Machine-Learning-Augmented Simulation of Thin Metal Film Growth on Weakly-Interacting Substrates

Decoration of 2D-material, insulator, and semiconductor surfaces with thin metal films is relevant for a wide array of key enabling devices and technologies, including solar cells, energy-saving windows, catalysts, sensors, and nanoelectronics. Such films are typically synthesized via condensation from the vapor phase, whereby device functionality crucially depends on film morphology. Achieving morphology control is, however, not trivial, as metal atoms may exhibit weak interaction with the underlying substrate leading to uncontrolled morphology of three-dimensional metal island agglomerates. [1]

Prior experimental reports have shown that metal film morphology can be manipulated in a non-invasive fashion by deploying minority gaseous [2,3] or metal species [4,5] (i.e., surfactants) at the film growth front. In the present work, we seek to unravel atomic-scale mechanisms by which surfactants affect morphological evolution of thin-metal films on weakly-interacting substrates by means of kinetic Monte-Carlo (kMC) simulations.

From a simulation point of view, modelling of multi-elemental thin film growth poses a considerable challenge: atomic interactions must be described accurately in the complex and a priori unknown chemical environments at the film growth front, while maintaining computational efficiency to reach millisecond or even longer timescales. To address this challenge, we have been developing a machine-learning (ML) augmented kMC model for Ag thin film growth on weakly-interacting substrates in the presence of Cu and Au surfactant atoms. The model — built upon our previous work where we utilized neural networks in simulating Cu surface diffusion [6] — has two key components: molecular dynamics (MD) for on-the-fly nudged elastic band migration barrier calculations, and a Gaussian process regression (GPR) [7] ML model for concurrently training a fast surrogate barrier predictor to eventually replace the relatively slow MD calculations. The GPR approach draws inspiration from the Gaussian approximation potentials (GAP) [8], and utilizes the same code base, but the atomic environments of the migration events are mapped directly to activation barriers, instead of potential energies and forces. We have used classical, embedded-atom method potentials for barrier calculations, but the model can utilize any potential that the LAMMPS [9] back-end accepts. Our preliminary results for Ag homoepitaxy show that the kMC simulation reproduces the growth mode and the island shapes in accordance with the underlying potential energy function.

[1] K. Sarakinos, Thin Solid Films 688, 137312 (2019).
[2] A. Jamnig et al., ACS Appl. Nano Mater. 3, 4728 (2020).
[3] N. Pliatsikas et al., Journal of Vacuum Science & Technology A 38, 043406 (2020).
[4] A. Jamnig et al., Applied Surface Science 538, 148056 (2021).
[5] A. Jamnig et al., Journal of Vacuum Science & Technology A 40, 033407 (2022).
[6] J. Kimari et al., Computational Materials Science 183, 109789 (2020).
[7] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (2005).
[8] A. P. Bartók et al., Physical review letters 104, 136403 (2010).
[9] S. Plimpton, Journal of Computational Physics 117, 1 (1995).