Applicability of the three-dimensional Alexander-Haasen model for the analysis of dislocation distributions in single-crystal silicon

Applicability of the three-dimensional Alexander-Haasen (AH) model for the analysis of dislocation distributions in single-crystal silicon has been estimated. The numerical results obtained from the AH model agree well with the experimental data for both CZ-Si and FZ-Si crystals with the axis in the [001] direction but do not completely agree with the experimental data for the FZ-Si crystal with the axis in the [111] direction. The inapplicability of the AH model in a crystal with the axis in the [111] direction may arise from the neglect of dislocation propagation in this model, because the dislocation propagation in a crystal with the axis in the [111] direction is more active than that in a crystal with the axis in the [001] direction. Therefore, to increase the applicability of the AH model, it is necessary to include the effect of dislocation propagation.