Scatterometry Model Parameter Constraint for Substrate Structure Measurement
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Solution Overview
Problem
In lithographic processes, existing measurement techniques face challenges in accurately determining microscopic structure parameters due to the high number of degrees of freedom in models, leading to inaccuracies and computational inefficiencies, especially when dealing with complex structures or materials.
Innovation Solution
The method involves defining a mathematical model with variable parameters, applying constraints to reduce the number of degrees of freedom without fixing parameters, and using these constrained models to generate and compare candidate structures to identify the best matching signal for measurement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of variable parameters in the model is increased to accurately represent complex structures, then measurement accuracy is improved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent segments the parameter space by dividing it into multiple subspaces, each with its own reduced set of variable parameters. This allows the complex measurement problem to be broken down into smaller, more manageable subproblems that can be solved independently and then combined, reducing overall computational complexity while maintaining measurement accuracy.
Solution Approach 2:
The patent introduces a new dimension by adding a subspace identification step to the traditional parameter matching process. Instead of directly searching through the high-dimensional parameter space, the system first identifies which subspace the measurement belongs to, then performs parameter matching within that specific subspace. This dimensional transformation reduces the effective search space and computational burden.
2Measurement precision
If more parameters are treated as variable to capture complex structure characteristics, then reconstruction accuracy is improved, but the size of the parameter space and computational tasks become unacceptably large
Solution Approach 1:
The patent divides the large parameter space into multiple smaller subspaces, each characterized by a reduced set of variable parameters. This segmentation allows the system to perform faster local searches within each subspace rather than performing a single exhaustive search through the entire parameter space, significantly reducing computational processing time while maintaining reconstruction accuracy.
Solution Approach 2:
The patent performs preliminary action by first identifying which subspace the measurement data belongs to before performing the actual parameter matching. This preliminary classification step narrows down the search space in advance, allowing subsequent parameter optimization to be performed more efficiently on a reduced set of candidate parameters.
3Productivity
If parameters are fixed to nominal values to reduce model complexity, then computational efficiency is improved, but measurement accuracy deteriorates due to distortion in the matching process
Solution Approach 1:
The patent makes the model dynamic by allowing the set of variable parameters to change depending on which subspace is identified. Instead of fixing parameters to nominal values or allowing all parameters to vary uniformly, the system dynamically selects which parameters should be variable based on the measured data characteristics, optimizing both computational efficiency and measurement accuracy for each specific case.
Solution Approach 2:
The patent changes parameters based on the identified subspace. Each subspace has its own optimized set of variable parameters, allowing the system to adapt the model complexity to match the actual measurement requirements. This parameter adaptation ensures that only the necessary parameters are varied for each measurement, improving computational efficiency without sacrificing accuracy.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for more accurate and efficient measurement of structure parameters by reducing the number of degrees of freedom, improving reconstruction accuracy without compromising computational practicality.
Implementation Method 1
a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured
Implementation Method 2
properties of the scattered or reflected beam are measured
Implementation Method 3
model, e.g., simulated, diffraction signals calculated from a parameterized model
Data Source
AI summary
Diffraction models and scatterometry are used to reconstruct a model of a microscopic structure on a substrate. A plurality of candidate structures are defined, each represented by a plurality of parameters (p1, p2, etc.)). A plurality of model diffraction signals are calculated by simulating illumination of each of the candidate structures. The structure is reconstructed by fitting one or more of the model diffraction signals to a signal detected from the structure. In the generation of the candidate structures, a model recipe is used in which parameters are designated as either fixed or variable. Among the variable parameters, certain parameters are constrained to vary together in accordance with certain constraints, such as linear constraints. An optimized set of constraints, and therefore an optimized model recipe, is determined by reference to a user input designating one or more parameters of interest for a measurement, and by simulating the reconstruction process reconstruction. The optimized model recipe can be determined automatically by a parameter advisor process that simulates reconstruction of a set of reference structures, using a plurality of candidate model recipes. In the generation of the reference structures, restrictions can be applied to exclude unrealistic parameter combinations.