Three-Dimensional Dislocation Density Analysis of Bulk Semiconductor Single Crystal During CZ Growth Process

Abstract

A three-dimensional finite element computer program is developed for calculating dislocation density in bulk single crystal during Czochralski (CZ) growth process. In this program, crystal anisotropy in elastic constants and slip systems is taken into account. The Hassen-Sumino model is used as a uni-axial creep constitutive equation, which is extended to multi-axial stress state by using the theory of crystal plasticity. Dislocation density analyses of a silicon bulk single crystal are performed in the cases of both <001> and <111> pulling directions by use of this program. It is found that the dislocation density increases very rapidly from initial state to steady state. Significant differences are found between both pulling directions in distribution pattern of stress and dislocation density.