The University of Southampton
University of Southampton Institutional Repository

The effect upon Czochralski growth of periodic modulation of the growth rate

Wheeler, A.A. (1982) The effect upon Czochralski growth of periodic modulation of the growth rate Journal of Crystal Growth, 56, (1), pp. 67-76. (doi:10.1016/0022-0248(82)90013-6).

Record type: Article

Abstract

In this paper we describe the results of a mathematical treatment of the Czochralski growth system when the growth rate is periodically modulated. Such a modulation simulates the effect of fluctuations in temperature which occur in the melt from which the crystal is grown. In this treatment we consider the system in the limits Sc? ?, R? ?, ?? 0, ??0, where Sc is the Schmidt number, R is the Reynolds number of the liquid phase, ? the Prandtl number, and ? the ratio of the solution diffusivities in the liquid and solid phases. Here we describe the effect of the modulation upon the solute, temperature and velocity fields. The velocity filed is perturbed by an amount O(Sc-1/2) from the steady-state flow induced by the rotation of the crystal, while the temperature field in the liquid exhibits a three-region structure. (Here the symbol O(x) means of order x. We use it here in its mathematical sense. That is if y = O(x), then there exists a constant k independent of y and x such that -kx <y < kx for all x.) A solute boundary layer of thickness O((Sc)-1/2) forms adjacent to the crystal interface in the liquid. When the crystal does not melt back the effect of solute diffusion in the solid is confined to a perturbation O(?). However if the crystal melts back the effect of solute diffusion in the crystal becomes important, producing a time dependent solute boundary layer in the crystal.

Full text not available from this repository.

More information

Published date: 1982

Identifiers

Local EPrints ID: 833
URI: http://eprints.soton.ac.uk/id/eprint/833
ISSN: 0022-0248
PURE UUID: 870c9b62-900e-4ffd-80ae-fc506d8c8249

Catalogue record

Date deposited: 05 Apr 2004
Last modified: 17 Jul 2017 17:17

Export record

Altmetrics

Contributors

Author: A.A. Wheeler

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×