Coupling atomistic and continuum length scales in heteroepitaxial systems: Multiscale molecular-dynamics/finite-element simulations of strain relaxation inSi∕Si3N4nanopixels

Abstract

A hybrid atomistic-continuum simulation approach has been implemented to study strain relaxation in lattice-mismatched Si/ Si3N4 nanopixels on a Si111 substrate. We couple the molecular-dynamics MD and finite-element simulation approaches to provide an atomistic description near the interface and a continuum description deep into the substrate, increasing the accessible length scales and greatly reducing the computational cost. The results of the hybrid simulation are validated against full multimillion-atom MD simulations. We find that strain relaxation in Si/ Si3N4 nanopixels may occur through the formation of a network of interfacial domain boundaries reminiscent of interfacial misfit dislocations. They result from the nucleation of domains of different interfacial bonding at the free edges and corners of the nanopixel, and subsequent to their creation they propagate inwards. We follow the motion of the domain boundaries and estimate a propagation speed of about 2.5 10 3 m / s. The effects of temperature, nanopixel architecture, and film structure on strain relaxation are also investigated. We find: i elevated temperature increases the interfacial domain nucleation rates; ii a thin compliant Si layer between the film and the substrate plays a beneficial role in partially suppressing strain relaxation; and iii additional control over the interface morphology may be achieved by varying the film structure.