Bayesian-optimized kinetic Monte Carlo modeling of Na electrodeposition on Cu

Kinetic Monte Carlo simulations were combined with Bayesian optimization to identify the kinetic conditions that favor compact early-stage Na deposition on Cu at room temperature. Rather than specifying all parameters from electronic-structure inputs, we adopt a morphology-first strategy in which only the dominant kinetic terms—overpotential, terrace diffusion, and lateral binding—are varied within literature-motivated bounds. Bayesian optimization provides a data-efficient means of exploring this reduced parameter space, while ensemble averaging yields a statistically stable kinetic optimum. Under the identified conditions, Na growth at two monolayers remains laterally continuous and quasi-layer-by-layer, with minimal roughness relative to nearby parameter combinations within the explored kinetic landscape. Phase-map analyses reveal a narrow compact-growth basin surrounded by increasingly rough morphologies at high driving forces or reduced mobility. Skewness serves as a supporting diagnostic, highlighting an early-time asymmetry regime at very low-magnitude overpotentials, while roughness remains the most reliable indicator of compact growth. Although motivated by Na/Cu electrodeposition, this combined Kinetic Monte Carlo and Bayesian optimization framework offers a general, data-efficient approach for locating kinetic regimes consistent with smooth alkali-metal electrodeposition.