University of East Anglia
Norwich, England
The Czochralski crystal growth system for pulling single crystals from a melt by first dipping a seed crystal into that melt owes its origins to the pioneering work of Czochralski, whose prime concern was to measure the speed of crystallisation of a number of low melting-point metals. It was not until 30 years later, in the late 1940's, that the technique was developed and exploited by the electronics industry. During the second half of this century it has become the dominant technique for the production of bulk single crystals of a wide range of materials for the electronics and electro-optics industries. In the 1940's there was virtually no understanding of the technique. However, over the last 50 years it has been subjected to intense study, with size and purity of the end-product the main goal. In this lecture we demonstrate that within the Czochralski system there is a kaleidescope of phenomena that are familiar to us as applied mathematicians. For example, in the cooling crystal there are dislocations to be modelled, whilst at the crystal-melt interface we have a moving boundary problem, where the net heat transport determines the growth rate of the crystal. Within the melt which is typically a binary alloy, for example silicon doped with phosphorous, a thin dopant boundary layer forms at the freezing interface.There we may expect not only hydrodynamic but also morphological instabilities. Finally, the introduction of a magnetic field to both damp melt turbulence, and control the distribution of impurities, involves a study of magnetohydrodynamic effects, not only at the interface but also within the bulk melt.