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Related Concept Videos

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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Sampling Plans01:23

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
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Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
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Cluster Sampling Method01:20

Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Sampling Methods: Overview01:06

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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Cluster sampling and scalable Bayesian optimization with constraints for negative tone development resist model

Le Ma, Xingyu Ma, Shaogang Hao

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    This study introduces a new method for calibrating negative tone development (NTD) resist models, improving accuracy and efficiency for advanced semiconductor lithography. The approach uses cluster sampling and scalable Bayesian optimization (BO) with constraints.

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    Area of Science:

    • Semiconductor Manufacturing
    • Lithography Technology
    • Materials Science

    Background:

    • Shrinking semiconductor technology nodes present challenges in achieving smaller critical dimensions in lithography.
    • Negative tone development (NTD) processes are crucial for advanced nodes due to their wide process windows.
    • NTD resist model calibration is complex due to unique characteristics like shrinkage effects.

    Purpose of the Study:

    • To develop a more accurate and computationally efficient method for NTD resist model calibration.
    • To address the limitations of traditional Gradient Descent (GD) and heuristic methods in NTD model calibration.
    • To enhance the global optimization of high-dimensional parameter spaces in resist modeling.

    Main Methods:

    • Proposed a novel approach combining cluster sampling and scalable Bayesian optimization (BO) with constraints.
    • Utilized cluster sampling for enhanced global initial sampling.
    • Employed scalable BO with constraints for optimizing high-dimensional parameter spaces.

    Main Results:

    • Significantly enhanced calibration accuracy compared to GD and heuristic methods.
    • Substantially improved computational efficiency compared to GD.
    • Demonstrated a robust method for complex NTD resist model calibration.

    Conclusions:

    • The proposed cluster sampling and scalable BO with constraints method offers a superior alternative for NTD resist model calibration.
    • This approach overcomes local optima issues and reduces computational time.
    • Provides a new, efficient, and accurate solution for advanced semiconductor lithography challenges.