Czochralski Crystal Growth System Research Articles

3D Simulation of the Coil Geometry Effect on the Induction Heating Process in Czochralski Crystal Growth System

AbstractHerein, influence of coil geometry in a Czochralski crystal growth system is studied using 3D finite element method. Three different geometries for the helical RF‐coil including solenoid, conical solenoid, and rectangular are considered and distribution of magnetic flux density (through the system), produced heat in the RF‐coil and the graphite crucible, as well as heat volume integral are calculated. The obtained numerical results show that every considered coil produces a special heating structure due to its shape with some advantages and disadvantages.

Influence of magnetic flux concentrator on the induction heating process in crystal growth systems-geometry investigation

In this paper, a magnetic flux concentrator (MFC) is reported, and its geometry effect on the induction heating process has been calculated in a Czochralski crystal growth system using the 2D finite element method.

Influence of crucible and coil geometry on the induction heating process in Czochralski crystal growth system

A 2D finite element method is employed to compute electromagnetic field as well as volumetric heat generation in an oxide Czochralski crystal growth system considering different shapes of metal crucible and different configurations of induction coil. The results show undeniable roles of crucible corner shape and setup of the RF-coil under the crucible in producing desirable heat pattern and avoiding common issues in the CZ growth systems.

Numerical Modeling of Induction Heating in Crystal Pulling Method Change in the Coil Radius

An induction coil with two different radiuses for oxide Czochralski crystal growth systems is considered and corresponding results of electromagnetic field and volumetric heat generation have been computed using a finite element method (FlexPDE package). The calculation results show the importance of the coil radius on the heat generation distribution in a CZ growth system.

Ultrasonic flow measurements in a model of a Czochralski puller

An experimental study of the buoyancy-induced flow in a model of a Czochralski crystal growth system was conducted. Ultrasonic velocimetry was used to measure fluid velocities. To approach the thermal boundary conditions in an industrial growth facility, a double-walled glass crucible, which is flown through by a heating fluid, was chosen to hold the fluid. Similarity of the heat transfer conditions was achieved by selecting a liquid metal as the fluid under investigation, which was the ternary alloy GaInSn having a Prandtl number of 0.021. Because of the double-walled crucible, measurements through the container wall are difficult if ever possible. Since the availability of relatively short ultrasonic transducers it is practicable to have the sensor immersed into the fluid. Measurements of the radial velocity component shortly below the melt surface across the entire diameter of the crucible at various azimuthal angles reveal the complex flow structure of natural convection in a Czochralski crucible. As it is not to be expected to grow high quality mono-crystalline crystals from such a non-axisymmetric flow, rotating magnetic fields (RMF) are often proposed to render the flow more axisymmetric. This paper also addresses the question what happens to the buoyancy-driven flow when such an RMF is applied.

Review of some Aspects of Single Crystal Growth Using Czochralski Crystal Growth Technique

Abstract Single crystal that semiconductor industry thrive on, are grown using Czochralski (CZ) crystal growth technique. Over the years many researchers have investigated the problems related to CZ crystal growth system and number of studies related to different aspects of CZ crystal growth is available in open literature. Some of the important aspects related to Czochralski (CZ) crystal growth system used for growing single crystal are discussed. Origin of melt convection due to buoyant forces, forced convection due to crystal and crucible rotation and Marangoni convection due to thermo-capillary forces, and their effect on heat and species transport phenomena in the melt pool has been reviewed. Flow in present day large size crystal growth using CZ crystal growth system becomes oscillatory. Oscillations in melt can be damped using externally applied magnetic field. Effect of axial, transverse and inhomogeneous (CUSP) magnetic field on different melt convection has been a subject of interest for various research efforts. Oxygen release from silica crucible during growth of silicon crystal and mechanism for its incorporation into the growing crystal has also been reviewed. Conditions leading to growth of low oxygen concentration silicon crystal are elaborated.

Computational Study of Induction Heating Process in Crystal Growth Systems—The Role of Input Current Shape

A set of 2D steady state finite element numerical simulations of electromagnetic fields and heating distribution for an oxide Czochralski crystal growth system was carried out for different input current shapes (sine, square, triangle and sawtooth waveforms) of the induction coil. Comparison between the results presented here demonstrates the importance of input current shape on the electromagnetic field distribution, coil efficiency, and intensity and structure of generated power in the growth setup.

Numerical simulation of Cz crystal growth in rotating magnetic field with crystal and crucible rotations

Three-dimensional numerical simulations were carried out to analyze the effect of crystal and crucible rotating directions on heat and oxygen transport in Czochralski crystal growth system under rotating magnetic field. A low-Reynolds number k-ε model was used for the description of the turbulent processes. The computational results show that when rotations of crystal, melt and crucible are in the same direction, the oxygen concentration in the melt is the lowest and a low concentration crystal can be obtained. Under rotating magnetic field, the heat transport is dominated by lorentz force induced streaming field and the influence of crystal and crucible rotations on heat transport is weak. Moreover, the effect of crystal rotation on the melt turbulent flow and oxygen transport is stronger than that of crucible.

Influence of active afterheater on the fluid dynamics and heat transfer during Czochralski growth of oxide single crystals

For an oxide Czochralski crystal growth system, the influence of an active afterheater on the characteristics of the growth process such as temperature and flow fields, crystal-melt interface and the structure of heat transfer have been studied numerically using the finite element method. Several types of heat transfer mechanism, which are convection and conduction within the melt, conduction and radiation within the grown crystal, gas convection and radiative heat exchange between the exposed surfaces, have been taken into account. A comparison between the obtained results demonstrates the role and importance of an active afterheater on the basic parameters of the growth process such as thermal environment and heat transfer structure in oxide Czochralski growth systems.

Large eddy simulation of Marangoni convection in Czochralski crystal growth

AbstractLarge eddy simulation model is used to simulate the fluid flow and heat transfer in an industrial Czochralski crystal growth system. The influence of Marangoni convection on the growth process is discussed. The simulation results agree well with experiment, which indicates that large eddy simulation is capable of capturing the temperature fluctuations in the melt. As the Marangoni number increases, the radial velocity along the free surface is strengthened, which makes the flow pattern shift from circumferential to spiral. At the same time, the surface tension reinforces the natural convection and forces the isotherms to curve downwards. It can also be seen from the simulation that a secondary vortex and the Ekman layer are generated. All these physical phenomena induced by Marangoni convection have great impacts on the shape of the growth interface and thus the quality of the crystal. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical study of induction heating in melt growth systems—Frequency selection

A set of 2D finite element numerical simulation of induction heating process for an oxide Czochralski crystal growth system has been made for a range of f=1–100 kHz applied frequency of driving current. It was shown that the frequency selection has a marked effect in all basic induction phenomena, including electromagnetic field distribution, skin depth, coil efficiency, and intensity and structure of heating in the growth setup.

Influence of crucible geometry and position on the induction heating process in crystal growth systems

A series of 2D finite element numerical simulations of induction heating process for an oxide Czochralski crystal growth system has been done for different shapes and locations of a metal crucible. Comparison between the computational results shows the importance of crucible shape, geometry and its position with respect to the RF-coil on the electromagnetic field and heat generation distribution in the growth setup.

Influence of coil geometry on the induction heating process in crystal growth systems

Different shapes and orientations of the RF-coil turns in oxide Czochralski crystal growth systems are considered and corresponding results of electromagnetic field and volumetric heat generation have been computed using a finite element method. For the calculations, the eddy current in the induction coil (i.e. the self-inductance effect) has been taken into account. The calculation results show the importance of cross section shape, geometry and position of the RF-coil turns with respect to the crucible and afterheater on the heat generation distribution in a Czochralski growth system.

Influence of active afterheater on the induction heating process in oxide Czochralski systems

AbstractDifferent shapes and orientations of an active afterheater for oxide Czochralski crystal growth systems are considered and corresponding results of electromagnetic field and volumetric heat generation have been computed using a finite element method (Flex‐PDE package). For the calculations, the eddy current in the induction coil (i.e. the self‐inductance effect) has been taken into account. The calculation results show the importance of an active afterheater, its shape as well as its geometry and position with respect to the crucible on the heat generation distribution in a CZ growth system. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of Induction Heating in Oxide Czochralski Systems—Advantages and Problems

Two mathematical models of induction heating for oxide Czochralski crystal growth systems are reviewed, and additional results of electromagnetic field and volumetric heat generation have been computed for both models using a finite element method (ENTWIFE package). In the first model, the eddy current in the RF coil (i.e., the self-inductance effect) has been neglected while for the second model, it is taken into account. For the calculations, the electrical current input and total voltage of induction coil are set to be 1000 A and 200 ν, respectively, with a frequency of 10 kHz; the heat generation in all metallic parts, that is, crucible, afterheater, RF coil, and chamber, has been calculated for a real Czochralski setup. It has been found that by including the self-inductance effect in the RF coil the results change dramatically. Also, it was shown that the spatial distribution of the heat generation in the crucible is more realistic in the second model than in the first model. Concerning the distribu...

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

AbstractIn this paper, the role of seed rotation on the characteristics of the two‐dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two‐dimensional quasi‐steady state numerical simulations were carried out to analyze the seed‐melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ωseed = 5‐30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed‐melt interface during the seeding process. The seed‐melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed‐melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed‐melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ωseed) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical study of induction heating and heat transfer in a real Czochralski system

The equations of induction heating and heat transport have been solved for a real Czochralski crystal growth system, using the ENTWIFE package (finite-element method). The configuration usually used in dielectric crystal growth consists of a crucible, afterheater, induction coil with two parts and insulation. At first the electromagnetic field produced by the RF coil in the whole system and the generated heat inside the metal crucible and afterheater was calculated. Using this as a heat source then the temperature field and air convection inside the crucible and afterheater was determined. We have considered two cases: (1) configuration without a gap between crucible and afterheater and (2) with a gap corresponding to an often used growth situation. In both cases it was observed that there are two separate eddies of air convection with approximately equal strength and opposite rotation. Concerning the temperature field, the maximum temperature is in the crucible wall and the minimum is in the bottom corner of the crucible insulation. Along the axis of symmetry, in the first case the temperature is approximately constant and then drops close to the afterheater hole. But in the second case the temperature in the crucible is constant, decreases in the gap and is constant in the afterheater until it drops near its hole. This behavior has been observed during experimental measurements in the lab, too.

Development of a PC-Based Automatic Diameter Controlled Czochralski Crystal Growth System Using a Versatile Algorithm

A new algorithm for automatic diameter control in a Czochralski crystal growth system is developed. This has been successfully implemented in a system where a nonconventional device is used for crystal weighing, and proved to be very effective. The developed system was found capable of controlling the growth of several grown crystals. The diameter of all the crystals was controlled within a millimeter to the set values. The same algorithm was also successfully incorporated to a system having an entirely different configuration.

Mechanism of Heat and Oxygen Transfer under Electromagnetic CZ Crystal Growth with Cusp-Shaped Magnetic Fields

The three-dimensional time-dependent flow of the silicon melt in an electromagnetic Czochralski (EMCZ) crystal growth system with cusp-shaped magnetic fields was numerically investigated. Calculations were carried out using five different configurations of the melt and cusp-shaped magnetic fields. The results indicated that oxygen was transferred from a part of a sidewall of the crucible on which a cusp plane of the magnetic fields exists. The results also showed that the oxygen concentration at the solid-liquid interface of silicon increased when the cusp plane of the cusp-shaped magnetic fields shifted from the bottom of the crucible to the surface of the melt. © 2003 The Electrochemical Society. All rights reserved.

Simulation of large-scale silicon melt flow in magnetic Czochralski growth

We have modeled the silicon melt flow and temperature as well as the applied and induced magnetic fields in a large-scale, cylindrically symmetric Czochralski crystal growth system. The validity of a cylindrically symmetric model is evaluated by comparing melt flow simulations to previously published three-dimensional simulations and experimental measurements in identical setups. The applied magnetic field, due to a given external magnet configuration and its current distribution, is first solved. Subsequently, the coupled magnetohydrodynamical system, i.e., the Navier–Stokes, heat and induction equations, is solved in the melt region. The mathematical model is discretized by the finite element method. The numerical methods used are explained in this article. The applied external magnetic fields we have considered are time-independent and axisymmetric. The magnetohydrodynamical problem is time-dependent, and the velocity and the induced magnetic field have azimuthal components. The velocity distributions and temperature time series for various cusp-type fields are compared. It is found that a magnetic field of the order of 25 mT strongly damps the temperature oscillations in the melt outside about half the crucible radius. A higher field of about 100 mT stabilizes the flow in most of the melt.