|
Most of Single crystals is produced by the Czochralski(cz)
procress. The dislocations are frist introduced during
the Czochralski growth of GaAs that is crystallographic glid
caused by the excessive thermal stress. The dislocations formed
in bulk single crystals during Czochralski growth have adverse
effect on the performance of electronic and optical devices.
Most of studies have used the elastically isotropic model
characterized by the young''s modulus and the Poisson
ratio, which enables an axisymmetric thermal stress analysis.
This model is not correct. Strictly speaking, a three-
dimensional analysis, which takes account of elastic
anisotropic, should be conducted. Experimental evidence
indicates that in reality the solid-liquid interface is curved
during the Czochralski growth. Therefore, a parobolic-shape
interface is considered in this article. Moreover, in
order to accurately reflect the nature of material, the
physical properties are taken as function of temperature. A
powerful numerical method, consisting of discretizing the
space domain by F.E.M. , and treating the time domain by
Laplace and inverse Laplace transform,is adopted in this
article . The magnitude of stress and dislocation density
parameter are compared between anisotropic and isotroic
analyses.Numerical results indicate that the thermal stress
analyzed anisotropic theory is generally larger than
that by isotropic theory. Furthermore, significant
differences can be found in their distribution patterns
between both analyses. It is also observed that higher stress
level is concenrated around the bottom and top of interface.
Moreover,the larger the curvature of interface , the higher
the stress level concentrated in the top of interface.
|