Multi-Sided Variations for Statistical Static Timing Analysis
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Solution Overview
Problem
Current statistical static timing analysis (SSTA) methods face challenges in accurately modeling and projecting timing variations across a large multiple parameter process space, leading to pessimistic results and increased computational costs, especially when dealing with complex non-linear, non-separable models.
Innovation Solution
The method divides the process space into regions that can be modeled linearly, using statistical timers to propagate models for each region and create multi-sided sensitivities, allowing for more accurate projections at multiple points within the process space with reduced delay library requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current statistical static timing analysis methods are used to model timing variations across a large multiple parameter process space, then coverage of the process space is achieved, but the results become pessimistic and computational costs increase
Solution Approach 1:
The patent segments the process space into multiple regions, each modeled with linear variations. This segmentation allows the complex non-linear process space to be divided into manageable linear segments, reducing computational complexity while maintaining accuracy. The timing analysis is performed separately for each region and then combined, avoiding the need to compute across the entire large parameter space in one operation.
Solution Approach 2:
The patent introduces a new dimension by creating multi-sided timing quantities that can project to any point within the process space. Instead of computing timing for each corner separately, the multi-sided approach creates a unified model that can be evaluated at multiple points simultaneously, reducing computational cost while maintaining comprehensive coverage.
2Measurement precision
If complex non-linear, non-separable models are used to accurately model timing variations, then modeling accuracy improves, but computational costs and pessimism increase
Solution Approach 1:
The complex non-linear model is segmented into multiple linear regions. Each region is modeled with simpler linear variations, reducing the complexity of individual models while collectively covering the entire non-linear process space. This segmentation transforms one complex non-separable model into multiple simpler linear models that are easier to compute.
Solution Approach 2:
The patent changes the parameter representation by introducing multi-sided timing quantities with associated sensitivities. Instead of using fixed corner-based parameters, the model uses variable-sided parameters that can adapt to different regions of the process space, allowing accurate representation of non-linear behavior through linear segments with varying parameters.
3Reliability
If traditional corner-based timing analysis is performed to cover the process space, then all corners are analyzed, but results become pessimistic
Solution Approach 1:
The patent transitions from traditional corner-based analysis to a multi-sided approach that adds a new dimension of flexibility. Instead of being constrained to fixed corners, the multi-sided model can project timing quantities to any point within the process space, including interior points that provide more realistic timing estimates and reduce pessimism while maintaining complete coverage.
Solution Approach 2:
The process space is segmented into multiple regions with different timing characteristics. By analyzing each region separately and combining results, the method achieves complete coverage without the pessimism of worst-case corner analysis, as each segment can be evaluated with appropriate local variations rather than global worst-case assumptions.
Data Source
AI summary
Creating an integrated circuit with non-linear variations, the computer identifies an integrated circuit design; identifies a timing model associated with the identified integrated circuit design; defines one or more static single sided variables; defines one or more regions of one or more of the defined one or more static single sided variables that are treated linearly; defines one or more multi-sided variables based on the defined one or more regions of the one or more of the defined one or more static single sided variables; identifies one or more timing paths within the identified integrated circuit design; performs a statistical static timing analysis on the identified timing model for the identified one or more timing paths within the identified integrated circuit design utilizing the defined one or more multi-sided variables; provides one or more timing quantities that project within a multi-parameter space based on the performed statistical static timing analysis.