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Simulation of Mirror Electron Microscopy Caustic Images in Three-Dimensions

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posted on 2024-09-18, 10:25 authored by SM Kennedy, David JessonDavid Jesson

Three-dimensional (3D) image simulation methods are applied to interpret mirror electron microscopy (MEM)images obtained from a movie of GaAs droplet epitaxy. The data for the 3D surface height map of the t = 20 min shape is in Fig2a in the format (x, y, height) with units in microns. The equations used to generate this height function are contained in Fig2a_Eqns. The surface profile (a slice through the 3D height map) and equipotential traces of Fig. 2b are contained in Fig2b_Height and Fig2b_Eqp1-5 respectively, and similarly for Fig. 2c. The format is (x, height) with units in microns.

Figure 3 gives an example of the Voronoi method. Figure 3a contains a sample grid of positions contained in file Fig3a in the format (x, y) in arbitrary units (e.g. microns). Figure 3b is made up of a list of electron positions in Fig3b_Points in (x, y) format, and the file generated by the software package qHull (obtained from http://www.qhull.org) is in Fig3b_Voronoi. In this 'Voronoi' file, the first line is the number of dimensions (2); the second line is in the format (total number of Voronoi vertices (V) which form the Voronoi regions, the number of positions (P), the number one); the next 'V' lines give the positions of the Voronoi vertices in (x, y) format starting with the position representing infinity; and the remaining 'P' lines describe the Voronoi region for each position, in the format of (number of vertices used to define the region, the label of each vertex used). Similarly, Fig3c_Points and Fig3c_Voronoi are the relevant data files for Figure 3c.

Fig4ab is the experimental MEM image data in (red, green, blue) format. Fig4c,d are the atomic force microscope height data, giving surface height values in nm at equally spaced points or pixels on a 128 by 128 grid. The grid separation is 6229.9/127 nm in x and y. Fig4e,f are line traces through the 3D data in the format of (y, height) in nm. (e) corresponds to a line trace in y along the 71st x pixel in (c), and (f) corresponds to a line trace in y along the 69th x pixel in (d).

Figure 5 uses the same format and data file structure as Fig. 2 but for the t = 15 min shape.
Data files Fig6a and Fig6b contain simulated MEM images in the format (x, y, intensity) for the surfaces in Fig. 5a and Fig.2a, respectively, with distances in nm and the intensity normalised so that '1' corresponds to uniform or background intensity.

Research results based upon these data are published at https://doi.org/10.1142/S0218625X19500136


Funding

Quantum Dot Architecture Nanodynamics

Engineering and Physical Sciences Research Council

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