Silicon Melt Convection Research Articles

Simulation of the superconducting magnet for a silicon single crystal growth

The magnetic Czochralsky (MCz) technique is the most common and widely used approach to producing single crystal silicon. The magnetic field is applied to control the temperature fluctuations and suppress silicon melt convection. However, the magnetic field quality and manufacturing costs were mainly determined by the shape of the coils. In order to generate the transverse magnetic field, two pairs of coils are arranged around the crucible and face each other in opposite directions to construct the superconducting magnets system, which has an inner diameter of 1600 mm and an outer diameter of 2400 mm. The simulating results indicate the magnetic flux density (B) in the center of molten silicon is 0.4 T, and the magnetic field inhomogeneity in the X-Y plane is about 20%. The electrical power consumption and cooling capacity will be reduced. Furthermore, a smaller cryostat is required to hold the curve shape coils, which results in lower cost and lower weight of the superconducting magnet.

Improving Performance of Cast Silicon Ingot by Forcing Silicon Melt Convection with Mechanical Stirring

Improving Performance of Cast Silicon Ingot by Forcing Silicon Melt Convection with Mechanical Stirring

Convective instabilities in the Czochralski model with different radii ratios

In this work, we explore the instability of the complex convection in the Czochralski model concerning the effects of the radii ratio, melt materials, and crystal rotation. Particularly, linear stability analysis is conducted based on the spectral element method for three groups of cases with the same interval for the variation of the radii ratio (Λ) but different material Prandtl number (Pr) and dimensionless crystal rotation velocity ωs. We observe that, for both ωs = 0 and ωs = 300, the mixed convection of silicon melt (Pr = 0.011) becomes less stable with the increase in radii ratio and the instability is of purely inertial mechanism. In contrast, as for the LiCaAlF6 melt (Pr = 1.4), a larger radii ratio would improve the stability and the instability is dominated by buoyancy mechanism for ωs = 300. Moreover, two times of critical wavenumber transitions occur in the critical stability curve for silicon melt (Pr = 0.011). Each transition associates with a convex turning point of the critical stability curve for ωs = 0, while only one turning point remains when ωs shifts to 300.

Comparative evaluation of RANS eddy-viscosity turbulence models for calculating the silicon melt convection in crystal growth systems

Comparative evaluation of RANS eddy-viscosity turbulence models for calculating the silicon melt convection in crystal growth systems

Design and Numerical Study of Argon Gas Diversion System Using Orthogonal Experiment to Reduce Impurities in Large-Sized Casting Silicon

To reduce oxygen and carbon impurities while casting silicon, an argon gas diversion system is proposed. A series of two-dimensional global transient numerical simulations are carried out using Fluent software according to the orthogonal experimental design, including heat transfer, convection of silicon melt and argon gas, and the fully coupling transport of impurities. The numerical results show that when the distance between the outer tube outlet and the cover is 10 mm, the backflow is inhibited by lateral outflow, thus the generation of CO is suppressed and the penetration of impurities into the silicon melt is decreased. The larger the flow rate, the more obvious the effect is. When the outer tube outlet is far from the cover, the effect of removing impurities is no longer significant. In addition, too large or too small an inner tube flow rate is not conducive to impurity reduction. The optimal parameter combination of outer tube flow rate, inner tube flow rate, and the distance between outer tube outlet and the cover are determined by the orthogonal experiment. Compared with the original furnace, the average concentration of oxygen and carbon in casting silicon ingots could be decreased by 7.4% and 59.9%, respectively, by using the optimized argon gas diversion system.

3D numerical simulation with experimental validation of a traveling magnetic field stirring generated by a Bitter coil for silicon directional solidification process

Silicon is the most widely used raw material in photovoltaic industry; however, the quality of the silicon photovoltaic solar cells depends on the quality of the raw material (i.e. metallurgical silicon or poly-silicon) and the solidification methods used for the production of the silicon ingot from which the solar cells are produced. This study is related to how improve the quality of the final ingot in the directional solidification process; it is necessary to control the impurity segregation of silicon raw material during the processing. This control can be accomplished by adding an electromagnetic Bitter coil which can generate an external traveling magnetic field (TMF) stirring to control the hydrodynamic flow of silicon melt during the solidification process without contaminating it. To carry out this study, we used a Bridgman vertical directional solidification furnace, equipped with a cylindrical Bitter coil stirrer used in order to have the control of the silicon melt convection on the principal parameters of the solidification process, such as the growth rate, the thermal gradient and the natural convection of silicon melt. For the electromagnetic, heat exchange and silicon melt flow modelling, we used 3D numerical Multiphysics coupled models. Parallel to the numerical results we carried out experimental investigations relating to the characterization of the electromagnetic parameters. This study shows a promising effect of the applied traveling magnetic field on the final ingot quality; indeed, we have the ability to control the silicon melt flow which can affect the thermal configuration, the solidification interface shape and the segregation of impurities by changing the electric current input configuration of the Bitter coil stirrer.

Three-dimensional effect of high frequency vibration on convection in silicon melt

The effect of high-frequency vibrations with different orientations on the convective flow in a liquid metal inside a cubic cell heated from the side is investigated using the collocation spectral method. The vibration is in three dimensions with a vibration vector contained in one of the three principal planes of the cavity ($x\phantom{\rule{0}{0ex}}z$, $x\phantom{\rule{0}{0ex}}y$, and $y\phantom{\rule{0}{0ex}}z$ planes). In either weightlessness or gravity conditions, the influence of the vibrations on the flow is found to strongly depend on their direction: each vibration orientation has its own features and affects the flow intensity and pattern differently.

Eddy-resolving numerical simulation of silicon melt convection in a Czochralski crucible: effects of radiation from the free surface at various crucible rotation rates

The contribution covers results of numerical study based on conjugate heat transfer formulation of turbulent silicon melt convection in an industrial system for CZ Si-crystal growth of 100 mm diameter crystals. The computations have been performed using an eddy-resolving method treated as Implicit LES for two values of the emissivity from the melt free surface (0.25 and 0.3) and the crucible rotation rate of 2 and 5 rpm. The effects of these parameters on melt convection and characteristics of heat transfer are analyzed.

Analysis of the Effect of a Vertical Magnetic Field on Melt Convection and Oxygen Transport During Directional Solidification of Multi-Crystalline Silicon by Numerical Simulation

Melt convection during the directional solidification process of multi-crystalline silicon plays a critical role in the transport of impurities. The utilization of a static magnetic field is an effective way to control the melt convection pattern. Studying the effect of the Lorentz force induced by the vertical magnetic field (VMF) on the melt convection of silicon in detail is beneficial to optimize the magnetic field parameters in the production process. Based on the numerical simulation method of multi-physics coupling, this paper explores the effects of different VMF intensities on the convection of silicon melt and the transport of oxygen in the melt during the directional solidification of polycrystalline silicon. The results show that in the first 125 minutes of the crystallization stage, the melt convection velocity is affected significantly by the magnetic field intensities. When different convection circulations are present in the silicon melt, the upper circulation easily transports oxygen to the furnace atmosphere, and the subjacent circulation easily lead to the retention and accumulation of oxygen. Enhancing the VMF intensity to a certain extent can reduce the size of the oxygen retention region in the silicon melt, and the time of the first disappearance of the subjacent circulation near the sidewall of the crucible is shortened. Then the average oxygen concentration in the silicon melt can be reduced. However, a larger vertical magnetic field intensity can result in greater average oxygen concentration in the oxygen retention region.

Influence of silicon melt convection on interface instability in large-size silicon carbide solution growth

The interface instability in large-size silicon carbide solution growth has been investigated with a focus on the influence of silicon solution convection. Indications have shown that solution convection produces a substantial effect on the instability of the growth interface. As the SiC size increases, the instability becomes more evident. Therefore, improved solution convection is required for growing large-sized silicon carbide ingots by the solution method.

Thermocapillary convection with bidirectional temperature gradients in a shallow annular pool of silicon melt: Effects of ambient temperature and pool rotation

In order to understand the characteristics and instability of thermocapillary convection of silicon melt with bidirectional temperature gradients, a series of unsteady three-dimensional numerical simulations were carried out in a shallow annular pool. The imposed radial temperature gradient is established by the temperature difference between the outer and inner walls, while the imposed vertical temperature gradient is formed by adding a constant heat flux at the bottom and the thermal radiation on the top free surface. Two kinds of critical heat fluxes are determined. The first type is to ensure the whole silicon in the pool is in the molten state, and the second type is to judge the onset of oscillatory flow. When Marangoni number is small, a three-dimensional steady flow is common without pool rotation, but it becomes oscillatory at a higher ambient temperature or a small rotation Reynolds number. An axisymmetric steady flow can be observed at a large rotation Reynolds number in the case of small or moderate Marangoni number. Furthermore, the transition from the radial temperature gradient dominated flow to the vertical temperature gradient dominated flow is discussed.

Effects of argon flow on impurities transport in a directional solidification furnace for silicon solar cells

A global simulation including coupled oxygen and carbon transport was carried out to study the argon flow effects on the impurities transport in a directional solidification furnace for silicon solar cells. The simulation is based on a fully coupled calculation of the thermal and flow fields in a furnace including argon gas flow and melt convection. Five chemical reactions are considered in the impurity transport model. The effects of both the argon flow rate and the furnace pressure were examined. It was found that the argon flow has an important effect on the silicon melt convection, which will further influence the evaporation characteristic of SiO at the melt free surface. The amount of SiO carried away by the argon flow increases with increase in the argon flow rate while the CO gas can be prevented from being transported to the melt free surface. There exists a peak value for the concentration of impurities in the furnace chamber regarding argon flow rate due to the correlation among SiO evaporated, reacted and taken away. The pressure also influences the impurity transport in the furnace by modifying the pattern of argon flow. The numerical results demonstrate a method to control the oxygen and carbon transport in a directional solidification furnace by adjusting the argon flow rate and the furnace pressure.

Stability of Thermocapillary Convection in Rotating Shallow Annular Pool of Silicon Melt

In order to understand the effect of pool rotation on stability of thermocapillary convection, the critical conditions for the incipience of oscillatory flow in rotating shallow annular pools of silicon melt (Pr = 0.011) are investigated by means of linear stability analysis (LSA) under different pool rotation rates ranging from Ta = 0 to 1,513.9 and under microgravity condition. The results indicate that with increase of Ta numbers, the critical Marangoni for the incipience of hydrothermal wave (HTW) increases, i.e., pool rotation stabilizes the steady axisymmetric thermocapillary convection of silicon melt. The critical azimuthal wave number mc decreases linearly with increase of Ta number when Ta ≤ 378.5. However, when Ta > 378.5, mc almost keeps constant with mc = 34. When Ta 550.

Effect of zero-Gauss plane and magnetic intensity on oxygen concentration in cusp-magnetic CZ crystals

The control of oxygen concentration in 200 mm-diameter Si single crystals is studied in the cusp-magnetic Czochralski method, and the effects of zero-Gauss plane (ZGP), ZGP shape, which is due to magnetic ratio (MR) of the lower to upper current densities in the configurations of the cusp-magnetic field, and magnetic intensity (MI) on the oxygen concentration and its distribution in the crystal are experimentally investigated. The shape of ZGP is not only flat but also parabolic due to MR. The oxygen concentration depends on MR, ZGP and MI. The oxygen concentration decreases with increasing MR. As ZGP decreases, which is moved from the crucible bottom toward the free surface, the oxygen concentration decreases. There is no significant influence of ZGP on the radial distribution of the oxygen concentration. With increasing melt-charge size, oxygen concentration increases because the contact-area between crucible wall and silicon melt increases and convection in the larger amount of the melt is much stronger. The experimental results are compared with other studies.

Geostrophic turbulence in CZ silicon melt under CUSP magnetic field

Due to the Coriolis force caused by crucible rotation, the CZ silicon melt convection develops into a geostrophic turbulence (J. Crystal Growth 116 (1992) 447) at higher Taylor number conditions (J. Crystal Growth 198/199 (1999) 135). This study investigates the effect of a CUSP magnetic field on the geostrophic turbulence by CCD melt surface observations (J. Crystal Growth 180 (1997) 487) in a conventional CZ furnace and corresponding numerical fluid simulations. The estimated Taylor number of the present study lies between 3×10 9 and 2×10 12, Hartmann number lies between 0 and 2000, and Rayleigh number lies between 2×10 7 and 2×10 8. CCD melt surface observations indicated that the fluctuating polka dot patterns consisting of a high temperature spot, which is a typical property of the geostrophic turbulence, were not broken by the CUSP magnetic field. Moreover, increasing of the magnetic field intensity enhanced the size and amplitude of the polka dots. On the other hand, increasing of crucible rotation caused the polka dot pattern to fade, which is similar to the case of zero magnetic field conditions. As regard the numerical fluid dynamic simulation, 3D differential equations containing the magnetic induction equation were solved on a cylindrical lattice of 80×60×65 points. The result of the simulations agreed with the melt surface observations mentioned above, and indicated the reduction in the kinetic energy of the entire melt. These facts delineates that a CUSP magnetic field will suppress the averaged fluctuation of the melt convection as expected by the usual understanding (J. Crystal Growth 113 (1991) 305), but will enhance the melt surface fluctuation in a geostrophic turbulence regime of a large crucible.

Effect of high frequency magnetic field on CZ silicon melt convection

Melt flow structure during the silicon single crystal growth process strongly affects the crystal quality. Therefore, melt convection control technique should be developed to obtain the high quality single crystal. For this purpose, we proposed a high frequency magnetic field applied method, and numerically investigated the effect of high frequency magnetic field on Czochralski (CZ) silicon melt convection. The results revealed that the melt convection was strongly affected by the applied electric current and frequency. The temperature distribution just below the crystal became flat if the applied electric current and frequency were selected as optimized value.

Suppression of Marangoni convection of silicon melt by a non-contaminating method

A set of numerical simulation of the effect of the gas shearing flow over a silicon melt free surface on Marangoni convection under microgravity condition was conducted by using finite element method. For given gas channel width, Marangoni number and aspect ratio a remarkable reduction of Marangoni convection in silicon liquid bridge can be achieved by choosing the optimal gas velocity in accordance with the correlation proposed in the paper. The effectiveness of the reduction of the gas flow under different conditions shows that, in some cases, Marangoni convection reduction of 99% can be realized by this non-contaminating method.

Silicon melt convection in large size Czochralski crucibles

The melt flow in large diameter crucibles during the growth of silicon (Si) single crystals of 300 mm diameter is characterized by turbulent large-scale velocity and temperature fluctuations. Strong efforts of the crystal growth industry are dedicated to the control of the interface shape and the related point defect distribution in the crystal, of the oxygen and particle transport in the melt, of the crucible overheating and of the conditions for dislocation free growth. Static and time-dependent electromagnetic fields offer new possibilities to meet the continuously increasing demands on crystal quality and yield improvement. Numerical simulation helps to investigate a wide range of possible process conditions, and to reduce experimental costs and time to market significantly. Depending on the required accuracy and available computation resources, two-dimensional (2D) or three-dimensional (3D) models are used. Temperature measurements in the melt, carried out during crystal growth and in model facilities, provide data for the verification of the numerical models, for direct process optimization and for a better understanding of the heat and mass transport behavior.

E162 CZ 法シリコン融液内自然対流に対する高周波磁場の影響

E162 CZ 法シリコン融液内自然対流に対する高周波磁場の影響

Oxygen distribution in silicon melt under inhomogeneous transverse-magnetic fields

This paper aims to report an effect on inhomogeneous transverse-magnetic fields to melt convection and oxygen distribution in silicon melt and at a solid–liquid interface during single crystal growth. The inhomogeneous transverse-magnetic fields were obtained by the calculation based on Biot–Savart equation with an assumption of finite-diameter solenoids. We studied how Lorenz force, which was formed by the inhomogeneous magnetic fields, modified convection of the melt and oxygen transfer as a function of relative position between the solenoids and the melt. We showed the possibility that oxygen concentration in the melt and near the solid–liquid interface can be controlled by relative position between the melt and the inhomogeneous transverse-magnetic fields. We discuss the effects of Lorenz force and electric potential distributions on the melt and oxygen transfer on the basis of calculated results obtained by three-dimensional and time-dependent calculation.