Segregation coefficient

Table 3. Equilibrium Segregation Coefficients for Impurities in Silicon...

An example of an analysis done on polysilicon and single-crystal Czochralski silicon (CZ) is shown in Table 1. As can be seen, polysilicon, which was used to grow the crystal, is dirtier than the CZ silicon. This is expected, since segregation coefficients limit the incorporation of each element into the crystal boule during the crystal growth process. All values shown in the table are from bulk analysis. Table 2 shows NAA data obtained in an experiment where surface analysis was accom-... 

Zhang Weihan, Yan Shuxia, Ji Zhijiang. Effective segregation coefficient and steady state segregation coefficient of germanium in Czochralski silicon. J Cryst Growth 169 598, 1996. 

Figure 4. Neutral stability diagrams from linear analysis for values of the thermophysical properties considered in this paper, (a) Diagram for properties given as Case I in Table I as a function of the segregation coefficient k. Continued on next page.

This illustrates the fact that impurity segregation and purification processes are dependent upon the type of impurity involved and its individual segregation coeffleient. As we illustrated above in 6.8.1., the problem is that the impurity is initially rejected from the solid, but its concentration builds up in front of the growing OTStal. The segregation coefficient, k,, then operates on that increased concentration and the product, ki Co. increases. 

Equilibrium segregation coefficients, for silicon impurities, 22 493t Equilibrium stages, calculation of, 10 756-759... 

Before the curves of Figure 5 can be used, two things must be determined the variation of the segregation coefficient, k, with the temperature of the coolant outside the tubes and the time required to freeze a zone of ice in the tube (not needed for simulation, because it does not affect the product salinity) which affects the production rate from a given unit. 

The effect of temperature difference on the segregation coefficient was determined experimentally. Although the segregation coefficient data vary with concentration, the effect is small in this type of system and was considered to have no significance in the economic study. Tubes ranging in size from 7/16 to 1 inch containing salt water were immersed in a constant temperature bath and the segregation coefficient was determined. 

Figure 5. Conversion and segregation coefficient required to produce water with 500 p.p.m. salt for various number of stages...

It was found that, although tube size has no effect, the temperature difference has a large effect on the segregation coefficient, as shown in Figure 6. 

Figure 6. Effect of temperature difference on segregation coefficient...

Figure 5. Idealized phase diagram for a binary alloy. The liquidus slope m and equilibrium segregation coefficient k are defined in the text.

The effective segregation coefficient keS is defined in tenns of the stagnant-film thickness as... 

Figure 12 shows a sample profile from the growth of gallium-doped germanium by Wang (6). The profile fits equation 21, with an equilibrium segregation coefficient k of 0.087 and keS of 0.09-0.11... 

Several groups (84-86) have extended the similarity analysis of Burton et al. (73) to the case in which an axial magnetic field is imposed on the melt with sufficient strength such that Ha >> 1 and N 1. With these limits, a closed-form asymptotic expression describes the variation in the flow field across the thin 0(Ha 1/2) Hartmann layer adjacent to the disk. Axial solute segregation across this layer was analyzed by assuming that the melt outside of the Hartmann layers is well mixed. The effective segregation coefficient approaches 1 when the field strength is increased, as expected for any mechanism that damps convection near the crystal. 

In order to integrate equation 1, it is necessary to have a relationship between and If there is equiHbrium between the bulk melt and the soHd freezing out, phase-diagram data may be used. As shown in Figure 2, in the limit of very small impurity contents, w is often proportional to ie, = kW/ where k is the distribution or segregation coefficient. Equation 1 may then be integrated ... 

The conditions for stable growth of a crystal are closely associated with segregation of dopants or impurities. Crystal growth theory includes an expression for the effective segregation coefficient K, for a crystal growing from a medium in which the dopant distribution is characterized by a boundary layer of thickness 5 ... 

Over the past decades, several papers were published regarding purification of Si using molten aluminium as solvent [13-16]. Yoshikawa and Morita [17] have estimated the segregation coefficient for various elements between solid Si and the Si-Al melt (Table 1.3). 

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