An improved RC model for VLSI interconnects with applications to buffer insertion

A general platform to generate the RC, RLC and RLCG models of interconnects using global approximation method, two-port networks, and asymptotic waveform evaluation (AWE) is presented. Using the delay of transmission-line-modeled interconnects from HSPICE as a bench mark, we show that among all 18 models studied, the π-configuration of AWE-RLC model yields the best accuracy. To reduce complexity subsequently computational cost without sacrificing accuracy, the AWE-RLC model is mapped to a complex RC model using moment matching. The complex RC model is further mapped to an improved RC model utilizing the principle of charge reservation. The improved RC model is employed to estimate the delay of long interconnects with buffer insertion. As compared with the conventional RC model, the improved RC model reduces the delay of interconnects with buffer insertion, the number of buffers, and the size of the buffer by 20.5, 24, and 32 %, respectively.     

Global interconnect width and spacing optimization for latency, bandwidth and power dissipation

This paper addresses a novel methodology optimizing global interconnect width and spacing for International Technology Roadmap for Semiconductors technology nodes. Global interconnects with and without buffer insertion are considered. The effects of the width and spacing of global interconnects on performance, such as delay, bandwidth, total repeater area and energy dissipation, are analyzed. The product of delay and bandwidth is used as the figure of merit for simultaneous short latency and large bandwidth and the proposed methodology can optimize global interconnects for the maximal figure of merit. It is demonstrated that buffers should not be inserted in global interconnects if interconnect length is shorter than a critical length, which is a constant for a given technology. For global interconnects with buffer insertion, the optimal width and spacing have analytical expressions and are constants for a given technology. For global interconnects without buffer insertion, the optimal width and spacing are dependent on both the technology parameters and interconnect length and can be computed numerically.     

Current-mode signaling in deep submicrometer global interconnects

This paper addresses propagation delay and power dissipation for current mode signaling in deep submicrometer global interconnects. Based on the effective lumped element resistance and capacitance approximation of distributed RC lines, simple yet accurate closed-form expressions of delay and power dissipation are presented. A new closed-form solution of delay under step input excitation is first developed, exhibiting an accuracy that is within 5% of SPICE simulations for a wide range of parameters. The usefulness of this solution is that resistive load termination for current mode signaling is accurately modeled. This model is then extended to a generalized delay formulation for ramp inputs with arbitrary rise time. Using these expressions, the optimum-line width that minimizes the total delay for current mode circuits is found. Additionally, a new power-dissipation model for current-mode signaling is developed to understand the design tradeoffs between current and voltage sensing. Based on the results and derived formulations, a comparison between voltage and current mode repeater insertion for long global deep submicrometer interconnects is presented.     

Design of DG FinFET based driver circuits for energy efficient sub threshold global interconnects

The proliferation of portable electronics has imposed a pressing need on design of low power circuits. Sub threshold circuits are the ideal candidate to quench the demand of ultra-low power. However, degraded performance and exacerbated variability are the major concerns of sub threshold circuits. Furthermore, the global interconnects significantly affects the performance and power dissipation in sub threshold circuits. The obvious reason is the increased capacitance of long global interconnects which is further augmented with increase in sub threshold CMOS driver resistance. This paper explores the performance of sub threshold global interconnect with six different configurations of DG FinFET driver circuit viz. FinFET SG, TGIG, THYBRID, TGSG, TPIGNSG and TPSGNIG. Performance analysis indicates that FinFET SG configuration exhibits 60.7, 0.8, 2.3, 37 and 40% better energy efficiency compared to TGIG, THYBRID, TGSG, TPIGNSG and TPSGNIG respectively at 225 mV supply voltage. Furthermore, the crosstalk analysis results shows that the glitch amplitude in TGSG driven interconnect and THYBRID driven interconnect is increased by 89.6 and 74% respectively compared to FinFET SG driven interconnect. This work also investigates the suitability of conventional buffer insertion technique for enhancing the performance of DG FinFET driven sub threshold global interconnects. The buffered and un-buffered interconnect shows comparable delay, PDP and EDP in sub threshold region. Furthermore, Monte Carlo analysis results indicate that spread in delay exhibited by FinFET SG driven un-buffered interconnect circuit is lesser by 25% compared to FinFET SG driven buffered circuit in sub threshold region.

     

Delay analysis of buffer inserted sub-threshold interconnects

In this paper, an analysis of interconnect delay minimization by CMOS buffer insertion in sub-threshold regime is presented. Analytical expressions are developed to calculate the total delay and optimum number of buffers required for delay minimization in sub-threshold interconnects. Considering delay minimization by buffer insertion, the effects of voltage-scaling on the delay and optimum number of buffers have been analyzed. It is demonstrated that voltage scaling in sub-threshold regime reduces the number of buffers required to attain the minimum delay. This is one more advantage of voltage-scaling in addition to the usual reduction in power dissipation, in the sense that lesser silicon area is consumed. For a wide variety of typical interconnect loads, analytically obtained results are in good agreement with SPICE extracted results for most of the cases more than 90 %. Finally, the variability analysis of sub-threshold interconnects is investigated using Monte Carlo analysis.     

基于精确时延模型考虑缓冲器插入的互连线优化算法

随着VLSI电路集成度增大和特征尺寸的不断减小,连线的寄生效应不可忽略,互连线的时延在电路总时延中占了很大的比例,成为决定电路性能的主要因素.在互连时延的优化技术中,缓冲器插入是最有效的减小连线时延的方法.本文提出了一个在精确时延模型下,在布线区域内给定一些可行的缓冲器插入位置,对两端线网进行拓扑优化,并同时插入缓冲器以优化时延的多项式时间实现内的算法.我们的算法不但可以实现时延的最小化,也可以在满足时延约束的条件下,最小化缓冲器的插入数目,从而避免不必要的面积和功耗的浪费.     

一种低延迟低功耗的片上全局互连方法

提出了一种用于片上全局互连的混合插入方法. 该方法利用中继驱动器和低摆幅差分信号电路在驱动不同长度连线时的优点，将它们混合插入到连线的合适位置，从而降低互连的延时和功耗. 模拟结果表明，该方法与已有方法相比在延时、能耗、能耗延时积以及面积等方面都获得了一定程度的改善.     

Analysis and optimization of shielded RLC global interconnects for gigascale integration

Compact physical models are presented for on-chip double-sided shielded transmission lines, which are mainly used for long global interconnects where inductance effects should not be ignored. The models are then used to optimize the width and spacing of long global interconnects with repeater insertion. The impacts of increasing line width and spacing on various performance parameters such as delay, data-flux density, power dissipation and total repeater area are analysed. The product of data-flux density and reciprocal delay per unit length are defined as a figure of merit (FOM). By maximizing the FOM, the optimal width and spacing of shielded RLC global interconnects are obtained for various international technology roadmap for semiconductors (ITRS) technology nodes.     

Differential current-sensing for on-chip interconnects

This paper presents a differential current-sensing technique as an alternative to existing circuit techniques for on-chip interconnects. Using a novel receiver circuit, it is shown that, delay-optimal current-sensing is a faster (20% on an average) option as compared to the delay-optimal repeater insertion technique for single-cycle wires. Delay benefit for current-sensing increases with an increase in wire width. Unlike repeaters, current-sensing does not require placement of buffers along the wire, and hence, eliminates any placement constraints. Inductive effects are negligible in differential current-sensing. Current-sensing also provides a tighter bound on delay with respect to process variations. However, current-sensing has some drawbacks. It is power inefficient due to the presence of static-power dissipation. Current-sensing is essentially a low-swing signaling technique, and hence, it is sensitive to full swing aggressor noise.     

Study of swing potential on deep submicron on-chip interconnect

The low energy limit of signal on deep submicron on-chip interconnect is deduced from Shannon's communication theorem considering the influence of noise. Based on this energy limit, the analytic model of minimum swing potential considering transmission line effects is constructed. Applying the analytic model to interconnect in deep submicron technology nodes from 0.18 to 0.05 μm, it is shown that the swing potential with present low-swing technique such as SDVST could be reduced further by 70–95% according to the analysis of this work. Correspondingly, by using the low-swing interconnect technique with the minimum swing potential obtained in this work, the decrement of interconnect dynamic power dissipation can be further decreased by about 10–20% of their original one by using SDVST technique, and that of interconnect propagation delay, by one third. Furthermore, the maximum interconnect length is evaluated with a minimum swing potential value in interconnect design. All the results are valuable for interconnect performance optimization, such as repeater insertion in deep submicron circuits. As an application, the design of low swing potential interconnect with interface circuit is introduced.     

POMR: a power-aware interconnect optimization methodology

As VLSI technologies scale down, the average die size is expected to remain constant or to slightly increase with each generation. This results in an average increase in the global interconnect lengths. To mitigate their impact, buffer insertion has become the most widely used technique. However, unconstrained buffering is expected to require several hundreds of thousands of global interconnect buffers. This increased number of buffers is destined to adversely impact the chip power consumption. In this paper, an optimal power maze routing and buffer insertion/sizing problem for a two-pin net is formulated, as a shortest paths ranking problem. The pseudopolynomial time bound of the new formulation fits well within the context of the increased number of buffers. In fact, power savings as high as 25% for the 130-nm technology with a 10% sacrifice in delay is achieved. Furthermore, with the advent of dual threshold technologies, power sensitive applications can substantially benefit from adopting dual threshold buffers. Accordingly, the proposed problem formulation is extended to incorporate the selection of the buffer threshold voltage, where a twofold increase in power savings is observed. During the assessment of the impact of technology scaling using a set of MCNC Benchmarks, an average power saving as high as 35% with a 10% sacrifice in delay is observed. In addition, there is a 10% variation in the power savings when accounting for the process variations.     

Optimal wire sizing and buffer insertion for low power and ageneralized delay model

We present efficient, optimal algorithms for timing optimization by discrete wire sizing and buffer insertion. Our algorithms are able to minimize a cost function subject to given timing constraints; we focus on minimization of dynamic power dissipation, but the algorithm is also easily adaptable to, for example, area minimization. In addition, the algorithm efficiently computes the complete, optimal power-delay trade-off curve for added design flexibility. An extension of our basic algorithm accommodates a generalized delay model which takes into account the effect of signal slew on buffer delay which can contribute substantially to overall delay. To the best of our knowledge, our approach represents the first work on buffer insertion to incorporate signal slew into the delay model while guaranteeing optimality. The effectiveness of these methods is demonstrated experimentally     

Effects of temperature in deep-submicron global interconnect optimization in future technology nodes

The resistance of on-chip interconnects and the current drive of transistors are strongly temperature-dependent. As a result, the interconnect performance in Deep-Submicron technologies is affected by temperature in a substantial proportion. In this paper we evaluate thermal effects in global RLC interconnects and quantify their impact in a standard optimization procedure based on repeaters insertion. By evaluating the difference between a simple RC and an accurate RLC model, we show how the temperature induced increase of resistance may reduce the impact of inductance. We also project the evolution of such effects in future CMOS technologies, according to the semiconductor roadmap.     

Thermally-aware modeling and performance evaluation for single-walled carbon nanotube-based interconnects for future high performance integrated circuits

Given the performance and reliability limits of conventional copper interconnects in the tens of nanometer regime, carbon-nanotube (CNT) based interconnects emerge as a potential reliable alternative for future high performance VLSI industry. In this paper, we present an accurate thermally-aware model for single-walled carbon-nanotube (SWCNT) based interconnects. Our thermally-aware model is an integration of temperature-dependent electrical parasitics model and thermal equivalent circuit that captures both self-heating and heat conduction phenomena. We verify the accuracy of our electro-thermal model against recently reported experimental measurements. By leveraging the presented electro-thermal model, we present a simulation platform to estimate the performance of SWCNT-based interconnects under different temperature conditions. Our thermally-aware model achieves improvement in the delay estimation accuracy of about 51.3% on average. Based on our simulation results, SWCNT-based interconnects offer more than 5×reduction in delay at dimensions of about 10-20 nm for 27- 127 °C temperature range.     

An accurate model for dynamic crosstalk analysis of CMOS gate driven on-chip interconnects using FDTD method

An accurate and time efficient model of CMOS gate driven coupled-multiple interconnects is presented in this paper for crosstalk induced propagation delay and peak voltage measurements. The proposed model is developed using the finite difference time domain (FDTD) technique for coupled RLC interconnects, whereas the alpha power law model is used to represent the transistors in a CMOS driver. As verified by the HSPICE simulation results, the transient response of the proposed model demonstrates high accuracy. Over the random number of test cases, crosstalk induced peak voltage and propagation delay show average errors of 1.1% and 4.3%, respectively, with respect to HSPICE results.     

Minimizing power dissipation in optical interconnects at low voltage using optimal modulator design

A strong motivation for insertion of optical interconnects in short-distance applications such as chip-to-chip or back-plane communication, apart from high bit rates, is their potential to achieve these bit rates at low power compared to the currently prevalent copper based interconnects. Thus, it is imperative to construct design methodologies which minimize the total optical link power dissipation. We present one such methodology, where we optimize the quantum-well modulators to minimize the power dissipation in modulator-based optical interconnects. In the first part of the paper, the focus is on obtaining the optimal modulator metrics [contrast ration (CR) and insertion loss], which yield the lowest total power (receiver and the modulator). The trends are studied as a function of the input laser power and bit rate. Having obtained the desirable modulator metrics and the corresponding power dissipation, in the second part, the focus is on the feasibility of these metrics in the light of voltage swing constraints. The biggest concern with the modulator based optical link is the low CR, especially at low voltage swing. While studying these concerns, we also provide insight into the physical design of the modulator including, its intrinsic region thickness, pre-bias voltage, and the size and the number of quantum-wells. Specifically, we outline the method to obtain the design parameters, which allows minimum power dissipation with the least laser power. This ultimately yields higher aggregate I/O bandwidth for chip to chip communication in power limited chips.     

An analysis of interconnect delay minimization by low-voltage repeater insertion

The effect of voltage-scaling on interconnect delay minimization by CMOS-repeater insertion is analyzed. Analytical models are developed to calculate the optimum number of repeaters as function of CMOS supply voltage. The analytically obtained results are in good agreement with SPICE extracted results. Analysis shows that voltage-scaling decreases power dissipation and the optimum number of repeaters required for delay minimization in long interconnects. Both resistive and inductive interconnects have been considered. At highly scaled voltages, the inductive interconnect has the advantage of lower power-delay product. It is also seen that voltage-scaling affects delay improvement due to repeater insertion.     

Minimization of delay and crosstalk in high-speed VLSIinterconnects

Design optimization of time responses of high-speed VLSI interconnects modeled by distributed coupled transmission line networks is presented. The problem of simultaneous minimization of crosstalk, delay and reflection is formulated into minimax optimization. Design variables include physical/geometrical parameters of the interconnects and parameters in terminating/matching networks. A recently published simulation and sensitivity analysis technique for multiconductor transmission lines is expanded to directly address the VLSI interconnect environment. The new approach permits efficient physical/geometrical oriented interconnect design using exact gradient based minimax optimization. Examples of interconnect optimization demonstrate significant reductions of crosstalk, delay, distortion and reflection at all vital connection ports. The technique developed is an important step towards optimal design of circuit interconnects for high-speed digital computers and communication systems     

Design and analysis of a low-swing driver scheme for long interconnects

Market forces are continually demanding devices with increased functionality/unit area; these demands have been satisfied through aggressive technology scaling which, unfortunately, has impacted adversely on the global interconnect delay subsequently reducing system performance. Line drivers have been used to mitigate the problems with delay; however, these have large power consumption. A solution to reducing the power dissipation of the drivers is to use lower supply voltages. However, by adopting a lower power supply voltage, the performance of the line drivers for global interconnects is impaired unless low-swing signalling techniques are implemented. The paper describes the design of a low-swing signalling scheme which consists of a low-swing driver, called the nLVSD driver which is an improved version of the MJ-driver [1] designed by Juan A. Montiel-Nelson and Jose C. Garcia. Subsequently, both low-swing driver schemes are analysed and compared focusing on their power consumption and performance characteristics, which are the main issues in present day IC design. A comparison between the two driver schemes showed that the nLVSD driver exhibited a 34% improvement regarding power consumption and a 28% improvement in delay when driving a 10 mm length of interconnect. A comparison between the two schemes was also undertaken in the presence of ±3σ Process and Voltage (PV) variations. The analysis indicated that the nLVSD driver scheme was more robust than the MJ-driver with a 33% and 44% improvement with respect to power consumption and delay variations. In order to further improve the robustness of the nLVSD scheme against process variation, the scheme was further analysed to identify which process variables had the most impact on circuit delay and power consumption. For completeness the effects of process variation on interconnect delay and power consumption was also undertaken.