0000000000273675
AUTHOR
A. Krauze
showing 12 related works from this author
Mathematical modelling of the industrial growth of large silicon crystals by CZ and FZ process
2003
The present paper gives an overview of the complex mathematical modelling of industrial Czochralski (CZ) and floating‐zone (FZ) processes for the growth of large silicon single crystals from melt. Extensive numerical investigations of turbulent Si‐melt flows in large diameter CZ crucibles, global thermal calculations in growth facilities and analysis of the influence of various electromagnetic fields on CZ process are presented. For FZ process, a complex system of coupled 2D and 3D mathematical models is presented to show the possibilities of modelling from the calculation of the molten zone shape till the resistivity distribution in the grown crystal. A special developed program code is pr…
Application of enthalpy model for floating zone silicon crystal growth
2017
Abstract A 2D simplified crystal growth model based on the enthalpy method and coupled with a low-frequency harmonic electromagnetic model is developed to simulate the silicon crystal growth near the external triple point (ETP) and crystal melting on the open melting front of a polycrystalline feed rod in FZ crystal growth systems. Simulations of the crystal growth near the ETP show significant influence of the inhomogeneities of the EM power distribution on the crystal growth rate for a 4 in floating zone (FZ) system. The generated growth rate fluctuations are shown to be larger in the system with higher crystal pull rate. Simulations of crystal melting on the open melting front of the pol…
Crystal shape 2D modeling for transient CZ silicon crystal growth
2013
Abstract A non-stationary axisymmetric model of Czochralski silicon single crystal growth is presented. The model describes transient behavior of crystal–melt, melt–gas and crystal–gas interfaces in connection with PID-based control of crystal diameter by changing crystal pulling velocity and heater power. To calculate significant crystal shape changes, unstructured finite element mesh is used in crystal and melt together with automatic element size control. Heater temperature changes are modeled with a simplified integral model. A numerical simulation example of start cone growth is given.
Numerical 3D modelling of turbulent melt flow in a large CZ system with horizontal DC magnetic field. II. Comparison with measurements
2004
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 …
Warming of water in a glass
2016
The article focuses on the process of water warming from 0 °C in a glass. An experiment is performed that analyses the temperature in the top and bottom layers of water during warming. The experimental equipment is very simple and can be easily set up using devices available in schools. The temperature curves obtained from the experiment help us to understand the process of convection in the glass and to determine the temperature at which the density of water is maximum. In addition, computational fluid dynamics—CFD modeling is carried out to facilitate better comprehension of the phenomenon observed in the experiment.
Applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field
2010
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…
Thermo acoustic - MHD electrical Generator
2011
Abstract The thermo-acoustic generators offer a unique means of converting thermal energy into mechanical energy without any moving parts and without fluid circulation. They are comparable to the Stirling engine with the advantage of much greater simplicity. They are therefore natural candidates for special uses where interventions are limited. The problem to solve is transforming the mechanical energy into electrical energy. MHD generators offer excellent opportunities in this area, particularly by using the mechanisms of induction. The work concerns the combination of a thermo-acoustic generator with an induction generator of a new concept for obtaining electric current with adjustable vo…
Mathematical modelling of the feed rod shape in floating zone silicon crystal growth
2017
Abstract A three-dimensional (3D) transient multi-physical model of the feed rod melting in the floating zone (FZ) silicon single-crystal growth process is presented. Coupled temperature, electromagnetic (EM), and melt film simulations are performed for a 4 inch FZ system, and the time evolution of the open melting front is studied. The 3D model uses phase boundaries and parameters from a converged solution of a quasi-stationary axisymmetric (2D) model of the FZ system as initial conditions for the time dependent simulations. A parameter study with different feed rod rotation, crystal pull rates and widths of the inductor main slit is carried out to analyse their influence on the evolution …
Validation of a 3D mathematical model for feed rod melting during floating zone Si crystal growth
2019
Abstract A mathematical model of global 3D heat transfer in floating zone silicon single crystal growth process is used to predict the shape of the open melting front of the feed rod. The model is validated using measurement data from research-scale growth experiments. Shape profiles of the open melting front are obtained from the feed rod leftover using a movable dial gauge. Azimuthal asymmetry of the rim of the open melting front is revealed in both simulations and measurements, quantitatively indicating the influence of the main slit of the inductor.
Numerical 2D modelling of turbulent melt flow in CZ system with dynamic magnetic fields
2004
Abstract The paper presents results of 2D axisymmetric mathematical modelling of laboratory CZ model facility that corresponds well to a large industrial silicon CZ growth system. The purpose of the investigation is to examine turbulent melt flow features that develop in the model crucible, when various dynamic magnetic fields (travelling, alternating) are applied, and to test the applicability of the modified low Re k–e turbulence model for the calculation of flows in these cases by extensive comparisons between calculated and measured data. The electromagnetic field is calculated with a self-developed program, and the calculations of the melt motion are carried out with the user modified …
3D modeling of growth ridge and edge facet formation in 〈100〉 floating zone silicon crystal growth process
2019
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.
Convective phenomena in large melts including magnetic fields
2007
The set of characteristic parameters which describe modern large industrial CZ silicon single crystal growth systems is introduced. The main melt flow driving mechanisms are considered, and the characteristic density values of various in the melt acting forces are estimated. The analysis is illustrated with examples of numerical simulation and comparisons with experiments.