A computer code was developed for the simulation of dislocation densities in a bulk single crystal during liquid-encapsulated Czochralski, or Czochralski, growth. The shape of the crystal/melt interface, and the temperature in the crystal at an arbitrary time, were determined by the linear interpolation of discrete data that were obtained via a heat-conduction analysis of a Czochralski single-crystal growth system. A dislocation kinetics model was used as a constitutive equation. By using this model, the creep strain-rate was related to the dislocation density. The model, after extension to multi-axial stress-states, was incorporated into a finite-element elastic-creep analysis program for axisymmetrical bodies. Dislocation-density simulations were performed by applying the program to bulk InP single crystals which were about 20cm in diameter. The effect of dopant atoms upon the dislocation density was examined. In the case of a lightly-doped single crystal, the dislocations were predicted to be distributed throughout the whole crystal. In the case of a highly-doped single crystal, the dislocations were localized in the central and peripheral regions of the crystal.

Finite-element analysis of the dislocation density during bulk single crystal growth N.Miyazaki, Y.Kuroda: Journal of Crystal Growth, 1999, 196[1], 62-6