Data Filter for Scanning Metrology Noise Reduction
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Solution Overview
Problem
Conventional data processing methods are inadequate for handling non-equispaced samples obtained from scanning sensors in lithographic apparatuses, leading to noise and distortion in height maps, particularly near wafer edges and in regions with varying scanning speeds.
Innovation Solution
A method involving a kernel defined by a probability density function, such as a Gaussian kernel, is convoluted over data samples to perform a weighted average, followed by a first-order regression, which allows for effective filtering and processing of data samples at variable spacings, maintaining a constant kernel area based on sensor spot size and sample interval.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-affected harmful factors
If conventional low-pass filters are used to process non-equispaced samples, then noise removal is achieved, but measurement precision deteriorates due to inadequate handling of variable spacing
Solution Approach 1:
The patent transforms the filtering approach by changing the parameter of sample spacing from variable to uniform through interpolation. Non-equispaced samples are interpolated to create equispaced samples, allowing conventional low-pass filters to operate effectively. This parameter transformation resolves the contradiction by enabling noise removal while preserving measurement precision through proper spacing normalization.
Solution Approach 2:
The patent introduces an intermediary processing step between sample acquisition and filtering. An interpolation function acts as a mediator that converts non-equispaced samples into equispaced samples, bridging the gap between the actual variable spacing and the requirements of conventional filters. This intermediary transformation enables effective noise removal without compromising accuracy.
2Measurement precision
If sampling rate is increased to improve measurement accuracy, then data quality improves, but processing complexity increases due to larger data sets
Solution Approach 1:
The patent extracts and separates the interpolation step from the main filtering process. By isolating the complex interpolation operation as a preliminary preprocessing step, the subsequent filtering operates on uniformly spaced data, reducing overall processing complexity. This extraction allows high-rate sampling to improve accuracy while managing complexity through staged processing.
Solution Approach 2:
The patent segments the data processing into distinct stages: first interpolating non-equispaced samples to equispaced samples, then applying conventional low-pass filtering. This segmentation allows each stage to be optimized independently, reducing overall computational complexity while maintaining high sampling accuracy benefits.
3Productivity
If conventional filtering methods are applied to non-equispaced data, then processing speed is maintained, but measurement precision deteriorates due to inadequate noise filtering
Solution Approach 1:
The patent performs preliminary interpolation to convert non-equispaced samples into equispaced samples before applying conventional low-pass filters. This preliminary action prepares the data in the format required for efficient conventional filtering, maintaining processing speed while enabling effective noise filtering and improving measurement precision.
Solution Approach 2:
The patent changes the spacing parameter from variable to uniform through interpolation, enabling the use of efficient conventional filtering algorithms. This parameter transformation maintains processing speed by allowing the use of optimized equispaced filtering methods while significantly improving noise filtering effectiveness and measurement accuracy.
Data Source
AI summary
A method of processing a data set including equispaced and/or non-equispaced data samples is disclosed. The method includes filtering of the data, wherein a kernel defined by a probability density function is convoluted over samples in the data set to perform a weighted average of the samples at a plurality of positions across the data set, and wherein a first order regression is applied to the filtered data to provide a processed data output.