Combined global 2D–local 3D modeling of the industrial Czochralski silicon crystal growth process

A global, axisymmetric thermal model of a Czochralski furnace is coupled to an external, local, 3D, time-dependent flow model of the melt via the inclusion of turbulent heat fluxes, extracted from the 3D melt model, into the 2D furnace model. Boundary conditions of the 3D model are updated using results from the 2D model. In the 3D model the boundary layers are resolved by aggressive mesh refinement towards the walls, and the Large Eddy Simulation approach is used to model the turbulent flow in the melt volume on a relatively coarse mesh to minimize calculation times. It is shown that by using this approach it is possible to reproduce fairly good results from Direct Numerical Simulations obtained on much finer meshes, as well as experimental results for interface shape and oxygen concentration in the case of growth of silicon crystals with 210 mm diameter for photovoltaics by the Czochralski method.

► Time-dependent 3D LES model reproduces good results from DNS.
► Coupled 2D–3D model reproduces measured s/l interface for industrial Si Cz process.
► Coupled 2D–3D model also reproduces measured oxygen concentration.
► Converged results from the coupled 2D–3D model are typically obtained after five days.