A finite-element computer program was developed for the continuous simulation of the dislocation density in bulk single crystals during Czochralski growth. The shape of the crystal/melt interface, and the temperature in the crystal at a given time, were determined by linear interpolation of discrete results which were obtained via heat-conduction analysis of a Czochralski single-crystal growth system. A dislocation kinetic model was used as the constitutive equation for the single crystal. Dislocation-density analyses were performed for 20cm-diameter semiconductor single crystals. The analyses predicted the existence of W-type dislocation density distributions across the diameters.

Development of Finite Element Computer Program for Dislocation Density Analysis of Bulk Semiconductor Single Crystals during Czochralski Growth. N.Miyazaki, S.Okuyama: Journal of Crystal Growth, 1998, 183[1], 81-8