Application of machine learning to reflection high-energy electron diffraction images for automated structural phase mapping

We have developed a phase mapping method based on machine learning analysis of reflection high-energy electron diffraction (RHEED) images. RHEED produces diffraction patterns containing a wealth of static and dynamic information and is commonly used to determine the growth rate, the growth mode, and the surface morphology of epitaxial thin films. However, the ability to extract quantitative structural information from the RHEED patterns that appear during film growth is limited by the lack of versatile and automated analysis techniques. We have created a deep learning-based analysis method for automating the identification of different RHEED pattern types that occur during the growth of a material. Our approach combines several supervised and unsupervised machine learning techniques and permits the extraction of quantitative phase composition information. We applied this method to the mapping of the structural phase diagram of ${\mathrm{Fe}}_{\mathrm{x}}{\mathrm{O}}_{\mathrm{y}}$ thin films grown by pulsed laser deposition as a function of growth temperature and oxygen pressure close to the hematite-magnetite phase boundary. The in situ RHEED-based mapping method produces results that are qualitatively similar to postsynthesis x-ray diffraction analysis.

Figure 1

Schematic diagram of U-Net and example results: (a) A simplified schematic of the U-Net model that takes in an RHEED pattern and outputs a binary mask of features of interest. (b) An example of input RHEED pattern to the U-Net model. Note that this pattern contains both spot and streak features. (c) The predicted masks for spot and streak features are shown in gray and orange colors, respectively.

Figure 2

Different stages of the analysis of RHEED images: (a) Labeled bounding boxes overlaid on an RHEED image. Each rectangular bounding box is drawn around a region labeled by the connected component algorithm. (b) Detected direct beam spot, bound by a box. The red dot shows the center of gravity of the intensity of the beam.

Figure 3

An illustration of a region covering two features of overlapping diffraction patterns from two phases: (a) The region, bound by a red rectangle, although not visible by eyes at this intensity scale, contains two streak patterns. The zoom-in on the right contains the same box, but with intensity rescaled for better visualization. (b) The integrated one-dimensional intensity variation of the region. The detected peaks are marked with triangles.

Figure 4

Analysis of the peak location periodicities: (a) Diagram illustrating how peaks are grouped based on the distance from the origin. Solid lines show peak locations. Step 1: lists all the peaks discovered by our algorithm. Step 2: The peak closest to the origin is selected and labeled in red. Based on this peak, its multiplicity is constructed and shown in the red dash line with an error box. Step 3: Any peaks that are within the range of the error box are considered to be in the same base distance and are labeled in red. (b) All labeled peaks overlaid on the original diffraction pattern. The number shows the average peak distance from the origin normalized by the multiplicity. The red dash line highlights the position of peaks that are analyzed and grounded in (a).

Figure 5

Phase mapping of iron oxide films: (a) Raw RHEED images recorded at the end of each deposition. (b) The extracted regions' intensities of each base distance from the RHEED pattern form a feature vector. Each feature vector is represented by a pie chart where each pie slice's area shows the relative intensity of each base distance. The color encodes the base distance of the region intensity as shown in the legend. The unit of the distance is $\mathrm{n}{\mathrm{m}}^{–1}$. (c) The red and blue scatter points show the XRD phase map of the hematite ($\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$) and magnetite (${\mathrm{Fe}}_3{\mathrm{O}}_4$) phases, respectively. The presence of a phase is plotted as a circle. The size of the circle indicates if the phase is major or trace material in a particular sample. Sample identifier notation: sample made at ${10}^{–A}\mathrm{Torr}$ at B °C is denoted as $A\text{−}B$. For instance, the sample 5-600 was made at ${10}^{–5}\mathrm{Torr}$ of $P_{O2}$ at the substrate temperature of 600 °C.