Statistical Timing Model Simplification via Sensitivity Analysis
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Solution Overview
Problem
Current statistical timing analysis methods for integrated circuits are cumbersome due to the need to simulate numerous independent geometry parameters, leading to an excessive number of evaluations and large data sets, which complicates the process and increases resource usage.
Innovation Solution
A method is introduced to simplify the statistical model by selecting only the derived process parameters with high sensitivity for timing analysis, which are linear combinations of process parameter variations, thereby reducing the number of calculations required.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional statistical timing analysis simulates all independent geometry parameters (width, thickness, isolator stacks) for every wire level, then the analysis comprehensively covers process variations, but the number of evaluations becomes impossible (2^24 geometries for 6-level metal technology)
Solution Approach 1:
The patent extracts and identifies only the dominant geometry parameters that have the most significant impact on timing delays. By analyzing sensitivity coefficients, the method separates critical parameters (such as wire width and thickness) from less influential ones, evaluating only the essential subset rather than all possible parameter combinations.
Solution Approach 2:
The patent transforms the timing analysis by changing from evaluating all geometry parameters to evaluating only the dominant ones. The method uses sensitivity analysis to identify which parameter variations most significantly affect delay, then focuses computational resources on those specific parameters while using linear interpolation for others.
2Manufacturing precision
If the timing tool evaluates all 2^24 geometries with nine geometry variations per metal level, then complete timing coverage is achieved, but the computational burden and storage requirements become unmanageable
Solution Approach 1:
The patent applies partial action by evaluating only the necessary subset of geometry parameters rather than all possible combinations. The sensitivity analysis identifies which parameters require full evaluation and which can be handled through linear interpolation, performing exactly the right amount of computation needed for acceptable accuracy.
Solution Approach 2:
The patent uses linear interpolation to estimate timing values for intermediate geometry parameters based on evaluations at extreme points (min and max values). This creates approximate copies of the full evaluation results without actually performing all the computations, significantly reducing the computational burden while maintaining reasonable accuracy.
3Reliability
If separate, independent variations of dielectric thickness between wire levels are simulated, then the statistical model captures more process variations, but the number of process variations and calculations increases
Solution Approach 1:
The patent extracts only the dominant sources of variation that significantly impact timing. By analyzing sensitivity coefficients for each parameter including dielectric thickness variations, the method identifies which independent variations contribute most to timing uncertainty and focuses on those while reducing or eliminating less significant variations.
Data Source
AI summary
Forming of a statistical model for a set of independently variable parameters for analysis of a circuit design is disclosed. In one embodiment, a method includes establishing a timing model including delay and delay changes due to process parameter variations (Pi) that impact timing; selecting an element of the circuit design that dominates circuit delay in the timing model; determining a delay sensitivity of each of a set of derived process parameters (Vj) for the element that are linear combinations of the process parameter variations (Pi); and selecting only those derived process parameters with a high sensitivity for use in the statistical model. The invention simplifies the statistical model and reduces the number of calculations require for timing analysis. A method of performing a timing analysis using the simplified statistical model is also disclosed.