Method for the Manual Analysis of Moiré Structures in STM images

A method is presented to manually determine the lattice parameters of commensurate hexagonal moiré structures resolved by STM. It solves the problem that lattice parameters of moiré structures usually cannot be determined by inspection of an STM image, so that computer‐based analyses are required. T...

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Bibliographic Details
Published in:Chemphyschem 2021-05, Vol.22 (9), p.870-884
Main Authors: Günther, Sebastian, Zeller, Patrick, Böller, Bernhard, Wintterlin, Joost
Format: Article
Language:English
Subjects:
Fourier transforms
graphene
Inspection
Lattice parameters
layered materials
Mathematical analysis
moiré structures
scanning tunneling microscopy
Substrates
two-dimensional solids
Vectors (mathematics)
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Summary:A method is presented to manually determine the lattice parameters of commensurate hexagonal moiré structures resolved by STM. It solves the problem that lattice parameters of moiré structures usually cannot be determined by inspection of an STM image, so that computer‐based analyses are required. The lattice vector of a commensurate moiré structure is a sum of integer multiples both of the two basis vectors of the substrate and of the adsorbed layer. The method extracts the two factors with respect to the adsorbed layer from an analysis of the Fourier transform of an STM image. These two factors are related to the two factors with respect to the substrate layer. Using the cell augmentation method, six possible moiré structures are identified by algebra. When the orientation and lattice constant of the substrate are roughly known, this information is usually sufficient to determine a unique moiré structure and its lattice parameters. Manual analysis: A method is presented to analyze STM images of commensurate, hexagonal moiré structures on surfaces. Precise lattice constants and rotational angles can usually not be derived by simple inspection. However, the equations describing moiré structures can be solved analytically, from which a step‐by‐step recipe is developed that gives exact lattice parameters. Trial‐and‐error approaches as well as numerical computations are avoided. The method makes use of the Fourier transform, as illustrated for the simulated data in the table of content image.
ISSN:1439-4235
1439-7641
DOI:10.1002/cphc.202001034