e-News - February, 2006 Printable version
Table of Contents
Gas flow simulation.
Accurate point defect prediction.
Forthcoming features.
Forthcoming events. 		 
Temperature distribution and argon gas velocity vectors in a Czochralski crystal puller.
Pulling rate: V = 6.0 cm/h; Argon pressure: P0 = 30 mbars; Volumetric flow rate at P0: Q0 = 0.03 m^3/s.
Isotherms are separated by 200 K. The reference velocity vector is printed.
   
Gas flow simulation

Gas flow effects when modelling the global heat transfer in a Czochralski furnace have been neglected in previous FEMAG-CZ releases, assuming that the convective heat transfer is much smaller than the radiative heat transfer. A more accurate prediction of heat and mass transfer however requires that gas flow be taken into account.

From FEMAG-CZ version 2.8, the gas flow is computed both in quasi-steady and time-dependent simulations (crystal growth and post-growth stages). A RANS model is used that includes a turbulent model taking crystal and crucible rotations into account.

The effect of gas flow on the melt free surface, which might locally influence the prediction of oxygen distribution in melt and crystal is, however, still neglected. This feature will be included in next FEMAG-CZ release.
 
   
Accurate point defect prediction

FEMAG-CZ dynamic simulations correctly predict the inherently time-dependent behaviour of point defect distribution.

Dynamic effects influence deeply the defect distribution in Czochralski-grown silicon crystals for two reasons. On the one hand, the solidification interface deformation caused by any change of the operating conditions (pull rate, heater power...) and in particular, the rapid change of interface shape that occurs during the shouldering, directly affects the thermal gradient above the interface and the resulting interstitial and vacancy densities according to the well-known V/G criterion. On the other hand, since point defects are transported while diffusing and reacting, the defect distribution inside the crystal is a picture of the history of defect generation and cannot be correctly predicted by means of a quasi-steady model.

Another key feature of FEMAG-CZ is to provide up-to-date material data governing the formation, diffusion and recombination of point defects in Silicon crystals. In fact, a very significant discrepancy (which can reach more than two orders of magnitude) can be found in the literature between the material parameters determined by direct experiments and the corresponding values proposed for simulation. A major objective of FEMAGSoft Company is to provide FEMAG users with the material data required for point defect simulations that match the experimental results.
 

Comparison of quasi-steady (left) with time-dependent (right) point defect predictions for a Czochralski-grown silicon crystal by means of FEMAG simulations. Isolines of the CI-CV distributions. The CI-CV=0 isoline is indicated in bold. Crystal radius: R = 7.5 cm. Pulling rate: V = 4.5 cm/h. The Sinno-Dornberger model has been used.
     
Forthcoming Features

Time-dependent simulations with melt convection calculated at each time step.

Advanced gas flow module (including gas flow effect on the melt flow through forces exerted on the melt-gas interface).

Calculation of oxygen and dopant concentration in the melt and the crystal.

Influence of horizontal magnetic fields on the melt flow. 		  Forthcoming Events

From September 10 to 13, 2006: 5th International Workshop on Modeling in Crystal Growth.
   
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