Modelling of the Czochralski flow

Abstract

The Czochralski method of the industrial production of a silicon single crystal consists of pulling up the single crystal from the silicon melt. The flow of the melt during the production is called the Czochralski flow. The mathematical description of the flow consists of a coupled system of six P.D.E. in cylindrical coordinates containing Navier-Stokes equations (with the stream function), heat convection-conduction equations, convection-diffusion equation for oxygen impurity and an equation describing magnetic field effect.

Keywords

• mathematical modelling
• viscous flow
• Czochralski method
• single crystal growth
• weak solution
• operator equation
• existence theorem
• weighted Sobolev spaces
• Rothe method.