0000000000400401
AUTHOR
A. Muižnieks
Numerical 3D modelling of turbulent melt flow in a large CZ system with horizontal DC magnetic field. II. Comparison with measurements
This paper presents a comparison between numerically calculated and measured temperature distributions in turbulent flow in a laboratory model for a CZ large silicon single crystal industrial growth system with a horizontal DC magnetic field. The laboratory model consists of an electrically heated 20” crucible with low-temperature InGaSn melt, a water-cooled metallic crystal model, and a magnet system creating a horizontal magnetic field in the range 0–. Distributions of time-averaged temperature values in various cross sections in the melt are obtained from measurements by a multichannel thermocouple system. A 3D numerical model for the scalar potential induced in the melt by the velocity …
Modelling of phase boundaries for large industrial FZ silicon crystal growth with the needle-eye technique
In order to facilitate the numerical calculations of the phase boundaries in large industrial floating zone silicon crystal growth with the needle-eye technique, the chain of improved mathematical models is developed. The phase boundaries are solved in a partly transient way and the modelling improvements cover the open melting front, the inner triple point and the free melt surface. The view factors model is applied for the radiative heat transfer. The electromagnetic field is calculated with account of a multiple-slit inductor.
Applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field
Abstract To examine the applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic fields, LES calculations with Smagorinsky–Lilly turbulence model and van Driest damping at the solid walls are carried out. The program package for the calculations was developed on the basis of the open-source code library OpenFOAM ® . A previously published laboratory model with low temperature melt InGaSn, a 20” crucible, and process parameters corresponding to industrial Czochralski silicon systems is considered. Flow regimes with two crystal and crucible rotation rates and with different strengths of the traveling magnetic field “down” are analyzed. The calcula…
Numerical investigation of the influence of EM-fields on fluid motion and resistivity distribution during floating-zone growth of large silicon single crystals
The floating-zone-process with needle-eye inductor is a complex process with many coupled parameters that have nonlinear influence on the process stability and resistivity distribution in the silicon single crystal. To fulfill the requirements of semiconductor industry for tighter specification of resistivity distribution, additional means like magnetic fields can be used to reach a more homogeneous resistivity distribution without disturbing process stability. The current paper analyses the influence of static and alternating fields on the fluid motion and macroscopic and microscopic resistivity profile by means of numerical calculations. It is found that with a lower frequency of the HF-i…
Numerical 3D study of FZ growth: dependence on growth parameters and melt instability
Three-dimensional modelling of the floating zone (needle-eye) crystal growth process is carried out to analyse numerically the stability of the melt flow and the influence of the crystal rotation rate and inductor slit width on the 3D flow field and on the grown crystal resistivity. The unsteadiness of the melt is simulated and it is found that for the considered growth parameters a steady-state flow can be a reasonable approximation to the unsteady melt motion. The parametric studies have shown that increasing the rotation rate essentially changes the flow pattern and weakens the rotational striations, while the inductor slit width has a more local influence on these characteristics.
Numerical study of transient behaviour of molten zone during industrial FZ process for large silicon crystal growth
The fully transient axisymmetric model has been developed for calculation of phase boundaries in large (up to 200 mm diameter) industrial floating zone (FZ) silicon single crystal growth with the needle-eye technique. The transient model is implemented in a specialized computer program. The model and program are based on a previously developed model and program for steady-state FZ process calculations. This transient approach allows studying of such substantially time-dependent process phases as the growth of the starting and ending cones of the crystal rod, which are particularly important for growth of large crystals in practice. Numerous calculations are carried out and the results for r…
Stress-induced dislocation generation in large FZ- and CZ-silicon single crystals—numerical model and qualitative considerations
When growing silicon crystals with higher diameter (presently up to 300 mm) the thermal stresses and possible dislocation generation in single crystals become a serious problem for both FZ- and CZ-methods. A two-dimensional problem oriented code for the FEM-package ANSYS has been developed to calculate the temperature field in the growing crystal considering radiation exchange with reflectors and environment and thermal stresses. Comparing calculated stresses with critical stresses, the dislocated zone is determined. A qualitative concept for the occurrence of dislocations using the metastable state is developed. In a parametric study for different thermal boundary conditions and crystal ge…