Optical Metrology for Semiconductor Devices Using Mueller Matrix
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Solution Overview
Problem
Existing optical metrology techniques face challenges in accurately differentiating dimensional parameters and asymmetric parameters in complex 3D semiconductor devices due to high correlation between the two, making it difficult to achieve precise measurements, especially in structures like Forksheet devices where process-induced errors are common.
Innovation Solution
The use of Mueller matrix paired off-diagonal elements in combination with machine learning approaches to generate predictions of asymmetric parameters, which are then fed forward to improve the accuracy of dimensional parameter measurements, thereby breaking the correlation between dimensional and asymmetric parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional optical metrology techniques are used to measure complex 3D semiconductor devices, then dimensional parameters can be obtained, but the high correlation between dimensional parameters and asymmetric parameters causes measurement inaccuracy
Solution Approach 1:
The patent segments the measurement process into two independent stages: first measuring asymmetric parameters using Mueller matrix paired off-diagonal elements, then measuring dimensional parameters using the remaining Mueller matrix elements with asymmetric parameters fixed. This segmentation breaks the correlation between parameter types and enables accurate measurement of complex 3D semiconductor devices.
Solution Approach 2:
The patent extracts asymmetric parameters from the full set of Mueller matrix elements by specifically using the paired off-diagonal elements (m13, m31, m24, m42). This extraction isolates the asymmetric parameter information from dimensional parameter information, allowing them to be measured independently without mutual interference.
2Loss of information
If all Mueller matrix elements are used simultaneously to determine both dimensional and asymmetric parameters, then comprehensive device information is obtained, but the correlation between parameter types reduces measurement accuracy
Solution Approach 1:
The patent segments the 16 Mueller matrix elements into two distinct groups: paired off-diagonal elements (m13, m31, m24, m42) for asymmetric parameter measurement, and remaining elements for dimensional parameter measurement. This segmentation prevents information mixing and maintains measurement precision for both parameter types.
Solution Approach 2:
The patent performs preliminary measurement of asymmetric parameters using paired off-diagonal elements before measuring dimensional parameters. By fixing asymmetric parameters in advance, the subsequent dimensional parameter measurement avoids correlation issues, enabling accurate determination of both parameter types from comprehensive Mueller matrix data.
3Measurement precision
If traditional modeling techniques are used for complex features, then parameter fitting can be achieved, but the process is time consuming and computationally intensive
Solution Approach 1:
The patent segments the parameter fitting process into two separate regression analyses: first fitting asymmetric parameters using paired off-diagonal elements, then fitting dimensional parameters using remaining elements with asymmetric parameters fixed. This segmentation reduces computational complexity and measurement time while maintaining fitting accuracy for complex semiconductor structures.
Solution Approach 2:
The patent performs preliminary determination of asymmetric parameters before the main dimensional parameter fitting process. This preliminary action simplifies the subsequent regression analysis by reducing the number of free parameters, thereby decreasing computation time while preserving measurement accuracy for complex 3D devices.
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 method enhances the accuracy of dimensional parameter measurements by suppressing the correlation with asymmetric parameters, leading to improved device performance and more efficient metrology solutions for complex structures.
Implementation Method 1
obtaining a plurality of Mueller matrix elements from ellipsometry measurements of the 3D device
Implementation Method 2
generating machine learning predictions of asymmetric parameters of the 3D device based on at least one Mueller matrix paired off-diagonal elements
Data Source
AI summary
Complex three-dimensional structures in semiconductor devices are measured using Mueller matrix paired off-diagonal elements to generate machine learning predictions of asymmetric parameters of the device and determine dimensional parameters based on one or more Mueller matrix elements and the asymmetric parameters. The measurements of the device may be performed at different azimuth angles selected based on sensitivity to the asymmetric parameters and the dimensional parameters. Additionally, the Mueller matrix elements may be generated based on measurements performed at azimuth angles that are 180° apart to eliminate asymmetric noise from the measurement tool. One or more models of the device may be used with the Mueller matrix elements to generate dimensional parameter information and optionally preliminary asymmetrical parameters. The determined asymmetric parameters may be fed forward to the one or more models for determining the dimensional parameters to suppress a correlation between dimensional parameters and asymmetric parameters of the device.