Model analysis of segregation phenomena for silicon single crystal growth from the melt

Abstract

Abstract Segregation model for silicon single crystal growth from the melt has been developed in order to explain the typical phenomena, which are the deviation of the effective segregation coefficient ( k e ) from that as expected by the BPS theory in the higher growth rate ( R ) region and the different behavior due to the growth directions in the k e − R relations. The model, with phosphorus as an example, is based on the combination of the temperature dependence of impurity diffusivity in liquid and the kinetic undercooling. The model can quantitatively explain not only the deviations but also the difference due to the orientations. Additionally, the following two ideas, both being important for understanding the crystal growth of silicon, can be introduced through the analysis. One possibility is that the existence of large kinetic undercooling even in the 〈100〉 continuous growth. The energy barrier is estimated as 1.24 eV. The other is a mixture of two “aggregates”, both having different diffusivities, and the large change of the ratio in temperature.