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Research Papers: Melting and Solidification

A Numerical Simulation Study on the Effects of Crucible Rotation and Magnetic Fields in Growth of SiGe by the Traveling Heater Method

[+] Author and Article Information
Youhei Takagi, Yasunori Okano

Division of Chemical Engineering,Department of Materials Engineering Science, Graduate School of Engineering Science,  Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japantakagi@cheng.es.osaka-u.ac.jp

Sadik Dost

Crystal Growth Laboratory,  University of Victoria, Victoria, BC, Canada V8W 3P6sdost@uvic.ca

J. Heat Transfer 134(1), 012301 (Oct 28, 2011) (7 pages) doi:10.1115/1.4004803 History: Received September 20, 2010; Revised July 27, 2011; Accepted July 28, 2011; Published October 28, 2011; Online October 28, 2011

A numerical simulation study was carried out to shed light on the effects of applied crucible rotation and static magnetic field during the traveling heater method growth of bulk SiGe single crystals. The simulation results show that the application of crucible rotation weakens the radial silicon concentration gradient due to the effect of centrifugal force. The effects of applied static magnetic field direction and strength on the concentration field in the melt were also studied. It was found that the simultaneous application of crucible rotation and static magnetic field is best to grow large crystals with uniform composition. An optimum combination of crucible rotation rates and applied magnetic field strengths is determined.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 11

Time dependence of concentration distribution near the growth interface z = 5.0 × 10−4 m for Ha = 40 and Ω = 5 rpm: (a) t = 300 s, (b) t = 301 s, (c) t = 302 s, (d) t = 303 s, (e) t = 304 s, (f) t = 305 s, and (g) t = 306 s

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Figure 12

Effect of crucible rotation on concentration distribution in radial direction for Ha = 20 and t = 300 s

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Figure 13

Instantaneous concentration distribution near the growth interface z = 5.0 × 10−4 m: (a) axial, (b) transversal and (c) oblique magnetic forces, respectively

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Figure 14

Effect of magnetic field direction for Ha = 40 and Ω = 10 rpm at t = 300 s

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Figure 10

Time dependence of concentration at some sampling points near the growth interface for Ha = 40 and Ω = 5 rpm

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Figure 9

Instantaneous concentration distribution in radial direction for Ha = 40 and Ω = 5 rpm at θ = 0 and π rad

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Figure 8

Effect of vertical magnetic field strength on concentration distribution in radial direction for Ω = 10 rpm at t = 300 s

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Figure 7

Effect of vertical magnetic field strength on concentration distribution in radial direction for Ω = 5 rpm at t = 300 s

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Figure 6

Velocity and silicon concentration distributions with vertical magnetic field Ha = 40 at t = 300 s: (a) vertical and (b) horizontal profiles at z = 5.0 × 10−4 m

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Figure 5

Velocity and silicon concentration distributions with crucible rotation Ω = 5 rpm at t = 300 s: (a) vertical and (b) horizontal profiles at z = 5.0 × 10−4 m

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Figure 4

Velocity and silicon concentration distributions without external force at t = 300 s: (a) vertical profiles of velocity vector (left) and concentration (right), and (b) horizontal profiles of concentration near the growth interface at z = 5.0 × 10−4 m (z1 in Fig. 4a)

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Figure 3

Comparison of the simplified thermal convection at RaT  = 200,000: (a) —– Lan and Liang [18], - - - Lan and Liang (Fluent) [18], – – – Baumgartl [19], and (b) present result

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Figure 2

Computational grid

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Figure 1

Schematic diagram of THM

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