WIAS Preprint No. 995, (2004)

On the modelling of semi-insulating GaAs including surface tension and bulk stresses



Authors

  • Dreyer, Wolfgang
  • Duderstadt, Frank

2010 Mathematics Subject Classification

  • 74N20 74A15 74N05 74B99

2008 Physics and Astronomy Classification Scheme

  • 82.60.-s 61.72.Bb 61.72.Qq 64.10.+h 64.30.-t 64.70.Dv

Keywords

  • thermodynamic, phase transition, phase diagrams, precipitates, surface stress, deviatoric stress, chemical potentials, elasticity, GaAs

Abstract

Necessary heat treatment of single crystal semi-insulating Gallium Arsenide (GaAs), which is deployed in micro- and opto- electronic devices, generate undesirable liquid precipitates in the solid phase. The appearance of precipitates is influenced by surface tension at the liquid/solid interface and deviatoric stresses in the solid.

The central quantity for the description of the various aspects of phase transitions is the chemical potential, which can be additively decomposed into a chemical and a mechanical part. In particular the calculation of the mechanical part of the chemical potential is of crucial importance. We determine the chemical potential in the framework of the St. Venant--Kirchhoff law which gives an appropriate stress/strain relation for many solids in the small strain regime. We establish criteria, which allow the correct replacement of the St. Venant--Kirchhoff law by the simpler Hooke law.

The main objectives of this study are: (i) We develop a thermo-mechanical model that describes diffusion and interface motion, which both are strongly influenced by surface tension effects and deviatoric stresses. (ii) We give an overview and outlook on problems that can be posed and solved within the framework of the model. (iii) We calculate non-standard phase diagrams, i.e. those that take into account surface tension and non-deviatoric stresses, for GaAs above 786°C, and we compare the results with classical phase diagrams without these phenomena.

Appeared in

  • Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 464 (2008) pp. 2693-2720.

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