Statisticalmodelingofscanningtransmission...
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Statistical modeling of scanning transmission electron microscopy images of crystal interfaces with atomic resolution Jenny Jonasson 1 Joint work with Mats Rudemo 1 , Nikolina Ljustina 2 and Eva Olsson 2 1 Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg 2 Applied Physics, Chalmers University of Technology
Transcript of Statisticalmodelingofscanningtransmission...
Statistical modeling of scanning transmission
electron microscopy images of crystal interfaces
with atomic resolution
Jenny Jonasson1
Joint work with Mats Rudemo1, Nikolina Ljustina2 and Eva Olsson2
1Mathematical Sciences, Chalmers University of Technology and the
University of Gothenburg2Applied Physics, Chalmers University of Technology
Crystal structure
B-siteA-site
Oxygen
Unit cell
High-Angle Annular Dark Field Scanning Transmission
Electron Microscopy
Annular detector
Crystal specimen
Electron beam
Scattered electrons
LaSr
Intensity proportional to atomic number (and number of atoms ina column).
Example
InterfaceLaAlSrTi
LaAlO3 in the film on the substrate SrTiO3
Detail
Goals
• Characterization of a particular crystal, grown with specificenvironmental conditions
• The position of the interface and its width, that is the degreeof intermixing between atoms across the interface in a narrowregion.
• The positions of atoms in the B-sites relative to the atoms inthe A-sites. Are they affected in the vicinity of the interface?
Problems
• Physical models are (too) complex
• Imaging. Not constant background. Row-wise dependence.
• A-site atoms have fixed positions in corners of a cube. Not soin images
Preliminary analysis
To the left, LaAlO3 in the film, to the right SrTiO3 in thesubstrate.
Preliminary analysis
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Bilinear transformation of each unit cell giving A-site atoms incorners of square. Average unit cell.
Preliminary analysis
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Gaussian function fitted to each A-site atom, then removed.Smoothed average unit cell.
Preliminary analysis
A-site atoms removed.
Preliminary analysis
Gaussian function fitted to B-site atoms.
Image
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Vertical averaging. Logistic function fit to A-site atoms.
Modeling ideas
1. Image results from a convolution of an object function (atomcolumn as seen by electrons) with a probe intensity profile
2. Probe intensity profile - ”known”.
3. Object function - possibly Gaussian. (Want to estimateposition and height for each atom)
4. Incorporate function describing the interface.
5. Estimate with maximum likelihood.
1-3 already in van Aert et al. (2009)
More future work
• More than one image of each sample with different rotationsin x-y plane
• Images with higher resolution. Possible to see oxygen atoms?
• Testing. Is there a significant difference of atom positions forcrystals grown at different oxygen pressure?
