Analyzing Synthesis–Structure Relationships in Epitaxially–Grown Semiconductors with Quantum and Classical Supervised Machine Learning

Thin film crystal growth experiments occur within highly multidimensional processing spaces often defined by sets of multiple experiment design parameters. Identifying the optimal values for each synthesis parameter is conventionally performed through an Edisonian, trial–and–error approach to experiment design that is often costly in terms of both time and resources. Considerable interest exists in the development of machine learning–based methodologies for the rapid and accurate identification of optimal materials designs and synthesis conditions that result in material samples exhibiting target properties of interest.<br/> <br/>In this work, data detailing several hundred distinct plasma–assisted molecular beam epitaxy (PAMBE) thin film crystal growth trials of ZnO as well as various nitride semiconductors have been organized into separate, material composition–specific data sets. For each growth record, the complete set of experiment parameters (substrate temperature, metal source effusion cell temperatures, plasma source forward power, growth duration, etc.) are associated with binary measures of crystallinity (1 for monocrystalline, 0 for polycrystalline) and surface morphology (1 for atomically flat, 0 for uneven) as determined by <i>in–situ</i> reflection high–energy electron diffraction (RHEED) patterns. A Bragg–Williams derived measure of lattice ordering (0 ≤ S² ≤ 1) is included as an additional, continuous figure of merit for investigation. Calculations of p–values, Pearson’s correlation coefficient, and decision tree splitting rules are utilized to assess the PAMBE operating parameters which are most statistically influential upon each of the three structural metrics. From these analyses, substrate temperature and nitrogen chamber pressure are determined to be most statistically influential upon the crystallinity of epitaxially–grown GaN thin film crystals as assessed via RHEED patterns. In the case of epitaxially–grown ZnO thin film surface morphology, the settings of oxygen gas flow rate and zinc effusion cell temperature are found to be the most statistically important operating parameters. Radio frequency plasma settings and substrate temperature values are shown to be influential upon S² in epitaxially–grown thin film crystals of ZnO as well as GaN.<br/><br/>Quantum as well as conventional supervised machine learning algorithms – including logistic regression, tree–based models, and quantum support vector machines – are trained on the data in order to investigate the relationships between the PAMBE process parameters and resulting sample crystallinity, surface morphology, and measured S². When predicting the occurrence of monocrystalline GaN via PAMBE, supervised learning algorithms designed to incorporate quantum computers display significant advantage over their classical machine learning counterparts. Predictions of InN crystallinity are most accurately made by an optimized and trained k–nearest neighbors algorithm. The class conditional probabilities of obtaining monocrystalline and atomically flat thin film crystals are predicted across processing spaces of the two PAMBE synthesis parameters determined to be most statistically significant, and S² is also forecasted across the same growth spaces. These predictions are compared to conventional experimental wisdom as well as the results described within published literature regarding the PAMBE synthesis of these materials. The predictions indicate that different growth conditions are of interest depending on whether a single crystalline sample, a flat surface, or a well–ordered lattice is the most desired outcome. The superior generalization performance displayed by the quantum machine learning algorithms when predicting GaN crystallinity implies the potential for quantum machine learning algorithms to be beneficial for studies of synthesis–structure relationships in other material systems.<br/> <br/>*This work was supported in part by the National Science Foundation (grant number DMR–2003581).