Hybrid Mask Filter for Semiconductor Lattice Strain Analysis
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Solution Overview
Problem
Existing methods for analyzing lattice strain in semiconductor devices face challenges in achieving high resolution and accuracy due to the trade-off between spatial resolution and noise levels in strain images, particularly when using cosine mask filters.
Innovation Solution
A method utilizing a hybrid mask filter based on a combination of Gaussian and Sigmoid functions, represented by F(x) = Ke^(-2r^2) + (1-K) * 1/(1+er), is applied to select peak frequencies in spectrum images, allowing for improved noise removal and spatial resolution through Fourier Transform and inverse Fourier Transform processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a cosine mask filter is used in existing commercial software for strain analysis, then the filtering process is simple and straightforward, but the spatial resolution of the strain image deteriorates and noise increases
Solution Approach 1:
The patent changes the functional form of the mask filter from a cosine function to a hybrid function combining Gaussian and Sigmoid functions. This parameter change in the filter's mathematical representation enables simultaneous achievement of high spatial resolution and effective noise suppression, resolving the contradiction between simple filtering and measurement precision.
Solution Approach 2:
The patent creates a composite mask filter by combining Gaussian function characteristics (noise suppression) and Sigmoid function characteristics (edge preservation) into a single hybrid function. This composite approach allows the filter to simultaneously achieve noise reduction and maintain spatial resolution, overcoming the limitations of using a single function type.
2Measurement precision
If the size of the cosine mask increases to improve spatial resolution, then the spatial resolution of the strain image improves, but noise increases
Solution Approach 1:
The patent introduces a new functional form with adjustable parameters (sigma for Gaussian width, threshold for Sigmoid transition) that independently control noise suppression and resolution characteristics. By optimizing these parameters, the system achieves high spatial resolution without the noise penalty associated with increasing cosine mask size.
Solution Approach 2:
The hybrid filter combines the noise-suppressing Gaussian component with the edge-preserving Sigmoid component, creating a composite filtering mechanism that selectively reduces noise while maintaining spatial resolution. This composite structure allows simultaneous optimization of both contradictory properties.
3Object-generated harmful factors
If a larger mask size is used to reduce noise, then noise levels decrease, but spatial resolution deteriorates
Solution Approach 1:
The patent uses parameter optimization to achieve the desired balance between noise reduction and resolution. By adjusting the sigma parameter of the Gaussian component and the threshold parameter of the Sigmoid component, the system can achieve effective noise suppression while maintaining high spatial resolution, eliminating the need to increase mask size at the cost of resolution.
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 enables the generation of strain images with enhanced spatial resolution and reduced noise, allowing for more accurate analysis of lattice strain in semiconductor devices, thereby improving the analysis of stress effects on device performance.
Implementation Method 1
generating a spectrum image by performing a Fourier Transform on an image of a semiconductor device
Implementation Method 2
generating a first strain image by performing an inverse Fourier Transform on the filtered spectrum image
Data Source
AI summary
A method of analyzing lattice strain of a semiconductor device includes generating a spectrum image by performing a Fourier Transform on an image of a semiconductor device, providing a first hybrid mask filter t filter designed to select at least one peak frequency from the spectrum image, filtering the spectrum image using the first hybrid mask filter to generate a filtered spectrum image, and generating a first strain image by performing an inverse Fourier Transform on the filtered spectrum image.