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Research on Flow Characteristics and Instabilities during Czochralski Crystal Growth Process

Author: WuChunMei
Tutor: LiYouRong
School: Chongqing University
Course: Power Engineering and Engineering Thermophysics
Keywords: Czochralski configuration Rotation Thermocapillary flow Thermocapillary-buoyancy flow Flow instability
CLC: O781
Type: PhD thesis
Year: 2013
Downloads: 75
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The Czochralski (Cz) crystal growth technology is one of the most importantmethods for producing single crystals, where both the crucible containing the melt andthe crystal growing at the melt surface are rotated in opposite directions to smooth theirregular heating. Thus, the forces that can drive the flow include the thermocapillary,buoyancy, centrifugal and Coriolis forces. These forces interact on different scalesmaking the Cz crystal growth process difficult to be controlled and characterized, andseveral flow instabilities may be triggered. These flow instabilities have a direct impacton the quality of the growing single crystal, such as the undesired creation of striations.Up to now, it appears that how the rotation influences the thermal and flow fields, thedetails about the complex flow driven by the combination of buoyancy andthermocapillary forces, Coriolis and centrifugal forces have not been investigatedsystematically, and the mechanisms of flow instabilities remain puzzling, although lotsof works have been reported on the flow behaviors during Cz crystal growth process.In this thesis, both numerical simulations and experiments are performed tocontribute further to the understanding of the complex flow during Czochralski crystalgrowth process. The critical conditions for the onset of flow instabilities are obtained,and the stability diagrams are mapped. Meanwhile, the effects of the aspect ratio, radiusratio, thermocapillary Reynolds number (ReT), as well as the rotation Reynolds number(Rec, Res) are presented. In addition, the mechanisms of flow instabilities are alsodiscussed. The results obtained herein can not only make progress in hydrodynamics butalso provide some new theoretical bases for the optimization of crystal growthtechnology. The main results are as follows:Firstly, the characteristics of the three-dimensional flow driven by the rotation ofcrucible and crystal are investigated by numerical simulation. Results show that whenthe rotation Reynolds number is small, the basic flow is axisymmetric and steady.However, when the rotation Reynolds number exceeds a critical value, the flow willundergo a transition to a three-dimensional oscillatory flow, which is characterized bythe velocity fluctuation waves travelling in the azimuthal direction. The propagatingdirection and velocity of the waves, as well as the wave number, are dependent on therotation rate and directions of the crucible and crystal. When the crystal counter rotateswith crucible, the mechanism of the flow transition is the shear instability. In the shallow Cz configuration, when the crystal rotates only or co-rotates with crucible, theelliptic instability is responsible for the flow transition. However, in the deepconfiguration, when the crystal co-rotates with crucible, the flow instability is ellipticinstability, and centrifugal instability is the origin of the flow transition for the case ofcrystal rotation only. In addition, the characteristics of flow also show an importantdependence on the radius ratio. Various polygonal flow patterns are presented atdifferent radius ratio.Secondly, the fundamental characteristics of the three-dimensional flow of lowPrandtl number fluid induced by crucible and/or crystal rotation and the surface tensiongradient during Czochralski crystal growth process are investigated through a series ofunsteady three-dimensional numerical simulations. The results indicate that the criticalthermocapillary Reynolds number varies with the rotation of crucible and crystal. Whenthe crucible rotates only, the critical thermocapillaty Reynolds number, ReT,c, decreasesfirst and then increases with the increase of Rec. If the crystal co-rotates with crucible,the ReT,cincreases with the increase of Rec, and the higher Resresults in a lower ReT,catthe same Rec. In particular, when the crystal counter-rotates with the crucible, threedifferent flow states are observed and mapped with different ReT. If the rotation-inducedflow is strong, the flow field is already located in the unstable state, as the increasinginfluence of the thermocapillary force, the flow strength is weakened, and the3-Dunsteady flow will transit to stable state. If ReTincreases further, the flow driven by thethermocapillary force is dominant and will lose its stability again, and then transit toanother unstable state.In addition, the flow driven by the coupled buoyancy and thermocapillary forces,Coriolis and centrifugal forces are discussed. It is indicated that the effect of buoyancyforce can instabilize the flow. For a high ReT, the thermocapillary-buoyancy convectionis dominant, thus the origin of the flow instability is Rayleigh-Bénard instability. Whenthe effects of the driving forces are comparable, the mechanism of the flow transitionhas been proved to be the baroclinic instability.Furthermore, the combined effects of temperature gradient and counter rotation ofcrucible and crystal on the flow instability in a liquid-encapsulated Czochralskiconfiguration are investigated through a series of direct numerical simulations. Resultsshow that when the ReTexceeds a threshold value, the unsteady multi-cellular structuresare developed. The oscillatory flow behaves as fluctuation waves propagating from thecrystal/fluid interface to the crucible sidewall. The amplitudes of the velocity and temperature fluctuations decrease with the increase of crystal rotation rate, but increasewith the crucible rotation rate. The critical conditions for the onset of flow instabilityare obtained. The stability diagram indicates that the rotation of crucible has adestabilizing effect on the flow, but the crystal rotation can depress the flow instabilitywhen the crystal rotation Reynolds number exceeds a certain value.Finally, the temperature filed of the complex flow in the Cz configuration isinvestigated experimentally by schlieren technique. For the shallow liquid layer, thetemperature disturbance pattern on the free surface is characterized by the curvedspokes. For the different temperature difference, two groups of hydrothermal waveswith different wave numbers are travelling in the opposite directions, especially for thecase of small radius ratio configuration, the typical Bénard cells are observed. When thedepth of liquid layer locates in the range of5~8mm, with the increase of temperaturedifference, the temperature disturbance transits from the straight spoke pattern to the"flower bud typed" pattern. When the depth is greater than8mm, the temperature profileon the surface is represented as striated pattern. In addition, the rotation of crucible hasmore serious inhibition to the flow instability with the higher depth.

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CLC: > Mathematical sciences and chemical > Crystallography > Crystal growth > Theories of crystal growth
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