TY - JOUR

T1 - The elastic field of a surface step

T2 - The Marchenko-Parshin formula in the linear case

AU - Connell, Cameron R.

AU - Caflisch, Russel E.

AU - Luo, Erding

AU - Simms, Geoff

N1 - Funding Information:
Research supported in part the ARO through Grant #DAAD19-02-1-0336 and by the NSF under Grant #DMS0402276.

PY - 2006/11/15

Y1 - 2006/11/15

N2 - 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 Marchenko-Parshin formula for the dipole moment in terms of the elastic surface stress.

AB - 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 Marchenko-Parshin formula for the dipole moment in terms of the elastic surface stress.

KW - Elasticity

KW - Epitaxial growth

KW - Marchenko-Parshin formula

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U2 - 10.1016/j.cam.2005.08.020

DO - 10.1016/j.cam.2005.08.020

M3 - Article

AN - SCOPUS:33746267067

SN - 0377-0427

VL - 196

SP - 368

EP - 386

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -