A Discrete Elastic Model for Epitaxial Systems and the Force Field at a Step

Strain has significance for both the growth characteristics and material properties of thin epitaxial films. In this work, the method of lattice statics is applied to an epitaxial system with cubic symmetry, using harmonic potentials. The energy density and force balance equations are written using a finite difference formalism that clearly shows their consistency with continuum elasticity. For simplicity, the atomic interactions are assumed to be maximally localized. For a layered material system with a material/vacuum interface and with surface steps, force balance equations are derived, and intrinsic surface stress at the material/vacuum interface is included by treating the atoms at the surface as having different elastic properties. By defining the strain relative to an appropriately chosen nonequilibrium lattice, as in the method of eigenstrains, analytic formulas in terms of microscopic parameters are found for the local force field near a step and for the macroscopic monopole and dipole moment forces due to a step. These results provide an atomistic validation of the MarchenkoParshin formula for the dipole moment in terms of the elastic surface stress. ∗Research supported in part by an NSF Focused Research Group grant # DMS0074152. †Mathematics Department, NJIT. Email: [email protected] ‡Mathematics Department, Department of Materials Science & Engineering, and California NanoSystems Institute, UCLA. Email: [email protected]. §Mathematics Department, UCLA. Email: [email protected] ¶HRL Laboratories. Email: [email protected]