Model Experiments for Flow Phenomena in Crystal Growth

Abstract

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.

Numerical Simulation of Ammonothermal Crystal Growth of GaN—Current State, Challenges, and Prospects

“…Such simulations appear to be limited to much more well-investigated crystal growth processes such as Czochralski growth of silicon, and even for this extremely well-established growth process, they are still an active area of research [96]. It is furthermore interesting to note that even for such well-established crystal growth processes, validation of simulations using physical models also remains an active area of research, as indicated by a recent review by Dadzis et al [97]. This indicates that even with comparatively well-established material properties, it is not always clear which simplifying assumptions yield the right balance of computational speed and accuracy.…”

“…Pure substance properties will be illuminated first, followed by a discussion of possible deviations due to the presence of decomposition products of ammonia and solutes. Thermophysical data for pure ammonia are available up to 426.9 °C in a database of the National Institute of Standards and Technology (NIST) [97]. To give an overview of how different fill levels alter the pure substance properties of ammonia, Figure 8 shows density, pressure, specific heat capacity, dynamic viscosity, and thermal conductivity at the upper end of the temperature range for which data are available in the database by NIST [97].…”

“…Thermophysical data for pure ammonia are available up to 426.9 °C in a database of the National Institute of Standards and Technology (NIST) [97]. To give an overview of how different fill levels alter the pure substance properties of ammonia, Figure 8 shows density, pressure, specific heat capacity, dynamic viscosity, and thermal conductivity at the upper end of the temperature range for which data are available in the database by NIST [97]. The fill level refers to the volume fraction of the reactor filled with liquid ammonia at the boiling point of ammonia (−33.36 °C).…”

“…Reprinted from [101], Copyright 2016, with permission from Elsevier. (b) Pressure as a function of specific volume of ammonia for selected temperatures (reprinted from[44], data from NIST database[97]). The hatched area in red marks the typical application range of supercritical fluids whereas the dark blue region approximately indicates the parameter range of ammonothermal GaN growth.…”

Model experiments for Czochralski crystal growth processes using inductive and resistive heating

“…Such "model experiments" are, therefore, predestined for the validation of numerical simulation and are of growing interest, e.g. for investigation of flow phenomena [8][9][10], process control [11,12], or phase boundary stability [13]. Within the NEMOCRYS (Next Generation Multiphysical Models for Crystal Growth Processes) project, we are developing a new generation of multiphysical models [14,15] and model experiments for crystal growth processes, where multiple physical phenomena can be observed simultaneously and hence validated in a coupled manner.…”