Theoretical distributions of point-defect concentration in a Si ingot grown inside a melt using the noncontact crucible method considering the accumulation effect of diffusion flux

Abstract

The noncontact crucible (NOC) method has a large and deep low-temperature region in the upper central part of a Si melt to grow a uniform large Si single ingot without contact with the crucible wall. The temperature distribution in the NOC ingot is quite different to that in an ingot grown by the Czochralski (CZ) method because the NOC ingot is grown inside the Si melt. However, the distributions of point defects such as vacancy and interstitial Si atom are not known for the NOC ingot. To clarify the distributions of point defects, a simulation model is proposed to calculate the distribution of point defects in the NOC ingot. The effect of accumulation of diffusion fluxes on the concentrations of both vacancy and interstitial Si atom is considered for NOC growth because these diffusion fluxes are expected to continuously affect such concentrations in the ingot grown with the moving interface under the relatively low temperature gradient inside the melt. This point is one of the large merits of NOC growth. The concentrations of vacancy and interstitial Si atom were also calculated after the dynamic equilibrium pair-annihilation process between the diffused point defects during growth. They were calculated as a function of distance from the growing interface. By selecting the growth conditions, the concentrations of vacancy and interstitial Si atom were found to be very close to each other all over the ingot. The cross point where the concentrations of vacancy and interstitial Si atom were the same was found to strongly depend on G, the temperature gradient in the crystal.