TECHNICAL PAPERS: Manufacturing Processes

Interface Shape and Thermally-Driven Convection in Vertical Bridgman Growth of Gallium Selenide: A Semiconductor With Anisotropic Solid-Phase Thermal Conductivity

[+] Author and Article Information
Hanjie Lee, Arne J. Pearlstein

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801

J. Heat Transfer 123(4), 729-740 (Feb 02, 2001) (12 pages) doi:10.1115/1.1372194 History: Received August 29, 2000; Revised February 02, 2001
Copyright © 2001 by ASME
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Grahic Jump Location
Schematic of vertical Bridgman growth with imposed ampoule-wall temperature distribution Tb(z)
Grahic Jump Location
Isotherms and streamlines for dTb(0)/dz=30°C cm−1. (a) U=0.25 μm sec−1 : ψmin=−0.0261,ψmax=0.0432; (b) U=1.0 μm sec−1 : ψmin=−0.0253,ψmax=0.0708; and (c) U=3.0 μm sec−1 : ψmin=−0.0233,ψmax=0.116.
Grahic Jump Location
Interface shapes for dTb(0)/dz=30°C cm−1.U=0.25 μm sec−1 , Δz/ri=0.120;U=0.50 μm sec−1 , Δz/ri=0.152;U=1.0 μm sec−1 , Δz/ri=0.215;U=3.0 μm sec−1 , Δz/ri=0.437.
Grahic Jump Location
Isotherms and streamlines for dTb(0)/dz=60°C cm−1, with L1=30 and L2=8. (a) U=0.25 μm sec−1 : ψmin=−0.0608,ψmax=0.0490; (b) U=1.0 μm sec−1 : ψmin=−0.0598,ψmax=0.0704; and (c) U=3.0 μm sec−1 : ψmin=−0.0572,ψmax=0.117.
Grahic Jump Location
Interface shapes for dTb(0)/dz=60°C cm−1.U=0.25 μm sec−1 , Δz/ri=0.102;U=0.50 μm sec−1 , Δz/ri=0.117;U=1.0 μm sec−1 , Δz/ri=0.150;U=3.0 μm sec−1 , Δz/ri=0.275.
Grahic Jump Location
Isotherms and streamlines for dTb(0)/dz=30°C cm−1,U=0.25 μm sec−1 , with Tc=900°C,Th=1050°C, and TM=937°C:ψmin=−0.0292,ψmax=0.0538.
Grahic Jump Location
Interface shapes for dTb(0)/dz=30°C cm−1, with Tc=900 °C,Th=1050°C, and TM=937°C.U=0.25 μm sec−1 , Δz/ri=0.146;U=0.50 μm sec−1 , Δz/ri=0.190;U=1.0 μm sec−1 , Δz/ri=0.274;U=3.0 μm sec−1 , Δz/ri=0.563.
Grahic Jump Location
Isotherms and streamlines for a fictitious material with isotropic solid-phase conductivity kiso=tr(ks)/3 and dTb(0)/dz=30°C cm−1. (a) U=0.25 μm sec−1 : ψmin=−0.0712,ψmax=0.893×10−4; (b) U=1.0 μm sec−1 : ψmin=−0.0507,ψmax=0.0; and (c) U=3.0 μm sec−1 : ψmin=−0.0572,ψmax=0.117.
Grahic Jump Location
Interface shapes for dTb(0)/dz=30°C cm−1 for a fictitious material with isotropic solid-phase thermal conductivity kiso=tr(ks)/3 and dTw(0)/dz=30°C cm−1.U=0.25 μm sec−1 , Δz/ri=−0.177;U=0.50 μm sec−1 , Δz/ri=−0.159;U=1.0 μm sec−1 , Δz/ri=−0.125;U=3.0 μm sec−1 , Δz/ri=4.9×10−3.
Grahic Jump Location
Isohterms and streamlines for localized ampoule-wall heating with χ=−0.1,z0/ri=−0.05,σ=2, and λ=0.4 cm−1 , corresponding to dTb(0)/dz=30°C cm−1 when χ=0. (a) U=0.25 μm sec−1 : ψmin=−0.0515,ψmax=0.0387; (b) U=0.5 μm sec−1 : ψmin=−0.0481,ψmax=0.0389; and (c) U=1.0 μm sec−1 : ψmin=−0.0425,ψmax=0.0402.
Grahic Jump Location
Interface shapes (below) for localized ampoule-wall heating with χ=0.1,σ=2,z0/ri=−0.05, and λ=0.4 cm−1 (corresponding to dTb(0)/dz=30°C cm−1 when χ=0).U=0.25 μm sec−1 , Δz/ri=0.080;U=0.50 μm sec−1 , Δz/ri=0.106;U=1.0 μm sec−1 , Δz/ri=0.156. Upper curves are for χ=0:U=0.25 μm sec−1 , Δz/ri=0.120;U=0.50 μm sec−1 , Δz/ri=0.152;U=1.0 μm sec−1 , Δz/ri=0.215.
Grahic Jump Location
Isotherms and streamlines for zero g at dTb(0)/dz=30°C cm−1,U=1.0 μm sec−1 : ψmin=−7.79×10−5max=−5.09×10−8.




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