The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing.

The numerical modelling of the melt flow in Si crystal growth plays an important role for improving the resistivity distribution of crystals grown in industrial processes. However, recent series of experiments have shown that the existing numerical model—a finite volume solver with incompressible laminar approximation of the melt flow—is not always accurate enough to describe the experimental results for 4″ crystals. To improve the simulation results, material properties have been revised. For some of them, such as the Marangoni or thermal expansion coefficients, the literature suggests different values varying by more than a factor of two. Therefore, simulations using different combinations of parameters were run to perform parameter calibration. The study demonstrated that the description of induced heat on the open melting front needs to be modified to obtain the shape of phase boundaries that provides the best agreement to the experiment. It was concluded that new values should be assigned to several material properties in the model, most importantly the Marangoni coefficient $M=-1.2·{10}^{-4}{\displaystyle \frac{\mathrm{N}}{\mathrm{m}·\mathrm{K}}}$, and that an appropriate turbulence model may help to describe the dopant transport more precisely.

The present study demonstrates the use of a transient multiphase flow model for the description of feed rod melting dynamics during the floating-zone silicon crystal growth process on a local scale. The presented numerical model is verified using a previously introduced analytical model of the thin melt layer on the open melting front. An artificial increase in viscosity on the liquid–gas boundary is used to minimize numerical effects, and good agreement with the analytical model is achieved in the system parameter range that describes a typical growth process. Simulations with a precise interface shape show that a stable solution is achieved in cases with different initial melt distributions, showcasing the re-establishment of melt flow after the thin melt layer breaks. The influence of flow rate fluctuations is investigated, and the obtained stable solution is maintained in the majority of the considered cases.