Optimal experimental design for nano-particle atom-counting from high-resolution STEM images

Area of Science:

• Materials Science
• Physics
• Microscopy

Background:

• Accurate atom counting is crucial for understanding material properties at the nanoscale.
• High-resolution scanning transmission electron microscopy (HR STEM) is a powerful tool for atomic-scale imaging.
• Quantifying the precision and error in atom counting from HR STEM images is essential for reliable analysis.

Purpose of the Study:

• To apply detection theory principles to quantify the probability of error in atom counting from HR STEM images.
• To investigate binary and multiple hypothesis testing for estimating the number of atoms in projected atomic columns.
• To determine the optimal STEM detector design for accurate atom counting.

Main Methods:

• Utilized detection theory to calculate the probability of error in atom counting.
• Evaluated different criteria for atom counting: STEM images, scattering cross-sections, and peak intensities.
• Analyzed the impact of object thickness on optimal detector design, specifically inner detector angle.

Main Results:

• Scattering cross-sections provide a highly accurate criterion for atom counting, performing comparably to direct image analysis.
• Peak intensities are less reliable for atom counting compared to scattering cross-sections and image-based methods.
• Derived an expression for the probability of error to guide optimal STEM detector design for atom counting.

Conclusions:

• Scattering cross-sections are a robust and accurate method for quantifying atom numbers in HR STEM.
• The optimal STEM detector configuration for atom counting depends on object thickness, favoring LAADF for thin samples.
• This work provides a framework for optimizing HR STEM imaging parameters to maximize atom-counting precision.