Transistor-level timing analysis using embedded simulation

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

Interconnect delays represent an increasingly dominant portion of overall circuit delays. During timing-driven physical synthesis process, timing analysis is repeatedly performed over several hundred thousand components. Thus, fast and accurate estimation of interconnect delays is crucial. Traditionally, lumped and elmore delay models have been widely used for computing interconnect delays in physical synthesis due to their computational efficiency. However, these delay models are known to be inaccurate since they ignore slew and resistive shielding effects. In this paper, we propose a new iterative refinement based delay estimation approach that considers resistive shielding along with driver slew. Experimental results show that the proposed approach gives not only highly accurate results for far end RC-line delays but also compares very favorably to more difficult to match source end delays and source slews. In addition, use of the proposed delay model in physical synthesis yields significant performance improvement on several large industrial ASICs.

A computer model for n parallel microstrip lines is developed for circuit simulation. This model for the lossy transmission line system can be readily implemented into circuit simulators and can accurately simulate the delay and crosstalk effects of interconnects in high-speed integrated circuits. Modal analysis is applied to decouple the n-coupled-line system into n independent lines, and the characteristic solutions of telegraph equations are represented by a set of simple time-varying equivalent circuits. The model has been implemented in a general-purpose circuit simulator, iSMILE, which is compatible with SPICE. Simulation results on propagation delay times and crosstalk are presented for high-speed GaAs HEMT (high-electron-mobility transistor) integrated circuits.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, we introduce a way of modeling the differences between the calculated delays and the real delays, and propose an efficient path selection method for path delay testing based on the model. Path selection is done by judging which of two paths has the larger real delay by taking into account the ambiguity of calculated delay, caused by imprecise delay modeling as well as process disturbances. In order to make precise judgment under this ambiguity, the delays of only the unshared segments of the two paths are evaluated. This is because the shared segments are presumed to have the same real delays on both paths. The experiments used the delays of gates and interconnects, which were calculated from the layout data of ISCAS85 benchmark circuits using a real cell library. Experimental results show the method selects only about one percent of the paths selected by the most popular method.

Article Free Access Share on Circuit delay models and their exact computation using Timed Boolean Functions Authors: William K. C. Lam View Profile , Robert K. Brayton View Profile , Alberto L. Sangiovanni-Vincentelli View Profile Authors Info & Claims DAC '93: Proceedings of the 30th international Design Automation ConferenceJuly 1993 Pages 128–134https://doi.org/10.1145/157485.164625Published:01 July 1993Publication History 18citation300DownloadsMetricsTotal Citations18Total Downloads300Last 12 Months7Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Timing analysis and verification is a critical stage in digital integrated circuit design. As feature sizes decrease to nanometer scale, the impact of process parameter variations in circuit performance becomes extremely relevant. Even though several statistical timing analysis techniques have recently been proposed, as a form of incorporating variability effects in traditional static timing analysis, corner analysis still is the current timing signoff methodology for any industrial design. Since it is impossible to analyze a design for all the process corners, due to the exponential size of the corner space, the design is usually analyzed for a set of carefully chosen corners, that are expected to cover all the worst-case scenarios. However, there is no established systematic methodology for picking the right worst-case corners, and this task usually relies on the experience of design and process engineers, many times leading to over design. This paper proposes an efficient automated methodology for computing the worst-delay process corners of a digital integrated circuit, given a linear parametric characterization of the gate and interconnect delays.

In this paper, we demonstrate that conventional Static Timing Anaysis (STA) based, functional, gate-level simulation of asynchronous circuits with cycles is only as accurate as the STA engine used. This is, firstly because cycle cuts create local slew errors at cutpoints, and secondly because slew propagation may not be upper bounded across multiple cut points in the same cycle. The use of an Asynchronous STA (ASTA) engine, which does not cut cycles, and properly bounds slews across cycles is a possible solution, which can indeed serve as an upper bound over SPICE transistor level similations. We contrast STA and ASTA-based gate-level simulations with transistor level SPICE simulations to demonstrate the impact of timing errors for 12 asynchronous control circuits, implemented by the Petrify tool, in a 0.25μm technology library. We show that STA-based simulation results are incorrectly more optimistic than ASTA, and it is possible for the simulation period to even be faster than SPICE, which is a major timing error.

As the device dimension is scaled down, interconnect RC delay becomes dominant performance limiter in high-performance VLSIs. Another issue in the submicron interconnects is a drastic increase of coupling capacitance due to the higher aspect ratio to reduce the interconnect resistance. The increase of the coupling capacitance degrades signal integrity, inducing noise problems and delay fluctuation problems. Buffer insertion (repeater insertion) is one of the most effective ways to decrease the interconnect delay. The original buffer insertion, however, cannot be applied to bi-directional buses because the buffer is uni-directional in nature. Some circuit configurations that can be applied to bi-directional buses have been proposed. These circuits turn out to be prone to malfunctions when there is a noise from adjacent lines in scaled down interconnect systems where capacitive coupling is large. A new buffer insertion scheme for bi-directional buses, namely the dual-rail bus (DRB) scheme, which does not have noise problems is proposed and measured in this paper. Another proposal is on a high-speed buffer insertion scheme for uni-directional buses by making use of staggered firing. The staggered firing bus (SFIB) is proposed and measured.

With recent advances in reverse engineering, attackers can reconstruct a netlist to counterfeit chips by opening the die and scanning all layers of authentic chips. This relatively easy counterfeiting is made possible by the use of the standard simple clocking scheme, where all combinational blocks function within one clock period, so that a netlist of combinational logic gates and flip-flops is sufficient to duplicate a design. In this article, we propose to invalidate the assumption that a netlist completely represents the function of a circuit with unconventional timing. With the introduced wave-pipelining (WP) paths, attackers have to capture gate and interconnect delays during reverse engineering, or to test a huge number of combinational paths to identify the WP paths. To hinder the test-based attack, we construct false paths with WP to increase the counterfeiting challenge. The experimental results confirm that WP true paths and false paths can be constructed in benchmark circuits successfully with only a negligible cost, thus thwarting the potential attack techniques.

Most modern microprocessors use a balanced tree to distribute the clock. However, at gigahertz clock speeds an increasing fraction of skew and jitter comes from random variations in gate and interconnect delay. The majority of jitter in a clock tree is introduced by buffers and inter-line coupling to the clock wires. A relatively small amount comes from noise in the source oscillator. This distributed clock network generates the clock signal with phase locked loops (PLLs) at multiple points (nodes) across a chip, and distributes each only to a small section of the chip (tile). Phase detectors (PD) at the boundaries between tiles produce error signals that are summed by an amplifier in each tile and used to adjust the frequency of the node oscillator.

FIDER: A Force-Balance-Based Interconnect Delay Driven Re-Synthesis Algorithm for Data-Path Optimization After Floorplan

In todayýs deep-submicron designs, the interconnect delays contribute an increasing part to the overall performance of an implementation. Particularly when targeting field programmable gate arrays (FPGAs), interconnect delays are crucial, since they can easily vary by orders of magnitude. Many existing performance-directed retiming methods use simple delay models which either neglect routing delays or use inaccurate delay estimations. In this paper, we propose a retiming approach which overcomes the problem of inaccurate delay models. Our retiming technique uses delay information extracted from a fully placed and routed design and takes account of register timing requirements. By applying physical constraints, we ensure that the delay information remains valid during retiming. In our experiments, we achieved up to 27% performance improvement.

In this paper, we propose a calculation method of gate delay for SSTA (Statistical Static Timing Analysis) considering MIS (Multiple Input Switching). In SSTA, statistical maximum/minimum operation is necessary to calculate the latest/fastest arrival time of multiple input gate. Most SSTA approaches calculate the distribution in the latest/fastest arrival time under SIS (Single Input Switching assumption), resulting in ignoring the effect of MIS on the gate delay and the output transition time. MIS occurs when multiple inputs of a gate switch nearly simultaneously. Thus, ignoring MIS causes error in the statistical maximum/minimum operation in SSTA. We propose a statistical gate delay model considering MIS. We verify the proposed method by SPICE based Monte Carlo simulations. Experimental results show that the neglect of MIS effect leads to 80% error in worst case. The error of the proposed method is less than 20%.

In this paper, a model of the propagation delays in the interconnection lines on GaAs‐based very high‐speed integrated circuits is presented. The model includes the very high‐frequency effects, such as geometric dispersion, substrate losses, and conductor losses. The model is used to simulate the dependence of interconnect delays on the frequency of operation, interconnect length, width, material resistivity, load capacitance, and the driving source resistance. © 2001 John Wiley &amp; Sons, Inc. Microwave Opt Technol Lett 31: 229–233, 2001.

The importance of effective lower bound estimation (LBE) techniques is well established in high-level synthesis (HLS) since it allows more efficient exploration of the design space while providing other HLS tools with the capability of predicting the effect of specific tools on the design space. Much of the previous work has focused on LBE techniques that use very simple cost models which primarily focus on the functional unit resources. With the push toward submicron technologies, simple models that use functional unit resources alone are not accurate enough to allow effective design space exploration since the effects of storage and interconnect can indeed dominate the cost function. In this paper, we present an integrated approach aimed at predicting lower bounds on hardware resources needed to implement a behavioral description within a given amount of time. Our area cost model accounts for storage (register) and interconnect resources (buses) in addition to functional resources. Our timing model uses a finer granularity that permits the modeling of functional unit, register, and interconnect delays. Our approach is integrated because we consider the dependencies between the different types of resources as well as the ordering in which the resources are allocated. We tested our technique for functional unit, storage, and interconnect requirements on several high-level synthesis benchmarks, and observed near-optimal results. We believe that our comprehensive LBE approach can lead to better quality HLS solutions in less time, and we demonstrate this approach in our paper.