Crystal rotation rate

Figures 19a-c show the results of a numerical simulation by a finite difference method for a 2-dimensional axially symmetric viscous fluid system. The left-hand and right-hand part of each picture show the stream lines of the melt and isotherms, respectively, within the right-hand halves of the vertical section of the crucible (see also Seeflelberg et al. 1997b). Convection below the crystal is induced by the crystal rotation and the natural convection near the crucible wall. As the crystal rotation rate and/or the crystal diameter increases, the forced convection becomes stronger and the meeting point of the forced and the natural convections near the melt surface moves from the crystal to the crucible wall. The isotherms are coupled strongly to the convection, and the temperature at the crystal growth interface increases with the acceleration of forced convection (increasing the crystal rotation rate) as well as with increasing the size of the crystal.

Crystal pulling under certain conditions for the forced convection exhibits a potentiality of both flat or concave crystal production (Namikawa et al. 1996a, sect. 6.2). To attain suitable growth conditions for a flat crystal, the crystal rotation rate should satisly simultaneously at least the following three requirements ... 

The process of growing a pure crystal is sensitive to a host of process parameters that impact the iacorporation of impurities ia the crystal, the quality of the crystal stmcture, and the mechanical properties of the crystal rod. For example, the crystal-pulling mechanism controls the pull rate of the crystallisa tion, which affects the iacorporation of impurities ia the crystal, and the crystal rotation, which affects the crystal stmcture. 

We find that the rotation rate affects both the "interface angle", i.e.- the angle between crystal and melt, cuid control of crs tal diameter, as shown in the following diagram, given as 6.4.7. on the next page. 

The best compromise seems to be fast- rotation for the crystal and slow or no rotation for the crucible. Of all the possible methods of stirring the melt, the static-crucible method seems to be the best, and this is the method used by most crystal-growers. The next best method seems to be rotating the crucible at a slow rate, counter to the direction of the crystal rotation. It is clear that crystal- rotation needs to dominate the stirring pattern so that mixing of the melt continues while the crystal is growing. 

The crystal growth rate has been found in many eases to be extremely rapid, more rapid than can be accounted for on the diffusion hypothesis thus Tammann (foe. cit.) found for benzophe-none a maximum crystallisation velocity of 2 4 mm. per minute (Walton and Judd, J. Phys. Ohem. xvni, 722,1914). Much higher values, e.g. 6840 mm. per minute for water and 60,000 mm. per minute for phosphorus (Gernez, O.R, xcv. 1278, 1882) have been recorded. In some cases the rate was found independent of the speed of rotation of the stirrer and occasionally the reaction velocity followed a bimolecular law instead of the simple unimolecular expression which holds true for solution. 

The Czochralski Technique. Pulling from the melt is known as the Czochralski technique. Purified material is held just above the melting point in a cmcible, usually of Pt or Ir, most often powered by radio-frequency induction heating coupled into the wall of the crucible. The temperature is controlled by a thermocouple or a radiation pyrometer. A rotating seed crystal is touched to the melt surface and is slowly withdrawn as the molten material solidifies onto the seed. Temperature control is used to widen the crystal to the desired diameter. A typical rotation rate is 30 rpm and a typical withdrawal rate, 1—3 cm/h. Very large, eg, kilogram-sized crystals can be grown. 

Secondary nucleation results from the presence of solute particles in solution. Recent reviews [16,17] have classified secondary nucleation into three categories apparent, true, euid contact. Apparent secondary nucleation refers to the small fragments washed from the surface of seeds when they are introduced into the crystallizer. True secondary nucleation occurs due simply to the presence of solute particles in solution. Contact secondary nucleation occurs when a growing particle contacts the walls of the container, the stirrer, the pump impeller, or other particles, producing new nuclei. A review of contact nucleation, frequently the most significant nucleation mechanism, is presented by Garside and Davey [18], who give empirical evidence that the rate of contact nucleation depends on stirrer rotation rate (RPM), particle mass density, Mj>, and saturation ratio. 

Ko+ l-Ko)sxpi-vd/D) with other symbols defined above. This equation describes semiquantitatively the variation of dopant concentration in the crystal with growth rate v and with changes in rotation rate co, which change the boundary layer thickness, <5 (5 oc... 

The equations have been verified experimentally in apparatus to be described later. After the cylinder begins rotating, only a few minutes are needed for the falling crystal to establish an orbit. The rotation rate of the crystal matches that of the mechanics, for the 1-mm crystals to... 

The drive shaft and bowl assembly are designed to function under water in the temperature bath. Supported above the water are the drive motor, I, timing belt and pulleys, H, the speed controller, J, and upper section of the chain drive housing, K. The use of a glass water bath and glass growth chamber permits the operator to see the crystal in motion. With submillimeter seeds, the initial rotation rate is several rpm and can be increased as needed. 

Figure 18.55 shows the predicted steady-state temperature and meridional flow streamlines for (a) no melt convection and stationary crystal, (b) no crystal rotation with buoyancy-induced melt flow, (c) modest rotation and mixed melt convection, and (d) high rotation rates with mixed melt convection [213], The emissivity of the crystal-vapor interface of the system was specified to be 0.3, while the melt-crystal interface emissivity was set to 0.9 for the GGG crystal of refractive index 1.8. Additional property values and geometric details are listed elsewhere [215]. The crucible diameter is 200 mm, the crystal diameter is 100 mm, and thermocapillary convection was not included in the analysis. 

The next best method seems to be rotating the crucible at a slow rate, counter to the direction of the crystal rotation. It is clear that crystal-rotation needs to dominate the stirring pattern so that mixing of the melt continues while the crystal is growing. 

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