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Crystal growth as a challenge for multi-physics coupling

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Crystal growth as a challenge for multi-physics coupling

Abstract

Many technologically relevant crystalline materials are produced in complex high-temperature processes involving a large variety of physical phenomena such as heat transfer including radiation and phase change, electromagnetism, melt and gas flows, thermal stresses. Numerous specialized or general-purpose simulation tools (e.g., Comsol, OpenFOAM) have been applied to these processes, however, two key issues are still not solved. First, insufficient data for model validation due to limited possibilities of in-situ measurements. Second, incomplete knowledge about coupling effects between various physical phenomena and lack of appropriate models. We are addressing these issues within the framework of a Starting Grant from the European Research Council (ERC). An experimental platform will be developed for in-situ analysis of crystal growth processes of model materials with modern measurement techniques. The obtained data will be used to establish a new level of physical understanding and a new generation of multiphysical models for crystal growth. The present contribution discusses the practical challenges in this project with a focus on multi-physics coupling. ****************************************************************************************** A recording of this conference presentation is available on YouTube: https://www.youtube.com/watch?v=mqYs7Ljdv8s
vMax-Born-Str. 2 v12489 Berlin vGermany vwww.ikz-berlin.de v
LEIBNIZ -INSTITUT FÜR KRISTALLZÜCHTUNG
Crystal growth as a challenge for
multi-physics coupling
Kaspars Dadzis
Leibniz Institute for Crystal Growth, Berlin
preCICE Workshop 2020
February 1718, Technical University of Munich
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v2
17.02.2020
Contents
Crystal growth and the floating zone process
Multi-physical modeling
EXAMPLE 1: FZone
EXAMPLE 2: Comsol & ...
Model development strategy
Conclusions
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v3
17.02.2020
Contents
Crystal growth and the floating zone process
Multi-physical modeling
EXAMPLE 1: FZone
EXAMPLE 2: Comsol & ...
Model development strategy
Conclusions
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v4
17.02.2020
Motivation for (silicon) crystal growth
International prototype of the kilogram 1889−2019
ptb.de
Pt (90%) and Ir (10%) cylinder with height and diameter of
approximately 39 mm stored in Paris.
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v5
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Motivation for (silicon) crystal growth
Re-definition of kilogram unit in 2019
ptb.de
1 kg = 2.152538397 x 1025 atoms of Si28 determined by
"counting atoms" in a perfect sphere of crystalline silicon
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v6
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Motivation for (silicon) crystal growth
The "age of silicon" is not yet over!
Re-definition of kilogram unit 2019 Quantum computer
ptb.de ibm.com
1 kg = 2.152538397 x 1025 atoms of Si28 determined by
"counting atoms" in a perfect sphere of crystalline silicon Crystalline silicon is one of the materials
considered for applications in quantum computers
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v7
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The crystal growth process
Growth furnace
(3x5 m)
Silicon raw
material rod Growth process
(>1500 °C)
Animation!
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v8
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Floating zone growth of 4 inch silicon crystals (2h in 30s)
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v9
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The crystal growth process
The floating zone growth process ensures the highest material purity
and structural perfection for silicon.
Growth furnace
(3x5 m)
Silicon raw
material rod Silicon crystal
(ø100 mm)
Growth process
(>1500 °C)
Animation!
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v10
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Contents
Crystal growth and the floating zone process
Multi-physical modeling
EXAMPLE 1: FZone
EXAMPLE 2: Comsol & ...
Model development strategy
Conclusions
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v11
17.02.2020
Physics of the crystal growth process
Complex interaction of multi-physical phenomena on various time and length scales.
Inductor
Feed rod
Crystal
Molten zone
Molten
thin film Heat induction
Heat radiation
Electromagnetic
field
1412 C
Stress
Gas flow
Photo of the growth process (1/2) Schematic & physical phenomena
Melt
flow
1412 C
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v12
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Numerical modeling
Heat transfer
Electromagnetism
Melt flow
Gas flow
Stresses
Basic physical theory
Heat
conduc. & convec.
Heat radiation
Phase change
Electromagnetic
induction
Incompressible
fluid
flow incl. buoyancy
Thermo
-elastic stress
Surface tension
Main
equations
(selection)

 





 

 





Field variables
T
temperature
v
gboundary velocity
A
magnetic vector pot.
V
electric scalar pot.
u
flow velocity
p
pressure
σ
elastic stress
z
surface coordinate
Length
scale
1 mm
1 m
0.1 mm
1 m
0.1 mm
0.1 m
0.1 m
1 m
1 mm
0.1 m
Time scale
1 min
1 h
1 min
1 h
0.1 s
1 h
1 min
1 h
1 min
1 h
Suitable numerical
methods
Finite
elements
View factors
Boundary
elements
Finite
elements
Finite volumes
Finite
elements
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v13
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Software landscape
StressesMelt/gas flowEM fieldsHeat transfer
Crystal growth
simulators General-purpose 3D (multi-physics) software packages
CGSim & Flow
module []
(STR Group)
CrysMAS []
(Fraunhofer IISB)
FEMAG []
(FEMAGSoft)
ANSYS
Fluent
ANSYS
Mechanical
CFD-ACE+ []
COMSOL []
STAR-CCM+
ANSYS
EMAG []
COMSOL
Opera
(Cobham)
ANSYS
CFX []
ANSYS
Fluent []
CFD-ACE+ []
COMSOL []
STAR-CCM+
Abaqus
ANSYS
Mechanical
COMSOL []
Elmer
SYRTHES
Commercial
Open source
(free) Elmer
GetDP []
Code Saturne
OpenFOAM []
Calculix
Code Aster
Elmer
Useful pre/post-processing utilities: FreeCAD, Gmsh, NETGEN, ParaView, SALOME
Popularity at Internat.
Workshops on Modeling
in Crystal Growth
≥2 uses ()
≥5 uses ()
≥10 uses ()
Numerical tools are available for all physical topics. But how about coupling between models?
[ Dadzis et al., J. Cryst. Growth 474 (2017) ]
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v14
17.02.2020
Contents
Crystal growth and the floating zone process
Multi-physical modeling
EXAMPLE 1: FZone
EXAMPLE 2: Comsol & ...
Model development strategy
Conclusions
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v15
17.02.2020
EXAMPLE 1: FZone 2D
Initial mesh
Thermal and EM fields,
phase boundary shapes
[G. Ratnieks et al., J. Cryst. Growth 255 (2003) 227]
[K. Surovovs et al., J. Cryst. Growth 401 (2014) 120]
Melt flow
vSpecialized code developed over >15 years at the
University of Latvia and Siltronic AG
vUni-/bi-directional, surface/volume, transient/steady-
state coupling of a thermalelectromagneticmoving
phase boundarymelt flow problem in at least 3 loops
Only 2D solvers. In-house code exclusive for industry.
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v16
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EXAMPLE 1: FZone 2D + 3D extensions
[K. Lacis et al., Magnetohydrodynamics 46(2) (2010) 199]
[K. Surovovs et al., J. Cryst. Growth 401 (2014) 120]
Melt flow (OpenFOAM)
vThe 2D model is coupled with 3D models:
Electromagnetic induction using BEM
AC magnetic fields using FEM
Melt flow & DC magnetic field in OpenFOAM
vUnidirectional, surface/volume steady-state
coupling
Can the feedback from 3D to 2D be neglected?
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v17
17.02.2020
Contents
Crystal growth and the floating zone process
Multi-physical modeling
EXAMPLE 1: FZone
EXAMPLE 2: Comsol & ...
Model development strategy
Conclusions
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v18
17.02.2020
EXAMPLE 2: Comsol 2D/3D
Induced heat (on boundaries)

Azimuthal average
ACDC module (3D)
Magnetic field of the inductor
Induced currents
Heat transfer module (2D)
Heat conduction and radiation
(Shapes of phase boundaries)
vPower control may require a feedback from 2D to 3D
vBoundary motion may require coupling to an external routine to correct
discontinuities and calculate free surface shape with EM pressure
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v19
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EXAMPLE 2: Comsol & coupling
Comsol: Fluid flow & Chemical
species modules (2D)
Melt flow with buoyancy
Species transport
EM
force
OpenFOAM (3D)
Melt flow with buoyancy
Species transport
Geometry & boundary cond.
EM
force
Geometry & boundary cond.
[m/s]
Challenges: stable model coupling within Comsol & bi-directional coupling with OpenFOAM.
Comsol: ACDC module (3D)
Magnetic field of the inductor
Induced currents
Comsol: heat transfer module (2D)
Heat conduction and radiation
(Shapes of phase boundaries)
Heat sources
Heat convection
(nearly all coupling is needed on
surfaces)
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v20
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Contents
Crystal growth and the floating zone process
Multi-physical modeling
EXAMPLE 1: FZone
EXAMPLE 2: Comsol & ...
Model development strategy
Conclusions
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v21
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Model development strategy
2. Verification
“solving the equations right
3. Benchmarking
“solving the equations fast
Physical model (theory)
Mathem. (numerical) model
Reality
Virtual model (computer)
[ Dadzis et al., J. Cryst. Growth 474 (2017) ]
Theory for the
magnetic field of
the Earth?
University of Maryland
[Science News, 2013]
Reality: Earth's outer core
Diameter of 7000 km
Molten iron & nickel at 5000 °C
Model experiment
Diameter of 3 m
Liquid sodium at 100 °C
Virtual models should be: (1) physically correct; (2) numerically accurate;
(3) computationally efficient. Model experiments support the first task.
Validation using model experiments (example)
1. Validation
“solving the right equations”
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v22
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Multi-physical model experiments
Starting Grant funded by the European
Research Council (ERC): Feb 2020 Jan 2025
NEMOCRYS: Next Generation Multiphysical
Models for Crystal Growth Processes
Goals for all 5 physical topics:
vSelect key open questions for modeling
vDo experiments in the MultiValidator
vCreate validated coupled models
A new research group "Model experiments"
at the IKZ.
Preliminary design
(0.5 x 1 m, 30700 °C)
Silicon growth furnace
(3x5 m, >1500 °C)
Physics of
crystal growth
MultiValidator with modern
measurement techniques
Open PhD position for Multi-physics
simulation at the IKZ!
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v23
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Conclusions
Conclusions
Floating zone growth of silicon crystals requires
efficient coupling of multi-physical models
There are many software libraries for multi-
physical modeling. However, both model coupling
and model validation need further work.
These topics are investigated at the IKZ within the
project NEMOCRYS funded by ERC.
Selected challenges for model coupling
Uni-/bi-directional, surface/volume, transient/
steady-state coupling of a thermal
electromagneticmoving phase boundarymelt
flow problem in multiple loops (e.g., with Comsol)
Bi-directional coupling between the above 2D
solver and 3D flow solvers (e.g., OpenFOAM).
Can these and similar problems be solved in the
preCICE environment?
Acknowledgments
J. Virbulis and the Crystal growth modeling group at the University of Latvia
R. Menzel and the Floating zone group at the IKZ
vKaspars Dadzis vCrystal growth as a challenge for multi- physics coupling v24
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Backup
vMax-Born-Str. 2 v12489 Berlin vGermany vwww.ikz-berlin.de v
LEIBNIZ -INSTITUT FÜR KRISTALLZÜCHTUNG
Inductor
Feed rod
Crystal
Molten zone
Molten
thin film Heat induction
Heat radiation
Electromagnetic
field
1412 C
Stress
Gas flow
Photo of the growth process (1/2) Schematic & physical phenomena
Melt
flow
1412 C
Crystal growth as a challenge for multi-physics coupling
Kaspars Dadzis, Leibniz Institute for Crystal Growth (IKZ), Berlin
The challenges:
vSolve the coupled problem:
moving boundaries heat
transport electromagnetism
stress flows species transport
vDevelop efficient coupling
between 2D (e.g., Comsol) and 3D
(e.g., OpenFOAM) models. With
preCICE?
vValidate coupled models using
multiphysical model experiments
Physics in silicon crystal growth Coupled model in Comsol
preCICE Workshop 2020
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