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.     

A global interconnect optimization scheme for nanometer scale VLSI with implications for latency, bandwidth, and power dissipation

This paper addresses the critical problem of global wire optimization for nanometer scale very large scale integration technologies, and elucidates the impact of such optimization on power dissipation, bandwidth, and performance. Specifically, this paper introduces a novel methodology for optimizing global interconnect width, which maximizes a novel figure of merit (FOM) that is a user-defined function of bandwidth per unit width of chip edge and latency. This methodology is used to develop analytical expressions for optimum interconnect widths for typical FOMs for two extreme scenarios regarding line spacing: 1) spacing kept constant at its minimum value and 2) spacing kept the same as line width. These expressions have been used to compute the optimal global interconnect width and quantify the effect of increasing the line width on various performance metrics such as delay per unit length, total repeater area and power dissipation, and bandwidth for various International Technology Roadmap for Semiconductors technology nodes.     

A power-optimal repeater insertion methodology for global interconnects in nanometer designs

This paper addresses the problem of power dissipation during the buffer insertion phase of interconnect performance optimization. It is shown that the interconnect delay is actually very shallow with respect to both the repeater size and separation close to the minimum point. A methodology is developed to calculate the repeater size and interconnect length which minimizes the total interconnect power dissipation for any given delay penalty. This methodology is used to calculate the power-optimal buffering schemes for various ITRS technology nodes for 5% delay penalty. Furthermore, this methodology is also used to quantify the relative importance of the various components of the power dissipation for power-optimal solutions for various technology nodes.     

An Interconnect Scaling Scheme with Constant On-Chip Inductive Effects

This paper introduces a new global-tier interconnect scaling scheme which ensures that inductance effects do not start dominating the overall interconnect performance. It is shown that for unscaled global lines, inductance effects increase as technology scales while for the scaling scheme proposed by ITRS [1], interconnects become extremely resistive and, while inductance effects diminish with scaling but the performance, specifically, delay per unit length, degrades with scaling. The effect of the proposed global interconnect scaling scheme on optimized driver size, interconnect length, delay per unit length and total buffer area is quantified and compared with the unscaled and the ITRS cases. It is shown that the proposed scaling scheme improves the delay per unit length without degrading inductive effects or increasing buffer area with scaling.     

Interconnect design strategy: structures, repeaters and materialswith strategic system performance analysis (S2PAL) model

In this paper, we propose a novel methodology for scheming an interconnect strategy, such as what interconnect structure should be taken, how repeaters should be inserted, and when new metal or dielectric materials should be adopted. In the methodology, the strategic system performance analysis model is newly developed as a calculation model that predicts LSI operation frequency and chip size with electrical parameters of transistors and interconnects as well as circuit configuration. The analysis with the model indicates that interconnect delay overcomes circuit block cycle time at a specific length; D_c-cross. Here tentatively, interconnects shorter than D_c-cross are called local interconnects, and interconnects longer than that as global ones. The cross-sectional structures for local and global tiers are optimized separately. We also calculate global interconnect pitch and the chip size enlarged by the global interconnect pitch and the inserted repeaters, and then estimate the effectiveness of introducing new materials for interconnects and dielectrics     

Low-power and high-performance techniques in global interconnect signaling

In this article, two accurate and efficient approaches are proposed to optimize the power and delay of global interconnects in VLSI ICs. We modify the conventional buffer insertion and low swing methods for delay and power optimization of various lengths of the global interconnects. As such, we address non-equidistance buffer insertion (NEBI) and current-mode driver and receiver (CMDR) techniques along with our smart optimization procedure. It is shown that the optimized low swing CMDR technique is efficient for global interconnects of the length equal or longer than 5 mm, and the improved buffer insertion technique, NEBI, is a perfect choice for the short global interconnects. Additionally, a random search algorithm known as simulated annealing (SA), improved by an intelligent method using a piecewise linear and exponential cost function, is employed for optimization of the power and delay. To this end, we have implemented a smart CAD tool that works interactively with HSPICE to achieve accurate and reliable design results. For verification purposes, several circuits are designed and simulated in 0.25, 0.18, and 0.13 μm CMOS technologies. The simulation results verify a significant reduction in the power and delay of global interconnects compared to other methods in the literature.     

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.     

Optimal global interconnects for GSI

Performance of a high-speed chip is largely affected by both latency and bandwidth of global interconnects, which connect different macrocells. Therefore, one of the important goals is to design high-bandwidth and fast buses that connect a processor and its on-chip cache memory or link different processors within a multiprocessor chip. In this paper, the width of global interconnects is optimized to achieve a large "data-flux density" and a small latency simultaneously. Data-flux density is the product of interconnect bandwidth and reciprocal wire pitch, which represents the number of bits per second that can be transferred across a unit-length bisectional line. The optimal wire width, which maximizes the product of data-flux density and reciprocal latency, is independent of interconnect length and can be used for all global interconnects. It is rigorously proved that the optimal wire width is the width that results in a delay that is 33% larger than the time-of-flight (ToF). Using the optimal wire width decreases latency, energy dissipation, and repeater area considerably, compared to a sub-optimal wire width (e.g., 42% smaller latency, 30% smaller energy-per-bit, and 84% smaller repeater area compared with the W/sub opt//2 case) at the cost of a small decrease in data-flux density (e.g., 14% smaller compared with W/sub opt//2 case). A super-optimal wire width, however, causes a slight decrease in latency (e.g., 14% for 2W/sub opt/) at the cost of a large decrease in data-flux density (e.g., 35% for 2W/sub opt/).     

基于单壁碳纳米管束的三维互连线设计与分析

Metallic carbon nanotubes(CNTs) have been proposed as a promising alternative to Cu interconnects in future integrated circuits(ICs) for their remarkable conductive, mechanical and thermal properties. Compact equivalent circuit models for single-walled carbon nanotube(SWCNT) bundles are described, and the performance of SWCNT bundle interconnects is evaluated and compared with traditional Cu interconnects at different interconnect levels for through-silicon-via-based three dimensional(3D) ICs. It is shown that at a local level, CNT interconnects exhibit lower signal delay and smaller optimal wire size. At intermediate and global levels, the delay improvement becomes more significant with technology scaling and increasing wire lengths. For 1 mm intermediate and 10 mm global level interconnects, the delay of SWCNT bundles is only 49.49% and 52.82% that of the Cu wires, respectively.     

Predictions of CMOS compatible on-chip optical interconnect

Interconnect has become a primary bottleneck in the integrated circuit design process. As CMOS technology is scaled, the design requirements of delay, power, bandwidth, and noise due to the on-chip interconnects have become more stringent. New design challenges are continuously emerging, such as delay uncertainty induced by process and environmental variations. It has become increasingly difficult for conventional copper interconnect to satisfy these design requirements. On-chip optical interconnect has been considered as a potential substitute for electrical interconnect. In this paper, predictions of the performance of CMOS compatible optical devices are made based on current state-of-the-art optical technologies. Electrical and optical interconnects are compared for various design criteria based on these predictions. The critical dimensions beyond which optical interconnect becomes advantageous over electrical interconnect are shown to be approximately one-tenth of the chip edge length at the 22 nm technology node.     

Circuit Modeling and Performance Analysis of Multi-Walled Carbon Nanotube Interconnects

Metallic carbon nanotubes (CNTs) have received much attention for their unique characteristics as a possible alternative to Cu interconnects in future ICs. Until this date, while almost all fabrication efforts have been directed toward multiwalled CNT (MWCNT) interconnects, there is a lack of MWCNT modeling work. This paper presents, for the first time, a detailed investigation of MWCNT-based interconnect performance. A compact equivalent circuit model of MWCNTs is presented for the first time, and the performance of MWCNT interconnects is evaluated and compared against traditional Cu interconnects, as well as Single-Walled CNT (SWCNT)-based interconnects, at different interconnect levels (local, intermediate, and global) for future technology nodes. It is shown that at the intermediate and global levels, MWCNT interconnects can achieve smaller signal delay than that of Cu interconnects, and the improvements become more significant with technology scaling and increasing wire lengths. At 1000- global or 500- intermediate level interconnects, the delay of MWCNT interconnects can reach as low as 15% of Cu interconnect delay. It is also shown that in order for SWCNT bundles to outperform MWCNT interconnects, dense and high metallic-fraction SWCNT bundles are necessary. On the other hand, since MWCNTs are easier to fabricate with less concern about the chirality and density control, they can be attractive for immediate use as horizontal wires in VLSI, including local, intermediate, and global level interconnects.     

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.

     

Compact Performance Models and Comparisons for Gigascale On-Chip Global Interconnect Technologies

The on-chip global interconnect with conventional Cu/low-k and delay-optimized repeater scheme faces great challenges in the nanometer regime owing to its severe performance degradation. This paper describes the analytical models and performance comparisons of novel interconnect technologies and circuit architectures to cope with the interconnect performance bottlenecks. Carbon nanotubes (CNTs) and optics-based interconnects exhibit promising physical properties for replacing the current Cu/low-k-based global interconnects. We quantify the performance of these novel interconnects and compare them with Cu/low-k wires for future high-performance integrated circuits. The foregoing trends are studied with technology node and bandwidth density in terms of latency and power dissipation. Optical wires have the lowest latency and power consumption, whereas a CNT bundle has a lower latency than Cu. The new circuit scheme, i.e., “capacitively driven low-swing interconnect (CDLSI),” has the potential to effect a significant energy saving and latency reduction. We present an accurate analytical optimization model for the CDLSI wire scheme. In addition, we quantify and compare the delay and energy expenditure for not only the different interconnect circuit schemes but also the various future technologies, such as Cu, CNT, and optics. We find that the CDLSI circuit scheme outperforms the conventional interconnects in latency and energy per bit for a lower bandwidth requirement, whereas these advantages degrade for higher bandwidth requirements. Finally, we explore the impact of the CNT bundle and the CDLSI on a via blockage factor. The CNT shows a significant reduction in via blockage, whereas the CDLSI does not help to alleviate it, although the CDLSI results in a reduced number of repeaters due to the differential signaling scheme.      

Optimization of throughput performance for low-power VLSI interconnects

The technique of optimal voltage scaling and repeater insertion is analyzed in this paper to reduce power dissipation on global interconnects. An analytical model for the maximum bit-rate of a very large scale integration interconnect with repeaters has been derived and results are compared with HSPICE simulations. The analytical model is also used to study the effects of interconnect length and scaling on throughput. The throughput-per-bit-energy is analyzed to determine an optimum combination of supply voltage and repeaters for a low-power global interconnect with 250 nm /spl times/ 250 nm cross-sectional dimensions implemented with the 180 nm micro-optical silicon system technology node. It is shown that the optimal supply voltage is approximately equal to twice the threshold voltage. A case study illustrates that a combination of 1 V supply along with one repeater per millimeter increases the throughput-per-bit-energy to over three times that of a latency-centric interconnect of 2 V, which results in a 70% reduction in power dissipation without any loss of throughput performance.     

Logic Gates as Repeaters (LGR) for Area-Efficient Timing Optimization

Logic gates as repeaters (LGRs)-a methodology for delay optimization of CMOS logic circuits with resistance-capacitance (RC) interconnects is described. The traditional interconnect segmentation by insertion of repeaters is generalized to segmentation by distributing logic gates over interconnect lines, reducing the number of additional, logically useless inverters. Expressions for optimal segment lengths and gate scaling are derived. Considerations are presented for integrating LGR into a VLSI design flow in conjunction with related methods. Several logic circuits have been implemented, optimized and verified by LGR. Analytical and simulation results were obtained, showing significant improvement in performance in comparison with traditional repeater insertion, while maintaining low complexity and small area     

On Modeling of Parallel Repeater-Insertion Methodologies for SoC Interconnects

Parallel repeaters are proven to outperform serial repeaters in terms of delay, power and silicon area when regenerating signals in system-on-chip (SoC) interconnects. In order to avoid fundamental weaknesses associated with previously published parallel repeater-insertion models, this paper presents a new mathematical modeling for parallel repeater-insertion methodologies in SoC interconnects. The proposed methodology is based on modeling the repeater pull-down resistance in parallel with the interconnect. Also, to account for the effect of interconnect inductance, two moments were used in the transfer function, as opposed to previous Elmore delay models which consider only one moment for RC interconnects. A direct consequence of this new type of modeling is an increased challenge in the mathematical modeling of interconnects. HSpice electrical and C++/MATLAB simulations are conducted to assess the performance of the proposed optimization methodology using a 0.25-$mu$m CMOS technology. Simulation results show that this repeater-insertion methodology can be used to optimize SoC interconnects in terms of propagation delay, and provide VLSI/SoC designers with optimal design parameters, such as the type as well as the position and size of repeaters to be used for interconnect regeneration, faster than with conventional HSpice simulations.      

Thermal-Aware Methodology for Repeater Insertion in Low-Power VLSI Circuits

In this paper, the impact of thermal effects on low-power repeater insertion methodology is studied. An analytical methodology for thermal-aware repeater insertion that includes the electrothermal coupling between power, delay, and temperature is presented, and simulation results with global interconnect repeaters are discussed for 90- and 65-nm technology. Simulation results show that the proposed thermal-aware methodology can save 17.5% more power consumed by the repeaters compared to a thermal-unaware methodology for a given allowed delay penalty. In addition, the proposed methodology also results in a lower chip temperature, and thus, extra leakage power savings from other logic blocks.     

Maximizing throughput over parallel wire structures in the deep submicrometer regime

In a parallel multiwire structure, the exact spacing and size of the wires determine both the resistance and the distribution of the capacitance between the ground plane and the adjacent signal carrying conductors, and have a direct effect on the delay. Using closed-form equations that map the geometry to the wire parasitics and empirical switch factor based delay models that show how repeaters can be optimized to compensate for dynamic effects, we devise a method of analysis for optimizing throughput over a given metal area. This analysis is used to show that there is a clear optimum configuration for the wires which maximizes the total bandwidth. Additionally, closed form equations are derived, the roots of which give close to optimal solutions. It is shown that for wide buses, the optimal wire width and spacing are independent of the total width of the bus, allowing easy optimization of on-chip buses. Our analysis and results are valid for lossy interconnects as are typical of wires in submicron technologies.     

Low-power repeaters driving RC and RLC interconnects with delay and bandwidth constraints

Interconnect plays an increasingly important role in deep-submicrometer very large scale integrated technologies. Multiple design criteria are considered in interconnect design, such as delay, power, and bandwidth. In this paper, a repeater insertion methodology is presented for achieving the minimum power in an RC interconnect while satisfying delay and bandwidth constraints. These constraints determine a design space for the number and size of the repeaters. The minimum power is shown to occur at the edge of the design space. With delay constraints, closed form solutions for the minimum power are developed, where the average error is 7% as compared with SPICE. With bandwidth constraints, the minimum power can be achieved with minimum-sized repeaters. The effects of inductance on the delay, bandwidth, and power of an RLC interconnect with repeaters are also analyzed. By including inductance, the minimum interconnect power under a delay or bandwidth constraint decreases as compared with an RC interconnect.     

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.