Mathematical modelling of the industrial growth of large silicon crystals by CZ And FZ process

authored by: Alfred Mühlbauer, Andris Muiznieks, Gundars Ratnieks, Armands Krauze, Georg Raming, Thomas Wetzel
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.
Organisation(s): Institute of Electrothermic Process Engineering
External Organisation(s): University of Latvia
Siltronic AG
Type: Article
Journal: COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Volume: 22
Pages: 158-169
No. of pages: 12
ISSN: 0332-1649
Publication date: 01.03.2003
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computer Science Applications, Computational Theory and Mathematics, Electrical and Electronic Engineering, Applied Mathematics
Sustainable Development Goals: SDG 9 - Industry, Innovation, and Infrastructure
Electronic version(s): https://doi.org/10.1108/03321640310452259 (Access: Closed)