STEADY-STATE FLOW IN A CZOCHRALSKI CRUCIBLE

A separate solution for steady state melt flow is obtained for each of five driving forces: (a) crystallization, (b) crystal rotation, (c) crucible rotation, (d) buoyancy force, and (e) surface tension gradient. Mixed flows with crystal and/or crucible rotation, with crystal rotation and buoyancy force, and with crystal rotation, buoyancy force, and surface tension gradient are examined. It is found that the final flow depends on the flow history. The rigid body rotation is not always a stable solution in Czochralski geometry. When the driving forces for buoyancy and crystal rotation are comparable, the mixed flow becomes unstable.