Effects of interface roughness on cohesive strength of self-assembled monolayers

Self-assembled monolayers (SAMs) are aggregates of small molecular chains that have the property to form highly ordered assemblies. The choice of terminal groups on the chains makes them excellent contenders of molecular-level tailoring. Molecular dynamics (MD) simulations and experimental observations of spallation of two SAM-enhanced gold-film/silicon-substrate interfaces have shown that the cohesive strength of SAM-enriched transfer-printed interfaces is strongly dependent on the choice of terminal groups. Though the MD results of perfectly ordered atomistic surfaces show the same qualitative trend as the experiments, they over-predict the interfacial cohesive strengths by a factor of about 50. Results from AFM studies have revealed that the roughness of these interfaces is of the same order (∼1 nm) as the range of atomistic interactions. Hence, surface roughness is a key contributor in significantly reducing interfacial cohesive strength in these systems. In this manuscript, a continuum-level study is performed to investigate the influence of surface roughness on the cohesive strength of the interface between a Si/SAM substrate and a transfer-printed gold film. We approximate the film as a deformable continuum interacting with a rough substrate of SAMs represented by a harmonic function. Using a cohesive law derived from MD, spallation is simulated to evaluate the effective traction-separation characteristics for the rough SAM-gold interface. Our analysis shows that incorporating roughness may reduce the interfacial cohesive strength by an order of magnitude depending on the film properties and the surface roughness. Additionally, we observe that the gold film adopts unique separation attributes based on roughness parameters and material properties.