0000000000522533
AUTHOR
G. Ratnieks
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.
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…
Numerical study and comparisons with experimental data for transient behaviour of phase boundaries during industrial FZ process for silicon crystal growth
Abstract In our numerical transient model developed previously for the industrial FZ crystal growth process with the needle-eye technique, the meshing algorithms are essentially improved and a significant amount of numerical studies are carried out for model verification. Transient modelling for the experimental growth process with step-like time dependences of inductor current and feed rod velocity has shown that time dependencies of the crystal radius and zone height calculated numerically agree with the data from praxis. The fully transient simulation for growth process of crystal starting cone has shown that the model is capable of performing the simulation even if the crystal diameter …
3D modeling of growth ridge and edge facet formation in 〈100〉 floating zone silicon crystal growth process
Abstract A 3D quasi-stationary model for crystal ridge formation in FZ crystal growth systems for silicon is presented. Heat transfer equations for the melt and crystal are solved, and an anisotropic crystal growth model together with a free surface shape solver is used to model the facet growth and ridge formation. The simulation results for 4″ and 5″ crystals are presented and compared to experimental ridge shape data.
Influence of the three dimensionality of the HF electromagnetic field on resistivity variations in Si single crystals during FZ growth
Abstract Three-dimensional numerical modelling is carried out to analyse the floating zone crystal growth with the needle-eye technique used for the production of high-quality silicon single crystals with large diameters ( ⩾100 mm ). Since the pancake inductor has only one turn, the EM field and the distribution of heat sources and EM forces are only roughly axisymmetric. The non-symmetry together with crystal rotation reflects itself on the hydrodynamic, thermal and dopant concentration fields in the molten zone and causes variations of resistivity in the grown single crystal, which are known as the so-called rotational striations. The non-symmetric high-frequency electromagnetic field of …