Combined 3D and 2.5D modeling of the floating zone process with Comsol Multiphysics

Wünscher, Michael; Menzel, Robert; Riemann, H.; Lüdge, Anke

doi:10.1016/j.jcrysgro.2013.03.052

Cited by 19 publications

(6 citation statements)

References 8 publications

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“…To have realistic interface shapes and temperature field in the crystal, initially a converged state of quasi-steady calculations using the program FZone [16] with inductor shape from [7] is obtained for the given crystal diameter and the pull rate. Shape of the crystallization interface is found by solving global heat transfer problem which couples the temperature field in the silicon with radiation on the surfaces using view factors, and the heat sources are taken from 3D high-frequency electromagnetic field calculation [17].…”

Section: Numerical Model 21 Boundary Conditionsmentioning

confidence: 99%

“…Reduction of the thermal stresses with the introduction of a crystal radiation reflector was shown as well. Global model of FZ system which includes axissymmetric stress field using Comsol Multiphysics has been developed at the Leibniz Institute for Crystal Growth [7]. The case study revealed that higher pull rate leads to an increase of thermal stress, and presence of the reflector decreases the stress.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional modelling of thermal stress in floating zone silicon crystal growth

Plāte¹,

Krauze

Virbulis

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract.During the growth of large diameter silicon single crystals with the industrial floating zone method, undesirable level of thermal stress in the crystal is easily reached due to the inhomogeneous expansion as the crystal cools down. Shapes of the phase boundaries, temperature field and elastic material properties determine the thermal stress distribution in the solid mono crystalline silicon during cylindrical growth. Excessive stress can lead to fracture, generation of dislocations and altered distribution of intrinsic point defects. Although appearance of ridges on the crystal surface is the decisive factor of a dislocation-free growth, the influence of these ridges on the stress field is not completely clear. Here we present the results of thermal stress analysis for 4" and 5" diameter crystals using a quasi-stationary three dimensional mathematical model including the material anisotropy and the presence of experimentally observed ridges which cannot be addressed with axis-symmetric models. The ridge has a local but relatively strong influence on thermal stress therefore its relation to the origin of fracture is hypothesized. In addition, thermal stresses at the crystal rim are found to increase for a particular position of the crystal radiation reflector.

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Section: Numerical Model 21 Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three-dimensional modelling of thermal stress in floating zone silicon crystal growth

Plāte¹,

Krauze

Virbulis

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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“…The typical working frequency is 2.5 MHz, leading to very small skin depth both in the copper inductor (0.04 mm) and graphite parts (1.4 mm). Such skin depths can be hardly resolved for realistic 3D geometries; therefore, the Boundary coil model is applied to the inductor while the Surface impedance boundary condition (SIBC) is applied to all other electrically conducting surfaces [3]. Several aspects of these modeling assumptions have not been yet discussed in the literature:…”

Section: Numerical Modelsmentioning

confidence: 99%

High-frequency Heat Induction Modeling for a Novel Silicon Crystal Growth Method

Dadzis¹,

Menzel²,

Ziem³

et al. 2017

Proceedings of the VIII International Scientific Colloquium "Modelling for Materials Processing"

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A new method for silicon crystal growth using granulate as feedstock material has been proposed recently. This method bears resemblance to the well-known float zone growth but also places new challenges for both hardware design and numerical modeling. In this study we focus on the high-frequency induction heating. We compare and validate numerical models implemented in the commercial software package Comsol and open source software GetDP, using both analytical solutions and measurements of the 3D magnetic field distribution for real inductor shapes. The options to improve the overall modeling accuracy are discussed. Results from direct measurements of the inductor current and of the temperature-dependent electrical conductivity of silicon granulate are presented.

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“…Wü nscher et al [66] and Menzel [12] applied COMSOL for 3D and 2.5D modeling of EM, temperature, and stress fields as well as the shapes of free surface, melting, and crystallization interfaces for 4 00 and 5 00 process.…”

Section: Historical Overviewmentioning

confidence: 99%

Floating Zone Growth of Silicon

Muižnieks

Virbulis

Lüdge

et al. 2015

Handbook of Crystal Growth

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Combined 3D and 2.5D modeling of the floating zone process with Comsol Multiphysics

Cited by 19 publications

References 8 publications

Three-dimensional modelling of thermal stress in floating zone silicon crystal growth

Three-dimensional modelling of thermal stress in floating zone silicon crystal growth

High-frequency Heat Induction Modeling for a Novel Silicon Crystal Growth Method

Floating Zone Growth of Silicon

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