Thermal history simulation of Czochralski silicon crystals and its application to the study of defects formation during crystal growth

A finite element quasi-steady-state modeling of temperature distribution during the growth of a silicon crystal by the Czochralski (CZ) method is presented. Computations are performed for a comprehensive geometrical model of an actual CZ puller, accounting for detailed radiation heat exchange and introducing a reviewed set of temperature-dependent thermophysical properties. The crystal growth process is simulated step-wise, with automatic update of the mesh at each successive growth step. Temperature and pull rate data are then input to a mathematical routine for the calculation of the dwell time for user-defined temperature intervals and crystal position. Applications of this simulation tool for the interpretation of crystal quality characteristics such as oxygen precipitation and light scattering defect axial profiles are presented.