Li-C. Wang

False-path-aware statistical timing analysis and efficient path selection for delay testing and timing validation

We propose a false-path-aware statistical timing analysis framework. In our framework, cell as well as interconnect delays are assumed to be correlated random variables. Our tool can characterize statistical circuit delay distribution for the entire circuit and produce a set of true critical paths.

REDO-random excitation and deterministic observation-first commercial experiment

For many years, non-target detection experiments have been simulated by using AND/OR bridges or gross delay faults as surrogates. For example, the defective part level can be estimated based upon surrogate detection when test patterns target stuck-at faults in the circuit. For the first time, test pattern generation techniques that attempt to maximize non-target defect detection have been used to test a real, 100% scanned, commercial chip consisting of 75 K logic gates. In this experiment, the defective part level for REDO-based patterns was 1,288 parts per million lower than that achieved by DC stuck-at based patterns generated using todays state of the art tools and techniques.

A Circuit SAT Solver With Signal Correlation Guided Learning

Boolean Satisfiability has attracted tremendous research effort in recent years, resulting in the developments of various efficient SAT solver packages. Based upon their design architectures, researchers have tried to develop better heuristics to further improve its efficiency, by either speeding up the Boolean Constraint Propagation (BCP) procedure or finding a better decision ordering (or both). In this paper, we propose an entirely different SAT solver design concept that is circuit-based. Our solver is able to utilize circuit topological information and signal correlations to enforce a decision ordering that is more efficient for solving circuit-based SAT problem instances. In particular, for unsatisfiable circuit examples, our solver is able to achieve from 2x up to more than 75x speedup over a state-of-the-art SAT solver.

Critical path selection for delay fault testing based upon a statistical timing model

Critical path selection is an indispensable step for testing of small-size delay defects. Historically, this step relies on the construction of a set of worst-case paths, where the timing lengths of the paths are calculated based upon discrete-valued timing models. The assumption of discrete-valued timing models may become invalid for modeling delay effects in the deep submicron domain, where the effects of timing defects and process variations are often statistical in nature. This paper studies the problem of critical path selection for testing small-size delay defects, assuming that circuit delays are statistical. We provide theoretical analysis to demonstrate that the new path-selection problem consists of two computationally intractable subproblems. Then, we discuss practical heuristics and their performance with respect to each subproblem. Using a statistical defect injection and timing-simulation framework, we present experimental results to support our theoretical analysis.

New challenges in delay testing of nanometer, multigigahertz designs

Less predictable path delays and many paths with delays close to the clock period are the main trends affecting the delay testability of deep-submicron designs. We examine the challenges in meeting the quality requirements of gigascale integration, and explore functional testing as well as statistical models and methods that could alleviate some of those problems.

TranGen: a SAT-based ATPG for path-oriented transition faults

This paper presents a SAT-based ATPG tool targeting on a path-oriented transition fault model. Under this fault model, a transition fault is detected through the longest sensitizable path. In the ATPG process, we utilize an efficient false-path pruning technique to identify the longest sensitizable path through each fault site. We demonstrate that our new SAT-based ATPG can be orders-of-magnitude faster than a commercial ATPG tool. To demonstrate the quality of the tests generated by our approach, we compare its resulting test set to three other test sets: a single-detection transition fault test set, a multiple-detection transition fault test set, and a traditional critical path test set added to the single-detection set. The superiority of our approach is demonstrated through various experiments based on statistical delay simulation and defect injection using benchmark circuits.

On correlating structural tests with functional tests for speed binning of high performance design

The use of functional vectors has been an industry standard for speed binning purposes of high performance ICs. This practice can be prohibitively expensive as the ICs become faster and more complex. In comparison, structural patterns can target performance related faults in a more systematic manner. To make structural testing an effective alternative to functional testing for speed binning, structural patterns need to correlate with functional test frequencies closely. We investigate the correlation between functional test frequency and that of various types of structural patterns on MPC7455, a Motorola processor executing to the PowerPC/spl trade/ instruction set architecture.

Defect-oriented testing and defective-part-level prediction

After an integrated circuit (IC) design is complete, but before first silicon arrives from the manufacturing facility, the design team prepares a set of test patterns to isolate defective parts. Applying this test pattern set to every manufactured part reduces the fraction of defective parts erroneously sold to customers as defect-free parts. This fraction is referred to as the defect level (DL). However, many IC manufacturers quote defective part level, which is obtained by multiplying the defect level by one million to give the number of defective parts per million. Ideally, we could accurately estimate the defective part level by analyzing the circuit structure, the applied test-pattern set, and the manufacturing yield. If the expected defective part level exceeded some specified value, then either the test pattern set or (in extreme cases) the design could be modified to achieve adequate quality. Although the IC industry widely accepts stuck-at fault detection as a key test-quality figure of merit, it is nevertheless necessary to detect other defect types seen in real manufacturing environments. A defective-part-level model combined with a method for choosing test patterns that use site observation can predict defect levels in submicron ICs more accurately than simple stuck-at fault analysis.

Using logic models to predict the detection behavior of statistical timing defects

In this paper, we study the possibility of using logic defect-level prediction models to predict the detection behavior of statistical timing defects. We compare two known logic models: the Williams-Brown (WB) model and the Mercer-Park-GrimailaDworak (MPGD) model. In the WB-model, the defect coverage is replaced by the n-detection transition fault coverage. We first demonstrate that both logic models may fail to predict the detection of statistical timing defects. Then, we propose an improved WB model based upon selection of the hard-to-detect transition faults. We show that, by selecting a proper subset of the hard-to-detect transition faults, the detection behavior of these faults can correlate well to the detection behavior of statistical timing defects. We explain our findings through statistical delay defect injection and simulation, and report results based upon various benchmark circuits.

Speedpath prediction based on learning from a small set of examples

In high performance designs, speed-limiting logic paths (speedpaths) impact the power/performance trade-off that is becoming critical in our low power regimes. Timing tools attempt to model and predict the delay of all the paths on a chip, which may be in the millions. These delay predictions often have a significant error and when silicon is measured there is a large variation of path delays as compared to the prediction of the tools. This variation may be caused by process, environmental or other effects that are often unpredictable. It is therefore desirable to use early silicon data to better predict and model potential speedpaths for subsequent silicon steppings. In this paper, we present a novel machine learning-based approach that uses a small number of identified speedpaths to predict a larger set of potential speedpaths, thus significantly enhancing the traditional timing prediction flows post-silicon. We demonstrate the feasibility of this approach and summarize our findings based on the analysis of silicon speedpaths from a 65 nm P4 microprocessor.