Phase-field modeling and n-point polytope characterization of nanostructured protuberances formed during vapor-deposition of phase-separating alloy films

The formation of surface features, such as grooves, protruding grains, or hillocks, in vapor-deposited phase-separating films is typically attributed to internal residual stresses arising due to a difference in thermal expansion coefficients of the film and the substrate. Even though such protuberances are typically observed on the film’s surface, the current understanding of how interfacial energies and surface contact angles influence this nanostructural evolution is very limited. In view of this knowledge gap, we adopt a three-dimensional phase-field approach to numerically investigate the role of seed morphology and contact angles on the morphological evolution of surface protuberances in phase-separating alloy films. Film nanostructures are quantified using a statistical morphological descriptor, namely, n-point polytope functions, which provides a host of insights into the kinetic pathways while unraveling a hidden length scale correlation present at all contact angles. Finally, we also apply this characterization technique on previously reported micrographs of Cu–Ta and Cu–Mo–Ag films to highlight similarities between our simulation-based findings with those obtained from co-deposition experiments.