Unified Statistical Model for IC Process Variations
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Solution Overview
Problem
Conventional modeling of process variations in integrated circuits is inaccurate, leading to over-design due to the assumption that all devices are sampled at the same process corner, ignoring over-chip variations and double counting local variations, which results in wasted design margins and inefficient scaling with transistor size reduction.
Innovation Solution
A unified statistical modeling method that separates and accurately determines global and local variations by generating total variation sigma from intra-die and inter-die data, allowing for the generation of corner models for each, thereby reducing over-design and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional corner modeling assumes all devices are sampled at the same process corner, then the modeling process is simple, but the accuracy of variation prediction deteriorates due to ignoring over-chip variations and double counting local variations
Solution Approach 1:
The patent segments the total variation into two distinct components: global variation (sigma_global) representing over-chip variations sampled at different process corners, and local variation (sigma_local) representing intra-die variations. This segmentation allows accurate prediction of device behavior at different locations without double counting, while maintaining a manageable modeling process through separate corner models for global variation and mismatch models for local variation.
2Reliability
If designers apply local variations on the corners of total variations, then robust designs are ensured, but design margins are wasted due to double counting of local variations
Solution Approach 1:
The patent separates total variation into global and local components, allowing designers to apply only the appropriate variation model for each design scenario. Corner models use sigma_global for global variation while mismatch models use sigma_local for local variation, eliminating double counting and reducing wasted design margin while maintaining robustness.
Solution Approach 2:
The patent introduces separate mismatch models as intermediaries that specifically handle local variations. These mismatch models act as a bridge between the corner models and the actual local device behavior, allowing accurate prediction of local variation effects without requiring designers to apply local variations on top of corner models, thus eliminating the double counting problem.
3Measurement precision
If the 1/sqrt(W*L) rule is used for sigma_local, then the modeling is simple, but the accuracy deteriorates in advanced technologies with smaller transistor scales
Solution Approach 1:
The patent moves away from the fixed 1/sqrt(W*L) rule for determining sigma_local and instead uses extraction from intra-die measurement data. This parameter change allows sigma_local to be determined based on actual observed variations in the specific technology node being modeled, significantly improving accuracy for advanced technologies while the extracted parameters can be reused across designs to manage complexity.
Data Source
AI summary
A method of developing a statistical model for integrated circuits includes providing a set of test patterns; collecting a set of intra-die data from the set of test patterns; collecting a set of inter-die data from the set of test patterns; generating a total variation sigma (sigma_total) from the set of intra-die data and the set of inter-die data; appointing one of a global variation sigma (sigma_global) and a local variation sigma (sigma_local) as a first sigma, and a remaining one as a second sigma; generating the first sigma from one of the set of intra-data and the set of inter-data; generating the second sigma by removing the first sigma from the sigma_total; generating a corner model for global variations based on sigma_global and the set of inter-die data; and generating a corner model for local variations based on sigma_local and the set of intra-die data.