Variability in digital integrated circuits makes timing verification an extremely challenging task. In this paper, a canonical first order delay model is proposed that takes into account both correlated and independent randomness. A novel linear-time block-based statistical timing algorithm is employed to propagate timing quantities like arrival times and required arrival times through the timing graph in this canonical form. At the end of the statistical timing, the sensitivities of all timing quantities to each of the sources of variation are available. Excessive sensitivities can then be targeted by manual or automatic optimization methods to improve the robustness of the design. This paper also reports the first incremental statistical timer in the literature which is suitable for use in the inner loop of physical synthesis or other optimization programs. The third novel contribution of this paper is the computation of local and global criticality probabilities. For a very small cost in CPU time, the probability of each edge or node of the timing graph being critical is computed. Numerical results are presented on industrial ASIC chips with over two million logic gates.

First-order incremental block-based statistical timing analysis

Recent changes in CMOS device structures and materials motivated by impending atomistic and quantum-mechanical limitations have profoundly influenced the nature of delay and power variability. Variations in process, temperature, power supply, wear-out, and use history continue to strongly influence delay. The manner in which tolerance is specified and accommodated in high-performance design changes dramatically as CMOS technologies scale beyond a 90-nm minimum lithographic linewidth. In this paper, predominant contributors to variability in new CMOS devices are surveyed, and preferred approaches to mitigate their sources of variability are proposed. Process-, device-, and circuit-level responses to systematic and random components of tolerance are considered. Exploratory, novel structures emerging as evolutionary CMOS replacements are likely to change the nature of variability in the coming generations.

High-performance CMOS variability in the 65-nm regime and beyond

VLSI Test Principles and Architectures: Design for Testability (Systems on Silicon)

The growing packing density and power consumption of very large scale integration (VLSI) circuits have made thermal effects one of the most important concerns of VLSI designers The increasing variability of key process parameters in nanometer CMOS technologies has resulted in larger impact of the substrate and metal line temperatures on the reliability and performance of the devices and interconnections Recent data shows that more than 50% of all integrated circuit failures are related to thermal issues This paper presents a brief discussion of key sources of power dissipation and their temperature relation in CMOS VLSI circuits, and techniques for full-chip temperature calculation with special attention to its implications on the design of high-performance, low-power VLSI circuits The paper is concluded with an overview of techniques to improve the full-chip thermal integrity by means of off-chip versus on-chip and static versus adaptive methods

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Thermal Modeling, Analysis, and Management in VLSI Circuits: Principles and Methods

Variability in digital integrated circuits makes timing verification an extremely challenging task. In this paper, a canonical first-order delay model that takes into account both correlated and independent randomness is proposed. A novel linear-time block-based statistical timing algorithm is employed to propagate timing quantities like arrival times and required arrival times through the timing graph in this canonical form. At the end of the statistical timing, the sensitivity of all timing quantities to each of the sources of variation is available. Excessive sensitivities can then be targeted by manual or automatic optimization methods to improve the robustness of the design. This paper also reports the first incremental statistical timer in the literature, which is suitable for use in the inner loop of physical synthesis or other optimization programs. The third novel contribution of this paper is the computation of local and global criticality probabilities. For a very small cost in computer time, the probability of each edge or node of the timing graph being critical is computed. Numerical results are presented on industrial application-specified integrated circuit (ASIC) chips with over two million logic gates, and statistical timing results are compared to exhaustive corner analysis on a chip design whose hardware showed early mode timing violations

First-Order Incremental Block-Based Statistical Timing Analysis

Uncertainty in circuit performance due to manufacturing and environmental variations is increasing with each new generation of technology. It is therefore important to predict the performance of a chip as a probabilistic quantity. This paper proposes three novel algorithms for statistical timing analysis and parametric yield prediction of digital integrated circuits. The methods have been implemented in the context of the EinsTimer static timing analyzer. Numerical results are presented to study the strengths and weaknesses of these complementary approaches. Across-the-chip variability continues to be accommodated by EinsTimer's "Linear Combination of Delay (LCD)" mode. Timing analysis results in the face of statistical temperature and V/sub dd/ variations are presented on an industrial ASIC part on which a bounded timing methodology leads to surprisingly wrong results.

/pdf/statistical-timing-for-parametric-yield-prediction-of-5g949scgtz.pdf

Statistical timing for parametric yield prediction of digital integrated circuits

A method of removing pessimism in static timing analysis is described. Delays are expressed as a function of discrete parameter settings allowing for both local and global variation to be taken in to account. Based on a specified target slack, each failing timing test is examined to determine a consistent set of parameter settings which produces the worst possible slack. The analysis is performed on a path basis. By considering only parameters which are in common to a particular data/clock path-pair, the number of process combinations that need to be explored is reduced when compared to analyzing all combinations of the global parameter settings. Further, if parameters are separable and linear, worst-case variable assignments for a particular clock/data path pair can be computed in linear time by independently assigning each parameter value. In addition, if available, the incremental delay change with respect to each physically realizable process variable may be used to project the worst-case variable assignment on a per-path basis without the need for performing explicit corner enumeration.

System and method for correlated process pessimism removal for static timing analysis

Uncertainty in circuit performance due to manufacturing and environmental variations is increasing with each new generation of technology. It is therefore important to predict the performance of a chip as a probabilistic quantity. This paper proposes three novel path-based algorithms for statistical timing analysis and parametric yield prediction of digital integrated circuits. The methods have been implemented in the context of the EinsTimer static timing analyzer. The three methods are complementary in that they are designed to target different process variation conditions that occur in practice. Numerical results are presented to study the strengths and weaknesses of these complementary approaches. Timing analysis results in the face of statistical temperature and Vdd variations are presented on an industrial ASIC part on which a bounded timing methodology leads to surprisingly wrong results

/pdf/statistical-timing-for-parametric-yield-prediction-of-2ehxqzsf8f.pdf

Kerim Kalafala

Papers

First-order incremental block-based statistical timing analysis

First-Order Incremental Block-Based Statistical Timing Analysis

Statistical timing for parametric yield prediction of digital integrated circuits

System and method for correlated process pessimism removal for static timing analysis

Statistical Timing for Parametric Yield Prediction of Digital Integrated Circuits