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A Finite Element Framework for Burton-Cabrera-Frank Equation

  • Frank Haußer
  • Axel Voigt
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 149)

Abstract

A finite element framework is presented for the Burton-Cabrera-Frank (BCF) equation. The model is a 2 + 1-dimensional step flow model, discrete in the height but continuous in the lateral directions. The problem consists of adatom diffusion equations on terraces of different atomic height; boundary conditions at steps (terrace boundaries); and a normal velocity law for the motion of such boundaries determined by a two-sided flux, together with one-dimensional edge-diffusion. Two types of boundary conditions, modeling either diffusion limited growth or growth governed by attachment-detachment kinetics at the steps, are considered. We review the basic ideas of the algorithms, already described in [1, 2] and extent it to incorporate anisotropy of the step free energy, the edge mobility and the kinetic coefficients (attachment-detachment rates). The problem is solved using two independent meshes: a two-dimensional mesh for the adatom diffusion and a one-dimensional mesh for the step dynamics governed by an anisotropic geometric evolution law. Finally results on the anisotropic growth of single layer islands are presented.

Keywords

step-flow model anisotropic geometric evolution laws parametric finite elements discrete-continuous coupling 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Frank Haußer
    • Axel Voigt
      • 1
    1. 1.Crystal Growth groupresearch center caesarBonnGermany

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