| The Czochralski technique is the widely used method in industrial silicon single crystal growth. The condition in the furnace is complex including internal structure, heating system, melt property, etc. Aiming to get convection and heat transfer information accurately, global analysis model should be build on taking whole parts into consideration in the furnace, which is also the way to master the characteristics of global convection and furnace structure. What this paper study including: (1) In the Czochralski crystal growth process, thermal radiation is one of the main method of heat transfer, the radiation transfer between surfaces takes the principle actor as the gas in the furnace has less affect in radiation process. Typical radiation models are taken for radiation simulation in closed chamber, the result indicates that surface to surface radiation model have more accuracy and convenience on closed space radiation simulation than other models. (2) Analysis is taken on traditional Boussinesq approximation under a strong rotational flow for non-isothermal flow, which approximation is widely adopted on Czochralski crystal growth simulation. A revised Boussinesq approximation model is addressed by considering centrifugal and Coriolis forces. Results indicate that the revised Boussinesq model is valid on strong rotational non-isothermal flow while traditional Boussinesq approximation cannot get reasonable result. (3) Numerical model on melt is built and used on melt convection and heat transfer analysis, result indicates that natural convection induced by temperature gradient and forced convection induced by rotation of crystal or crucible will influence the melt convection. The result can serve as a reference for global analysis in practical conditions. (4) Phase change interface is a moving boundary issue which shape is important to crystal growth quality,a porosity medium assumption on phase change area is adopted on the interface shape simulation. A global numerical model is established coupling with thermal radiation, conduct and convection. In this model, the thermcapillary and phase change interface shape are also taken into consideration. Having the control equation uniformed into one whole differential equation form, the global model equation is discretized and solved successfully. Furthermore, the distributions of temperature and velocity, as well as the interface shape of crystal-melt for small size silicon single crystal growth are investigated. The result indicates the present model can well predict the small size silicon crystal growth, and it is useful for the optimal furnace design and growth condition. |
