Crystal pulling rate

Figure 19 shows sample isotherms and interface shapes predicted by the QSSM for calculations with decreasing melt volume in the crucible, as occurs in the batchwise process. Because the crystal pull rate and the heater temperature are maintained at constant values for this sequence, the crystal radius varies with the varying heat transfer in the system. Two effects are noticeable. First, decreasing the volume exposes the hot crucible wall to the crystal. The crucible wall heats the crystal and causes the decrease in... 

Process Stability and Control. Operationally, automatic control of the crystal radius by varying either the input power to the heater or the crystal pull rate has been necessary for the reproducible growth of crystals with constant radius. Techniques for automatic diameter control have been used since the establishment of Czochralski growth. Optical imaging of the crystal or direct measurement of the crystal weight has been used to determine the instantaneous radius. Hurle (156) reviewed the techniques currently used for sensing the radius. Bardsley et al. (157,158) described control based on the measurement of the crystal weight. 

Fig. 6.2 Temperature distribution and argon velocity vectors in the Ekz-1300 system. The crystal pulling rate is 2 mm min, argon pressure and flow rate are ISmbar and 1500 SLH, respectively, the crystal/crucible rotation rates are 20 and —5 rpm, respectively.

Figure 7.7 shows the interface deflection toward the melt as a function of the ratio between the crystal-pulling rate (Vp) and the temperature gradient in the crystal near the interface (G). The interface moves upward to the crystal side with increase in either the magnetic field intensity or the value of the parameter Vp/G. This trend is consistent with that of the axial temperature gradient in the crystal near an interface, as shown in Fig. 7.6. This is because the interface shape is mainly determined by the temperature distribution in the crystal close to the interface and the melt convection in a crucible.

As one can gather from Eq. (14.17), during crystal pulling from the variable cross section crucible, several possibilities emerge to control the volatile activator in crystal. The direct path is variation of C(q. Besides, C(S) depends on the crystal pulling rate and the relation of the values of crystal transverse cross section vs. free melt surface ds l(d — ds ). In the variable cross section crucible, the value of this relation can be easily varied, the volatile activator concentration for ingots of various diameters being kept constant and made the same. 

The presence of defects and impurities is unavoidable. They are created during tire growtli or penetrate into tlie material during tlie processing. For example, in a crystal grown from tire melt, impurities come from tire cmcible and tire ambient, and are present in tire source material. Depending on factors such as tire pressure, tire pull rate and temperature gradients, tire crystal may be rich in vacancies or self-interstitials (and tlieir precipitates). 

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. 

The second justification for the angular condition is that this condition is necessary for the determination of the radius of the crystal at the trijunction as a function of heat-transfer conditions and pull rate. This argument is simple. The dimensionless Young-Laplace equation of capillary statics gives the shape of an axisymmetric melt-ambient meniscus as... 

Equation 37 describes the relationship between the rate of change of the crystal radius at the trijunction and the deviation of the local angle from the equilibrium value < >o. In this expression, < )(t) is the dynamic angle formed between the local tangents to the melt-ambient and crystal-ambient surfaces, and Vg(T) is the dimensionless pull rate of the crystal. For steady-state growth, equation 37 simply sets the angle with what must be a solid cylinder of constant radius. The importance of the dynamical form equation 37 is brought out in the next section. 

The main difference between the methods of Kyropoulos (see Figure 7.19a) and Czochralski (see Figure 7.19b) is that in the former the seed is permitted to grow into the melt, while in the latter the seed is withdrawn at a rate that keeps the solid-liquid interface more or less in a constant position. Pull rates depend on the temperature gradient at the crystal-melt interface and can vary from 1 to 40mmh . The steeper the gradient the faster the growth rate and, hence, the faster the permissible rate of withdrawal. 

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