Czochralski heat flows

The next most importtmt parameters in Czochralski growth of crystals are the heat flow and heat losses in the system. Actually, aU of the parameters (with the possible exception of 2 and 9) are strongly ciffected by the heat flow within the crystal-pulling system. A tj pical heat-flow pattern in a Czochralski sjretem involves both the crucible and the melt. The pattern of heat-flow is important but we will not expemd upon this topic here. Let it suffice to point out that heat-flow is set up in the melt by the direction of rotation of the cr5rstal being pulled. It is also ctffected by the upper surface of the melt and how well it is thermally insulated from its surroundings. The circular heat flow pattern causes the surface to radiate heat. The crystal also absorbs heat and re-radiates it... 

The next most important parameters in Czochralski growth of crystals are the heat flow and heat losses in the system. Actually, all of the parameters (with the possible exception of 2 and 9) are strongly affected by the heat flow within the crystal-pulling stem. The next section addresses this factor. 

A typical heat-flow pattern in a Czochralski system involves both the crucible and the melt, as shown in the following diagram ... 

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. 

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