
298 Crystal Growth and Evaluation of Silicon for VLSI and ULSI
the ratio of the pull rate and the temperature gradient at the solidication interface ratio
is equal to a critical value C
crit
of 1.4 × 10
–3
cm
2
/K min, as shown in Figure 9.4. Crystals
become fully interstitial rich at low pull rates, where C
crit
is lower than 1.4 × 10
–3
cm
2
/K
min over the complete radius. In a relatively narrow window of approximately ±10% of
the critical ratio, neither vacancy nor interstitial reaches the critical supersaturation for
the nucleation of larger defects. This explains most of the defects generated during crystal
growth, since they depend on the ratio ...