Effects of cusp-shaped magnetic field on melt convection and oxygen transport in an industrial CZ-Si crystal growth

Liu, Xin; Liu, Lijun; Li, Zaoyang; Wang, Yuan

doi:10.1016/j.jcrysgro.2012.06.004

Cited by 33 publications

(12 citation statements)

References 28 publications

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“…This study investigated heat and oxygen transfer in a CMCZ furnace with 300-mm-diameter crystals with a previously reported furnace configuration. [11] Two kinds of grid systems were used to calculate heat and mass transfer, and oxygen transfer. Figure 1a shows the grid used for the calculation of heat and convection (including electric current and potential) in both the crystal and the melt.…”

Section: Modeling and Numerical Methodsmentioning

confidence: 99%

“…Several papers [11][12][13][14] report numerical results in a 2D global analysis on oxygen transfer as well as heat and mass transfer under the CMCZ system. Yokoyama et al, [15] Kalaev et al, [16] and P. Daggolu et al [17] reported on the effects of the temperature and convection velocity of the silicon melt in a 300-mm-diameter crystal growth system using TMCZ or CMCZ obtained via 3D global analysis.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Effect of Cusp‐Shaped Magnetic Fields on Heat, Mass, and Oxygen Transfer Using a Coupled 2D/3D Global Model

Kakimoto

Liu

Nakano

2021

Crystal Research and Technology

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The recent development of power devices requires silicon wafers in the radial direction as well as in the depth direction in a low oxygen concentration. Magnetic fields such as transverse or cusp-shaped magnetic fields are then applied to the silicon melt to reduce the oxygen concentration in the crystal, especially those 300 mm in diameter or larger. Several studies reported calculated results of reduced oxygen concentration in the melt with cusp-shaped magnetic fields. However, few studies have reported on the 3D transfer processes of oxygen in the melt. This paper reports on the transfer mechanism of oxygen in silicon melts with 300-mm-diameter crystals under cusp-shaped magnetic fields during the growth of silicon crystals via the Czochralski method. Using in-house software with a coupled 2D/3D global model, this study examines the effects of the flow fields in the melt on heat, mass, and oxygen transfer as a function of the relative position between the zero-Gauss plane and the melt.

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Section: Modeling and Numerical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of the Effect of Cusp‐Shaped Magnetic Fields on Heat, Mass, and Oxygen Transfer Using a Coupled 2D/3D Global Model

Kakimoto

Liu

Nakano

2021

Crystal Research and Technology

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“…In recent times, there has been an increasing demand for large-diameter silicon wafers, leading to the use of larger crucibles. However, this results in turbulent flow in the melt, causing fluctuations in temperature and impurity levels [2]. This turbulent flow worsens the instability within the melt and leads to inconsistencies in the crystal's composition at both the macro-and microscopic levels [3].…”

Section: Introductionmentioning

confidence: 99%

“…However, there are important issues regarding CMF that require further investigation, particularly the optimal position of the zero-Gaussian plane (ZGP). A two-dimensional simulation of 300 mm CZ-Si crystal growth demonstrated that different CMF configurations lead to various melt convection structures, and that adjusting the ZGP position can result in a flatter growth interface shape [2]. Threedimensional transient simulations have shown that different ZGP positions can cause thermal waves to travel around the melt free surface, potentially leading to temperature oscillations at the interface [3,9].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Simulation of Melt Convection and Oxygen Transport in CZ-Si Crystal Growth with Cusp Magnetic Fields

Cen,

Guo

2023

Crystals

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The application of magnetic fields has become a standard control technique in the CZ-Si growth industry. To investigate the impact of cusp-shaped magnetic fields (CMF) on heat and mass transfer in the melt, a series of transient three-dimensional simulations were conducted for the growth of a 100 mm CZ-Si crystal with a cylindrical crucible. The turbulent melt motion was modeled using the large eddy simulation (LES) method. Six configurations of CMF with various zero-Gaussian plane (ZGP) positions were examined and numerically compared. The computed results showed that different ZGP positions resulted in distinct types of melt convection, buoyant plumes, and thermal waves. Additionally, it was observed that the studied CMF configurations effectively reduced oxygen dissolution from the crucible wall along with oxygen impurity incorporation into the crystal. These findings demonstrate the potential for precise control of the heat and mass transfer process in CZ-Si growth through the application of suitable CMF.

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“…Liu et al studied the effect of temperature and external magnetic field on the deformation of solid-liquid interface [5]. Asadi et al studied the change of solid-liquid interface at different rotating speeds of crystals and crucibles [6]. Voronkov and Falster studied the effect of growth parameters on crystal quality from the factors of crystal defects and proposed a criterion V/G for evaluating the probability of vacancies and self-gap in crystals [7].…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Optimization of Process Parameters of Silicon Single Crystal Growth

Huang

Zhang

Wang

2022

Wireless Communications and Mobile Computing

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In order to obtain higher quality silicon single crystal, a hybrid strategy for modeling of Czochralski silicon crystal growth and optimizing of process parameters is presented in the paper. The hybrid strategy includes the computational fluid dynamics (CFD) method, neural network of group method of data handing (GMDH), and improved nondominated sorting genetic algorithm II (NSGA-II). The shape variable of solid-liquid interface h and the defect evaluation criteria V / G are set to objective functions according to engineering experience and process requirement. The polynomial of the objective functions is produced by GMDH and CFD. Ultimately, an improved elitist strategy and crowding distance NSGA-II is proposed in the paper to obtain the Pareto optimum solution by the objective functions identified by the GMDH. Compared with other optimization algorithms, the improved NSGA-II can increase the lateral diversity and the uniform distribution of the nondominated solutions. Engineering validation proved that the proposed hybrid strategy can effectively solve the complex uncertain multiobjective optimization problem of system and provides a new method for obtaining high-quality crystal growth process parameters.

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Effects of cusp-shaped magnetic field on melt convection and oxygen transport in an industrial CZ-Si crystal growth

Cited by 33 publications

References 28 publications

Analysis of the Effect of Cusp‐Shaped Magnetic Fields on Heat, Mass, and Oxygen Transfer Using a Coupled 2D/3D Global Model

Analysis of the Effect of Cusp‐Shaped Magnetic Fields on Heat, Mass, and Oxygen Transfer Using a Coupled 2D/3D Global Model

Three-Dimensional Simulation of Melt Convection and Oxygen Transport in CZ-Si Crystal Growth with Cusp Magnetic Fields

Multiobjective Optimization of Process Parameters of Silicon Single Crystal Growth

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