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Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a

Scott D Findlay1, Hamish G Brown2,3, Philipp M Pelz2,4

  • 1School of Physics and Astronomy, Monash University, Clayton, VIC3800, Australia.

Microscopy and Microanalysis : the Official Journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada
|July 27, 2021
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Summary

This study reconstructs the electron scattering matrix using 4D scanning transmission electron microscopy (STEM) data. This method enables accurate atomic-resolution imaging and sample thickness determination, even with multiple scattering and noise.

Keywords:
4D STEMphase retrievalscattering matrix

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Electron Microscopy

Background:

  • The scattering matrix formulation is crucial for understanding electron scattering in transmission electron microscopy (TEM).
  • Advancing toward atomic-resolution structure determination requires robust methods to handle multiple scattering events.
  • Visualizing the scattering matrix aids in comprehending its properties and applications.

Purpose of the Study:

  • To develop and demonstrate a method for reconstructing the scattering matrix from 4D scanning transmission electron microscopy (STEM) data.
  • To showcase the utility of this reconstruction for atomic-resolution imaging and accurate sample thickness determination.
  • To investigate the impact of noise and multiple scattering on the reconstruction process.

Main Methods:

  • Utilizing a simulation-based case study with incorporated shot noise.
  • Applying regularization techniques based on the continuity of the scattering matrix.
  • Reconstructing the scattering matrix from 4D STEM measurements acquired at a single defocus value.

Main Results:

  • Successful reconstruction of the scattering matrix from limited experimental data (single defocus value).
  • Demonstrated capability to simulate STEM images at different defocus values using the reconstructed matrix, validating its accuracy.
  • Achieved nanometer-accurate sample thickness determination for crystalline samples without prior structural information.

Conclusions:

  • The scattering matrix formulation, when regularized for continuity, provides a powerful pathway for advanced electron microscopy.
  • This approach facilitates atomic-resolution imaging and precise thickness measurements, overcoming challenges of multiple scattering and noise.
  • The method offers a significant step towards routine atomic-resolution structure determination using STEM.