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Mathematical modelling of the Czochralski crystal growth process
Includes bibliographical references (leaves 142-149).
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613230082293760 |
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| access_status_str | Open Access |
| author | Brakel, Thomas W |
| author2 | Myers, Timothy G |
| author_browse | Brakel, Thomas W Myers, Timothy G |
| author_facet | Myers, Timothy G Brakel, Thomas W |
| author_sort | Brakel, Thomas W |
| collection | Thesis |
| description | Includes bibliographical references (leaves 142-149). |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/4868 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:50.328Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/4868 Mathematical modelling of the Czochralski crystal growth process Brakel, Thomas W Myers, Timothy G Mathematics and Applied Mathematics Includes bibliographical references (leaves 142-149). In this document a mathematical model for the Czochralski crystal growth process is developed. The trend in current research involves developing cumbersome numerical simulations that provide little or no understanding of the underlying physics. We attempt to review previous research methods, mainly devoted to silicon, and develop a novel analytical tool for indium antimonide (lnSb) crystal growth. This process can be subdivided into two categories: solidification and fluid mechanics. Thus far, crystal solidification of the Czochralski process has been described in the literature mainly qualitatively. There has been little work in calculating actual solidification dynamics. Czochralski crystal growth is a very sensitive process, particularly for lnSb, so it is crucial to describe the system as accurately as possible. A novel ID quasi-steady method is proposed for the shape and temperature field of an lnSb crystal, incorporating the effects of the melt. The fluid mechanics of the Czochralski melt have been modelled by numerous researchers,with calculations performed using commercial software. However, a descriptionof the buoyancy and rotation interaction in the melt has not been adequatelyperformed. Many authors have presented flow patterns but none have indicated either: melt conditions preferential for crystal growth or at least a description of a typical melt structure. In this work, a scale analysis is performed that implies an idealized flow structure. An asymptotic model is then derived based on this order of magnitude analysis, resulting in a fast and efficient fluid flow calculation. The asymptotic model is validated against a numerical solution to ensure that the macroscopic features of the flow structure are present. The asymptotic model does not show exact agreement, but does provide an estimate of the melt heat flux that is necessary for the solidification calculation. The asymptotic model is also used to predict macroscopic changes in the melt due to rotation. 2014-07-31T08:06:23Z 2014-07-31T08:06:23Z 2006 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/4868 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Brakel, Thomas W Mathematical modelling of the Czochralski crystal growth process |
| thesis_degree_str | Doctoral |
| title | Mathematical modelling of the Czochralski crystal growth process |
| title_full | Mathematical modelling of the Czochralski crystal growth process |
| title_fullStr | Mathematical modelling of the Czochralski crystal growth process |
| title_full_unstemmed | Mathematical modelling of the Czochralski crystal growth process |
| title_short | Mathematical modelling of the Czochralski crystal growth process |
| title_sort | mathematical modelling of the czochralski crystal growth process |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/4868 |
| work_keys_str_mv | AT brakelthomasw mathematicalmodellingoftheczochralskicrystalgrowthprocess |