Progress in modeling of fluid flows in crystal growth processes

Modeling of fluid flows in crystal growth processes has become an important research area in theoretical and applied mechanics.Most crystal growth processes involve fluid flows,such as flows in the melt,solution or vapor.Theoretical modeling has played an important role in developing technologies used for growing semiconductor crystals for high performance electronic and optoelectronic devices.The application of devices requires large diameter crystals with a high degree of crystallographic perfection,low defect density and uniform dopant distribution.In this article,the flow models developed in modeling of the crystal growth processes such as Czochralski,ammono- thermal and physical vapor transport methods are reviewed.In the Czochralski growth modeling,the flow models for thermocapillary flow,turbulent flow and MHD flow have been developed.In the ammonothermal growth modeling,the buoyancy and porous media flow models have been developed based on a single-domain and continuum approach for the composite fluid-porous layer systems.In the physical vapor transport growth modeling,the Stefan flow model has been proposed based on the flow-kinetics theory for the vapor growth.In addition,perspectives for future studies on crystal growth modeling are proposed.