**100 mm Si Czochralski growth**

Fig. 1.
Temperature distribution |

Calculation of the
global heat and mass transport in industrial Cz growth setups is extremely
complicated as several interrelated physical phenomena should be resolved
simultaneously.
Engineering model of
global heat transfer in the Cz systems that is currently used in CGSim includes
self-consistent calculation of melt turbulent convection, inert gas flow and
melt-crystal interface geometry. This model was used to study the effect of
the inert gas flow on turbulent melt convection and global heat transfer in
an industrial Cz system Leybold EKZ 1300 [1].

To illustrate the CGSim's
capability of handling such a complex task as heat simulation in Cz silicon growth,
we compared
the simulation results obtained using CGSim with the temperatures measured
in the crystal as well as
inside the lateral and bottom insulations, Figure 2 (a,b). Detailed discussion
of the experiment on the temperature measurements in the growing crystal
carried out at Siltronic AG can be found in [2]. Comparison of the results
shows that CGSim can adequately predict temperature distribution in the
industrial growth setup and inside the growing silicon crystal.

(a) |
(b) |

Fig. 2. Verification of the temperature predictions
by comparing the computational results (b) with experimental data obtained
at the points shown in (a). |

Fig. 3.
3D grid in the crystallization zone including the melt, crucibles,
and the crystal |

Adequate prediction of the electrical
properties of silicon depends on the accurate calculation of characteristics
of point defects in the growing crystal that, in turn, depend on
thermal regime during the crystal pulling and concentrations of impurities.
Temperature gradients in the growing crystal are noticeably affected by
the geometry of the melt-crystal interface, while the geometry itself is
unknown

*a priori* and is to be found during the calculation.

To predict the geometry of the melt-crystal interface,
detailed thermal regime in the crystallization zone and eventually defect
incorporation and evolution, we use 3D unsteady analysis of melt
turbulent convection coupled with the heat transfer analysis in the crystal and
the crucible. At the first step, we calculate heat and mass transfer in
the whole system using 2D approximation. The results are used to set thermal
boundary conditions for the 3D computations in the crystallization zone.
One can see that 3D unsteady behavior of melt flow results in strongly asymmetric instant
distributions of the crystallization rate over the interface and the temperature
under the crystal, Fig. 4 (a,b).

T(K) (a) |
V(mm/min) (b) |
(c) |

Fig. 4. Temperature under the crystal (a),
crystallization rate over the interface (b), geometry of the crystallization front for the crystal heights
of 240 and 300 mm. |

Accurate analysis of temperature gradients and thermal
stresses is possible in Module Defects and in Flow Module. For predicting initial spatial
distributions of defects in
the growing crystal, a 2D model of vacancy and interstitial dynamics is applied.
The model considers initial defect formation at the crystallization front and
their further incorporation by convective and diffusive transport with clusterization
and reciprocal recombination. The difference between vacancy and interstitial
concentrations shows the type of dominating defects and the position of OSF ring,
see Figure 5.

(a) |
(b) |
(c) |

Fig. 5. Temperature gradients (a),
thermal stresses (b), the difference between vacancy and interstitial concentrations (c). |

1. "Gas flow effect on global heat transport and melt convection in Czochralski
silicon growth",
V.V. Kalaev, I.Yu. Evstratov, Yu.N. Makarov,
E.V. Eskov, M.V. Nikolenko, V.S. Postolov,
Journal of Crystal Growth 249 (2003) pp. 87-99.

2. "Thermal simulation of the Czochralski silicon growth process
by three different models and comparison with experimental results",
E. Dornberger, E. Tomzig, A. Seidl, S. Schmitt, H.-J. Leister, Ch. Schmitt,
G. Muller,
Journal of Crystal Growth 180 (1997) pp. 461-467.