NUCLEATION AND GROWTH OF OXIDE PRECIPITATES IN CZ-SI WAFERS

When N(B) is moles of oxygen atoms dissolved into an Si wafer of N(A) moles, the concentration of oxygen atoms in the Si wafer is given by mole fraction as X(B) = N(B)/(NA + NB), and the degree of supersaturation is defined by sigma = (X(B)/X(BS,T)) - 1 where X(BS,T) is the mole fraction of the saturated state at temperature T. We have proved that sigma is equal to the chemical potential difference of oxygen atoms in between saturated and supersaturated states if sigma much less than 1. Here the spontaneous generation rate is proportional to sigma(gamma), where gamma is the number of the oxygen atoms in the critical oxide particles in the Si wafers. Duration time of a low temperature heating (at about 700-degrees-C) will determine the number of nuclei for oxide precipitates, and a treatment near 950-degrees-C is very effective on growth of oxide particles, because growth of the oxide particles is determined by diffusion of the atoms. Before the low temperature treatments, preheating at a temperature higher than 1000-degrees-C is effective in dissolving Si-O pairs and making interstitial oxygen atoms, where the Si-O pairs have been generated by the cooling stage after the crystal growth.