Parametric numerical study of dislocation density distribution in Czochralski-grown germanium crystals

Dislocations strongly affect the quality of Czochralski-grown germanium crystals used for various applications, however, the influence of different growth parameters on the dislocation distribution has not been extensively studied in the literature. In the present work, a simplified parametric crystal growth model is introduced which is suitable for large-scale numerical studies. The time-dependent temperature and dislocation density distributions in the crystal are calculated and analyzed. The Alexander-Haasen model is applied for dislocation modeling. Model parameters are taken from previously published discrete dislocation dynamics simulations, establishing a novel coupling between mesoscopic and macroscopic simulations. A W-shaped radial distribution of the dislocation density is obtained in the simulations. It is shown that the effective ambient temperature and crystallization front deflection have the strongest influence on the dislocation distribution. The results are compared to the experiment, showing a qualitative agreement, but also several deviations. Limitations of the considered dislocation modeling approach and the simplified thermal model are discussed.