Interpretable self-driving sputtering epitaxy reveals human-usable growth rules for β-Ga₂O₃ films

Self-driving laboratories are powerful tools for navigating high-dimensional process spaces, yet Bayesian-optimization decision layers optimize black-box objective functions without distilling transferable process understanding. Here, we demonstrate a mathematically interpretable self-driving laboratory framework that transforms autonomous optimization data into human-executable growth rules. As a benchmark, we apply this framework to sputtering, addressing a challenge in sputtering epitaxy: realizing high-quality β-Ga₂O₃ heteroepitaxy and single-crystalline β-Ga₂O₃ homoepitaxy. By combining Bayesian optimization with automated optical evaluation of the Urbach energy as a sub-bandgap disorder metric, the self-driving system identifies heteroepitaxial conditions yielding an Urbach energy of 182 meV, below previously reported values for sputtered β-Ga₂O₃ films. Importantly, the optimized growth window is transferable across substrates, realizing single-crystalline β-Ga₂O₃ homoepitaxy, corroborated by scanning transmission electron microscopy. To convert closed-loop data into interpretable growth rules, we train a random forest surrogate and reveal that the growth landscape is described by additive contributions from four growth parameters, with a temperature-oxygen interaction. This structure suggests a human-executable strategy with sequential one-dimensional tuning followed by focused two-dimensional refinement, validated by human-executed re-optimization, yielding a reduced Urbach energy of 163 meV. This establishes an interpretable self-driving workflow that converts autonomous optimization data into validated, human-usable growth rules.