Testing the accuracy of the two-dimensional object model in HAADF STEM.

Area of Science:

• Materials Science
• Electron Microscopy
• Solid State Physics

Background:

• High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) commonly employs a 2D object-function approximation and image convolution model for crystalline samples.
• This model assumes the sample can be represented by sharp peaks at atomic column positions, convolved with the focused STEM illumination's point spread function (PSF).

Purpose of the Study:

• To experimentally validate the 2D object-function approximation for HAADF-STEM imaging of crystalline materials.
• To determine the thickness limit for the validity of the 2D model in HAADF-STEM.
• To explore the implications of the findings for image reconstruction and aberration diagnosis.

Main Methods:

• Acquisition of HAADF-STEM focal series from MgO smoke cubes.
• Analysis of laterally resolved image information using Fourier transforms and tracking intensity changes with defocus.
• Comparison of experimental results with simulated STEM probe depth resolution capabilities to determine apparent sample thickness.

Main Results:

• The 2D object-function and image convolution model was experimentally validated for sample thicknesses up to 250 nm.
• The 2D object model holds true for individual frames within a focal series.
• The focal series can be described as a convolution of a 2D object function with a 3D probe function.

Conclusions:

• The 2D object-function approximation is a valid model for HAADF-STEM imaging of crystalline samples within a certain thickness range (up to 250 nm).
• Treating focal series as a convolution with a 3D probe function offers new possibilities for diagnosing remnant aberrations and improving image reconstruction techniques.