Physics-Augmented Regression for Large-Pitch Critical Dimension Metrology
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Solution Overview
Problem
Current metrology methods struggle to accurately determine critical dimensions of large pitch targets like deep trench and through-silicon via structures due to local minima issues in chi-square-based regression algorithms, leading to inaccurate and inefficient depth and bottom CD parameter extraction, which compromises precision and speed.
Innovation Solution
A physics augmented regression algorithm that isolates depth parameters from other model parameters, using a novel objective function to iteratively match simulated and detected signals, enhancing precision and speed in determining critical dimensions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If chi-square-based regression algorithms are used to determine critical dimensions of large pitch targets, then the measurement process can be performed, but the algorithms encounter local minima issues leading to inaccurate depth and bottom CD parameter extraction
Solution Approach 1:
The patent segments the critical dimension extraction process into multiple independent parameters (top CD, bottom CD, depth) and uses separate objective functions for each parameter optimization. This segmentation allows the algorithm to avoid local minima by optimizing each parameter independently rather than simultaneously, resolving the convergence reliability issue while maintaining measurement precision.
Solution Approach 2:
The patent changes the objective function from the traditional chi-square-based function to a physics-augmented objective function that incorporates optical transfer functions and spectral sensitivity information. This parameter change in the objective function formulation enables the algorithm to navigate the solution space more effectively, avoiding local minima and achieving both accurate parameter extraction and reliable convergence.
2Measurement precision
If iterative regression algorithms are used to extract critical dimensions, then measurement precision can be improved, but the calculation time increases reducing productivity
Solution Approach 1:
The patent performs preliminary actions by pre-calculating and storing optical transfer functions and spectral sensitivity information before the actual measurement. This preliminary computation allows the iterative regression algorithm to access ready-to-use physics models during execution, reducing the computational burden per iteration and thus decreasing total calculation time while maintaining high measurement precision.
Solution Approach 2:
The patent introduces an intermediary physics-augmented objective function that mediates between the raw measurement data and the critical dimension parameters. This intermediary function incorporates optical physics models that provide physical constraints and guidance, enabling the algorithm to converge faster to accurate solutions by avoiding unnecessary iterations in the parameter space.
3Measurement precision
If complex physics models are used to simulate target signals, then measurement accuracy improves, but the computational complexity increases
Solution Approach 1:
The patent segments the complex physics modeling into separate, modular components: optical transfer functions for different layers, spectral sensitivity functions for detectors, and material optical properties. This segmentation allows the complex physics to be managed through composition of simpler functions, reducing algorithmic complexity while maintaining accurate signal simulation through the combined effect of these modular physics models.
Data Source
AI summary
Methods and systems for determining information for a specimen are provided. One system includes a metrology subsystem that detects signals responsive to illumination of a target structure on a specimen. The system also includes a physics augmented regression algorithm and an objective function. The objective function is configured for separation of relationships between the detected signals and different physical characteristics of the target structure. The physics augmented regression algorithm determines one or more of the different physical characteristics of the target structure from the detected signals.