Kip Killpack

Statistical static timing analysis: how simple can we get?

With an increasing trend in the variation of the primary parameters affecting circuit performance, the need for statistical static timing analysis (SSTA) has been firmly established in the last few years. While it is generally accepted that a timing analysis tool should handle parameter variations, the benefits of advanced SSTA algorithms are still questioned by the designer community because of their significant impact on complexity of STA flows. In this paper, we present convincing evidence that a path-based SSTA approach implemented as a post-processing step captures the effect of parameter variations on circuit performance fairly accurately. On a microprocessor block implemented in 90nm technology, the error in estimating the standard deviation of the timing margin at the inputs of sequential elements is at most 0.066 FO4 delays, which translates in to only 0.31% of worst case path delay.

A multi-port current source model for multiple-input switching effects in CMOS library cells

The problem of multiple-input switching (MIS) has been mostly ignored by the timing CAD community. Not modeling MIS for timing can result in as much as 100% error in stage delay and slew calculation. The impact is especially severe on stages immediately after a bank of flops, where the inputs have a high probability of arriving simultaneously. Other problems such as modeling of interconnect loads, complex (nonlinear/nonmonotonic) input waveforms, power-droop impact on cell delay, nonlinear input capacitances, delay variations due to cross-capacitance, etc. are also known sources of error. In this paper, we introduce the multi-port current source model (MCSM). MCSM can efficiently handle an arbitrary number of simultaneously switching inputs, including single-input switching (SIS). Moreover, MCSM is comprehensive in that other modeling problems associated with delay and noise computation are elegantly covered. We demonstrate the applicability of MCSM on a large 65 nm industrial test-case. For cells experiencing MIS, the model yields delay and slew-rate errors within plusmn5% for 88.3% and 93.0% of the cases, respectively. We also present data that show that MCSM is an effective receiver model which captures active loading effects without incurring significant additional error. MCSM makes combined cell-level timing, noise, and power analysis a possibility

Silicon speedpath measurement and feedback into EDA flows

Timing, test, reliability, and noise are modeled and abstracted in our design and verification flows. Specific EDA algorithms are then designed to work with these abstracted models, often in isolation of other effects. However, tighter design margins and higher reliability issues have increased the need for accurate models and algorithms. We propose utilizing silicon data to tune and improve the EDA tools and flows. In this paper we describe a silicon methodology to isolate silicon speedpath environments and feed these into a simulation framework to temporally and spatially isolate specific speedpaths in order to model and understand the real effects. This is done using accurate electrical speedpath modeling techniques which may be used to tune the accuracy and correlation of the design models. The effort required to distinguish the many different electrical effects will be outlined.

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.

Case Study on Speed Failure Causes in a Microprocessor

In this article, we identify the underlying speed paths and perform a detailed analysis on the effects of multiple input switching, cross-coupling noise, and localized voltage drop on microprocessor. We employ cycle-wise clock shrinks on a tester combined with a CAD methodology to unintrusively identify and analyze these speed paths. Understanding the causes of speed failures can help designers make better power and performance tradeoffs.

Silicon feedback to improve frequency of high-performance microprocessors: an overview

In modern high-performance microprocessors designed using advanced process technologies, the frequency of the part is often slower than what the static timing analysis tools predict before tape out. We give an overview of techniques used to observe the failing path on the tester, identify the dominant devices impacting the delay of the path, and learn from the failing path to fix other similar paths in the design. In particular, we describe a support vector machine based approach for learning from speedpaths observed in silicon.

FA-STAC: A Framework for Fast and Accurate Static Timing Analysis with Coupling

This paper presents a framework for fast and accurate static timing analysis considering coupling. With technology scaling to smaller dimensions, the impact of coupling induced delay variations can no longer be ignored. Timing analysis considering coupling is iterative, and can have considerably larger run-times than a single pass approach. We propose a novel and accurate coupling delay model, and present techniques to increase the convergence rate of timing analysis when complex coupling models are employed. Experimental results obtained for the ISCAS benchmarks show promising accuracy improvements using our coupling model while an efficient iteration scheme shows significant speedup (up to 62.1%) in comparison to traditional approaches.

Pessimism reduction in coupling-aware static timing analysis using timing and logic filtering

With continued scaling of technology into nanometer regimes, the impact of coupling induced delay variations is significant. While several coupling-aware static timers have been proposed, the results are often pessimistic with many false failures. We present an integrated iterative timing filtering and logic filtering based approach to reduce pessimism. We use a realistic coupling model based on arrival times and slews and show that non-iterative pessimism reduction algorithms proposed in previous research may give potentially non- conservative timing results. On a functional block from an industrial 65nm microprocessor, our algorithm produced a maximum pessimism reduction of 11.18% of cycle time over converged timing filtering analysis that does not consider logic constraints.

FA-STAC: An Algorithmic Framework for Fast and Accurate Coupling Aware Static Timing Analysis

This paper presents an algorithmic framework for fast and accurate static timing analysis considering coupling. With technology scaling to smaller dimensions, the impact of coupling induced delay variations can no longer be ignored. Timing analysis considering coupling is iterative, and can have considerably larger run-times than a single pass approach. We propose two different classes of coupling delay models: heuristic-based coupling model and current source-based coupling model, and present techniques to increase the convergence rate of timing analysis when such coupling models are employed. Our proposed coupling model show promising accuracy improvements compared to SPICE. Experimental results on ISCAS85 benchmarks validates the effec tiveness of our efficient iteration scheme. Our iteration algorithm obtained speedups of up to 62.1 % using a heuristic coupling model while 2.7 x using a current-based coupling model in comparison to traditional approaches.

Pessimism Reduction in Coupling-Aware Static Timing Analysis Using Timing and Logic Filtering

With continued scaling of technology into nanometer regimes, the impact of coupling induced delay variations is significant. While several coupling-aware static timers have been proposed, the results are often pessimistic with many false failures. We present an integrated iterative timing filtering and logic filtering based approach to reduce pessimism. We use a realistic coupling model based on arrival times and slews, and show that non-iterative pessimism reduction algorithms proposed in previous research may give potentially non-conservative timing results. On a functional block from an industrial 65 nm microprocessor, our algorithm produced a maximum pessimism reduction of 11.18% of cycle time over converged timing filtering analysis that does not consider logic constraints.