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 0–0.16T. 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 field in the horizontal DC magnetic field is implemented in the HD program package CFD-ACE+TM(V2003). For 3D HD calculations, moderate grids and the RNG k-ϵ turbulence model are used. Comparisons between calculated and measured temperature distributions in various cross sections are carried out for the cases with and without crucible and crystal rotation and with and without the magnetic field. The agreement is generally good, but some local discrepancies appear in the cases with the crystal rotation.

A model approach for a modification of the effective heat conductivity in the turbulent melt flow simulation for 28″ Si CZ crucibles is presented, which helped to overcome deficiencies in the growth interface shape prediction for industrial 300mm Si CZ growth. The model has been incorporated into a CZ simulation tool based on the simulation software codes FEMAG for the global heat transfer and CFD-ACE for the turbulent melt flow simulation. The model predictions are compared to results from 300mm Si CZ growth experiments with 200kg charge weight in 28″ crucibles in a growth parameter range covered by standard industrial processes. The model is an engineering approach. Nevertheless, some physical background is briefly discussed on a phenomenological basis, including results of recent model experiments.

The reported investigations concern physical modelling of Czochralski growth of silicon large-diameter single crystals. InGaSn eutectic was used as a modelling liquid, employing actual criteria of the real process (Prandtl, Reynolds, Grashof numbers, etc.) and geometric similarity. A multi-channel measuring system was used to collect and process the temperature and flow velocity data. The investigations were focused on the study of heat transfer, in particular, the instability of the “cold zone” of the melt at the crystallization front.

Contactless melt flow control is important in many crystal growth technologies. Typically, steady magnetic fields are used to damp convective flow. On the other hand active flow driving forces like in a rotating magnetic field can be of stabilizing character, too. We present numerical results for the combined action of steady and alternating magnetic fields for the silicon Czochralski crystal growth process. The melt flow is determined by various flow driving sources: besides the thermal convection and rotation of crystal and crucible, there are also the influence of driving and/or damping electromagnetic forces and the thermocapillarity-driven flow at the free deformable melt surface.

The melt flow in large diameter crucibles during the growth of silicon (Si) single crystals of 300mm diameter is characterized by turbulent large-scale velocity and temperature fluctuations. Strong efforts of the crystal growth industry are dedicated to the control of the interface shape and the related point defect distribution in the crystal, of the oxygen and particle transport in the melt, of the crucible overheating and of the conditions for dislocation free growth. Static and time-dependent electromagnetic fields offer new possibilities to meet the continuously increasing demands on crystal quality and yield improvement. Numerical simulation helps to investigate a wide range of possible process conditions, and to reduce experimental costs and time to market significantly. Depending on the required accuracy and available computation resources, two-dimensional (2D) or three-dimensional (3D) models are used. Temperature measurements in the melt, carried out during crystal growth and in model facilities, provide data for the verification of the numerical models, for direct process optimization and for a better understanding of the heat and mass transport behavior.

We present a computational model of 3D turbulent melt convection in Czochralski Si-crystal growth systems, based on the hybridization of Reynolds-averaged approach and large eddy simulation. The effect of superimposed magnetic field action on the melt flow is introduced in the model to account for the suppression of turbulent melt fluctuations. The model has been verified using experimental data for temperature in the melt and along the melt–crucible surface. Effects of axial magnetic field on the change in melt convection are studied in an industrial configuration.

The increase of diameter in the silicon single crystal growth from 200 to 300mm for industrial application, and to 400 or 450mm for research, respectively, has triggered off the development of numerous new technologies like crystal-growth-supporting systems, low-power hot zones, high strength of static magnetic fields and new quartzglas qualities. At Wacker Siltronic, new kinds of magnetic fields have been developed for 300mm CZ growth. In this paper, the results of dynamic and combined (static and alternating) magnetic fields are discussed. Instead of buoyancy-driven convection, a magnetic-field-controlled melt flow has been obtained in large melt volumes. The crucible wall temperature and, in turn, the quartzglas corrosion has been reduced. Furthermore, the application of the magnetic fields allows the control of oxygen in a wide range.

Magnetic fields are of growing interest for improvement of the silicon Czochralski crystal growth process. The use of steady magnetic fields provides suppression of turbulent fluctuations due to their damping action on the melt flow. Recent literature data on magnetic fields show that a relatively low field strength allows to control heat and mass transfer in laboratory scale melts. This contribution presents experimental results of temperature measurements in industrial scale silicon Czochralski melts under different magnetic field conditions. Temperature distributions are obtained by using thermocouples to detect temperatures in the melt and at the crucible wall during a crystal growth process. In addition we report on results of numerical simulations carried out for growth parameters and magnetic fields as used in the experiments. All experimental data are compared with the results from numerical simulation and discussed with respect to their implication on improving the quality of the grown crystals.

The paper describes a numerical simulation tool for heat and mass transfer processes in large diameter CZ crucibles under the influence of several non-rotating AC and CUSP magnetic fields. Such fields are expected to provide an additional means to influence the melt behaviour, particularly in the industrial growth of large diameter silicon crystals. The simulation tool is based on axisymmetric 2D models for the AC and CUSP magnetic fields in the whole CZ facility and turbulent hydrodynamics, temperature and mass transport in the melt under the influence of the electromagnetic fields. The simulation tool is verified by comparisons to experimental results from a laboratory CZ setup with eutectics InGaSn model melt.

A computational model combining calculations of global heat and mass transfer in the entire CZ system with Large Eddy Simulation (LES) of turbulent melt convection is presented. Global heat and mass transport is calculated using an axisymmetrical quasi-steady-state approximation with accounting for radiative heat exchange, heat conduction in solid parts, inert gas flow, and turbulent melt convection. The global transport calculations provide adequate boundary conditions for comprehensive investigation of melt turbulent convection using 3D LES. The LES of the melt flow describes the temperature distribution and impurity transport in the melt much better than 2D turbulent flow models. Moreover, the 3D calculations provide complete information with respect to thermal fluctuations in the melt and to non-uniformity of the crystallization process at the melt–crystal interface.

Turbulent silicon melt flows are studied in large diameter Czochralski crucibles under the influence of alternating, steady and combined magnetic fields. The investigations are based on the experimentally verified two-dimensional axisymmetric mathematical models. The influence of steady, alternating and combined magnetic fields on the flow pattern and temperature field is investigated. Global heat transfer and melt flow calculations are coupled and the influence of melt convection on the interface shape is studied and compared with experimental data.

We describe a computational model based on Large Eddy Simulation to calculate 3D unsteady turbulent melt convection in Czochralski systems for Si-crystal growth. The model has been verified using temperature measurements inside the melt and along the melt-crucible surface. The effect of the crucible rotation rate on 3D turbulent structures developed in the melt is analyzed. Transformation of the melt flow with increasing argon flow rate is predicted, and the controlling effect of the argon flow on the oxygen content in the crystal is evaluated.