The Effect of an Axial Magnetic Field at the Interface of a Crystal Grown by the Czochralski Method

A mathematical model has been developed which aims to give insight into the transport phenomena in the vicinity of the interface of a crystal grown by the Czochralski method in the presence of an axial magnetic field. The fluid flow, temperature and concentration fields in this region have a strong...

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Bibliographic Details
Published in:IMA journal of applied mathematics 1985-09, Vol.35 (2), p.175-194
Main Authors: CARTWRIGHT, R. A., EL-KADDAH, N., SZEKELY, J.
Format: Article
Language:English
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Summary:A mathematical model has been developed which aims to give insight into the transport phenomena in the vicinity of the interface of a crystal grown by the Czochralski method in the presence of an axial magnetic field. The fluid flow, temperature and concentration fields in this region have a strong effect on the distribution of impurities and the occurrence of cracks, dislocations and other physical defects in the crystal and so knowledge and ultimately control of these factors is of great practical importance. The model incorporates rotation of both the crystal and crucible by considering the crystal to be an infinite disc rotating in a semi-infinite fluid which may be rotating at infinity. Axial symmetry is assumed and the magnetic Prandtl number is considered to be very much less than unity. This means that induced currents can be neglected and allows a similarity solution to be developed. The system of partial differential equations can then be replaced by an ordinary differential boundary-value problem which is solved numerically.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/35.2.175