Mg segregation at inclined facets of pyramidal inversion domains in GaN:Mg

Structural defects in Mg-doped GaN were analyzed using high-resolution scanning transmission electron microscopy combined with electron energy loss spectroscopy. The defects, in the shape of inverted pyramids, appear at high concentrations of incorporated Mg, which also lead to a reduction in free-hole concentration in Mg doped GaN. Detailed analysis pinpoints the arrangement of atoms in and around the defects and verify the presence of a well-defined layer of Mg at all facets, including the inclined facets. Our observations have resulted in a model of the pyramid-shaped defect, including structural displacements and compositional replacements, which is verified by image simulations. Finally, the total concentration of Mg atoms bound to these defects were evaluated, enabling a correlation between inactive and defect-bound dopants.

1 Shape and polarity of the PIDs Figure S1: Horizontal line profile of atomic columns belonging to pyramids. Top example shows the <1100> projection while the bottom shows <1120>. The acquired HAADF images are shown and the top profile of each pyramid are marked with a red line. This line shows the extent of the profile. Profiles are normalized between 0 and 1 and shifted vertically for comparison. Insets for each pyramid shows the projected direction of the pyramid shape and the plotted profiles agrees with the thickness being a pointed corner for the <1100> projection and semi-flat middle section for the <1120> projection. Note the uneven intensity in the top-layer (blue) for both projections. This is due to the random replacement of Ga with Mg. Figure S2: High magnification ABF-STEM image of the top of one pyramid. The lattice is overlayed with the structure of WZ and lines highlight the lateral positions in the ABABAB stacking. However, the top layer of Mg (arrow) positions itself on the blue lines, the C-position. Also, the structure within the pyramid is inverted, following ABABAB stacking. Here it is seen with some overlap from the ambient matrix. Figure S3: Schematic and simulated cases of TEM imaging of the pyramids in the <1120> projection. a) and e) show lamellas projected in the TEM of different thicknesses, where a) has matrix overlapping the whole pyramid in projection (slightly thicker than the pyramid) and e) clips the pyramid, creating a region that has only pyramid domain in projection (slightly thinner than the pyramid). b) and f) show the cases respectively in a simulated atomic model of half the pyramid, including the apex at the bottom right. Colors in the atomic model: green -Ga, blue -N, yellow -Mg. c)-d) simulate STEM images for the first case in HAADF and ABF modes respectively, and g)-h) do the same for the second case (green circles mark the apex). Scalebars in the bottom left of the simulated images are all 1 nm. Figure S4: Illustration of the plasmon peaks for the ambient matrix GaN compared to MgO. They have different intensity but are here matched to be compared. The plasmon-regions and up (> 15 eV) are multiplied with different factors for comparison. As can be seen for GaN, there are multiple plasmon peaks/features as high as 50 eV with diminishing intensity. From the MgO signal we see the Mg-L 2,3 just above 50 eV (edge marked by an arrow with corresponding color). This illustrates the potential overlap and motivates the use of MLLS as described in the main text, as the background for Mg (∼51 eV) can not be properly subtracted. The minor edge of Ga with a delayed onset at ∼103 eV is faintly seen here (also marked by an arrow with corresponding color), but not included in the MLLS analysis in the main text. Figure S5: Illustration of size and concentration measurement of PIDs from one of the sites. a) shows a higher magnification making measurements of PIDs with clear width in <1100> projection possible. This is used to estimate an average size in the specific region. b) shows manual counting of the PIDs in an image. Since the width and height of the image is known and the thickness is measured through mean-free-path the concentration PIDs can be estimated. The range of Mg concentration presented arises from multiple sites measured for improved statistics and some variation of size are present. The method of manually counting defects in a region also accounts for some margin of error. Figure S6: MLLS EELS mapping of two components, just as in the example shown in the main text (figure 4). The components are: the ambient matrix and the interface, shown in left and right columns respectively. The three scans are made using the same settings described in the main text and made just after each other, in series. The results clearly show a degradation of the Mg-interface structure, indicate electron-beam induced damage.

Import the needed packages
Below follows a workflow to create the figure of MLLS fitting. The data is loaded, fitted and displayed, with comments throughout.

Load and treat the data
Select which scan to use and set parameters. Then load the data (dm3) using Hyperspy.
In [1]: #Import packages #%matplotlib qt #comment for in-line figures and uncomment for separate windows import hyperspy.api as hs import matplotlib.pyplot as plt import scipy.misc import numpy as np from scipy import ndimage import matplotlib.font_manager as fm import matplotlib.patches as patches from mpl_toolkits.axes_grid1.anchored_artists import AnchoredSizeBar import matplotlib.gridspec as gridspec import warnings warnings.filterwarnings("ignore") In  Define the two regions of interest (ROI) used as components. Add these two spectra to "component_list". The positions are manually selected as two rectangles.
First the components are added to the model ("m") and then the fitting is performed ("m.multifit()"), then the resulting fit of each component is saved to "image_list"

Presentation of data
Collect the data into presentable figures. The fitted maps of "image_list" are displayed, followed by the two components plotted as spectra (including their difference). Lastly the image of the region is shown with rectangles marking the positions of the ROIs. Create the finialized figure with the subfigures collected. Here the data is also rotated 90 deg to match the displayed pyramids in the rest of the images.
a) The overview image with rectangle of the location of the spectrum image is displyed. Scalebar size is calculated and displayed b) The image (same as above) is shown with the ROIs marked in correct colors. Also here a scalebar is shown.
c) The two fitted maps are shown as rgb-images (their intensity times the "color_components") d) Finally the components shown above are plotted normalized to the max-value of each of them in the range (for comparison). The max-value is the first in each of them. Below this plot the difference is displayed with zero marked with a red line.
(Total figure is then saved for inclusion in the manuscript) In