The Czochralski (CZ) process is one of the most common techniques used to grow single crystals, that are the basis of many technologies such as computer chips, solar cells or power electronics. It involves a variety of physical phenomena from heat transfer to thermal stresses. Various simulation models investigating CZ growth 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 closed-source software or not published at all. In the ERC-funded NEMOCRYS project, therefore, a new generation of open source crystal growth models is being developed and validated using model experiments. Figure 1: visualization of the coupling between heat transfer and gas flow simulation We have selected finite element method (FEM) for modelling of heat transfer and induction heating in CZ growth, and two separate models have been implemented in the software Elmer  and FEniCS . For gas flow modelling we use the finite volume method (FVM) in OpenFOAM software . In this contribution, a 2D surface coupling of the heat transfer and gas flow simulation using the preCICE library  is presented. The coupling is performed in steady-state on a 2D axisymmetric domain using a Dirichlet-Neumann approach, see figure 1. Results obtained with both Elmer-OpenFOAM and FEniCS-OpenFOAM coupling are compared and validated with the model experiments for different growth conditions. Further extensions of the numerical simulation are discussed with focus on melt flow simulation. REFERENCES  K. Dadzis, P. Bönisch, L. Sylla and T. Richter, Validation, verification, and benchmarking of crystal growth simulations. J. Cryst. Growth, Vol. 474, pp. 171–177, 2017.  P. Råback, M. Malinen, J. Ruokolainen, A. Pursula and T. Zwinger, Elmer Models Manual, 2020.  J.S. Dokken, The FEniCSx tutorial, https://jorgensd.github.io/dolfinx-tutorial/, 2021.  OpenFOAM Foundation. http://openfoam.org. Version: 9, 2021.  H.-J. Bungartz, F. Lindner, B. Gatzhammer, M. Mehl, K. Scheufele, A. Shukaev, and B. Uekermann. Comput Fluids, Vol. 141, pp. 250–258, 2016.
Crystal growth simulations involve a variety of physical phenomena, e.g., heat transfer, gas and melt flows, electromagnetism and thermal stresses. The Finite element (FEM) and Finite volume methods (FVM) have been selected as the main simulation tools for a new crystal growth model. Currently, 2D axisymmetric heat transfer including radiation, phase change and inductive heating are implemented using FEM in Elmer and FEniCSx. The FVM solver OpenFOAM has been chosen for gas flow simulations. In this contribution, the coupling strategy between Elmer-OpenFOAM / FEniCSx-OpenFOAM using preCICE library is discussed. First test cases are evaluated for both couplings, and requirements for future development are analyzed. --- A recording of the talk is available here: https://youtu.be/8ivCDyz2FlI
The Czochralski (CZ) growth technique is widely applied in crystal growth, using both induction and resistance heaters. In this work, a novel model experiment platform with comprehensive in-situ measurement capability is introduced. Growth experiments with the model material tin applying both heating concepts are performed and analyzed, e.g., in terms of the maximum achievable crystal diameter. Strong asymmetries in the magnetic field of the induction heater are measured and temperature distribution on the resistance heater is found to be non-uniform. Furthermore, significant losses are observed in the power supplies of the resistance heater. The heating efficiency of both concepts is compared considering different insulation geometries. The obtained results show the capability of model experiments for design optimization and will provide valuable input for further validation of numerical simulations.
Presentation at DKT 2021 Conference. File will be made available upon request.
MODEL EXPERIMENTS FOR HEATER CONCEPTS IN CZOCHRALSKI CRYSTAL GROWTH PROCESSES Keywords: multiphysics, crystal growth, Czochralski method, model experiment, induction heater
For the application of Elmer FEM in crystal growth simulation, a new Python interface pyelmer has been developed at the Leibniz Institute for Crystal Growth. It uses an object-oriented approach to manage the dependencies between materials, geometric bodies, boundaries, solvers, etc. In combination with the already available Python interface of the mesh generator Gmsh, for which additional utility-functions are provided, pyelmer enables an integrated workflow in one of the most prominent modern programming languages and thus helps to reduce the complexity and error rate of the simulation setup. The focus of this talk is the workflow of pyelmer, its data structures and pre-defined setups. Examples from the simulation of crystal growth processes with the Czochralski method will be shown. We would like to discuss the applications of pyelmer in your projects and possible contributions to its further development. --- A recording of the webinar is available here: https://youtu.be/QIfAa_5pvHU
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
The NEMOCRYS project in the group “Model experiments” at the IKZ develops an open-source-based framework for coupled multiphysics simulation in crystal growth. Currently, Gmsh for FEM mesh generation and Elmer to solve the heat transfer problem including inductive heating are applied. These tools are wrapped in an easy-to-use python interface that allows for highly-parameterized models and enables automatized large-scale studies. A major challenge in the present implementation is the coupling between Elmer and Gmsh: The transient simulation involves moving boundaries and requires mesh updates. In future, an additional coupling to OpenFOAM will be needed to consider the fluid dynamics of the liquid and gas phase. This requires transient bi-directional multiscale coupling in 2D and 3D both on surfaces and in volumes. We consider preCICE a promising library to meet this challenge and would like to discuss the need for further adapters and coupling algorithms. --- You can watch the presentation here: https://youtu.be/jN3JfOB3tC8
The main goal of this presentation is to show how could YOU learn doing numerical simulation of crystal growth by yourself. The focus is on: 1) macroscopic aspects of crystal growth (from the melt); 2) Focus on physical understanding (instead of numerical methods). I consider Czochralski growth of tin as a case study and discuss experimental results as well as physical and numerical models. In the second part, the model development strategy consisting of validation, verification, and benchmarking is presented. Finally, a short introduction to the NEMOCRYS project is given.
The NEMOCRYS project funded by an ERC Starting Grant aims at the development of profoundly validated numerical models for crystal growth processes using the Czochralski (CZ) and Floating Zone (FZ) methods. These growth processes usually involve very high temperatures and have high requirements on the degree of purity, which prevents in-depth measurements in-situ. Therefore, in the NEMOCRYS project, a model system using model materials, e.g, tin instead of silicon, is investigated experimentally and numerically. The two-dimensional heat transfer simulation is an important tool for the study of crystal growth processes. First attempts of validation of a 2D-CZ numerical model using experimental data revealed a strong influence of convective cooling, which needs to be modeled without introducing a too high complexity. The application of heat transfer coefficients (HTC) is promising, however their computation using empirical formulas seems to be inaccurate. Parameter studies are performed to estimate the influence of the HTC, and different methods for their estimation and validation are discussed.
This is a model experiment for Czochralski growth and a challenging test case for multi-physics simulations. The attached PDF file contains a description of the experimental setup and main results. The attached MP4 file contains a video of the growth process (1h 40m real time).