Semiconductor Measurement Recipe Optimization With Regularization
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Solution Overview
Problem
Current metrology systems face challenges in generating measurement recipes efficiently due to the complexity of semiconductor structures, which require long computational times and are not robust to variations in hardware and geometric modeling errors, leading to delays and reduced performance.
Innovation Solution
A regularized measurement recipe optimization method that incorporates regularization terms to constrain the process space, using prior knowledge of the measurement application, to identify a minimum set of measurement system settings that are robust to variations and reduce computational effort.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional measurement recipe optimization is performed without regularization, then measurement precision can be improved, but computational time increases significantly and robustness to variations decreases
Solution Approach 1:
The patent applies preliminary action by incorporating regularization terms into the cost function before optimization begins. These regularization terms (L2 norm on weights, L1 norm on coefficients, or elastic net) pre-constrain the search space and guide the optimization toward physically meaningful solutions, reducing the need for extensive computational exploration while maintaining measurement precision.
Solution Approach 2:
The patent changes the parameter space by transforming the optimization problem into a regularized form. By modifying the cost function to include regularization components, the patent effectively changes the parameters being optimized, leading to faster convergence and reduced computational time while preserving the ability to achieve high measurement precision.
2Reliability
If comprehensive measurement system parameter settings are explored, then measurement robustness improves, but computational effort and time requirements increase
Solution Approach 1:
The patent applies local quality by making the optimization process sensitive to local variations in the data through regularization terms. The L2 and L1 normalization terms in the cost function create local penalties that encourage the optimization to focus on the most informative measurement parameters, achieving robustness without requiring exhaustive exploration of all possible settings.
Solution Approach 2:
The patent uses copying by creating a regularized cost function that replicates the essential characteristics of the measurement problem while adding constraining elements. This copied optimization problem maintains the robustness requirements but reduces computational complexity through the added regularization structure that simplifies the search space.
3Adaptability or versatility
If measurement recipe optimization is performed without regularization terms, then flexibility in parameter selection is maintained, but optimization stability and robustness to variations decrease
Solution Approach 1:
The patent applies beforehand cushioning by incorporating regularization terms that act as protective constraints during optimization. These terms (L2 norm on weights, L1 norm on coefficients) provide a cushion against overfitting and instability by penalizing extreme parameter values before they can cause optimization failures, thereby stabilizing the results while maintaining flexibility.
Solution Approach 2:
The patent changes the parameter space by transforming the optimization problem into a regularized form. By modifying the cost function to include regularization components, the patent effectively changes the parameters being optimized, leading to more stable and reliable results while preserving the ability to adapt to different measurement scenarios.
Data Source
AI summary
Methods and systems for optimizing a semiconductor measurement recipe that is robust to variations of hardware modeling parameters and geometric modeling errors are described herein. Robust measurement recipe optimization minimizes a cost function including one or more regularization terms that constrain the process space, and thus, significantly reduces the computational effort required to optimize a measurement recipe. This reduces overall process time and improves wafer throughput. In some examples, optimization is performed based on measurement data associated with multiple instances of a semiconductor structure; each instance characterized a different value of one or more geometric parameters of interest. In some examples, the search for optimized measurement recipes is limited to the discrete set of measurement system parameter values associated with the available measurement data set. In this manner, the performance of a particular measurement recipe is validated using existing measurement data.