Cryst. Res. Technol. 43, No. 2, 145 – 151 (2008) / DOI 10.1002/crat.200710993
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Influence of active afterheater on the induction heating process in
oxide Czochralski systems
M. H. Tavakoli*, F. Samavat, and M. Babaiepour
Physics Department, Bu-Ali Sina University, Hamedan, Iran
Received 17 July 2007, accepted 26 September 2007
Published online 19 October 2007
Key words computer simulation, Czochralski method, induction heating.
PACS 02.60.Cb, 02.70.Dh, 41.20.-q, 81.10.Fq
Different shapes and orientations of an active afterheater for oxide Czochralski crystal growth systems are
considered and corresponding results of electromagnetic field and volumetric heat generation have been
computed using a finite element method (Flex-PDE package). For the calculations, the eddy current in the
induction coil (i.e. the self-inductance effect) has been taken into account. The calculation results show the
importance of an active afterheater, its shape as well as its geometry and position with respect to the crucible
on the heat generation distribution in a CZ growth system.
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction
Today the method of radiofrequency induction heating is widely used in crystal growth technology. This
method is applied to generate directly the required thermal power in the metallic parts. In oxide Czochralski
(CZ) systems (Figure 1), this induction power is produced by an induction heater coil (copper) that surrounds
the metal crucible (usually iridium or platinum). A high frequency electric current (~10 kHz) in this coil
induces an eddy current distribution in the metal crucible and afterheater. The final product is the rate of
energy dissipation in the crucible and afterheater -Joulean heating (I
2
R) in the form of temporal and spatial
volumetric heating. This internal heat generation is partly transferred into the melt and gas via the inner wall
and bottom of the crucible and the afterheater wall and top cover, and partly lost to the surroundings via the
outer surfaces of insulation.
Using an active afterheater in oxide CZ growth is common for controlling the heat transfer mechanisms and
temperature field in the setup. Presence of an active afterheater in the CZ furnace affects markedly on the heat
generation and complicated thermal field in the system and also represents a challenging problem of numerical
modeling [1-4].
The goal of this article is to reveal the role of an active afterheater on the induction heating process and
compare the corresponding results of electromagnetic field and heat generation distribution for an oxide
Czochralski system using a FEM numerical approach. To do it, different shapes and orientations of an active
afterheater with respect to the crucible are considered corresponding to the real growth situations. Our
challenge is to extend the fundamental understanding of induction heating process used for crystal growth
technology, because this understanding will enable the growers to optimize existing procedures and design of
new growth methods.
2 Mathematical model
Following assumptions are made in our numerical calculations: (1) The system is axisymmetric. (2) All media
are linear, isotropic and stationary. (3) All materials are non-magnetic and have no net charge. (4) The
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* Corresponding author: e-mail: mht@basu.ac.ir