E. Tomzig

Numerical investigation of silicon melt flow in large diameter CZ-crystal growth under the influence of steady and dynamic magnetic fields

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.

Modeling analysis of unsteady three-dimensional turbulent melt flow during Czochralski growth of si crystals

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.

Numerical model of turbulent CZ melt flow in the presence of AC and CUSP magnetic fields and its verification in a laboratory facility

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.

Effects of various magnetic field configurations on temperature distributions in Czochralski silicon melts

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.

Analysis of turbulent flow in silicon melts by optical temperature measurement

Abstract Turbulent convection in silicon melts plays a decisive role for the transport of heat and oxygen during the silicon Czochralski crystal growth. Information on the state of turbulence is usually derived from the frequency behaviour of temperature fluctuations. Until now, temperature fluctuations were mostly detected by thermocouples, which are protected from the chemically aggressive melt by silica quartz tubes. The major disadvantage of this technique is the damping effect on amplitudes of temperature fluctuations at frequencies higher than 0.5 Hz. This drew back significantly the information available on the state of turbulence. A method to overcome this disadvantage is an optical technique of measuring temperatures that provides sampling rates up to 100 Hz. In this contribution, we present optical temperature measurements using silica rods as waveguides in large-diameter Czochralski silicon melts. The detected temperature fluctuations give slopes of power spectra that are approximately proportional to f−4 for higher frequencies, in the case of the smaller crucible of 14 inch diameter. This indicates a soft turbulence state where melt flow is stabilised by rotational forces. On the other hand, a hard turbulence state of melt flow, indicated by an f−5/3 behaviour of the power spectra, was found for the large crucible with 32 inch diameter. In contrast to the smaller crucible, we found no changes of the state of turbulence by increasing the crucible rotation rate. The results are discussed with respect to its consequences on the properties of silicon crystals grown by the Czochralski method from large-scale melts.

Crystal growth melt flow control by means of magnetic fields

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.

Physical modelling of the melt flow during large-diameter silicon single crystal growth

Abstract 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.

Numerical study of 3D unsteady melt convection during industrial-scale CZ Si-crystal growth

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. r 2002 Elsevier Science B.V. All rights reserved. PACS: 81.10.Aj; 81.10.Fq; 47.27.Eq; 47.27.Rc

Study of oxygen transport in Czochralski growth of silicon

Abstract The present status and special features of experimental analysis and numerical modelling of oxygen transport in the Czochralski growth of silicon is treated. The solubility of oxygen in liquid Si is discussed in detail as this parameter is used as a boundary condition (oxygen source) in the numerical process models. The possibility of in situ measurement of the oxygen distribution in the melt in dependence from boundary conditions by using an electrochemical sensor is shown. Model conceptions for a numerical simulation of the oxygen transport in Czochralski melts are discussed in detail. The problem of boundary layer resolution is analysed, examples how to solve it are given. A quantitative modelling of the oxygen transport suffers at present from the fact that the existing turbulence models are not adequate to predict the velocity field precisely enough.

Global model of Czochralski silicon growth to predict oxygen content and thermal fluctuations at the melt-crystal interface

Abstract 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.