Adaptive Smoothing for Plasma Emission Data Processing
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Solution Overview
Problem
Current data processing methods for numerical data, particularly in plasma etching, face challenges in achieving a high signal-to-noise ratio (S/N ratio) and reducing data delay time, leading to insufficient responsiveness and difficulty in detecting change points, especially in high-performance semiconductor devices with complex patterns and low aperture ratios.
Innovation Solution
The implementation of an adaptive double exponential smoothing method that adjusts smoothing parameters based on errors using a probability density function and exponential weighted moving averages, combined with the backward Savitzky-Golay method for data preprocessing, to enhance S/N ratio and responsiveness while minimizing data delay.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional data smoothing methods (e.g., simple exponential smoothing, moving average) are used, then data processing can be performed, but the S/N ratio is insufficient and change points cannot be detected with high precision
Solution Approach 1:
The patent applies dynamics by making the smoothing parameter adaptive rather than fixed. The smoothing parameter automatically adjusts its value based on the local characteristics of the data, allowing the filtering strength to vary dynamically across different regions of the signal. This enables precise detection of change points while maintaining high S/N ratio in stable regions.
Solution Approach 2:
The patent changes the parameter of the smoothing method from a fixed value to an adaptive value that varies with the data. By introducing an adaptive smoothing parameter that changes based on local data characteristics, the method achieves both high S/N ratio and precise change point detection simultaneously.
2Reliability
If strong smoothing is applied to improve S/N ratio, then noise is reduced, but data delay time increases and responsiveness decreases
Solution Approach 1:
The adaptive smoothing parameter dynamically adjusts the filtering strength based on local data characteristics. In regions with abrupt changes, the parameter reduces smoothing to minimize delay and maintain responsiveness. In stable regions, it increases smoothing to improve S/N ratio, thus resolving the time-delay versus quality trade-off.
Solution Approach 2:
The patent applies local quality by making the smoothing parameter location-dependent rather than uniform across the entire dataset. Each region of the data receives an appropriate smoothing strength tailored to its local characteristics, allowing simultaneous optimization of S/N ratio and responsiveness in different parts of the signal.
3Adaptability or versatility
If conventional smoothing methods are used, then data processing is simple, but the method lacks adaptability to varying data characteristics and cannot handle complex patterns effectively
Solution Approach 1:
The patent applies self-service by enabling the data itself to determine the appropriate smoothing parameter value. The method automatically adapts to local data characteristics without requiring external intervention or manual tuning, making the processing both adaptive and relatively simple to implement.
Data Source
AI summary
According to an embodiment of the present invention, a plasma processing apparatus includes: a processing chamber in which plasma processing is performed to a sample; a radio frequency power source that supplies radio frequency power for generating plasma in the processing chamber; and a data processing apparatus that performs processing to light emission data of the plasma. The data processing apparatus performs the processing to the light emission by using an adaptive double exponential smoothing method for varying a smoothing parameter based on an error between input data and a predicted value of smoothed data. A response coefficient of the smoothing parameter is derived by a probability density function including the error as a parameter.