A multizone adaptive process model for low and high pressure crystal growth

Zhang, H.; Prasad, V.

doi:10.1016/0022-0248(95)00257-x

Cited by 52 publications

(15 citation statements)

References 24 publications

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“…In the presence of rotation, all three components of velocity are non-zero, though a function of the radial and vertical coordinates. The numerical model is based on a primitive variable formulation, previously discussed by Zhang and Prasad (1995). The approach adopted in the present study is presented in detail by Banerjee (2004).…”

Section: Numerical Modelmentioning

confidence: 99%

“…Such cold model experiments reveal the complicated interaction of transport mechanisms existing in real Czochralski processes. Mathematical models have also been developed to explore these interactions (Derby and Xiao, 1991;Zhang and Prasad, 1995). These models help in conducting simulation under realistic conditions and optimizing process parameters for the growth of high quality crystals.…”

Section: Introductionmentioning

confidence: 99%

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Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Banerjee

Bharadwaj

Muralidhar

2006

J Vis

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Steady state temperature distribution in a model Czochralski crucible has been mapped by liquid crystal thermography (LCT). The crucible is a water-filled glass beaker. Water is used as the test fluid because of ease of experimentation, as well as the availability of correct thermo-physical properties. In addition, the Prandtl number of water matches those of molten oxides. A copper cylinder whose diameter is smaller than that of the beaker is placed centrally at the water surface. Convection patterns are set up by applying constant temperature difference between the crucible wall and the cylinder surface, in the temperature range of the liquid crystals. The cylinder is given a fixed rotation, thus creating mixed convection conditions in the test fluid. The LCT images recorded in the present study clearly reveal convective rolls, and the interaction of buoyancy-driven convection in the crucible with cylinder rotation. The resulting temperature distributions match numerical simulation quite well. The pure buoyancy and pure rotation experiments result in axisymmetric temperature fields, while in mixed convection, the field is unsteady and three dimensional.

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Section: Numerical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Banerjee

Bharadwaj

Muralidhar

2006

J Vis

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“…The melt convection is modeled. Our home-built code, developed from MASTRAPP [18], and a commercial code, COMSOL, are combined for the simulation. The furnace size is similar to that used in Ref.…”

Section: Resultsmentioning

confidence: 99%

Influence of furnace design on the thermal stress during directional solidification of multicrystalline silicon

Fang

Wang

Zhou

et al. 2012

Journal of Crystal Growth

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“…The in-house-built MASTRAPP program [24] is modified to simulate heat transfer and melt convection during the growth of Nd:YVO 4 crystals. The properties of Nd:YVO 4 crystals used in the simulations are summarized in Table 1 [25,26].…”

Section: Simulation and Experimental Resultsmentioning

confidence: 99%