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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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Figures

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Fig. 1

Typical PVT reactor for SiC crystal growth with simplified geometry

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Fig. 2

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

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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. 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. 5

Variations of marginal changes

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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. 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. 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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