Machine learning for in-situ composition mapping in a self-driving magnetron sputtering system

TL;DR

This work tackles the challenge of rapid, in-situ composition mapping in a multi-source vacuum deposition SDL. It combines in-situ QCM measurements with a geometric sputter-flux model and Bayesian active-learning Gaussian processes to learn single-source deposition as a function of $P$ and $p_{Ar}$, then interpolate multi-source deposition to generate composition maps across a substrate. Among the acquisition functions evaluated, a fully Bayesian GP with BALM proves most efficient, enabling learning in under $10$ experiments for each source, and enabling automatic prediction of co-sputtering compositions validated by Rutherford Backscattering Spectrometry with center-point compositions matching targets (e.g., $Cu/(Cu+Sn)=0.66$). The approach dramatically increases throughput, narrows the experimental parameter space, and demonstrates a path to ML-guided SDL-driven exploration of inorganic thin films, with potential extensions to reactive sputtering and multi-objective optimization. Overall, the paper shows that ML-driven process models integrated with in-situ sensing can accelerate synthesis-property mapping in self-driving magnetron sputtering systems, delivering quantitative composition and thickness maps in real time.

Abstract

Self-driving labs (SDLs), employing automation and machine learning (ML) to accelerate experimental procedures, have enormous potential in the discovery of new materials. However, in thin film science, SDLs are mainly restricted to solution-based synthetic methods which are easier to automate but cannot access the broad chemical space of inorganic materials. This work presents an SDL based on magnetron co-sputtering. We are using combinatorial frameworks, obtaining accurate composition maps on multi-element, compositionally graded thin films. This normally requires time-consuming ex-situ analysis prone to systematic errors. We present a rapid and calibration-free in-situ, ML driven approach to produce composition maps for arbitrary source combinations and sputtering conditions. We develop a method to predict the composition distribution in a multi-element combinatorial thin film, using in-situ measurements from quartz-crystal microbalance sensors placed in a sputter chamber. For a given source, the sensor readings are learned as a function of the sputtering pressure and magnetron power, through active learning using Gaussian processes (GPs). The final GPs are combined with a geometric model of the deposition flux distribution in the chamber, which allows interpolation of the deposition rates from each source, at any position across the sample. We investigate several acquisition functions for the ML procedure. A fully Bayesian GP - BALM (Bayesian active learning MacKay) - achieved the best performance, learning the deposition rates for a single source in 10 experiments. Prediction accuracy for co-sputtering composition distributions was verified experimentally. Our framework dramatically increases throughput by avoiding the need for extensive characterisation or calibration, thus demonstrating the potential of ML-guided SDLs to accelerate materials exploration.

Figures (15)

• Figure 1: The SDL workflow consists of the following steps each iteration: 1. PVD sputtering experiment, 2. model training with active learning, 3. obtain composition map to infer co-sputtering. Finally, external verification by RBS.
• Figure 2: Geometric model of the sputter flux. The sputter gun, which emits matter, is shown in grey. Isosurfaces with equal concentrations of emitted atoms are shown in different shades. The emission becomes increasingly directed and narrow as $n$ increases.
• Figure 3: The active learning cycle begins with training three models (one for each QCM sensor mass rate) on several initial experiments, then iteratively evaluating the acquisition function and querying the next experimental point, appending the new point to the training set and repeating until the budget is spent. After training, the three sensor models are used to fit a flux distribution model (described in Section \ref{['sec:flux_model']}) for the source. Subsequently, multiple such flux models can be combined to predict composition maps for co-sputtering depositions.
• Figure 4: "Ground truth" dataset of 225 data points collected while sputtering from a Zr target, where $\dot{m}_i$ is the mass deposition rate measured by sensor $i$.
• Figure 5: Comparison of various acquisition functions running on the Zr dataset in Figure \ref{['fig:zr_grid']} (a) Random query, (b) NIPV, (c) BALM and (d) BALD, for different choice of initial training points in Cases 1-3. The shaded region represents $\pm 1$ std. We see that BALM in Case 3 achieves the lowest $E_\text{RMS} [ngcm^{-2}s^{-1}]$ score in the fewest queries