In-situ observation of impurity diffusion boundary layer in silicon Czochralski growth

In-situ observation of the impurity diffusion boundary layer during single crystal growth of indium-doped silicon was carried out by X-ray radiography. The difference in the transmitted X-ray image compared with molten silicon just beneath the crystal-melt interface was attributed to the concentration of indium impurities having a larger absorption coefficient. The intensity profile of the transmitted X-ray can be reproduced by a transmittance calculation that considers the meniscus shape and impurity distribution. The impurity distribution profile near the crystal-melt interface was estimated using the Burton-Prim-Slichter (BPS) equation. The observed impurity diffusion boundary layer thickness was about 0.5 mm. It was found that the boundary layer thickness was not constant in the radial direction, which cannot be explained by the BPS theory, since it is based on a one-dimensional calculation.