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Model experiments for heater concepts in Czochralski crystal growth processes


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MODEL EXPERIMENTS FOR HEATER CONCEPTS IN CZOCHRALSKI CRYSTAL GROWTH PROCESSES Keywords: multiphysics, crystal growth, Czochralski method, model experiment, induction heater
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Topic*: 6. Solidification, crystal growth
J. Pal*, A. Enders-Seidlitz, and K. Dadzis
Leibniz-Institut für Kristallzüchtung (IKZ), Max-Born-Straße 2, 12489 Berlin, Germany
Key words: multiphysics, crystal growth, Czochralski method, model experiment, induction
Crystalline materials are produced in complex high-temperature processes involving a
large variety of physical phenomena from heat transfer to fluid dynamics. A new research group
"Model experiments" has been established at the IKZ recently. Within the NEMOCRYS (Next
Generation Multiphysical Models for Crystal Growth Processes) project funded by a Starting
Grant from the European Research Council (ERC), we are developing a new generation of
multiphysical models for crystal growth processes. This shall be achieved by a series of unique
crystal growth setups (model experiments) for materials with low working temperatures,
relaxed vacuum-sealing requirements and hence by easy experimental access for various in-situ
measurement techniques. Model experiments for crystal growth are of growing interest [1-6]
and allow one to investigate selected physical phenomena extracted from the complex real
crystal growth process. However, in previous studies, mostly a very limited number of physical
aspects have been addressed in such experiments (e.g., only melt flow).
The Czochralski (CZ) growth technique is widely applied in crystal growth, both with
induction heating and graphite resistance heaters. Each of these types of heater exhibits varying
energy efficiency, electromagnetic forces, temperature (in)stability in the melt, diameter
(in)stability during the growth process, relevant heat flows, as well as in-situ sensor access to
the process. In this study, we investigate the advantages and disadvantages of both heating
Figure 1: Picture of the experimental setup with sensors and induction heater (left); mounting of the
graphite heater (center) with surrounding thermal insulation (right).
The model experiment setup (see Figure 1) consists of a vacuum furnace equipped with
an optionally rotatable crucible support surrounded by a heater. The crucible is made of graphite
and filled with tin (TSn,m = 232 °C) the model material used for this experimental study. A thin
tin rod is used as seeding crystal. The setup is equipped with sensors of several types. Both
contact (thermocouples, resistance PT type) and contactless temperature sensors (pyrometer,
infrared camera) are used to measure and record the temperatures at various positions. The
complete growing process is recorded by common and high-speed optical cameras for
documentation purposes. Additionally, heater current is measured continuously.
First experiments with the presented setup applied the induction heater, and variations of
pulling velocity, crystal rotation, and pressure condition (furnace is evacuated or its door is
open with normal air pressure) were investigated. Figure 2 shows an optical and an infrared
image recorded during the process, and the diagram at the right side displays a typical
temperature recording. The very prominent orange-colored temperature was recorded by a
thermocouple placed very near to the induction coil; it exemplarily demonstrates a case where
the sensor positioning has to be optimized. We will further discuss the influence of the different
heater types on both the measurement setup and the growth process.
Figure 2: Pictures recorded during the process (left with the optical and center with the infrared
camera); temperature diagram of sensors inside the melt and the crucible wall (right).
In a next step, the obtained in-situ measurement data will be applied for validation of
numerical simulation of the process. For this purpose, a new thermal model of the Czochralski
process using the open source software Elmer FEM is currently being developed by the
NEMOCRYS project group. One aim will be to validate the convective cooling boundary
conditions for solid surfaces and the crystal diameter calculation. Furthermore, the presented
model experiments may be employed to optimize the techniques for in-situ observation as well
as to build a new basis for model benchmarking or for big data application in crystal growth.
Acknowledgements. This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme (grant
agreement No 851768).
K. DADZIS, O. PÄTZOLD, G. GERBETH. Model experiments for flow phenomena in crystal
growth. Crystal Research& Technology, vol. 55 (2019), no. 2, 1900096.
K. BERGFELDS, M. PUDZS, A. SABANSKIS, J. VIRBULIS. Experimental and numerical
investigation of laboratory crystal growth furnace for the development of model-based control of CZ
process. Journal of Crystal Growth, vol. 522 (2019), pp. 191-194.
P.-O. NAM, S.-S. SON, K.-W. YI. The effect of polycrystalline rod insertion in a low Prandtl
number melt for continuous Czochralski system. J. of Crystal Growth, vol. 312 (2010), pp. 1458-1462.
LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field. Journal
of Crystal Growth, vol. 312 (2010), pp. 3225-3234.
D. SCHWABE, R.R. SUMATHI, H. WILKE. The interface inversion process during the
Czochralski growth of high melting point oxides. J. of Crystal Growth, vol. 265 (2004), pp. 494-504.
U. EKHULT, T. CARLBERG. Czochralski growth of tin crystals under constant pull rate and IR
diameter control. Journal of Crystal Growth, vol. 76 (1986), pp. 317-322.
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Full-text available
The concept of a physical model experiment is introduced and discussed in the context of melt and gas flows in bulk crystal growth processes. Such experiments allow one to "extract" selected physical phenomena from the full complexity of a real crystal growth process and “transfer” them to material systems with an easier access for experimental measurements. Model experiments for the main techniques of melt growth are summarized in a literature review, and the applicability of the results to real crystal growth systems is analyzed. Recent examples of model experiments for melt and gas flows in Czochralski growth of silicon are used to demonstrate the state of the art and show the potential of such experiments to improve the understanding of complex multi‐physical multi‐scale phenomena occurring in every crystal growth process. The concept of a physical model experiment is discussed for melt and gas flows in bulk crystal growth processes, and previous results in the literature are reviewed. The state of the art is demonstrated with recent examples for melt flows in magnetic fields and for gas flows around the heat shield (see tracer image) in Czochralski growth of silicon.
The presented study is focused on laboratory Czochralski crystal growth experiments and their mathematical modelling. The developed small-scale CZ crystal growth furnace is described as well as the involved automation systems: crystal radius detection by image recognition, temperature sensors, adjustable heater power and crystal pull rate. The CZ-Trans program is used to model the experimental results – transient, 2D axisymmetric simulation software primarily used for modelling of the industrial-scale silicon crystal growth process. Poor agreement with the experimental results is reached; however, the proven ability to perform affordable, small-scale experiments and successfully model their transient behavior, creates a possibility to develop new process automation solutions in the future.
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 calculated distributions of averaged temperature and standard temperature deviations are compared with measured ones in the laboratory system, and a relatively good agreement between them is shown. The influence of chosen time steps and grid sizes is analyzed by comparing Fourier spectra of temperature time-autocorrelation functions and temperature spatial distributions, and it is shown that the used moderate meshes of few hundred thousand cells can be applied for practical calculations.
The increased wafer size results in greater instabilities and complexities within the silicon melt, and melt flow control through the application of magnetic fields is not adequate to stabilize the melt. Therefore, continuous Czochralski systems are being studied as a solution to these issues, with higher productivity and no change in size.The purpose of this study is to observe the effects of polycrystalline rod insertion on the melt for a continuous Czochralski system. In order to observe flow patterns within the melt both broadly and specifically, we employ experimentation on a model system in tandem with numerical simulation.The rod insertion do not significantly affect near the crystal edge. In the melt height from 0.14 to 0.09m, an asymmetric temperature distributions arise when the crystal rotation is counterclockwise direction (−15rpm) and the crucible rotation is clockwise direction (3rpm). The axis-symmetrical temperature distribution is formed at lower melt heights (0.08 and 0.07m). When the melt height is 0.07m, the axis-symmetric temperature distribution is maintained even after the rod insertion.
High melting point oxides show an interface inversion from a convex interface shape to a flat or concave interface when grown after the Czochralski method with constant crystal rotation rate and increasing crystal radius (as in the shoulder region). Under the described conditions one observes during YAG-growth a sudden and uncontrollable interface change, called interface flip, at a certain critical crystal rotation rate. We describe model experiments and numerical simulations of this inversion process. We show that it is connected with a flow transition at a certain critical rotational Reynolds number Rec. This Rec increases with the convex interface deflection and with the strength of the buoyant-thermocapillary flow near the free melt surface towards the crystal. A self-amplifying process, involving the back-melting of the crystal cone, starts when Rec is reached. The dynamics of the back-melting is explained. A more vigerous interface inversion process is expected for systems with large interface deflections and for systems with smaller dynamic Bond number, e.g. smaller crucibles.
Czochralski crystal growth experiments with auxiliary IR heating of the melt surface were carried out to investigate the feasibility of thermal diameter control. Tin crystals were grown under constant pull rate using IR control and with pull rate control. Temperature measurements were made in the melt during growth with IR diameter control and with growth rate diameter control. IR diameter control decreased the vertical and horizontal temperature gradients in the melt.