Transient phenomena in crystal growth systems

Abstract

In a model of the Czochralski crystal growth system the crystal is represented by a solid rotating plane adjacent to a semi-infinite region occupied by the melt from which the crystal is grown. The melt itself may be subjected to rotation at large distances from the interface. In a co-ordinate system advancing with the interface the crystal growth is modelled by a ‘suction’ velocity at the interface. A transient analysis is performed following a discontinuous change of solute concentration in the bulk of the melt. Two cases are considered, namely (i) solid body rotation of crystal and melt and (ii) no melt rotation at large distances from the interface. The paper represents a re-examination and re-interpretation of earlier work by Burton, Prim and Slichter [1].