WIAS Preprint No. 996, (2004)

Diffusion in the vicinity of an evolving spherical arsenic droplet


  • Dreyer, Wolfgang
  • Duderstadt, Frank
  • Qamar, Shamsul

2010 Mathematics Subject Classification

  • 74N25 82B24 82C26

2008 Physics and Astronomy Classification Scheme

  • 82.20.Wt 61.72.Bb 61.72.Qq 64.70.Dv


  • phase transition, diffusion, thermomecanical coupling, GaAs, precipitates


We study the diffusion problem of liquid droplets in single crystal semi-insulating Gallium Arsenide (GaAs). This problem is posed by an industrial application, where the droplets, also called precipitates, appear during a necessary heat treatment of GaAs wafer. The subsequent dissolution of the droplets is mandatory, in order to use the wafer after the heat treatment as a substrate material for micro- and opto- electronic devices.

In this study we consider a single droplet in a solid matrix, which is in contact with an arsenic gas, so that the arsenic can cross the solid/gas interface. The model equations have been derived by the authors. They consist of a nonlinear diffusion equation with diffusion controlled and kinetic boundary conditions, respectively, at the liquid/solid interface. Furthermore we study at the solid/gas interface alternatively zero flux and Dirichlet conditions.

Surface tension at the liquid/solid interface and deviatoric stresses in the solid are taken into account. The latter appear due to different densities of liquid and solid GaAs. There is a large influence of these effects on diffusion, interface motion and phase diagrams, which are used to identify regions, where coexistence of liquid and solid phases is possible.

In order to study the evolution of the droplet, and in particular possibilities to enforce its dissolution, we solve several initial and boundary value problems for the diffusion system.

Download Documents