LAUSR

In this article, the behavior of the dissolution process of silicon (Si) in molten germanium (Ge) was mathematically modeled and examined numerically. The transport phenomena during this process were modeled using the axisymmetric model (2D) and the equations of the model were solved numerically using the COMSOL multiphysics package. The numerical simulations were carried out exclusively to explain the experimental observations (carried out previously) on the effect of the presence of a free surface on the transport and the mixture of the solute and the shape of the interface of dissolution. The dissolution experimental work used a configuration in which the sample (source Si) was located at the bottom to mimic for instance the process in the melt replenishment Czochralski growth system. For the samples processed in the dissolution experiments, the dissolved heights of silicon were measured. This measurement gives the quantity of silicon dissolved in the experimental times and must be directly linked to the quantity of silicon transported in the melt. Measurement of the silicon composition profiles in the samples was carried out (in the experimental work previously carried out) using the energy dispersive X-ray spectrometer technique. The present numerical results confirm and complement the experimental observations and show that the effect indicates a tendency to more mixing and the presence of several complex convective melt flow regimes leading to rapid chaotic mixing with the presence of a free surface on the melt. In addition, the numerical and the experimental results reveal that it is necessary to take into account the geometry of the crystal growth system when the source Si material is located at the bottom. Indeed, the dissolution of silicon from the bottom of the melt in the presence of a free surface will occur much faster. This however may lead to instability and crystal growth with nonuniform composition.