Topology and Machine Learning Identify Hidden Relationship in Amorphous Silicon

Theoretical scientists used topological mathematics and machine learning to identify a hidden relationship between nano-scale structures and thermal conductivity in amorphous silicon. A study describing their work appeared in the Journal of Chemical Physics.

Amorphous solids, such as glass, obsidian, wax, and plastics, have no long-range repeating or crystalline structure to the atoms or molecules they are made of. Since they lack long-range order in their structure, their thermal conductivity can be far lower than a crystalline solid composed of the same material. There can still be some medium-range order on the scale of nanometers that should affect the propagation and diffusion of atomic vibrations, which carry heat.

Heat transport in disordered materials is important to physicists due to potential industrial applications, from solar cells to image sensors.

In experiments, the presence of medium-range order has been physically detected using fluctuation electron microscopy. At the theoretical level, it has been discussed by considering the distribution of dihedral angles or the use of ‘ring statistics.’

This draws on topology, which investigates the properties of an object that do not change. Focusing on topological invariance is useful for delivering a qualitative description. However, it is demanding to determine the atomic structure corresponding to a medium-range order and predict its physical properties only from simple topological invariants.

So, the researchers moved to an emerging technique called persistent homology, which has been used elsewhere to analyze complex structures ranging from proteins to amorphous solids. This method’s benefit is detecting topological features in complicated structures at different spatial scales. The medium-range order comprises quasi-repetitive structures at various scales, enabling us to extract the medium-range order hidden beneath what otherwise appears as randomness.

The researchers built computational models of amorphous silicon by classical molecular dynamics wherein the silicon temperature was increased above the melting point and then gradually cooled to room temperature. Changing the cooling rate introduced differences in structural characteristics by changing the cooling rate.

Then, the persistent diagram, which is the 2–D visualization of persistent homology, was computed for each model. They found that the persistent diagram fulfilled the creation of a good descriptor for use in the machine learning procedure, which in turn achieved accurate predictions about the thermal conductivities.