Algorithm of crystal profile control for automatic crystal growth by the Czochralski method

The new generation crystal growth systems should work in the automatic mode. To obtain high-quality crystals, accurate maintenance of the specified boule profile is required. In the systems using weight control, the programmed force is compared to the force acting upon the weight sensor. In this paper an algorithm for calculation of the programmed force is offered. It is based on the numerical solution of the Bardsley equation. This algorithm allows crystal profile setting both analytically and numerically.