SCS-OCV Statistical Corner Evaluation for On-Chip Variation
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Solution Overview
Problem
Current on-chip variation modeling techniques in integrated circuit timing analysis are hindered by high computational costs and pessimism introduced by simplifying assumptions, particularly in advanced technology nodes, which impedes widespread adoption and accuracy.
Innovation Solution
The Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV) methodology addresses these issues by introducing complex variation concepts, practical statistical min/max operations, and a corner evaluation method to accurately model and propagate random variations, reducing pessimism and computational burdens.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If statistical library characterization and statistical RC parasitic extraction are performed to enable accurate SSTA, then measurement precision and reliability are improved, but device complexity and computational cost increase significantly
Solution Approach 1:
The patent extracts and pre-characterizes statistical information (mean, standard deviation, skewness, kurtosis) of delay variations for standard cells and interconnects during the library characterization phase. This extracted statistical data is stored in lookup tables that can be directly used in timing analysis without performing expensive real-time statistical library characterization, thus reducing the complexity burden during actual timing analysis while maintaining accuracy.
Solution Approach 2:
The patent performs statistical characterization and RC parasitic extraction in advance during library characterization and creates pre-computed statistical models and lookup tables. This preliminary action eliminates the need to perform these expensive operations during actual timing analysis, significantly reducing the computational cost and complexity of SSTA while preserving measurement precision through the pre-computed statistical parameters.
2Device complexity
If single number OCV derating is used to model all on-chip variations, then device complexity is reduced, but reliability deteriorates due to increased pessimism
Solution Approach 1:
The patent transitions from uniform single-number OCV derating to location-aware statistical modeling where different statistical parameters (mean, standard deviation, skewness, kurtosis) are assigned to different locations and paths in the circuit based on their specific variation characteristics. This local quality approach allows each path to have its own statistically accurate timing model, eliminating the excessive pessimism of uniform derating while maintaining manageable complexity through automated statistical extraction and lookup table usage.
3Reliability
If complex statistical min/max operations are implemented to handle random variations, then reliability is improved, but computational cost increases
Solution Approach 1:
The patent uses statistical lookup tables that store pre-computed timing information for various statistical corners (e.g., 1-sigma, 2-sigma, 3-sigma points). During timing analysis, instead of performing complex real-time statistical calculations, the system queries these pre-computed lookup tables to obtain timing values for different statistical corners. This copying approach maintains reliability through accurate statistical corner evaluation while dramatically reducing computational cost by replacing complex calculations with table lookups.
Data Source
AI summary
The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV. This significantly reduces the learning curve and increases the usage of the technology, being more easily adopted by the industry.