Timeseries Analysis

Results extracted from multiple RHEED patterns taken over time (e.g. video).

Timeseries Analysis provides insight into physical measurables such as strain, growth rate, pattern topology, and changes in surface reconstruction.

For all rotating RHEED data, metrics are extracted from threads of the same or symmetrically-equivalent azimuthal angle automatically extracted from a frame-matching procedure. Multiple different high-symmetry scattering angles can be measured to leverage multi-azimuthal information from rotating RHEED data.

Strain

Extracted pattern data is used to track the evolution of diffraction feature spacing and calculate the accumulation of strain throughout a process.

Relative strain is calculated between neighboring patterns in time as the average of the percent change in the horizontal spacing, where the horizontal spacings are compared between diffraction features with the same relative positioning to the specular spot in neighboring patterns. At this time, one representative pattern is used for each region between transitions, although this is slated to change in the next update to AtomCloud.

Deposition Rate

Oscillation period is calculated from specular intensity oscillations, providing insights into growth rates where applicable. At this time, one representative pattern is used for each region between transitions, although this is slated to change in the next update to AtomCloud.

Pattern Topology

Spot count is used to quantify the evolution of RHEED patterns through the appearance or disappearance of diffraction features. Changes in the number of spots that are present can indicate phase transitions, phase separations, reconstructions, or that a target thickness has been reached.

Lattice Spacing

The tracking of relative pattern spacing and pattern periodicity can help identify surface reconstructions. Each colored scatter series in the example below gives the real-space lattice spacing (arbitrary units by default) of patterns extracted at a single azimuthal angle from a rotating RHEED timeseries. Lattice spacing in a given azimuthal angle is calculated by taking the minimum horizontal feature-to-feature distance in the RHEED pattern, corresponding to the longest periodic length scale in the surface lattice, and converting to real space by inverting. These arbitrary units are normalized by dividing by the minimum across all azimuthal angles measured.

A new reconstruction (change in the shade of background orange) emerges when the smoothed lattice spacing in a given azimuthal angle changes. The moving average window is determined by the oscillation period to scale with deposition rate.

Transitions

Transition Zones are indicated by green regions which indicates a shift in the underlying RHEED timeseries. These transitions are identified using unsupervised machine learning for non-linear dimensional reduction (PacMAP) and density-based clustering (HDBSCAN), which operate on the RHEED images directly. We highlight changes in physically measured quantities at these changepoints in the tooltip. In the example below, hovering over one transition shows that the growth rate and strain changed at the selected transition.

Transition Compare

With a file selected, you can inspect and compare the diffraction patterns of each cluster. Use the scrolling gallery below the RHEED Clusters plot to select which cluster you wish to view. Additional metrics are displayed for each cluster including, oscillation period, streak-to-spot ratio, and spot count.