A two‐dimensional model for the coupled effects of heat transfer and capillarity in a liquid encapsulated Czochralski growth system is analyzed by solving the full free‐boundary problem describing the temperature field in each phase, the shapes of the melt/solid and fluid/fluid interfaces, and the radius of a steadily growing crystal. Solutions are based on a finite element analysis with Newton iteration for all the variables. Heat transfer in the melt is taken to be dominated by conduction, and radiation to a uniform ambient is included for a transparent encapsulant. Calculations for a model normalGaAs system give reasonable predictions of crystal size and axial temperature gradient. The results are most sensitive to radiation through the encapsulant.

A finite element simulation of the anomalous out-diffusion of Mn in GaAs employing an interstitial-substitutional model combined with defect-chemical kinetics has been performed. The major species considered were Ga vacancies (VGa ), Mn substitutionals (MnGa), and interstitials (Mni) augmented by shallow donors (DAs ) and Ga vacancy-donor pairs (VGa-DAs). Mathematically, the model can be represented by two ordinary differential equations which are the kinetic relations describing the formation of MnGa and VGa-DAs coupled with three partial differential equations, including sink and source terms, for the diffusion of VGa, Mni, and DAs . The analysis required advanced numerical techniques using dynamic spatial and time meshes. We have achieved a very good theoretical description of Mn out-diffusion data for both 90 min and 24 h annealing cycles up to a depth of 0.5 μm from the surface [P.B. Klein, P. R. Nordquist, and P. G. Siebenmann, J. Appl. Phys. 51, 4861 (1980)]. Moreover, eventual depletion of the Mn contamination has been demonstrated. However, an inflection beyond 0.5 μm observed in the experimental results cannot be explained by the present treatment.

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