Shielding effect of on-chip interconnect inductance

Interconnect inductance introduces a shielding effect which decreases the effective capacitance seen by the driver of a circuit, reducing the gate delay. A model of the effective capacitance of an RLC load driven by a CMOS inverter is presented. The interconnect inductance decreases the gate delay and increases the time required for the signal to propagate across an interconnect, reducing the overall delay to drive an RLC load. Ignoring the line inductance overestimates the circuit delay, inefficiently oversizing the circuit driver. Considering line inductance in the design process saves gate area, reducing dynamic power dissipation. Average reductions in power of 17% and area of 29% are achieved for example circuits. An accurate model for a CMOS inverter and an RLC load is used to characterize the propagation delay. The accuracy of the delay model is within an average error of less than 9% as compared to SPICE.     

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.     

Figures of merit to characterize the importance of on-chipinductance

A closed-form solution for the output signal of a CMOS inverter driving an RLC transmission line is presented. This solution is based on the alpha power law for deep submicrometer technologies. Two figures of merit are presented that are useful for determining if a section of interconnect should be modeled as either an RLC or an RC impedance. The damping factor of a lumped RLC circuit is shown to be a useful criterion. The second useful figure of merit considered in this paper is the ratio of the rise time of the input signal at the driver of an interconnect line to the time of flight of the signals across the line. AS/X circuit simulations of an RLC transmission line and a five section RC II circuit based on a 0.25-μm IBM CMOS technology are used to quantify and determine the relative accuracy of an RC model. One primary result of this paper is evidence demonstrating that a range for the length of the interconnect exists for which inductance effects are prominent. Furthermore, it is shown that under certain conditions, inductance effects are negligible despite the length of the section of interconnect     

Effective on-chip inductance modeling for multiple signal lines and application to repeater insertion

/sup A/ new approach to handle inductance effects for multiple signal lines is presented. The worst-case switching pattern is first identified. Then a numerical approach is used to model the effective loop inductance (L/sub eff/) for multiple lines. Based on a look-up table for L/sub eff/, an equivalent single line model can be generated to decouple a specific signal line from the others to perform static timing analysis. Compared to the use of full RLC netlists for multiple lines, this approach greatly improves the computational efficiency and maintains accuracy for timing and signal integrity analysis. We apply these models to repeater insertion in critical paths and find that, for a single line, the RLC model minimizes delay with fewer number of repeaters than RC model. However, for multiple lines, we find that same number of repeaters is inserted for optimal delay according to both the RC and RLC models.     

A clock interconnect extractor for multigigahertz frequencies incorporating inductance effect

Due to decreasing device sizes and increasing clock speed, interconnect inductance is becoming an important factor in the on-chip delay analysis of deep submicrometer technologies. This delay has been represented as an RC model in the available electric design automation tools. In this paper, we model the on-chip interconnect as a RLC for systems running at multigigahertz frequencies. A static-extraction analysis method optimized for ASICs is detailed. It considers all the lines within the vicinity of the target signal line as return paths.     

考虑温度分布效应的RLC互连延时分析

基于等效Elmore延时模型和分段分布参数思想提出了一种RLC互连延时解析模型,该模型同时考虑了互连线温度分布效应和电感效应对延时的影响,更加贴近实际情况,在实际应用中具有重要意义. 仿真结果表明,对于简单的RLC互连树形结构而言,所提模型的延时误差在10%以内,且仿真效率高.     

DSM interconnects: importance of inductance effects and corresponding range of length

To analyze at which rise/fall times the inductance effect appears in DSM interconnects, the author develops a methodology versus the input line transition time to be technology-independent. These lines are modeled as RC and RLC distributed lines, and the two models are compared to define the effects caused by neglecting inductance. The goal of this study is, based upon the discrepancy between RC and RLC models, to define when inductance must be included in the modeling of interconnects. A simple rule permits the choice of the simplest model (RC or RLC) for a given accuracy. The length range concerned by the inductive effect is calculated from the complex propagation factor value. The theoretical limits are illustrated on several interconnection configurations, on a 0.18-/spl mu/m technology.     

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.      

Simulation of interconnect inductive impact in the presence of process variations in 90 nm and beyond

The on-chip inductive impact on signal integrity has been a problem for designs in deep-submicrometer technologies. The inductive impact increases the clock skew, max timing, and noise of bus signals. In this letter, circuit simulations using silicon-validated macromodels show that there is a significant inductive impact on the signal max timing (/spl sim/ 10% pushout versus RC delay) and noise (/spl sim/2/spl times/RC noise). In nanometer technologies, process variations have become a concern. Results show that device and interconnect process variations add /spl sim/ 3% to the RLC max-timing impact. However, their impact on the RLC signal noise is not appreciable. Finally, inductive impact in 65- and 45-nm technologies is investigated, which indicates that the inductance impact will not diminish as technology scales.     

Compact distributed RLC interconnect models. I. Single linetransient, time delay, and overshoot expressions

Novel compact expressions that describe the transient response of a high-speed distributed resistance, inductance, and capacitance (RLC) interconnect are rigorously derived with on-chip global interconnect boundary conditions. Simplified expressions enable physical insight and accurate estimation of transient response, time delay, and overshoot for high-speed global interconnects with the inclusion of inductance     

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.     

A multilevel parasitic interconnect capacitance modeling andextraction for reliable VLSI on-chip clock delay evaluation

This paper describes fringing and coupling interconnect capacitance models which include the nonlinear second-order effects of field interactions among multilevel parasitic interconnects for accurate circuit simulations. They are fitted well with numerical solutions by using a Poisson equation solver. A reliable parasitic distributed resistance-inductance-capacitance (RLC) extraction method is identified by using the solver with the bounded local three-dimensional (3-D) numerical analysis to reduce excessive central processing unit (CPU) time compared to full 3-D numerical simulation. We investigate the impact of input slew variations on the traversal clock delay within the slow ramp region of the driver gate as well as in the extracted parasitic interconnect networks. Input slew is found to be a dominant factor affecting clock delay sensitivity. In addition, we use indirect on-chip electron beam probing to confirm that the simulated clock delays are in reasonable agreement with the measured delays     

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     

互连线RC模型应用条件的仿真研究

研究结果表明,在L与RC比值较小时,阶跃响应的上升时间基本上由RC的乘积决定,电感对电路的影响可以忽略,互连线采用RC模型与RLC模型结果应无多大差别。在L与RC比值较大时,阶跃响应曲线出现振荡,此时使用RC模型需满足工作频率低于RC模型的“上限使用频率;当工作频率超过RC模型的“上限使用频率”时,互连线的模型就必须采用RLC模型。RC模型的“上限使用频率”仅与互连线长度有关:fmax106(Hz·m)。     

Performance Implications of Inductive Effects for Carbon-Nanotube Bundle Interconnect

In this letter, we investigate the impact of inductance on bundles of single-walled carbon nanotubes (SWCNT) for future very large scale integration interconnect applications. Leveraging a scalable equivalent circuit model, we assess the relative impact of magnetic inductance and the worst case theoretical value of kinetic inductance on both delay and voltage overshoot. Based on our results, even if the worst case theoretical value for kinetic inductance is assumed, it will only increase the delay and the voltage overshoot by a maximum of 6% and 3%, respectively. Therefore, kinetic inductance will not be a significant factor in the future SWCNT bundle-based interconnect solutions     

Wire shaping of RLC interconnects

The optimum wire shape to produce the minimum signal propagation delay across an RLC line is shown to exhibit a general exponential form. The line inductance makes exponential tapering more attractive for RLC lines than for RC lines. For RLC lines, optimum wire tapering achieves a greater reduction in the signal propagation delay as compared to uniform wire sizing. For RLC lines, exponential tapering outperforms uniform repeater insertion. As technology advances, wire tapering becomes more effective than repeater insertion, since a greater reduction in the propagation delay is achieved. Optimum wire tapering achieves a reduction of 36% in the propagation delay in long RLC interconnect as compared to uniform repeater insertion.

Wire tapering can reduce both the propagation delay and power dissipation. Optimum tapering for minimum propagation delay reduces the propagation delay by 15% and power dissipation by 16% for an example circuit. The optimum tapering factor to minimize the transient power dissipation of a circuit is described in this paper. An analytic solution to determine the optimum tapering factor that exhibits an error of less than 2% is provided. Wire tapering is also shown to reduce the power dissipation of a circuit by up to 65%.

Wire tapering can also improve signal integrity by reducing the inductive noise of the interconnect lines. Wire tapering reduces the effect of impedance mismatch in digital circuits. The difference between the overshoots and undershoots in the signal waveform of an example clock distribution network is decreased by 34% as compared to a uniformly sized network producing the same signal characteristics.     

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.     

Inductance model and analysis methodology for high-speed on-chip interconnect

With operating frequencies entering the multi-gigahertz range, inductance has become an important consideration in the design and analysis of on-chip interconnects. In this paper, we present an accurate and efficient inductance modeling and analysis methodology for high-performance interconnect. We determine the critical elements for a PEEC based model by analyzing the current flow in the power grid and signal interconnect. The proposed model includes distributed interconnect resistance, inductance and capacitance, device decoupling capacitances, quiescent switching currents in the grid, pad connections, and pad/package inductance. We propose an efficient methodology for extracting these elements, using statistical models for on-chip decoupling capacitance and switching currents. Simulation results show the importance of various elements for accurate inductance analysis. We also demonstrate the accuracy of the proposed model compared to the traditional loop-based inductance approach. Since the proposed model can consist of hundreds of thousands of RLC elements, and a fully dense mutual inductance matrix, we propose a number of acceleration techniques that enable efficient analysis of large interconnect structures.     

Optimal interconnection circuits for VLSI

The propagation delay of interconnection lines is a major factor in determining the performance Of VLSI circuits because the RC time delay of these lines increases rapidly as chip size is increased and cross-sectional interconnection dimensions are reduced. In this paper, a model for interconnection time delay is developed that includes the effects of scaling transistor, interconnection, and chip dimensions. The delays of aluminum, WSi2, and polysilicon lines are compared, and propagation delays in future VLSI circuits are projected. Properly scaled multilevel conductors, repeaters, cascaded drivers, and cascaded driver/ repeater combinations are investigated as potential methods for reducing propagation delay. The model yields optimal cross-sectional interconnection dimensions and driver/repeater configurations that can lower propagation delays by more than an order of magnitude in MOSFET circuits.