Details
| Original language | English |
|---|---|
| Pages (from-to) | 158-169 |
| Number of pages | 12 |
| Journal | COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |
| Volume | 22 |
| Issue number | 1 |
| Publication status | Published - 1 Mar 2003 |
Abstract
The present paper gives an overview of the complex mathematical modelling of industrial Czochralski (CZ) and floating-zone (FZ) processes for the growth of large silicon single crystals from melt. Extensive numerical investigations of turbulent Si-melt flows in large diameter CZ crucibles, global thermal calculations in growth facilities and analysis of the influence of various electromagnetic fields on CZ process are presented. For FZ process, a complex system of coupled 2D and 3D mathematical models is presented to show the possibilities of modelling from the calculation of the molten zone shape till the resistivity distribution in the grown crystal. A special developed program code is presented that is used to calculate the temperature field in the crystal including radiation exchange with reflectors, stress field due to thermal expansion and shape of the dislocated zone in the case of dislocation generation. Besides the macroscopic modelling of crystal growth processes, the crystallisation model on the atomistic level in the mean field approximation is also presented.
Keywords
- Crystal growth, Electromagnetic fields, Mathematical modelling, Silicon
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computational Theory and Mathematics
- Engineering(all)
- Electrical and Electronic Engineering
- Mathematics(all)
- Applied Mathematics
Sustainable Development Goals
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In: COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 22, No. 1, 01.03.2003, p. 158-169.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mathematical modelling of the industrial growth of large silicon crystals by CZ And FZ process
AU - Mühlbauer, Alfred
AU - Muiznieks, Andris
AU - Ratnieks, Gundars
AU - Krauze, Armands
AU - Raming, Georg
AU - Wetzel, Thomas
N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2003/3/1
Y1 - 2003/3/1
N2 - The present paper gives an overview of the complex mathematical modelling of industrial Czochralski (CZ) and floating-zone (FZ) processes for the growth of large silicon single crystals from melt. Extensive numerical investigations of turbulent Si-melt flows in large diameter CZ crucibles, global thermal calculations in growth facilities and analysis of the influence of various electromagnetic fields on CZ process are presented. For FZ process, a complex system of coupled 2D and 3D mathematical models is presented to show the possibilities of modelling from the calculation of the molten zone shape till the resistivity distribution in the grown crystal. A special developed program code is presented that is used to calculate the temperature field in the crystal including radiation exchange with reflectors, stress field due to thermal expansion and shape of the dislocated zone in the case of dislocation generation. Besides the macroscopic modelling of crystal growth processes, the crystallisation model on the atomistic level in the mean field approximation is also presented.
AB - The present paper gives an overview of the complex mathematical modelling of industrial Czochralski (CZ) and floating-zone (FZ) processes for the growth of large silicon single crystals from melt. Extensive numerical investigations of turbulent Si-melt flows in large diameter CZ crucibles, global thermal calculations in growth facilities and analysis of the influence of various electromagnetic fields on CZ process are presented. For FZ process, a complex system of coupled 2D and 3D mathematical models is presented to show the possibilities of modelling from the calculation of the molten zone shape till the resistivity distribution in the grown crystal. A special developed program code is presented that is used to calculate the temperature field in the crystal including radiation exchange with reflectors, stress field due to thermal expansion and shape of the dislocated zone in the case of dislocation generation. Besides the macroscopic modelling of crystal growth processes, the crystallisation model on the atomistic level in the mean field approximation is also presented.
KW - Crystal growth
KW - Electromagnetic fields
KW - Mathematical modelling
KW - Silicon
UR - http://www.scopus.com/inward/record.url?scp=0041701761&partnerID=8YFLogxK
U2 - 10.1108/03321640310452259
DO - 10.1108/03321640310452259
M3 - Article
AN - SCOPUS:0041701761
VL - 22
SP - 158
EP - 169
JO - COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
JF - COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
SN - 0332-1649
IS - 1
ER -