Growth of homogeneous mixed A1-xBx bulk crystals: Analytical prediction, phase-field modeling and experiment comparison

Abstract

An analytical model is proposed to predict the growth behavior of homogeneous mixed A1-xBx bulk crystals by the traveling liquidus-zone (TLZ) method. The solidification and melting rates at the cold and hot solid/liquid (S/L) interfaces are determined by the solute conservation equations, coupled with the non-linear concentration distribution in the liquid zone. A novel time-dependent critical translation rate is derived, which can completely suppress the composition segregation in the grown crystal with an arbitrary liquid zone width. The proposed model is validated by the thin interface phase-field model for the TLZ-grown Si0.5Ge0.5 crystal, regarding the growth kinetics and concentration distributions in the crystal and liquid phase. A good agreement between the analytical predictions and phase-field simulations is achieved. The growth kinetics and composition profiles in the grown crystals predicted by the present analytical model agree well with the experimental measurements reported in the literature. It is found that after an initial transient, the non-linear liquid concentration distribution reaches the quasi-stationary condition. The average crystal growth rate increases with increasing temperature gradient. The proposed critical translation rate can precisely match the time-dependent solidification rate at the cold S/L interface, leading to a completely homogeneous TLZ-grown Si0.5Ge0.5 bulk crystal for an arbitrary initial liquid zone width. It is demonstrated that the present analytical model with the non-linear liquid concentration distribution is applicable to predict the growth behavior of homogeneous mixed crystals with a wide region of temperature gradient, translation rate and initial liquid zone width.