Statistical Circuit Timing Analysis Using Generated PVT Corners
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Solution Overview
Problem
Existing circuit design analysis techniques face limitations in predicting failures due to design or manufacturing defects, particularly in very-large-scale integration circuits, as they often rely on deterministic timing analysis that assumes fixed values, leading to over-margining and potential hardware failures.
Innovation Solution
Generating additional PVT points using existing or known PVT points by pre-characterizing relationships between them, allowing for full parameterization and multi-dimensional statistical timing analysis without over-margining, thereby accounting for variability in process, voltage, and temperature.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If deterministic timing analysis is used, then analysis simplicity is maintained, but prediction accuracy deteriorates due to over-margining
Solution Approach 1:
The patent transforms deterministic timing analysis into statistical timing analysis by changing the parameter representation from fixed values to probability distributions. This involves modeling timing parameters as random variables with specific distributions (e.g., normal, log-normal) rather than using single deterministic values, thereby capturing variability in process, voltage, and temperature effects without sacrificing computational feasibility.
Solution Approach 2:
The patent extends timing analysis from a single-point determination to a multi-dimensional statistical space by incorporating multiple standard deviation points (e.g., μ-3σ, μ-2σ, μ-1σ, μ, μ+1σ, μ+2σ, μ+3σ). This dimensional expansion allows the analysis to capture the full distribution of possible timing outcomes rather than relying on a single worst-case or nominal value.
2Reliability
If statistical timing analysis with multiple PVT points is performed, then prediction accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent segments the statistical timing analysis into independent dimensional components, analyzing process, voltage, and temperature variations separately along each dimension before combining results through root-sum-square calculations. This segmentation allows complex multi-dimensional statistical analysis to be broken down into manageable one-dimensional analyses that can be performed systematically and combined efficiently.
Solution Approach 2:
The patent performs timing analysis at multiple discrete PVT corner points (e.g., μ-3σ to μ+3σ) which represents excessive sampling compared to a single deterministic analysis. By evaluating timing at these discrete statistical points and combining results through root-sum-square, the method achieves accurate statistical timing prediction without requiring exhaustive simulation of all possible continuous parameter combinations.
Data Source
AI summary
Examples described herein provide a computer-implemented method that includes receiving a circuit design and a set of known process, voltage, and temperature (PVT) points for components of the circuit design. The method further includes determining parameter ratios for the set of known PVT points. The method further includes performing a statistical static timing analysis on the circuit design using the set of known PVT points and at least one additional PVT point generated during the statistical static timing analysis. The method further includes performing projections and root sum squaring for possible corners in a parameter space based on a canonical model generated during performing the statistical static timing analysis.