Forecasting Active Species in Radio Frequency Nitrogen Plasma with Quantum and Conventional Machine Learning Algorithms

Radio frequency (RF) nitrogen plasma sources are of great importance for the epitaxial synthesis of nitride materials. The energetics and relative concentrations of the various active species within the plasma have a significant impact on the quality and structure of the grown sample. Thus, controlling the populations of these active species is critical to refining nitride material growth processes and producing high quality samples in both manufacturing and research and development contexts. Furthermore, enhancing control over the relative concentrations of active nitrogen species that are found in RF plasma can lead to an improved understanding of the influence that the various species have on the growth and processing of thin film material samples and devices.<br/><br/>RF plasma source operating parameters are traditionally optimized through Edisonian trial–and–error. This iterative approach to process refinement can be expensive in terms of both material resources and the time spent developing and implementing experiments. Previous work towards a more informed selection of operating parameters for RF nitrogen plasmas has involved calculating the ratio of active molecular to active atomic nitrogen species under various combinations of operating parameters and interpolating between the recorded data points; this approach yields plotted processing spaces from which operating parameters can be selected, but it is limited by the range of operating parameters spanned by the data points. Machine learning algorithms present a useful strategy for recognizing complex patterns and generalizing beyond recorded data points to forecast novel, unobserved information. To date, machine learning technologies have been successfully implemented to predict both electron density and electron temperature in RF nitrogen plasma from optical emission spectroscopy data. In the present work, we use supervised machine learning models, including those which incorporate quantum computation, to study the relationships between RF nitrogen plasma operating parameters and optical emission spectra features that are of interest for thin film deposition applications, including the ratio of active molecular to active atomic nitrogen species.<br/><br/>For a RF plasma source operated within a molecular beam epitaxy chamber, we have acquired optical emission spectroscopy data and measured the relative concentrations of the active nitrogen species for nearly 2000 different combinations of RF plasma source operating parameters spanning large portions of the parameter space that have not been previously studied. Each data point includes the full set of operating parameters as well as the resulting chamber pressure and the ratio of molecular to atomic active nitrogen species as measured from optical emission spectra. The relationships between these variables were first investigated by calculating matrices of both Pearson’s correlation coefficients and p–values for all possible pairings of the variables within the data set. These analyses were corroborative in describing the RF nitrogen plasma processing space as one defined by coupled variables that are highly interdependent upon one another. The splitting rules of regression tree models fit to the data further corroborated this assessment. Quantum and classical supervised learning models, including tree–based algorithms, quantum support vector regressors, and artificial neural networks, were trained upon the data and compared for generalization performance. The trained and tuned algorithms exhibiting superior generalization performance metrics were used to predict features such as the ratio of molecular to atomic active nitrogen for combinations of RF plasma operating parameters not contained within the recorded training data. This mapping displays trends that agree with conventional wisdom established through prior studies while also describing areas of the RF nitrogen plasma processing space that have not been previously investigated.