Quantum and Classical Supervised Learning Assessment of Transition Metal Dichalcogenide Monolayer Coverage

The potential for machine learning models to accurately recognize patterns in data has made them a top strategy for optimizing the simulation, synthesis, characterization, and processing of a broad range of thin film material systems. Learning algorithms have previously been shown to enhance both experimental and theoretical studies of few and single layer materials, including transition metal dichalcogenides (TMDs). For example, supervised learning has previously been implemented to optimize the chemical vapor deposition (CVD) of WTe₂ nanoribbons, and multiple investigations have been conducted to apply active learning, supervised classification and regression, as well as unsupervised learning to study the CVD of MoS₂ from solid state S and MoO₃ precursors. Building upon these efforts, we have applied quantum as well as conventional supervised learning algorithms to study the metal–organic chemical vapor deposition (MOCVD) of TMD thin films – including MoS₂, WS₂, and WSe₂ – as grown with dihydrogen chalcogenide gas and transition metal hexacarbonyl precursors.<br/> <br/>Several hundred discrete records of MOCVD–grown TMD thin films synthesized in a single laboratory have been organized into material–specific data sets. For each deposition experiment, Raman spectra characterizing the resulting sample have been utilized to assess monolayer coverage in the resulting thin film. The distance between the A_1g and E_2g Raman mode peaks in each spectrum was measured and associated with the respective growth record as an output variable in the data set. The MOCVD synthesis parameter data was subsequently mapped to the measured A_1g and E_2g Raman mode peak distance using supervised learning. A combination of p–value calculations, Pearson’s correlation coefficients, and regression tree splitting rules were used to investigate the statistical importance of each MOCVD operating parameter for influencing the expected value of the distance between the A_1g and E_2g Raman mode peaks. For MoS₂, agreement between the primary and secondary splitting rules of the regression tree as well as the magnitudes of the correlation coefficients indicate that two of the most influential synthesis parameters are the flow rate of the Mo(CO)₆ injector hydrogen gas during the growth step of the deposition process, as well as the flow of Mo(CO)₆ during the reaction temperature ramp up step.<br/> <br/>Various quantum as well as classical supervised machine learning algorithms – including k–nearest neighbors, tree–based algorithms, and quantum support vector regressors, were trained on the data and compared for generalization performance. The hyperparameters of each regression model were optimized for the data. The generalization performance of each optimized and trained algorithm was evaluated by calculating the mean squared error (MSE) of the values predicted by the model for a subset of the data that was withheld for testing. The algorithm demonstrating the lowest MSE on the testing data set was selected to forecast the distance between the A_1g and E_2g Raman mode peaks beyond the experimental data available for training. In the case of MoS₂, this generalization indicates that maximizing both the Mo(CO)₆ injector hydrogen gas flow during the growth step and the value of the Mo(CO)₆ flow during the reaction temperature ramp up step is forecasted to result in a minimization of the A_1g and E_2g Raman mode peak distance. This predicted reduction of the peak distance between the A_1g and E_2g vibrational modes in Raman spectra acquired of MoS₂thin films corresponds with improved monolayer coverage. The methodology demonstrated in this supervised learning investigation of synthesis–structure relationships can be applied to additional features of interest within Raman spectra, as well as to other TMDs, such as WS₂ and WSe₂.<br/> <br/>*This work was funded by Penn State 2DCC–MIP through the NSF cooperative agreement DMR–1539916 as well as by the National Science Foundation (grant number DMR–2003581).