Trends in Solute Segregation Behavior During Silicon Solidification
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implanted dopants in silicon by pulsed-laser melting (PLM) has been developed. The initial discovery that implantation damage could be repaired by pulsed-laser processing [1] was followed by several years of experimental measurements and the development of models to explain the phenomenon [2,31. However, a complete description of the redistribution of solute atoms during rapid solidification of silicon remains elusive. It has become clear that the enhanced dopant supersaturations observed in pulsed-laser melted ion-implanted silicon result from an increase in the partition coefficient during rapid solidification of silicon. The partition coefficient k is defined as the ratio of the solute concentration in the solid (xs) to that in the liquid (xL) at the solid/liquid interface: k a XS/XL
(1)
At the extremely high solidification speeds (up to 5 m/s) obtained in pulsed-laser melting, the partition coefficient increases from its equilibrium value ke toward unity. This trapping of solute during rapid solidification, observed several years earlier in Zn-Cd alloys [4], results in the observed enhanced concentrations of dopant elements. Several models have been advanced which attempt to explain the increase in k with solidification rate [5,6,7,8,9,10,111. Of these, the Aperiodic Stepwise Growth Model (ASGM) has been the most successful at matching experimental solute trapping data in silicon [10]. While the other models all predict that k should rise with increasing 479
Mat. Res. Soc. Symp. Proc. Vol. 321. -1994 Materials Research Society
solidification velocity, only the ASGM accounts for the observed dependence of solute trapping on crystallographic orientation. This model assumes that silicon solidification proceeds by the aperiodic lateral passage of (111) steps, as shown in figure 1. Figure 1: Solidificationat a speed v is accomplished by the lateral passage of (111) steps along the interface. Solute atoms are incorporated into the steps, and can only escape back to the liquid (at the ledge or on the terrace) until another step passes over the solute atom, permanently trappingit.
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The ASGM predicts that the partition coefficient should exhibit the following dependence on solidification speed and growth direction:
+vl(vf k)e1+ +vCos k+ keDcos vl(v Lsin si o)) k(v,O) =
__ / 1+ v/(vT cosO)
(2)
Here v is the solidification speed, 0 is the angle between the growth direction and the (111) axis of the crystal, and VT and vL are "diffusive speeds," the speeds at which a solute atom can diffuse from the solid into the liquid across the terrace and at the ledge, respectively. The orientation dependence predictions of the ASGM have been verified for the Si-Bi system, and in this work we test its validity for a much wider range of dilute Si alloys: As, Ga, Ge, In, Sb and Sn. In addition to testing the applicability of the ASGM, we hope to gain some insight into what determines the values of the terrace and ledge diffusive speeds. EXPERIMENTAL TECHNIQUES Silicon samples were cut from a single boule at misorientatio
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