Journal of Crystal Growth 303 (2007) 161–164 Development of a software for the numerical simulation of VCz growth under the influence of a traveling magnetic field Christiane Lechner à , Olaf Klein, Pierre-Etienne Druet Weierstrass Institute for Applied Analysis and Stochastics (WIAS), MohrenstraX e 39, 10117 Berlin, Germany Available online 2 February 2007 Abstract A software for the numerical simulation of crystal growth from the melt under the influence of a traveling magnetic field was developed by coupling a global stationary simulation of the temperature distribution and the electro-magnetic fields to a local transient simulation of the melt. Numerical results of the simulation of the vapor pressure controlled Czochralski (VCz) growth of GaAs are presented. r 2007 Elsevier B.V. All rights reserved. PACS: 44.25.+f; 47.11.+j; 47.65.+a; 81.10.Fq Keywords: A1. Computer simulation; A1. Convection; A1. Fluid flows; A1. Heat transfer; A2. Magnetic field assisted Czochralski method 1. Introduction During the recent years numerical simulations have become a powerful tool for aiding the design of crystal growth furnaces and of crystal growth processes. We develop a software for the numerical simulation of semiconductor crystal growth from the melt under the influence of a traveling magnetic field. The magnetic field is expected to influence the convective flows of the melt and to damp temperature fluctuations in the vicinity of the crystal thereby improving the quality of the crystal. 2. Global simulation The electro-magnetic fields and the temperature distribu- tion in the growth apparatus are computed with the software WIAS-HiTNIHS, the WIAS-High Temperature Numerical Induction Heating Simulator, see Refs. [1–3]. WIAS-HiTNIHS solves the energy balance equation in the whole growth apparatus assuming an axisymmetric setting and taking into account heat conduction and radiation between cavity surfaces. Fig. 1 shows a growth arrangement for vapor pressure controlled Czochralski (VCz) growth used at the Institute of Crystal Growth [4]. The right part of the figure shows the temperature distribution obtained by imposing a power of 4.8 kW in the resistance heater. The fixed triple point between crystal, melt and gas is at a temperature of 1512.7 K approximating 1511 K, the melting temperature of GaAs. WIAS-HiTNIHS determines the magnetic potential ~ A ¼ f ~ e W and the electric current ~ j ¼ j ~ e W by solving the Maxwell equations for an axisymmetric situation with a sinusoidal time dependence of all electromagnetic quantities, neglect- ing the movement of the fluid. The equations reduce to n div gradðrfÞ r 2 ¼ j r , (1) j ¼ 0 in insulators; ios c f þ s c v k 2pr in kth coil ring; ios c f in other conductors; 8 > > < > > : (2) with n ¼ 1=magnetic permeability, ðr; zÞ being the cylind- rical coordinates, i the imaginary unit, o ¼ 2p50 Hz the angular frequency, s c the electrical conductivity and v k the complex representation of a given total voltage at coil ring k. We consider three coils, each with two rings, that surround the growth apparatus and are placed above each other. When performing simulations with a prescribed total induction power we follow Ref. [5, Section 2] to compute v k ARTICLE IN PRESS www.elsevier.com/locate/jcrysgro 0022-0248/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2006.12.074 à Corresponding author. Tel.: +49 30 20372448; fax: +49 30 2044975. E-mail address: lechner@wias-berlin.de (C. Lechner).