Training of Neural Network Machine Learning Potentials for Activation Barrier Calculations in Predicting Growth Modes of Deposited Metals

Machine-learning interatomic potentials (MLIPs) are opening many new opportunities to extend the capabilities of computational materials science. MLIPs deliver increased throughput and simulations at time and length scales beyond first principles density functional theory (DFT), while maintaining near-DFT accuracy, thus allowing unravelling of chemical processes not accessible with DFT. In this work, we present an approach to training a neural network MLIP using DeepMD-kit software that delivers both accurate energies and forces, suitable for determining activation energies via nudged elastic band calculations. We use the deposition of metals on substrates, in particular Ru and Cu on TaN for semiconductor device interconnects, as the example system, for which activation barriers of metal atom migration at the metal-substrate interface and on the metal deposit are important in understanding the evolution of the film morphology during deposition. The structure of the metal-substrate interface directly affects the performance of devices, from catalysts and sensors, to interconnects and contacts in nanoelectronics. The activation barrier energies from our MLIP for all sizes of metal atom deposits reproduce the DFT activation energies to within an average error of 0.08 eV (6%) for Cu and 0.23 eV (19%) for Ru. The trends of the DFT barriers are preserved by the MLIP and the computing time is reduced from days using high performance computing to minutes on a personal laptop. This allows us to assess the activation energies for complex processes such as the transition of a 2-layer metal cluster to a 3-layer cluster-a key step in metal island growth. Morphology evolution occurs on multiple scales, from initial nucleation, to layer growth and cluster ripening. By demonstrating that MLIPs can be used to accurately and rapidly deliver activation energies for the relevant atomic scale processes, a multi-scale predictive atomistic model of metal deposition and growth chemistry becomes feasible.