Semiconductor Structure Metrology Using Multi-Pass MAP Estimation
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Solution Overview
Problem
Existing metrology techniques for semiconductor structures face challenges in accurately measuring complex structures due to insufficient information content, especially with increasing resolution requirements, multi-parameter correlation, and the use of opaque materials, leading to instability and inaccuracies in parameter estimation.
Innovation Solution
The integration of prior measurement information, such as physical process constraints and wafer-based models, into the optimization function using a Maximum A Posteriori (MAP) estimation approach, which combines current and prior data to enhance parameter estimation stability and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional metrology techniques are used to measure semiconductor structures, then measurement throughput is maintained, but measurement precision and accuracy deteriorate due to insufficient information content in complex structures
Solution Approach 1:
The patent applies preliminary action by incorporating prior measurement information and physical process constraints into the optimization function before performing the actual measurement analysis. This pre-integration of contextual knowledge enriches the information content available for parameter estimation, enabling accurate measurements of complex semiconductor structures without requiring additional physical measurements.
Solution Approach 2:
The patent uses an optimization function as an intermediary that bridges the gap between limited measurement data and the desired parameter estimates. By incorporating prior information and physical constraints into this intermediary function, the system compensates for insufficient information content in the raw measurements, enabling accurate parameter estimation for complex structures.
2Adaptability or versatility
If more parameters are floated to increase measurement flexibility, then adaptability improves, but measurement stability deteriorates due to parameter correlation and insufficient information
Solution Approach 1:
The patent applies feedback by incorporating physical process constraints and prior measurement information into the optimization function. This feedback mechanism provides stabilizing information that counteracts the instability introduced by floating multiple correlated parameters, enabling the system to maintain both flexibility and stability in parameter estimation.
Solution Approach 2:
The patent changes the parameterization approach by integrating prior information and physical constraints directly into the optimization function. This transformation allows the system to handle higher dimensional parameter spaces with improved stability, as the constrained optimization framework prevents unrealistic parameter combinations that would otherwise cause instability.
3Productivity
If measurement models are simplified to improve processing speed, then productivity increases, but measurement precision deteriorates due to inability to capture complex structure characteristics
Solution Approach 1:
The patent applies local quality by incorporating specific physical process constraints and prior measurement information relevant to particular semiconductor structures into the optimization function. This localized enrichment of information allows the use of computationally efficient models while maintaining high precision for specific parameter estimation, as the constraints provide structure-specific knowledge without requiring complex global models.
Data Source
AI summary
Methods and systems for measuring physical properties of a specimen by iterative solution of an optimization function including both current and prior measurement information are described herein. In one aspect, a Maximum A Posteriori (MAP) estimation approach is employed to integrate prior measurement information with current measurement information in the optimization function. In some examples, prior measurement information associated with the measurement of a semiconductor structure is available from a number of exogenous sources. In a further aspect, prior measurement information includes current measurements of a semiconductor structure under measurement as part of a multiple pass measurement. Prior statistics are determined based on an initial set of values of parameters of interest. The prior statistics are included in a subsequent MAP analysis of the same measurement data set employed in a first measurement pass. In another aspect, prior statistics are tracked to determine their impact on current measurements.