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Next Generation Multiphysical Models for Crystal Growth Processes

Periodic Reporting for period 1 - NEMOCRYS (Next Generation Multiphysical Models for Crystal Growth Processes)

Reporting period: 2020-02-01 to 2021-07-31

The NEMOCRYS project addresses the production process of crystalline materials used in microelectronics, telecommunication and many others fields of modern technology. These processes take place in crystal growth furnaces with high requirements for process control and efficiency. We are developing a new generation of models for crystal growth processes to raise the physical understanding and the possibilities for optimization to a qualitatively new level. In the first step, dedicated MODEL EXPERIMENTS are set up with the aim to investigate the heat transfer, fluid flows and other physical aspect of crystal growth processes in a dedicated environment that is easier to access for in-situ measurements than most crystal growth furnaces. In these experiments, model material with low melting points are applied. In the next step, new NUMERICAL MODELS are developed and validated in terms of physical assumptions and approximations using the experimental results. Finally, the improved physical understanding from model experiments and the new validated numerical models are applied to crystal growth processes of technologically relevant materials such as silicon or gallium oxide. This allows us to optimize the energy efficiency and the yield of the growth processes as well as the quality of the produced crystalline material and the resulting devices.
The development of a new EXPERIMENTAL PLATFORM for multiphysical model experiments has been realized in three stages: (1) desktop demonstration; (2) re-purposed test furnace; (3) novel and flexible furnace design - the MultiValidator. This stepwise approach reduces the technological risks and allows us to reach the scientific goals faster. Currently, we focus on the CZOCHRALSKI growth process, which is the most popular technique for crystal growth from the melt both in research and industry. The developed demonstration experiment is a low-cost (under 1000€) setup including full automation with a microcontroller/single-board computer and various sensors for thermal and electromagnetic measurements. This setup has been applied to grow crystals of model materials such as tin under ambient air atmosphere and temperatures up to 350 °C. The impact of various growth conditions has been investigated both in a scientific study and as training for students. The test furnace adds the possibility of vacuum or inert gas atmosphere, but also enables more realistic process geometries. Two cases with induction and resistance heating have been implemented and compared. The test furnace is equipped with comprehensive possibilities for in-situ measurements. These currently include thermocouples, resistance thermometers, pyrometers, heat flux sensors, infrared and optical cameras, sensors for the heater current, voltage, and magnetic field. In this way, we make the furnace "transparent" for observations of macroscopic physical phenomena during the growth process.

In the first project phase, the finite element software Elmer has been applied for numerical simulation. While it generally is a ready-to-use open source code with wide multiphysical capabilities, the setup of simulations becomes increasingly difficult for complex geometries and large-scale parametric studies. Therefore, a new Python-based interface pyelmer has been developed and published under an open-source license. Further simulation programs currently being tested are FEniCS, which offers more flexibility for coupling and modification of the components of multiphysical models, and OpenFOAM, which is based on the finite volume method and hence is better suited for fluid flow calculations. The selected simulation programs together with tools for pre-processing (e.g. Gmsh for grid generation) and post-processing (e.g. Paraview for visualization) will be integrated into a Python-based SOFTWARE PLATFORM for open-source crystal growth simulation - OpenCGS. Of course, the main goal of the project is the VALIDATION of the numerical models, where we have defined a three-step strategy: (1) sensitivity analysis to identify the most relevant model parameters; (2) parameter adjustment using in-situ measurements during a growth process or using dedicated experimental setups; (3) global accuracy estimation comparing simulations with series of growth experiments. Recently, we have applied this approach to thermal modeling of the Czochralski process and developed routines of parameter adjustment for convective heat transfer in the gas and in the melt in particular. This allowed us to reach a new level of accuracy for such practically relevant quantities as global power balance and crystal diameter.
The second stage of the experimental platform for multiphysical model experiments has already achieved an unprecedented in-situ insight into the physics of crystal growth processes (on a macroscopic scale). The MultiValidator as the third stage will enable model experiments closer to technologically relevant growth processes and also extend the scope of physics towards fluid phenomena and solid stresses. Furthermore, we will address other crystal growth processes such as FLOATING ZONE growth with inductive or optical heating. At the end, we expect to reach a new level of physical understanding of crystal growth process, which can be generalized to various materials and growth techniques.

The development of numerical models was preceded by a careful analysis of the current state of the art in the relevant literature to get an overview of open questions and unresolved challenges. We first addressed effects of convective heat transfer which have been neglected or simplified without appropriate justification in many cases in the past. We will continue with an analysis of heat generation in crystal growth processes to validate appropriate modeling approaches for complex three dimensional shapes of inductive and resistive heaters. Finally, after analyzing many other open modeling questions, we expect to obtain a "recipe book" of high practical relevance and large physical and technological scope leading to a new generation of multiphysical models for crystal growth processes.
Crystal growth setups for the validation of multiphysical models