The effect of fluctuating growth rates on segregation in crystals grown from the melt: II. Backmelting

Abstract

Using a time dependent extension of the Burton, Prim and Slichter model, we investigate the quantitative relationship between periodic variations in growth rate and compositional inhomogeneities in crystals grown by the Czochralski technique. In this paper we discuss the case in which the crystal experiences backmelting. If the amount of melting is moderate, the time dependent behavior of the diffusion layer is similar to that which occurs if there is no melting. If there is extensive backmelting, then during a portion of each rotational cycle the diffusion layer gradually changes into a region in which the concentration is depleted by comparison with that in the bulk of the melt. The composition in the crystal varies periodically and discontinuously along its length. If the amplitude A of the growth fluctuation is large enough, the spatially averaged value C of the dopant concentration in the crystal can be significantly less than that achieved during steady state growth. The fractional change △/ C in the concentration increases almost linearly with A.