Validation of a 3D mathematical model for feed rod melting during floating zone Si crystal growth

Plāte, M.; Dadzis, K.; Krauze, A.; Menzel, Robert; Virbulis, J.

doi:10.1016/j.jcrysgro.2019.05.034

Cited by 3 publications

(2 citation statements)

References 6 publications

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Section: D Model Simulation Resultsmentioning

confidence: 99%

“…[30]; Figure 14 shows the current density distribution of two kinds of 3D inductors. The inductor slit changes can directly affect the distribution of the current and the induced magnetic field [31]. It can be seen that the current distribution of the one-way inductor is concentrated in the center around the hole and the slit, the current distribution of the outer side of the current distribution is less; it is because the density of the ring-effect currents is greatest at the inner diameter of the coil, the electromagnetic field generated is most concentrated at the "waist" of the melting zone of the crystals, thus generating the most Joule heat close to the center of the melting surface and the least Joule heat close to the outer surface of the polycrystalline silicon melt, which results in a very uneven distribution of radial temperatures across the entire polycrystalline silicon melt.…”

Section: D Model Simulation Resultsmentioning

confidence: 99%

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Simulation of the Inductor Structure to Improve FZ Thermal Fields

Ai,

Sun,

Zhang

et al. 2023

Coatings

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The floating zone (FZ) is one of the important methods for pulling silicon single crystals, but there are still problems of an unstable thermal field and crystallization difficulties. They will directly affect the growth of single crystals, resulting in defects and even fractures, seriously reducing production efficiency. Based on this, the effect of the modified inductor structure on the FZ thermal field is investigated in this paper. Using COMSOL 6.0 simulation software, 2D and 3D FZ models are established. The inductor steps under the 2D model and the inductor slits under the 3D model are compared to analyze the effects of steps and slits on the 8-inch FZ thermal field and melt flow. The distributions of temperature fields and melt flow in the melting zone under the action of the axial magnetic field are calculated by finite element analysis. The results show that the melt under the introduction of steps in the 2D model and the cross-slit structure in the 3D model is the most stable and favorable for crystal growth, which matches the actual production.

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Section: D Model Simulation Resultsmentioning

confidence: 99%

Section: D Model Simulation Resultsmentioning

confidence: 99%

Simulation of the Inductor Structure to Improve FZ Thermal Fields

Ai,

Sun,

Zhang

et al. 2023

Coatings

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Numerical modelling of melting front structures during floating zone silicon crystal growth

Surovovs,

Sjomkane,

Virbulis

et al. 2024

Journal of Crystal Growth

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Simulation of flow field in silicon single-crystal growth using physics-informed neural network with spatial information

2022

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Melt convection plays a crucial role in the growth of silicon single crystals. In particular, melt flow transfers mass and heat, and it may strongly affect the crystal growth conditions. Understanding and controlling convection remains a significant challenge in industrial crystal production. Currently, the numerical methods such as the finite element method and the finite volume method are mainly used to simulate melt convection in the crystal growth process. However, these methods are not suitable for most applications with real-time requirements. Physics-informed neural networks (PINNs) have the advantages of fast calculation and wide application. They provide a new concept for the numerical solutions of nonlinear partial differential equations (PDEs). This paper proposes a PINN with spatial information to solve the silicon melt flow model, which does not depend on any simulation data. As the network depth (number of layers) increases, the derivative information in the PDE loss becomes weak, which reduces the expression of the original features in the loss function. Therefore, this study introduces spatial information into the hidden layer of the network, thereby enhancing the correlation between the network and the original input and improving the expression ability of the network. Specifically, silicon melt flow models under three rotating conditions are considered. Compared with other methods, the proposed algorithm can accurately capture regions with complex local morphology. The experimental results reveal the flow characteristics of the silicon melt and confirm the effectiveness of the proposed algorithm.

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Validation of a 3D mathematical model for feed rod melting during floating zone Si crystal growth

Cited by 3 publications

References 6 publications

Simulation of the Inductor Structure to Improve FZ Thermal Fields

Simulation of the Inductor Structure to Improve FZ Thermal Fields

Numerical modelling of melting front structures during floating zone silicon crystal growth

Simulation of flow field in silicon single-crystal growth using physics-informed neural network with spatial information

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