Interpretable self-driving sputter epitaxy: from black-box optimization to human-usable growth rules

Self-driving laboratories have emerged as powerful tools for navigating high-dimensional process spaces, yet systems remain black-box optimizers that yield limited transferable process understanding. Here, we demonstrate an interpretable self-driving laboratory framework that transforms autonomous optimization into human-usable growth rules. As a stringent benchmark, we apply this framework to RF magnetron sputtering, addressing a long-standing challenge of achieving high-quality beta-Ga2O3 heteroepitaxy and single-crystalline beta-Ga2O3 homoepitaxy via sputtering. By combining Bayesian optimization with automated optical evaluation of the Urbach energy as a metric of sub-bandgap disorder, the self-driving system efficiently identifies heteroepitaxial growth conditions yielding a minimum Urbach energy of 182 meV, the lowest value for sputtered beta-Ga2O3 films. Importantly, the optimized growth window is transferable, realizing single-crystalline beta-Ga2O3 homoepitaxy without further optimization, corroborated by scanning transmission electron microscopy. To convert the closed-loop dataset into interpretable growth rules, we train a random forest surrogate and distill it into response curves and quantified pairwise interactions across the four-dimensional growth-parameter space. This analysis identifies substrate temperature as the primary control knob, with RF power and gas flows acting largely additively and only a modest temperature-oxygen coupling delineating the narrow window for high-quality growth, establishing a general route from autonomous experimentation to transferable growth rules.