Lateral Impurity Segregation in Crystals Grown from the Melt

Abstract

The impurity distribution in crystals grown from the melt with an uneven interface revealed several interesting features. Generally, the lateral inhomogeneity in the impurity distribution through a slightly depressed crystallization front should be small [1]. The impurity distribution deviates little over much of the lateral crystal cross section in another limiting case, i.e., where the number β= vL/D (v is the growth rate, L is the lateral crystal dimension, and D is the diffusion coefficient) is large and the front is depressed nontrivially. The maximum inhomogeneity is attained at intermediate β values where inhomogeneity and the β values themselves depend strongly on the distribution coefficient [2]. However, the analytical solutions at slight depressions or large β values, as well as numerical calculations carried out in [2], suggest that the effect in fact is more profound and that the lateral impurity inhomogeneity can be very significant even at very slight front depressions if the distribution coefficient is also small.