTEMS

Tohoku University堀口 進課

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

Advanced modelling and design considerations for interconnects in ultra- low power digital system

PhD ThesisAs Very Large Scale Integration (VLSI) is progressing in very Deep submicron (DSM) regime without decreasing chip area, the importance of global interconnects increases but at the cost of performance and power consumption for advanced System-on- Chip (SoC)s. However, the growing complexity of interconnects behaviour presents a challenge for their adequate modelling, whereby conventional circuit theoretic approaches cannot provide sufficient accuracy. During the last decades, fractional differential calculus has been successfully applied to modelling certain classes of dynamical systems while keeping complexity of the models under acceptable bounds. For example, fractional calculus can help capturing inherent physical effects in electrical networks in a compact form, without following conventional assumptions about linearization of non-linear interconnect components. This thesis tackles the problem of interconnect modelling in its generality to simulate a wide range of interconnection configurations, its capacity to emulate irregular circuit elements and its simplicity in the form of responsible approximation. This includes modelling and analysing interconnections considering their irregular components to add more flexibility and freedom for design. The aim is to achieve the simplest adaptable model with the highest possible accuracy. Thus, the proposed model can be used for fast computer simulation of interconnection behaviour. In addition, this thesis proposes a low power circuit for driving a global interconnect at voltages close to the noise level. As a result, the proposed circuit demonstrates a promising solution to address the energy and performance issues related to scaling effects on interconnects along with soft errors that can be caused by neutron particles. The major contributions of this thesis are twofold. Firstly, in order to address Ultra-Low Power (ULP) design limitations, a novel driver scheme has been configured. This scheme uses a bootstrap circuitry which boosts the driver’s ability to drive a long interconnect with an important feedback feature in it. Hence, this approach achieves two objectives: improving performance and mitigating power consumption. Those achievements are essential in designing ULP circuits along with occupying a smaller footprint and being immune to noise, observed in this design as well. These have been verified by comparing the proposed design to the previous and traditional circuits using a simulation tool. Additionally, the boosting based approach has been shown beneficial in mitigating the effects of single event upset (SEU)s, which are known to affect DSM circuits working under low voltages. Secondly, the CMOS circuit driving a distributed RLC load has been brought in its analysis into the fractional order domain. This model will make the on-chip interconnect structure easy to adjust by including the effect of fractional orders on the interconnect timing, which has not been considered before. A second-order model for the transfer functions of the proposed general structure is derived, keeping the complexity associated with second-order models for this class of circuits at a minimum. The approach here attaches an important trait of robustness to the circuit design procedure; namely, by simply adjusting the fractional order we can avoid modifying the circuit components. This can also be used to optimise the estimation of the system’s delay for a broad range of frequencies, particularly at the beginning of the design flow, when computational speed is of paramount importance.Iraqi Ministry of Higher Education and Scientific Researc

Interconnect delay estimation models

With the continuous scaling down of very large scale integrated (VLSI) technologies and increased die size, the transistors are much smaller, and hence much faster. On the other hand, interconnects are narrower. So they are more resistive and slower in transmitting signals. This trend has led the interconnect delay to become a significant factor in determining the performance of VLSI designs. As the die size becomes larger, global interconnect length becomes longer. Thus, global interconnect delay is beginning to dominate a larger portion of the overall system performance. In order to take the impact of interconnect delay into account, it is very important to have computationally inexpensive and accurate interconnect delay models. The primary contribution of this thesis is to present two new interconnect delay models, called the Fitted Elmore Delay (FED) and the Improved Effective Capacitance Metric (IECM). The FED model is a simple, efficient and reasonably accurate interconnect performance estimation model. This model uses a curve fitting technique to approximate the accurate Hspice delay data. The functional form used in the curve fitting is derived based on the Elmore Delay (ED) model. Thus, our model has all the advantages of the Elmore Delay model. It has a closed form expression as simple as the ED model and is extremely efficient to compute. More importantly, it is significantly more accurate than the ED model. In fact, because of its striking similarity to the ED model, optimization of the delay with respect to the design parameters can be easily done. When applied to interconnect optimization techniques (i.e., wire sizing), the FED model is three to four times more accurate than the Elmore Delay model. On the other hand, like the ED model, the FED has the limitation of ignoring the resistive shielding problem. This problem occurs when the gate no longer sees the total net capacitance due to the high interconnect resistance. The Improved Effective Capacitance Metric (IECM) overcomes the resistive shielding problem. We adopt the methodology of computing the first three Taylor series coefficients of the driving-point admittance in the circuit. The IECM uses these Taylor coefficients to derive a closed form solution for the effective capacitance that captures the resistive shielding characteristics. The IECM can be implemented with similar simplicity as the Elmore Delay model. We have tested the IECM on a single-load circuit and multiple tree topologies. Experiments show that our model is significantly more accurate than other existing interconnect delay models in capturing the resistive shielding characteristics

An Efficient MRTD Model for the Analysis of Crosstalk in CMOS-Driven Coupled Cu Interconnects

This paper presents an efficient wavelet based numerical method for analyzing functional and dynamic crosstalk of CMOS driven coupled copper (Cu) interconnects known as Multi-Resolution Time Domain (MRTD),wherein, the CMOS drivers are modeled using nth-power law model. The performance of the proposed MRTD method is evaluated through recursive simulations in HSPICE environment and compared with the conventional Finite Difference Time Domain (FDTD) method at 32-nm technology node for global interconnects of length 1mm, where the computations of the proposed model and conventional FDTD are carried out using MATLAB. For different number of test cases, the proposed MRTD method gives an average error of 0.14 % and 1.9 % for peak crosstalk noise and peak noise timing, respectively, with respect to HSPICE results. Also, the dynamic crosstalk noise on victim line of the proposed MRTD method are in close agreement with those of HSPICE. The results show the dominance of the proposed MRTD method over the conventional FDT method regarding accuracy. The proposed MRTD method is also extended for three-mutuallycoupled interconnect lines for crosstalk analysis, with an average error less than 1 % when compared to that of more than 3 % using the conventional FDTD method. Moreover, for the transient analysis, the MRTD method is more time efficient than HSPICE

Selection of Voltage Thresholds for Delay Measurement

Since all physical devices have a finite non-zero responsetime, the notion of delay between the input and output logicsignals arises naturally once digital abstraction is done. Thisdelay should be positive and non-zero, since a physical devicetakes a finite amount of time to respond to the input. Defininga strictly positive delay is not a problem in the abstract domainof logic signals, since input and output ’’events‘‘ are preciselydefined. However, when the signal non-idealities are accountedfor, the notion of events is blurred and it is not obvious howto define delay such that it reflects the causal relationshipbetween the input and the output. By necessity, we define thestart and end points of these events by determining the timeinstants when the signals cross some appropriate voltage thresholds.The selection of these voltage thresholds for logic gates aswell as simple interconnect wires, is the subject of this paper.We begin by a discussion of what we mean by signal delay andhow it arises in a logic gate. With this background, startingfrom ideal inputs to ideal inverters and concluding with physicalinputs to physical inverters, we examine the problem of thresholdselection for inverters through a logical sequence of model refinement,using a combination of analytical and experimental techniques.Based on the insight gained through this analysis, we examinethe problem for multi-input (both static and dynamic) gates aswell as point-to-point interconnect wires. We show that thresholdsderived from the gate‘s DC voltage transfer characteristic removesthe anomalies, such as negative delay and large sensitivity toinput waveshape effects, that can arise with the widely used50% and 10%–90% thresholds. Despite its fundamentalnature, however, we note that the problem of threshold selectionhas received scant attention in the literature. To the best ofour knowledge, this is the first detailed study of this problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44035/1/10470_2004_Article_137059.pd