Static timing analysis taking crosstallk into account

We describe a procedure based on an existing static timing analysis tool for selecting path delay faults to target during test generation. The use of an existing static timing analysis tool ensures that a state-of-the-art process can be used for estimating path delays. However, static timing analysis, by itself, can be inaccurate as it does not take into consideration conditions that are necessary for detecting path delay faults. In the proposed method, these conditions are captured as what are called input necessary assignments, which static timing analysis tools are able to use. By providing the static timing analysis process with the input necessary assignments for a selected path, the static timing analysis process can estimate the delay of the path more accurately. It can also identify additional paths whose delays are at least as high as those of the selected paths. Thus, feeding back the input necessary assignments to the static timing analysis process enhances the correlation between static timing analysis and actual timing of tests on silicon. The result is a set of potentially detectable path delay faults associated with critical paths based on more accurate estimates of the path delays that can be exhibited by a test set, compared with the set that would be obtained by static timing analysis alone.

Recent static timing analysis (STA) tools have utilized task dependency graph (TDG) parallelism to enhance the STA runtime performance. Although TDG parallelism shows promising speedup, the overhead of scheduling a TDG can become dominant as the TDG becomes larger. To minimize the scheduling overhead, several TDG partitioning algorithms have been proposed to reduce the TDG size without affecting its task parallelism. Despite improved performance, existing TDG partitioners all fall short of incremental partitioning, limiting their practical use in STA tools that support timing-driven operations. To overcome this limitation, we propose iTAP, an incremental TDG partitioner to fully leverage the power of TDG partitioning in task-parallel STA applications. Compared to a state-of-the-art full TDG partitioner, iTAP enhances the overall STA performance by up to 2.97×.

Superconducting single-flux-quantum (SFQ) technology is a beyond-complementary metal–oxide–semiconductor (CMOS) technology, promising ultrahigh processing speed and low power consumption. A timing analysis tool for SFQ circuits should check circuit timing behavior, including working frequencies and hold time violations to determine the circuit performance. Unlike CMOS gates, generic SFQ gates are clocked gates, which produce their output pulses in response to a clock pulse and have a fan-out capability of one. An SFQ splitter, a special clockless gate that has a fan-out capability of two, is used to address the fan-out limitation. This gate is also utilized in the clock tree, which distributes clock pulses to various SFQ gates. The delay of a clock path in a clock tree is determined by the wire delays of connection nets and gate delays of splitters. However, the splitter delays in a clock path are significantly affected by process variations, resulting in a challenging skew problem. Furthermore, existing timing analysis tools of SFQ circuits are developed based on the timing definitions, rules, and constraints from CMOS technology with very few modifications. This article demonstrates the incompleteness of the existing SFQ technology timing definitions. Precisely, it presents a novel static timing analysis (STA) tool, qSTA, which checks the timing behavior of SFQ circuits based on revised definitions of the setup time and hold times. qSTA encompasses the common path pessimism removal technique, which removes the delays of the shared path segments between two clock paths to achieve a better approximation of real skew values. qSTA takes only 5.33 s to check the timing behavior of a 16-bit integer divider with 36 732 gates and 55 939 nets.

Process variations have become a critical issue in performance verification of high-performance designs. We present a new, statistical timing analysis method that accounts for inter- and intra-die process variations and their spatial correlations. Since statistical timing analysis has an exponential run time complexity, we propose a method whereby a statistical bound on the probability distribution function of the exact circuit delay is computed with linear run time. First, we develop a model for representing inter- and intra-die variations and their spatial correlations. Using this model, we then show how gate delays and arrival times can be represented as a sum of components, such that the correlation information between arrival times and gate delays is preserved. We then show how arrival times are propagated and merged in the circuit to obtain an arrival time distribution that is an upper bound on the distribution of the exact circuit delay. We prove the correctness of the bound and also show how the bound can be improved by propagating multiple arrival times. The proposed algorithms were implemented and tested on a set of benchmark circuits under several process variation scenarios. The results were compared with Monte Carlo simulation and show an accuracy of 3.32% on average over all test cases.

The impact of parameter variations on timing due to process variations has become significant in recent years. In this paper, we present a statistical timing analysis (STA) framework with quadratic gate delay models that also captures spatial correlations. Our technique does not make any assumption about the distribution of the parameter variations, gate delays, and arrival times. We propose a Taylor-series expansion-based quadratic representation of gate delays and arrival times which are able to effectively capture the nonlinear dependencies that arise due to increasing parameter variations. In order to reduce the computational complexity introduced due to quadratic modeling during STA, we also propose an efficient linear modeling driven quadratic STA scheme. We ran two sets of experiments assuming the global parameters to have uniform and Gaussian distributions, respectively. On an average, the quadratic STA scheme had 20.5times speedup in runtime as compared to Monte Carlo simulations with an rms error of 0.00135 units between the two timing cummulative density functions (CDFs). The linear modeling driven quadratic STA scheme had 51.5times speedup in runtime as compared to Monte Carlo simulations with an rms error of 0.0015 units between the two CDFs. Our proposed technique is generic and can be applied to arbitrary variations in the underlying parameters under any spatial correlation model

Given the sensitivity of circuit delay to supply and ground voltage values, static timing analysis (STA) must take into account supply voltage variations. Existing STA techniques allow one to verify the timing at different process corners which effectively only considers cases where all the supplies are low or all are high. Cases of mismatch between the supplies of driver and load are not considered. In practice, supply voltages are neither totally independent nor totally dependent. In this work, we consider the supply and ground nodes of a logic gate to be either totally independent variables, or to be directly tied or connected to those of some other gate(s) in the circuit. We also assume that the exact supply voltage values are not known exactly, but that only upper/lower bounds on them are known. In this framework, we propose new timing models for logic gates and identify the worst-case voltage configurations for individual gates and for simple paths. We then give an STA technique that provides the worst-case circuit delay taking supply variations into account.

In advanced technology nodes, incremental delay due to coupling is a serious concern. Design companies spend significant resources on static timing analysis (STA) tool licenses with signal integrity (SI) enabled. The runtime of the STA tools in SI mode is typically large due to complex algorithms and iterative calculation of timing windows to accurately determine aggressor and victim alignments, as well as delay and slew estimations. In this work, we develop machine learning-based predictors of timing in SI mode based on timing reports from non-SI mode. Timing analysis in non-SI mode is faster and the license costs can be several times less than those of SI mode. We determine electrical and logic structure parameters that affect the incremental arc delay/slew and path delay (i.e., the difference in arrival times at the clock pin of the launch flip-flop and the D pin of the capture flip-flop) in SI mode, and develop models that can predict these SI-aware delays. We report worst-case error of 7.0ps and average error of 0.7ps for our models to predict incremental transition time, worst-case error of 5.2ps and average error of 1.2ps for our models to predict incremental delay, and worst-case error of 8.2ps and average error of 1.7ps for our models to predict path delay, in 28nm FDSOI technology. We also demonstrate that our models are robust across designs and signoff constraints at a particular technology node.

Path tracing is a key requirement in providing various functionalities in a Static Timing Analysis (STA) tool. With growing design sizes and advancements in STA techniques like statistical timing analysis, path tracing techniques need to be more efficient and accurate. Naive extensions of path tracing techniques for statistical timing analysis are found to be inefficient and inaccurate. In this paper, we present a novel Statistical Path Tracing (SPT) approach and illustrate its application in Common Path Pessimism Removal (CPPR). We demonstrate that SPT is more efficient and accurate when compared to a Deterministic Path Tracing (DPT) approach.

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%.

As design size gets larger and becomes more complicated with feature integration, the runtime for Static Timing Analysis (STA) becomes more of a concern. Due to time-to-market pressure, the validation of the design is performed in parallel with the physical synthesis flow; therefore it is not uncommon to find last minute critical logic bugs during final design integration iterations. However, timing verification needs to be run on full-chip level to ensure that the check is comprehensive. This paper proposes a method to isolate only those logics which are affected by the Engineering Change Order (ECO) for STA. This simplification will allow faster ECO iteration to enable a more efficient timing convergence. The proposed method is also suitable to be used for multithreading in STA engines to speed-up timing verification due to ECO changes. Engineering Change Order (ECO), Static Timing Analysis (STA), Incremental Static Timing Analysis, VLSI design

Statistical static timing analysis (SSTA) tools have mostly addressed the process variations of devices and lumped interconnect RC effects. This paper provides an overview of interconnect process variations of capacitive coupling and its effect on crosstalk delay and noise. The correlations among parallel plate, lateral and total capacitance is shown. Correlations between resistance and capacitance are illustrated to enable development of a simple and efficient model for delay and noise analysis. Experimental results are shown to validate the assumptions on the linearity of sensitivity of delay and noise to process variations. A methodology to account for process variations in crosstalk delay and noise is proposed.

Static code analysis is widely used to support the development of high-quality software. It helps developers detect potential bugs and security vulnerabilities in a program's source code without executing it. While the potential benefits of static analysis tools are beyond question, their usability is often criticised and prevents software developers from using static analysis to its full potential. In the past decade, researchers have studied developer needs and contrasted them to available static analysis tool functionalities. In this paper, we summarize the main design challenges for building usable static analysis tools, and show that they revolve around the notion of explainability, which is a subarea of usability. We present existing analysis tools and current research in static analysis usability, and detail how they approach those challenges. This leads us to proposing potential lines of future work in explainability for static analysis, namely turning static analysis tools into assistants and teachers.

Static analyzers have become increasingly popular both as developer tools and as subjects of empirical studies. Whereas static analysis tools exist for disparate programming languages, the bulk of the empirical research has focused on the popular Java programming language. In this paper, we investigate to what extent some known results about using static analyzers for Java change when considering C#-another popular object-oriented language. To this end, we combine two replications of previous Java studies. First, we study which static analysis tools are most widely used among C# developers, and which warnings are more commonly reported by these tools on open-source C# projects. Second, we develop and empirically evaluate EagleRepair: a technique to automatically fix code in response to static analysis warnings; this is a replication of our previous work for Java [20]. Our replication indicates, among other things, that 1) static code analysis is fairly popular among C# developers too; 2) Re-Sharper is the most widely used static analyzer for C#; 3) several static analysis rules are commonly violated in both Java and C# projects; 4) automatically generating fixes to static code analysis warnings with good precision is feasible in C#. The EagleRepair tool developed for this research is available as open source.

Static timing analysis techniques are widely used to verify the timing behavior of large digital designs implemented predominantly in conventional static CMOS. These techniques, however, are not sufficient to completely verify the dynamic circuit families now finding favor in high-performance designs. In this paper, we describe an approach that extends static timing analysis to a high-performance dynamic CMOS logic family called self-resetting CMOS (SRCMOS). Due to the circuit structure employed in SRCMOS, designs naturally decompose into a hierarchy of gates and macros; timing analysis must address and preferably exploit this hierarchy. At the gate level, three categories of constraints on pulse timing arise from considering the effects of pulse width, overlap, and collisions. Timing analysis is performed at the macro level, by a) performing timing tests at macro boundaries and b) using macro-level delay models. We define various macro-level timing tests which ensure that fundamental gate-level timing constraints are satisfied. We extend the standard delay model to handle leading and trailing edges of signal pulses, across-chip variations, trading of signals, and slow and fast operating conditions. We have developed an SRCMOS timing analyzer based on this approach; the analyzer implemented as extensions to a standard static timing analysis program, thus facilitating its integration into an existing design system and methodology.

Early RTL delay prediction using neural networks