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Author: Miller, Wolfram × DDC: 540 ×

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    Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals
    (Weinheim : Wiley-VCH, 2021) Böttcher, Klaus; Miller, Wolfram; Ganschow, Steffen
    The Czochralski growth of NdScO3 single crystals along the [110]-direction is numerically analyzed with the focus on the influence of the optical thickness on the shape of the crystal–melt interface and on the generation of thermal stresses. Due to lack of data, the optical thickness (i.e., the absorption coefficient) is varied over the entire interval between optically thin and thick. While the thermal calculation in the entire furnace is treated as axisymmetric, the stress calculation of the crystal is done three-dimensionally in order to meet the spatial anisotropy of thermal expansion and elastic coefficients. The numerically obtained values of the deflection of the crystal/melt interface meet the experimental ones for absorption coefficients in the range between 40 and 200 m−1. The maximum values of the von Mises stress appear for the case of absorption coefficient between 20 and 40 m−1. Applying absorption coefficients in the range between 3 and 100 m−1 leads to local peaks of high temperature in the shoulder region and the tail region near the end of the cylindrical part.
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    Quasi-Transient Calculation of Czochralski Growth of Ge Crystals Using the Software Elmer
    (Basel : MDPI, 2019) Miller, Wolfram; Abrosimov, Nikolay; Fischer, Jörg; Gybin, Alexander; Juda, Uta; Kayser, Stefan; Janicskó-Csáthy, Jószef
    A numerical scheme was developed to compute the thermal and stress fields of the Czochralski process in a quasi-time dependent mode. The growth velocity was computed from the geometrical changes in melt and crystal due to pulling for every stage, for which the thermal and stress fields were computed by using the open source software Elmer. The method was applied to the Czochralski growth of Ge crystals by inductive heating. From a series of growth experiments, we chose one as a reference to check the validity of the scheme with respect to this Czochralski process. A good agreement both for the shapes of the melt/crystal interface at various time steps and the change in power consumption with process time was observed. © 2019 by the authors. Licensee MDPI, Basel, Switzerland.
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    Numerical modelling of the czochralski growth of β-Ga2O3
    (Basel : MDPI, 2017) Miller, Wolfram; Böttcher, Klaus; Galazka, Zbigniew; Schreuer, Jürgen
    Our numerical modelling of the Czochralski growth of single crystalline β-Ga2O3 crystals (monoclinic symmetry) starts at the 2D heat transport analysis within the crystal growth furnace, proceeds with the 3D heat transport and fluid flow analysis in the crystal-melt-crucible arrangement and targets the 3D thermal stress analysis within the β-Ga2O3 crystal. In order to perform the stress analysis, we measured the thermal expansion coefficients and the elastic stiffness coefficients in two samples of a β-Ga2O3 crystal grown at IKZ. Additionally, we analyse published data of β-Ga2O3 material properties and use data from literature for comparative calculations. The computations were performed by the software packages CrysMAS, CGsim, Ansys-cfx and comsol Multiphysics. By the hand of two different thermal expansion data sets and two different crystal orientations, we analyse the elastic stresses in terms of the von-Mises stress.