【International Papers】Interpretable self-driving sputtering epitaxy reveals human-usable growth rules for β-Ga₂O₃ films

Background

      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. β-Ga₂O₃ is a promising ultra-wide-bandgap semiconductor for next-generation power electronics and solar-blind deep-ultraviolet photodetectors, where device performance is highly sensitive to crystalline quality and optical disorder. High-quality epitaxial β-Ga₂O₃ can be realized by CVD and MBE techniques, but these approaches suffer from high-cost hardware. Radio-frequency magnetron sputtering is an industry-standard low-cost large-area deposition technique. Nevertheless, it is challenging to achieve high-quality epitaxy due to energetic growth environment, limited adatom mobility and narrow phase-stability margins, frequently resulting in amorphous, polycrystalline or mixed-phase films. There is a strong demand for interpretable self-driving workflows that go beyond black-box recipe searching and extract human-executable growth strategies from closed-loop experimental datasets.

Highlights

      An interpretable self-driving sputtering epitaxy platform is constructed, combining Bayesian optimization and automatic optical characterization. Urbach energy is adopted as objective metric for sub-bandgap disorder to realize closed-loop process optimization for β-Ga₂O₃ thin films;

      High-quality β-Ga₂O₃ heteroepitaxial films with low Urbach energy of 182 meV are achieved by sputtering. The obtained growth window is transferable, enabling single-crystal β-Ga₂O₃ homoepitaxy without extra optimization;

      Random-forest surrogate model is adopted to decode high-dimensional parameter space. Four growth parameters exhibit predominantly additive contributions, with only weak temperature-oxygen interaction;

      A human-executable tuning strategy is distilled: sequential one-dimensional parameter sweeping followed by focused two-dimensional refinement in temperature-oxygen space. Human-performed re-optimization further reduces Urbach energy down to 163 meV;

      It is demonstrated that self-driving experiment can deliver interpretable and transferable process knowledge rather than only optimal recipes, offering a new paradigm for oxide thin-film process development.

Conclusion

      In this work, we demonstrate that RF magnetron sputtering, when combined with an interpretable self-driving growth framework and automated optical analyses, can produce single-phase heteroepitaxial β-Ga₂O₃ films with high crystallographic and optical quality approaching that typically associated with CVD- and MBE-based epitaxy. Using the Urbach energy as a quantitative objective, the closed-loop campaign achieved Urbach energy =182 meV, below the lowest previously reported value for sputtered β-Ga₂O₃ films (280 meV) and below a representative MOCVD-grown report (220 meV). The rule-guided human re-optimization further reduced Urbach energy to 163 meV. While this performance remains above the best reported epitaxial films (~150 meV) and bulk single crystals (60-140 meV), the residual gap provides a clear roadmap for further improvement, namely, suppressing sub-gap disorder/defect states that are still detectable optically even in single-crystal films. Importantly, the same Bayesian-optimization-identified growth window discovered on C-plane Al₂O₃ was also sufficient to enable single-crystal β-Ga₂O₃ homoepitaxy. Given that RF sputtering is a mature, low-operating-cost technology already used for large-area oxide deposition in semiconductor and display manufacturing, these results point to self-driving sputter epitaxy as a promising, industry-compatible route for ultra-wide-bandgap β-Ga₂O₃ epitaxial layers and devices. Although the initial dataset in our campaign happened to include a sample with a moderately low Urbach energy (<350 meV), Bayesian optimization is not predicated on starting from a near-optimal recipe. Instead, the exploration-exploitation trade-off encourages broad sampling early on while progressively refining around promising regions. Consistent with this behavior, the Urbach energy values span a wide range across runs while the best-achieved Urbach energy decreases steadily. In our self-driving sputtering system, we further improved robustness against local trapping by adopting an adaptive prior-mean strategy, in which the Gaussian-process prior mean is resampled at each iteration from a uniform distribution bounded by the minimum and maximum observed Urbach energy values. This design promotes exploration of previously unseen regions and helps the search escape locally optimal regimes, and its effectiveness has been validated in benchmark simulations. A distinctive aspect of this study is that the self-driving workflow does not simply identify an optimized recipe, but also converts the closed-loop data into human-usable growth rules. While Bayesian optimization efficiently discovers growth conditions that minimize Urbach energy, process development ultimately requires an interpretable understanding of which parameters matter and how they should be adjusted. To bridge autonomous search and human-intuitive tuning, we analyzed the growth-parameter landscape explored by Bayesian optimization and distilled the closed-loop dataset into actionable process knowledge. Using a random forest as an explainable local surrogate, we identified a near-additive Urbach energy landscape with a dominant residual interaction between temperature and O₂ flow, rather than a fully entangled four-dimensional response. This structure yields a practical tuning logic consisting of sequential one-dimensional adjustments followed by a focused two-dimensional refinement in temperature and O₂ flow. The validity of this rule as an optimization strategy was supported by human-executed re-optimization, and its relevance to homoepitaxy was further examined by controlled cross-substrate tests within the tested process space.