Modeling Czochralski growth

Modelling dislocation generation in high pressure Czochralski growth of InP single crystals parts 1 and 11 , Model. SirmU. Mater. Sci. 

Modeling of Czochralski Growth of Large Silicon Crystals... 

Modeling of Czochralski growth process has a rich history [14-20]. First computations were done assuming the melt flow to be laminar, steady and axisymmetric ... 

A numerical model for simulation of the global heat transfer and the melt flow in the Czochralski growth of large silicon crystals is presented. The key model features are an extended 3D domain for the 2D/3D computations and a hybrid LES/RANS approach to turbulence modeling. It is shown that use of parallel computations on affordable multiprocessor systems assembled from the COTS hardware could reduce the turn-around time of simulation by an order of magnitude. The model validation using the experimental data on the growth of 100-mm and 300-mm silicon crystals in the industrial pullers Ekz-1300 and Ekz-2405 has proved its predictive power. 

D. Vizman, S. Eichler, J. Friedrich, G. Muller, 2004, Three-dimensional modeling of melt flow and interface shape in the industrial liquid-encapsulated Czochralski growth of GaAs , J. 

Figure 24. Streamlines and isotherms for the growth of silicon in a prototype Czochralski system with self-consistent calculation of interface and crystal shapes by using the quasi steady-state thermal-capillary model and the condition that the crystal radius remains constant. Calculations are for decreasing melt volume. The Grashof number (scaled with the maximum temperature difference in the melt) varies between 1.0 X 107 and 2.0 X 107 with decreasing...

E.M. Nunes et al., A volume radiation heat transfer model for Czochralski crystal growth processes. J. Cryst. Growth 236(4), 596-608 (2002). 

The calculations were carried out in the framework of the model of point defect dynamics, i.e., for the same crystals with the same parameters as in already the classical work on the simulation of microvoids and interstitial dislocation loops (A-microdefects) (Kulkarni et al., 2004). According to the analysis of the modern temperature fields used when growing crystals by the Czochralski method, the temperature gradient was taken to be G = 2.5 K/ mm (Kulkarni et al., 2004). The simulation was performed for crystals 150 mm in diameter, which were grown at the rates Vg = 0.6 and 0.7 mm/ min. These growth conditions correspond to the growth parameter Vg/ G >... 

Dornberger, E. Ammon, von W. Virbulis, J. Hanna, B. Sinno T. (2001). Modeling of transient point defect dynamics in Czochralski silicon crystal. Journal Crystal Growth, Vol. 230, No. 1-2, pp. 291-299, ISSN 0022-0248. 

Numerical models should be tested to prove their predictive power. The next two sections contain a discussion of general validation issues and an assessment of the model described above using available data on Czochralski silicon growth in... 

---