IC Static Timing With Equivalent-Parameter Variation Models
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for modeling combined global and local process variations in integrated circuit (IC) designs are inefficient and require significant processor time and memory, making them impractical for accurate static timing analysis (STA).
Innovation Solution
A set of equivalent parameters, including threshold voltage per device type and resistance/capacitance per interconnect layer, is used to model global process variations, combined with local variations through linear or root sum squared calculations, reducing the number of parameters needed and improving computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods use tens or hundreds of parameters to model global process variations, then modeling accuracy is improved, but processor time and memory usage increase significantly
Solution Approach 1:
The patent extracts only the most critical parameters from the full set of global process variation parameters. Specifically, it selects one parameter per device type (such as threshold voltage) and two parameters per interconnect layer (resistance per unit length and capacitance per unit length), reducing the parameter set from tens or hundreds to just a few key parameters that capture the dominant sources of variation.
Solution Approach 2:
The patent changes the parameter representation by using equivalent parameters that combine multiple physical effects into single representative values. The equivalent parameters (threshold voltage, resistance per unit length, capacitance per unit length) are calibrated to reproduce the statistical behavior of the full parameter set, enabling accurate modeling with fewer parameters.
2Measurement precision
If traditional methods use tens or hundreds of parameters to model global process variations, then modeling accuracy is improved, but memory usage increases significantly
Solution Approach 1:
The patent extracts only the most critical parameters from the full set of global process variation parameters. Specifically, it selects one parameter per device type (such as threshold voltage) and two parameters per interconnect layer (resistance per unit length and capacitance per unit length), reducing the parameter set from tens or hundreds to just a few key parameters that capture the dominant sources of variation.
3Measurement precision
If Monte-Carlo analysis is performed using many global parameters, then accuracy of global distribution determination is improved, but computational complexity increases
Solution Approach 1:
The patent extracts only the most critical parameters from the full set of global process variation parameters. Specifically, it selects one parameter per device type (such as threshold voltage) and two parameters per interconnect layer (resistance per unit length and capacitance per unit length), reducing the parameter set from tens or hundreds to just a few key parameters that capture the dominant sources of variation.
Solution Approach 2:
The patent changes the parameter representation by using equivalent parameters that combine multiple physical effects into single representative values. The equivalent parameters (threshold voltage, resistance per unit length, capacitance per unit length) are calibrated to reproduce the statistical behavior of the full parameter set, enabling accurate modeling with fewer parameters.
4Productivity
If a small set of equivalent parameters is used to model global process variations, then computational efficiency is improved, but modeling accuracy may deteriorate
Solution Approach 1:
The patent changes the parameter representation by using equivalent parameters that combine multiple physical effects into single representative values. The equivalent parameters (threshold voltage, resistance per unit length, capacitance per unit length) are calibrated to reproduce the statistical behavior of the full parameter set, enabling accurate modeling with fewer parameters.
Solution Approach 2:
The patent creates universal equivalent parameters that can represent multiple underlying physical variations. For example, the threshold voltage parameter captures the combined effect of multiple device fabrication variations, and the resistance/capacitance per unit length parameters capture interconnect variations, making these equivalent parameters multi-functional representations that maintain accuracy while reducing count.
Data Source
AI summary
A set of global parameters may be modeled using a set of equivalent parameters, where the set of global parameters represents global process variation in a circuit. A global distribution for a metric in the circuit may be determined by performing Monte-Carlo (MC) analysis using the set of equivalent parameters. Combined local and global variations for the metric may be calculated based on the global distribution for the metric and a local distribution for the metric.