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Development of an open-source-based framework for multiphysical crystal growth simulations

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Abstract

The NEMOCRYS project in the group “Model experiments” at the IKZ funded by an ERC Starting Grant aims at profoundly validated numerical models for crystal growth. These processes involve a variety of coupled physical phenomena such as heat transfer including radiation and phase change, electromagnetism, melt- and gas flows and thermal stresses. Numerous simulation studies (using e.g. Comsol, Ansys or OpenFOAM) have been published, however, their applicability remains limited: The validation is mostly insufficient due to missing in-situ measurements, and the models are either implemented in expensive closed-source software or not published at all. Therefore, a new open-source-based framework for multiphysics simulation in crystal growth is under development. It currently uses Gmsh for FEM mesh generation and Elmer to solve the heat transfer problem, which are wrapped in a python interface. A major challenge in the current implementation is the coupling between Elmer and Gmsh: The transient simulation involves a moving crystal and phase boundary, and thus the mesh needs to be updated. FEniCS is a promising tool providing additional flexibility to implement new models with more advanced coupling algorithms. For example, a dynamic simulation with varying crystal diameter could include heat transfer with phase change and electromagnetic heat induction in FEniCs. External coupling with finite volume libraries such as OpenFOAM could be applied for melt and gas flow calculations. --- https://fenics2021.com/talks/enders-seidlitz.html --- https://mscroggs.github.io/fenics2021/talks/enders-seidlitz.html
vMax-Born-Str. 2 v12489 Berlin vGermany vwww.ikz-berlin.de v
LEIBNIZ -INSTITUT FÜR KRISTALLZÜCHTUNG
Development of an open-source-based framework for
multiphysical crystal growth simulations
Arved Enders-Seidlitz
Josef Pal
Kaspars Dadzis
Leibniz Institute for Crystal Growth
FEniCS 2021 Conference
University of Cambridge / online, March 25, 2021
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Motivation
Simulation concept
Transient heat transfer simulation
Possible integration of FEniCS
Conclusion
Content
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https://www.sciencedirect.com/topics
/chemistry/czochralski-process
Motivation Silicon production
Czochralski growth
furnace
Silicon single crystal
http://www.knoda.org/back-history-discovery-
very-first-silicon-chip-digital-computers/
Computer technology,
solar energy
https://cen.acs.org/energy/solar-power/Supercharging-
silicon-solar-cell/97/web/2019/07 https://www.pvatepla-
cgs.com/anlagen/czochralski/
vArved Enders-Seidlitz vDevelopment of an open-source-based framework for multiphysical crystal growth simulations v4
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Motivation
Model experiments
Simplified geometry and material
Materials
oTin,  
oBismuth, NaNO3,
Conditions
oAir atmosphere
oVacuum
Measurements
oTemperatures
oThermocouples, Pt100
oIR Camera
oPyrometer
oElectromagnetism
oHeating power
oMagnetic field
oFlows, thermal stresses
vArved Enders-Seidlitz vDevelopment of an open-source-based framework for multiphysical crystal growth simulations v5
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Heat
transfer &
phase
change
Electro-
magnet-
ism
Gas flow Melt flow
Stresses
Crystal
Melt
Motivation
Numerical challenges
oComplex coupled physics
oMoving geometries
oDifferent timescales
o
Goals in NEMOCRYS Project
oValidation: Using model experiments
oOpen source implementation
vArved Enders-Seidlitz vDevelopment of an open-source-based framework for multiphysical crystal growth simulations v6
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Simulation concept
openCGS framework
(open crystal growth simulation)
Automatization,
pre-defined setups, etc.
Geometry
definition
Simulation setup
Post processing
Planned
Fluid dynamics
General purpose FEM
Coupling
External tools
additional tools
required
Meshing
Simulation
Visualization
vArved Enders-Seidlitz vDevelopment of an open-source-based framework for multiphysical crystal growth simulations v7
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Transient simulation setup
crucible
melt
air
inductor
crystal
symmetry axis Induction heating (harmonic)
 
   
Heat transfer

     
 
Phase change (steady-state approximation)
       ,    

Radiation (at solid/air boundaries)

 


P. Råback et al.: Elmer Models Manual, CSC – IT Center for Science,
10.11.2020. https://www.nic.funet.fi/pub/sci/physics/elmer/doc/
2D axisymmetric with Elmer
vArved Enders-Seidlitz vDevelopment of an open-source-based framework for multiphysical crystal growth simulations v8
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Transient simulation procedure
distortion
distortion
remeshing
t = 50 s
t = 50 s t = 100 s
t = 0 s
Steady state simulation
Mesh generation (with new L)
Transient simulation
with mesh distortion
Combination of sub-simulations to
one final result in Python
T
L, T
Mesh to mesh interpolation in Elmer
if    else
Procedure using Elmer / Gmsh
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Transient simulation implementation
from opencgs import geo,setup
def geometry(crystal_length):
geo.crystal(crystal_length,...)
geo.crucible(...)
geo.melt(...)
... # boundaries, mesh sizes
def simulation_setup(...):
setup.add_crystal(...)
... # bodies, boundaries
User input: Two functions
(simplified)
Mesh update loop in openCGS
(simplified)
sim =SteadyStateSim(geometry,
simulation_setup,
start_length)
sim.execute()
while start_length <max_length:
sim =TransientSim(geometry,
simulation_setup,
start_length,
length_increment,
sim)
sim.execute()
start_length += length_increment
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Transient simulation results
Numerical
oSimulation numerically stable
oNo visible errors introduced by mesh update
Physical
oIncrease in temperature with crystal length,
corresponds to experiment
oValidation ongoing: Convective cooling of crystal,
etc.
Future challenges
oVariable crystal diameters
New models required
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Possible integration of FEniCS
Need for advanced models
oPhase boundary modeling
oGrowth in axial and radial
direction
oInteraction with process control
oSemi-transparent materials
oInternal radiation
oInternal absorption
Possible implementations
oCoupling to Elmer (preCICE)
oComplete solver in FEniCS
radiation model required!
Semi-transparent materials
Phase boundary
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Transient thermal CZ growth simulation implemented
oPython-based framework using Elmer and Gmsh
oLimited to constant crystal diameters
Possible integration of FEniCS
oCoupling to Elmer using preCICE: Under development
oComplete solver in FEniCS: Radiation model required
Conclusion
13
vArved Enders-Seidlitz vDevelopment of an open-source-based framework for multiphysical crystal growth simulations v
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We’d like to acknowledge Peter Råback for his support regarding the usage of Elmer.
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).
Acknowledgements
Thank you for your attention!
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