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/ Si 3 N 4 nanopixels on a Si͑111͒ substrate. We couple the molecular-dynamics ͑MD͒ 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/ Si 3 N 4 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 ϳ2.5ϫ 10 3 m / s. The effects of temperature, nanopixel architecture, and film structure on strain relaxation are also investigated. We find: ͑i͒ elevated temperature increases the interfacial domain nucleation rates; ͑ii͒ a thin compliant Si layer between the film and the substrate plays a beneficial role in partially suppressing strain relaxation; and ͑iii͒ additional control over the interface morphology may be achieved by varying the film structure.

The study of deformation and stress—strain distribution of nano-scale thin sheet copper under the biaxial tensile loads by using molecular dynamics and finite-element method

“…Lidorikis et al [12] reported a hybrid atomisticcontinuum simulation approach, implemented to study strain relaxation in lattice-mismatched Si/Si 3 N 4 nanopixels on a Si(1 1 1) substrate. They coupled the MD and macro-scale finite-element simulation approaches to provide an atomistic description near the interface and a continuum description deep into the substrate, thereby, increasing the accessible length scales and significantly reducing the computational cost.…”

Pair distribution functions in molecular dynamics simulations of interfaces

“…The nitrogen atom is then bonded to three Si atoms across the interface with a bond length around 2.5 Å. It has been found that successive D1 -> D2 and D2 -> D1 slips relax the mismatch strain in form of a triangular superlattice of interfacial domains [Lidorikis et al, 2005]. In the simulation presented here the initial configuration was in phase D1.…”

“…After that, because the center piece is disconnected from the region on the left and the right that is being pulled, it can relax to almost the unstrained configuration which is reflected in the fact that the peak height of the first peak returns almost to its original value. Two different coherent interface phases leading to a local energy minimum configuration have been considered earlier [Lidorikis et al, 2005]. The phase D1 consists of the N atoms of type 4 in the interface plane of silicon nitride being positioned directly on top of the Si atoms of type 8 in the interface double layer of silicon (see figure 13.a)) with a bond length of 1.75 Å.…”