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Koprucki T, Maltsi A, Mielke A. Symmetries in transmission electron microscopy imaging of crystals with strain. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
Abstract
Transmission electron microscopy (TEM) images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries, we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion that might affect the image. For the imaging process, we prove mathematically that the intensities are invariant under specific transformations. A combination of these invariances with specific properties of the strain profile can then explain symmetries observed in TEM images. We demonstrate our approach to the study of symmetries in TEM images using selected examples in the field of semiconductor nanostructures such as quantum wells and quantum dots.
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Affiliation(s)
- Thomas Koprucki
- Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany
| | - Anieza Maltsi
- Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany
| | - Alexander Mielke
- Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany
- Humboldt-Universität zu Berlin, Institut für Mathematik,Rudower Chaussee 25, 12489 Berlin-Adlershof, Germany
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