Coarsening of 3D Thin Films under the Influence of Strong Surface Anisotropy, Elastic Stresses

Abstract

We develop a diffuse interface model to investigate the three dimensional coarsening in thin films. In this model, both strong surface anisotropy with linear Willmore regularization elastic stresses and deposition are included. The governing equation for the phase field parameter is a sixth order Cahn-Hilliard Equation due to the presence of surface anisotropy and the linear Willmore regularization. The simulated system is assumed to be in mechanical equilibrium with misfit in the film generated by lattice mismatch in the substrate. Thus the Cauchy-Navier equations are solved for elastic displacements which lead to the elastic energy. Both the Cahn-Hilliard equation and the Cauchy-Navier equations are solved with an non-stiff, adaptive nonlinear multigrid method. Simulation results of coarsening in three dimensions with different strengths of the surface anisotropy, misfit strain, and deposition rates are shown. Comparison and analysis of these results help to explain their influence on coarsening processes in thin films.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2009
Accession Number
ADA538820

Entities

People

  • John Lowengrub
  • Peng Shou
  • Steven G. Wise

Organizations

  • University of California, Irvine

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Anisotropy
  • Boundaries
  • Crystal Lattices
  • Crystal Structure
  • Crystals
  • Displacement
  • Energy
  • Equations
  • Films
  • Free Energy
  • Materials
  • Personal Information Managers
  • Perturbations
  • Simulations
  • Thin Films
  • Three Dimensional
  • Vapor Phases

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mechanical Engineering/Mechanics of Materials.
  • Thin Film Deposition Science.