Dislocation Density Analyses of Bulk Semiconductor Single Crystals during Czochralski Growth.

Abstract

A computer program was developed for continuous simulation of the dislocation density in a bulk single crystal during the Czochralski (CZ) growth process. In this computer program, the shape of the crystal melt interface and the temperature in a crystal at an arbitrary time were determined by linear interpolation of the discrete results that were obtained by heat conduction analysis of a CZ single crystal growth system. A dislocation kinetics model called the Hassen-Sumino model was used as the constitutive equation. In this model, the creep strain rate is related to the dislocation density, and this model extended to the multiaxial stress state was incorporated into a finite element elastic creep analysis program for axisymmetric bodies. Dislocation density analyses were performed using this computer program for Si, InP an GaAs bulk single crystals of about 8 inches diameter. The present analyses indicate a W-type dislocation density distribution across the diameter in InP and GaAs single crystals that can be observed in actual CZ growth of InP and GaAs.