Calibrating Optical Metrology Azimuth Error via Mueller Matrix Symmetry
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Solution Overview
Problem
Scatterometry systems face challenges in achieving high alignment accuracy due to uncontrolled angular errors in the plane-of-incidence (POI) azimuth angle, leading to variations in spectral signatures across different systems, making precise hardware alignment difficult, especially down to 0.2°.
Innovation Solution
The method involves calibrating the POI azimuth error by determining and correcting the azimuth angle offset using a calibration grating on a sample, measuring a partial Mueller matrix at multiple POI azimuth angles, and determining an axis of symmetry to calculate the offset, which can be applied to correct for angular errors in optical metrology devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If hardware alignment is performed to achieve high alignment accuracy, then measurement precision is improved, but device complexity increases due to the difficulty of achieving alignment down to 0.2°
Solution Approach 1:
The patent applies preliminary action by performing a calibration procedure before actual measurements. A calibration grating is measured at multiple POI azimuth angles to determine symmetry axes, from which an azimuth angle offset is calculated and stored. This pre-calibration step eliminates the need for complex real-time alignment adjustments during measurement, achieving high alignment accuracy (0.2° or better) while reducing operational complexity.
2Measurement precision
If POI azimuth angle is controlled to reduce angular error, then measurement precision is improved, but ease of operation deteriorates due to the difficulty of maintaining precise angular control
Solution Approach 1:
The patent implements feedback by measuring the calibration grating at multiple POI azimuth angles (e.g., -5° to +5° in 1° increments) and using the measured Mueller matrix data to calculate the symmetry axis and azimuth angle offset. This feedback mechanism identifies the actual angular deviation and provides correction information, allowing the system to compensate for angular errors without requiring complex real-time angular control during measurement operations.
3Ease of operation
If angular error in POI azimuth angle is left uncontrolled, then ease of operation is improved, but measurement precision deteriorates due to spectral signature variations across different systems
Solution Approach 1:
The patent applies self-service by enabling each optical metrology system to automatically determine its own azimuth angle offset through calibration. Each system measures its calibration grating, calculates its specific symmetry axes, determines its unique offset value, and uses this information to correct subsequent measurements. This self-calibration approach allows systems to operate with high measurement precision without requiring complex external alignment control or inter-system coordination.
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 accurate determination and correction of POI azimuth angle offsets, enhancing the alignment accuracy of optical metrology systems, enabling precise measurements and uniform calibration across multiple devices.
Implementation Method 1
measuring at least a partial Mueller matrix from a calibration grating on a sample that is held on a stage for a plurality of POI azimuth angles
Data Source
AI summary
Optical metrology is used to calibrate the plane-of-incidence (POI) azimuth error by determining and correcting an azimuth angle offset. The azimuth angle offset may be determined by measuring at least a partial Mueller matrix from a calibration grating on a sample held on a stage for a plurality of POI azimuth angles. An axis of symmetry is determined for a curve describing a value of a Mueller matrix element with respect to POI azimuth angle, for each desired wavelength and each desired Mueller matrix element. The axis of symmetry may then be used to determine the azimuth angle offset, e.g., by determining a mean, median or average of all, or a filtered subset, of the axes of symmetry. If desired, an axis of symmetry may be determined for data sets other than Mueller matrix elements, such as Fourier coefficients of measured signals.