Research Papers: Heat and Mass Transfer

Heat Transfer Inside the Physical Vapor Transport Reactor

[+] Author and Article Information
Zeyi Zhang

Department of Mechanical Engineering,
The University of Hong Kong,
Pokfulam, Hong Kong;
HKU-Zhejiang Institute of Research
and Innovation (HKU-ZIRI),
Hangzhou, Zhejiang 311300, China

Min Xu

Energy Research Institute,
Shandong Academy of Sciences,
Jinan, Shandong 250014, China

Liqiu Wang

Department of Mechanical Engineering,
The University of Hong Kong,
Pokfulam, Hong Kong;
HKU-Zhejiang Institute of Research and
Innovation (HKU-ZIRI),
Hangzhou, Zhejiang 311300, China
e-mail: lqwang@hku.hk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 6, 2015; final manuscript received April 26, 2016; published online June 7, 2016. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 138(10), 102002 (Jun 07, 2016) (13 pages) Paper No: HT-15-1705; doi: 10.1115/1.4033539 History: Received November 06, 2015; Revised April 26, 2016

The physical vapor transport (PVT) method is widely adopted to produce semiconductor materials including silicon carbide (SiC). This work focuses on the role of thermal radiation for the heat transfer inside the PVT reactor. The radiation is characterized by two dimensionless parameters relating to the SiC charge and to the growth chamber. A simulation program is set up with the finite-volume method (FVM), considering heat generation, conduction, and radiation under the steady-state condition. Comprehensive results are obtained by tuning values of dimensionless parameters and the associated controlling variables, such as the cooling temperature and the coil current density, and illustrated in the phase diagrams. From the study, we find that the charge size has negligible influence on the temperature field, the crucible conduction determines the temperature level, and the relative strength of the chamber radiation against the crucible conduction modifies the temperature field on the SiC ingot. Finally, design guidelines are proposed with the instructive phase diagram to achieve the optimized thermal performance of the PVT reactor.

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Chaussende, D. , Wellmann, P. J. , and Pons, M. , 2007, “ Status of SiC Bulk Growth Processes,” J. Phys. D: Appl. Phys., 40(20), pp. 6150–6158. [CrossRef]
Glass, R. C. , Henshall, D. , Tsvetkov, V. F. , and Carter, C. H. , 1997, “ SiC Seeded Crystal Growth,” Phys. Status Solidi B, 202(1), pp. 149–162. [CrossRef]
Matsunami, H. , and Kimoto, T. , 1997, “ Step-Controlled Epitaxial Growth of SiC: High Quality Homoepitaxy,” Mater. Sci. Eng.: B, 20(3), pp. 125–166. [CrossRef]
Ivanov, P. A. , and Chelnokov, V. E. , 1992, “ Recent Developments in SiC Single-Crystal Electronics,” Semicond. Sci. Technol., 7(7), pp. 863–880. [CrossRef]
Furusho, T. , Sasaki, M. , Ohshima, S. , and Nishino, S. , 2003, “ Bulk Crystal Growth of Cubic Silicon Carbide by Sublimation Epitaxy,” J. Cryst. Growth, 249(1–2), pp. 216–221. [CrossRef]
Chen, Q. S. , Zhang, H. , Prasad, V. , Balkas, C. M. , and Yushin, N. K. , 2001, “ Modeling of Heat Transfer and Kinetics of Physical Vapor Transport Growth of Silicon Carbide Crystals,” ASME J. Heat Transfer, 123(6), pp. 1098–1109. [CrossRef]
Sudarshan, T. S. , and Maximenko, S. I. , 2006, “ Bulk Growth of Single Crystal Silicon Carbide,” Microelectron. Eng., 83(1), pp. 155–159. [CrossRef]
Sugiyama, N. , Okamoto, A. , Okumura, K. , Tani, T. , and Kamiya, N. , 1998, “ Step Structures and Dislocations of SiC Single Crystals Grown by Modified Lely Method,” J. Cryst. Growth, 191(1–2), pp. 84–91. [CrossRef]
Wellmann, P. , Herro, Z. , Winnacker, A. , Pusche, R. , Hundhausen, M. , Masri, P. , Kulik, A. , Bogdanov, M. , Karpov, S. , Ramm, M. , and Makarov, Y. , 2005, “ In Situ Visualization of SiC Physical Vapor Transport Crystal Growth,” J. Cryst. Growth, 275(1–2), pp. E1807–E1812. [CrossRef]
Dhanaraj, G. , Dudley, M. , Ma, R. H. , Zhang, H. , and Prasad, V. , 2004, “ Design and Fabrication of Physical Vapor Transport System for the Growth of SiC Crystals,” Rev. Sci. Instrum., 75(9), pp. 2843–2847. [CrossRef]
Hofmann, D. , Eckstein, R. , Kolbl, M. , Makarov, Y. , Muller, S. G. , Schmitt, E. , Winnacker, A. , Rupp, R. , Stein, R. , and Volkl, J. , 1997, “ SiC-Bulk Growth by Physical-Vapor Transport and Its Global Modelling,” J. Cryst. Growth, 174(1–4), pp. 669–674. [CrossRef]
Selder, M. , Kadinski, L. , Durst, F. , Straubinger, T. , and Hofmann, D. , 1999, “ Numerical Simulation of Global Heat Transfer in Reactors for SiC Bulk Crystal Growth by Physical Vapor Transport,” Mater. Sci. Eng.: B, 61(2), pp. 93–97. [CrossRef]
Chen, X. J. , Liu, L. J. , Tezuka, H. , Usuki, Y. , and Kakimoto, K. , 2008, “ Optimization of the Design of a Crucible for a SiC Sublimation Growth System Using a Global Model,” J. Cryst. Growth, 310(7–9), pp. 1810–1814. [CrossRef]
Wang, X. L. , Cai, D. , and Zhang, H. , 2007, “ Increase of SiC Sublimation Growth Rate by Optimizing of Powder Packaging,” J. Cryst. Growth, 305(1), pp. 122–132. [CrossRef]
Liu, X. , Chen, B. Y. , Song, L. X. , Shi, E. W. , and Chen, Z. Z. , 2010, “ The Behavior of Powder Sublimation in the Long-Term PVT Growth of SiC Crystals,” J. Cryst. Growth, 312(9), pp. 1486–1490. [CrossRef]
Chen, X. J. , Nishizawa, S. , and Kakimoto, K. , 2010, “ Numerical Simulation of a New SiC Growth System by the Dual-Directional Sublimation Method,” J. Cryst. Growth, 312(10), pp. 1697–1702. [CrossRef]
Gao, B. , Chen, X. J. , Nakano, S. , Nishizawa, S. , and Kakimoto, K. , 2010, “ Analysis of SiC Crystal Sublimation Growth by Fully Coupled Compressible Multi-Phase Flow Simulation,” J. Cryst. Growth, 312(22), pp. 3349–3355. [CrossRef]
Meyer, C. , and Philip, P. , 2005, “ Optimizing the Temperature Profile During Sublimation Growth of SiC Single Crystals: Control of Heating Power, Frequency, and Coil Position,” Cryst. Growth Des., 5(3), pp. 1145–1156. [CrossRef]
Knippenberg, W. F. , 1963, Growth Phenomena in Silicon Carbide, Echt, Valkenburg, The Netherlands.
Raback, P. , Yakimova, R. , Syvajarvi, M. , Nieminen, R. , and Janzen, E. , 1999, “ A Practical Model for Estimating the Growth Rate in Sublimation Growth of SiC,” Mater. Sci. Eng.: B, 61(2), pp. 89–92. [CrossRef]
Ma, R. H. , Zhang, H. , Prasad, V. , and Dudley, M. , 2002, “ Growth Kinetics and Thermal Stress in the Sublimation Growth of Silicon Carbide,” Cryst. Growth Des., 2(3), pp. 213–220. [CrossRef]
Muller, S. G. , Glass, R. C. , Hobgood, H. M. , Tsvetkov, V. F. , Brady, M. , Henshall, D. , Malta, D. , Singh, R. , Palmour, J. , and Carter, C. H. , 2001, “ Progress in the Industrial Production of SiC Substrates for Semiconductor Devices,” Mater. Sci. Eng.: B, 80(1–3), pp. 327–331. [CrossRef]
Ma, R. H. , Zhang, H. , Dudley, M. , and Prasad, V. , 2003, “ Thermal System Design and Dislocation Reduction for Growth of Wide Band Gap Crystals: Application to SiC Growth,” J. Cryst. Growth, 258(3–4), pp. 318–330. [CrossRef]
Ma, R. H. , Zhang, H. , Ha, S. , and Skowronski, M. , 2003, “ Integrated Process Modeling and Experimental Validation of Silicon Carbide Sublimation Growth,” J. Cryst. Growth, 252(4), pp. 523–537. [CrossRef]
Pons, M. , Anikin, M. , Chourou, K. , Dedulle, J. M. , Madar, R. , Blanquet, E. , Pisch, A. , Bernard, C. , Grosse, P. , Faure, C. , Basset, G. , and Grange, Y. , 1999, “ State of the Art in the Modelling of SiC Sublimation Growth,” Mater. Sci. Eng.: B, 61(2), pp. 18–28. [CrossRef]
Mercier, F. , Dedulle, J. M. , Chaussende, D. , and Pons, M. , 2010, “ Coupled Heat Transfer and Fluid Dynamics Modeling of High-Temperature SiC Solution Growth,” J. Cryst. Growth, 312(2), pp. 155–163. [CrossRef]
Chen, Q. S. , Zhang, H. , Prasad, V. , Balkas, C. M. , Yushin, N. K. , and Wang, S. , 2001, “ Kinetics and Modeling of Sublimation Growth of Silicon Carbide Bulk Crystal,” J. Cryst. Growth, 224(1–2), pp. 101–110. [CrossRef]
Geiser, J. , Klein, O. , and Philip, P. , 2006, “ Transient Numerical Study of Temperature Gradients During Sublimation Growth of SiC: Dependence on Apparatus Design,” J. Cryst. Growth, 297(1), pp. 20–32. [CrossRef]
Klein, O. , and Philip, P. , 2003, “ Transient Numerical Investigation of Induction Heating During Sublimation Growth of Silicon Carbide Single Crystals,” J. Cryst. Growth, 247(1–2), pp. 219–235. [CrossRef]
Biro, O. , and Preis, K. , 1989, “ On the Use of the Magnetic Vector Potential in the Finite-Element Analysis of Three-Dimensional Eddy Currents,” IEEE Trans. Magn., 25(4), pp. 3145–3159. [CrossRef]
Kitanin, E. L. , Ramm, M. S. , Ris, V. V. , and Schmidt, A. A. , 1998, “ Heat Transfer Through Source Powder in Sublimation Growth of SiC Crystal,” Mater. Sci. Eng.: B, 55(3), pp. 174–183. [CrossRef]
Modest, M. F. , 2003, Radiative Heat Transfer, Academic Press, New York.
Ma, R. H. , Chen, Q. S. , Zhang, H. , Prasad, V. , Balkas, C. M. , and Yushin, N. K. , 2000, “ Modeling of Silicon Carbide Crystal Growth by Physical Vapor Transport Method,” J. Cryst. Growth, 211(1–4), pp. 352–359. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, CRC Press, Boca Raton, FL.
Roy, A. , Mackintosh, B. , Kalejs, J. P. , Chen, Q. S. , Zhang, H. , and Prasad, V. , 2000, “ A Numerical Model for Inductively Heated Cylindrical Silicon Tube Growth System,” J. Cryst. Growth, 211(1–4), pp. 365–371. [CrossRef]
Sparrow, E. M. , Eckert, E. R. G. , and Irvine, T. F. , 1961, “ The Effectiveness of Radiating Fins With Mutual Irradiation,” J. Aerosp. Sci., 28(10), pp. 763–772. [CrossRef]
Klein, O. , Philip, P. , Sprekels, J. , and Wilmanski, K. , 2001, “ Radiation- and Convection-Driven Transient Heat Transfer During Sublimation Growth of Silicon Carbide Single Crystals,” J. Cryst. Growth, 222(4), pp. 832–851. [CrossRef]
Su, J. , Chen, X. J. , and Li, Y. , 2014, “ Numerical Design of Induction Heating in the PVT Growth of SiC Crystal,” J. Cryst. Growth, 401, pp. 128–132. [CrossRef]


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Fig. 1

Typical PVT reactor for SiC crystal growth with simplified geometry

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Fig. 6

The magnetic vector potential field of case 0: (a) the dimensional magnitude Wb/m, (b) the dimensionless imaginary (left side) and real (right side) parts, and (c) the dimensionless eddy power

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Fig. 7

The dimensionless temperature field of case 0

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Fig. 8

Comparison of the temperature fields among four cases (thermal isolation not shown): (a) case 0, (b) case 1, (c) case 2, and (d) case 3

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Fig. 4

Grid layout (a) for the magnetic vector potential field, 111 × 65, (b) for the temperature field, 83 × 33, and (c) zoom-in view of the growth chamber and the ingot

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Fig. 2

Heat flow in the PVT reactor through three ways of heat transfer

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Fig. 5

Variations of marginal changes

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Fig. 9

(a)–(d) Temperature field in the ingot from case 0 to case 3, respectively, (e) temperature percentage difference (θ−θ2)/θ2 (%), and (f) normalized net radiative flux, −∇qradi″, around the growth chamber

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Fig. 3

Validation of the numerical solver for the thermal radiation model. The problem is adopted from Ref. [36], with ϵ=0.5 and α=120deg.

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Fig. 10

Variations of (a) radiation ratio, %, (b) (θmax−θ2)/θ2, %, (c) (θ1−θ2)/θ2, %, (d) θ2 (reoriented), and (e) Δθ, %, with respect to  log10(Π′cond/Πcond) (x-axis),  log10(Π′radi, J/Πradi, J) (y-axis), and d′/d (surfaces). The contour on zero-plane corresponds to d′/d=1. The values of d′/d are marked out besides the three surfaces when their differences are visible.

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Fig. 11

Variation of θ2 with respect to Π′cond/Πcond. The square and circle have Π′radi, J/Πradi, J=10Π′cond/Πcond, while the cross and asterisk have Π′radi, J/Πradi, J=0.1Π′cond/Πcond.

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Fig. 12

Variations of (a)  log10(λ) and (b) abs(Δθ), %, with respect to Π′cond/Πcond and Π′radi, J/Πradi, J. The curves with Δθ=0 and λ=1 are highlighted, and the four cases are located.

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Fig. 13

Overestimation ratio between the ideal radiative power and the actually net radiative power, received by the ingot surface

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Fig. 14

Phase diagrams: (a)  log10(Π′cond/Πcond) on x-axis and  log10(Π′radi, J/Πradi, J) on y-axis, and (b) T′∞/T∞ on x-axis and Jc′/Jc on y-axis



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