WIAS Preprint No. 1475, (2009)

Mean field diffusion models for precipitation in crystalline GaAs including surface tension and bulk stresses



Authors

  • Dreyer, Wolfgang
  • Kimmerle, Sven-Joachim

2010 Mathematics Subject Classification

  • 74Q99 35B27 35Q74 35R35 74A15 74F99 74N20 65P99

2008 Physics and Astronomy Classification Scheme

  • 02.30 Mv 02.30.Jr 61.72.uj 64.70.D- 66.30.-h

Keywords

  • mean field approximation, homogenisation, semi-insulating GaAs, Ostwald ripening including mechanics

Abstract

Based on a thermodynamically consistent model for precipitation in gallium arsenide crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose different mathematical models to describe the size evolution of liquid droplets in a crystalline solid. The first class of models treats the diffusion-controlled regime of interface motion, while the second class is concerned with the interface-controlled regime of interface motion. Our models take care of conservation of mass and substance. We consider homogenised models, where different length scales of the experimental situation have been exploited in order to simplify the equations. These homogenised models generalise the well-known Lifshitz-Slyozov-Wagner model for Ostwald ripening. Mean field models capture the main properties of our system and are well adapted for numerics and further analysis. Numerical evidence suggests in which case which one of the two regimes might be appropriate to the experimental situation.

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