Finite element analysis of dislocation density during bulk single crystal growth (effect of doping atoms in InP single crystal)

Abstract

A computer code for simulation of dislocation density in a bulk single crystal during liquid encapsulated Czochralski (LEC) or Czochralski (CZ) growth process. In this computer code, the shape of crystal–melt interface and the temperature in a crystal at an arbitrary time were determined by linear interpolation of the results that were discretely obtained by heat conduction analysis of a CZ single crystal growth system. A dislocation kinetics model called Haasen–Sumino model was used as a constitutive equation. In this model, creep strain rate is related to dislocation density, and this model extended to multiaxial stress state was incorporated into a finite element elastic creep analysis program for axisymmetric bodies. Dislocation density simulations were performed using this computer code for InP bulk single crystals with about 8″ in diameter. In the analysis, the effect of dopant atoms on the dislocation density was examined. In the case of a low doped InP single crystal, dislocations are distributed in the whole of the crystal. On the other hand, in the case of a highly doped InP single crystal, dislocations are localized at both the central and peripheral regions of the crystal.