Crystal Rotation Rate Research Articles

The interface inversion process during the Czochralski growth of high melting point oxides

High melting point oxides show an interface inversion from a convex interface shape to a flat or concave interface when grown after the Czochralski method with constant crystal rotation rate and increasing crystal radius (as in the shoulder region). Under the described conditions one observes during YAG-growth a sudden and uncontrollable interface change, called interface flip, at a certain critical crystal rotation rate. We describe model experiments and numerical simulations of this inversion process. We show that it is connected with a flow transition at a certain critical rotational Reynolds number Re c. This Re c increases with the convex interface deflection and with the strength of the buoyant-thermocapillary flow near the free melt surface towards the crystal. A self-amplifying process, involving the back-melting of the crystal cone, starts when Re c is reached. The dynamics of the back-melting is explained. A more vigerous interface inversion process is expected for systems with large interface deflections and for systems with smaller dynamic Bond number, e.g. smaller crucibles.

An experimental and numerical effort to simulate the interface deflection of YAG

Conical interface shapes like in YAG-growth are simulated using NaNO 3 melt growth systems. We have studied in detail the effect of the magnitude of the heat flux through the crystal on the interface deflection at crystal rotation rates near zero. The convection in the melt, driven by buoyancy and thermocapillary, was changed by varying either the radial temperature gradient in the melt, or by changing the melt level or by the application of cooling shields above the free melt surface. All these parameters have a significant influence on the crystal rotation rate which has to be applied to grow the crystal with flat interface. Comparison with numerical simulation is made using the experimental values as input parameters.

Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Three-dimensional numerical simulations of oxide melt flow in a large-scale Czochralski crucible (200 mm φ×100 mm h) have been carried out to investigate the effects of various factors such as the thermal boundary conditions at the crucible sidewall, the Marangoni effect at the melt free surface and the rotation rate of the crystal on the surface patterns and bulk flow structures of oxide melt. The block-structured boundary-fitting-coordinate technique was employed. It was found that the wave and wave-spoke patterns appear on the melt free surface depending on the factors. The change of the thermal boundary conditions at the crucible sidewall, from a constant temperature to a constant heat flux, and the Marangoni effect tended to cause the disappearance of the wave patterns because of the acceleration of the inward flow along the free surface toward the crystal. Unlike the case in a small crucible, the melt flows were always completely three-dimensional even though the surface temperature distribution was approximately axisymmetric. The increase of the crystal rotation rate could suppress the inward flow, and lead to a wave-spoke pattern when the Marangoni effect was taken into account. The spokes in the wave-spoke patterns were generated by an identical mechanism revealed in J. Crystal Growth 252 (2003) 550.

Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

AbstractHeat and mass transfer taking place during growth of Y3Al5O12 (YAG) crystals by the Czochralski method, including inner radiation, is analyzed numerically using a Finite Element Method. For inner radiative heat transfer through the crystal the band approximation model and real transmission characteristics, measured from obtained crystals, are used. The results reveal significant differences in temperature and melt flow for YAG crystals doped with different dopands influencing the optical properties of the crystals. When radiative heat transport through the crystal is taken into account the melt‐crystal interface shape is different from that when the radiative transport is not included. Its deflection remains constant over a wide range of crystal rotation rates until it finally rapidly changes in a narrow range of rotation rates. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Global analysis of a small Czochralski furnace with rotating crystal and crucible

In order to understand the influence of crystal and crucible rotations on the silicon melt flow and oxygen transport in a small Czochralski (Cz) furnace, a set of global numerical simulations, based on the pseudo-steady and axisymmetric laminar flow model, was conducted using the finite-element method. The crystal rotation rates ranged from 0 to 20 rpm and the crucible rotation rates from 0 to −2.5 rpm. The model evaluated the effects of the thermocapillary force on the radial distributions of oxygen concentration and ( V s,n/ G n) at the melt/crystal interface, where V s,n and G n are the crystal pulling rate and temperature gradient in the direction normal to the melt/crystal interface, respectively. Simulation results indicate that the thermocapillary force causes significant changes in the flow pattern and temperature distribution in the melt but gives small effect on the oxygen concentration in the crystal in the case of a small Cz furnace without a gas guide. On the contrary, installation of a gas guide has a significant effect on the flow fields and the oxygen concentration in the grown crystal.

Three-dimensional oscillatory convection of LiCaAlF6 melts in Czochralski crystal growth

Abstract Three-dimensional (3D) unsteady mixed thermal buoyancy, Marangoni and forced convection of LiCaAlF 6 (LiCAF) melts (Prandtl number Pr ≈1.4) are investigated numerically for model set up typically for Czochralski crystal growth. With increasing crystal rotation rate, convection evolves from steady axisymmetric to three-dimensional oscillatory convection with varying spatio-temporal features. The details of the oscillatory convection structures are presented.

Global simulation of a silicon Czochralski furnace in an axial magnetic field

Control of melt flow in crystal growth process by application of the magnetic field is a practical technique for silicon single crystals. In order to understand the influence of axial magnetic field on the silicon melt flow and oxygen transport in a silicon Czochralski (Cz) furnace, a set of global numerical simulations was conducted using the finite-element method for the magnetic field strength from 0 to 0.3 T, the crystal rotation rates from 0 to 30 rpm and the crucible counter-rotation rates from 0 to −15 rpm. It was assumed that the flow was axisymmetric laminar in both the melt and the gas, the melt was incompressible and a constant temperature was imposed on the outer wall of the Cz furnace. The results indicate significantly different flow patterns, thermal and oxygen concentration fields in the melt pool when a uniform axial magnetic field is applied.

Control of the facet plane formation on solid–liquid interface of LGS

The correlation of the facet plane that formed on the solid–liquid interface of Langasite (La 3Ga 5SiO 14) single crystals grown by the Czochralski method with its growth conditions was investigated. The crystal homogeneity was characterized by measuring leaky-surface acoustic wave velocity and X-ray topography. In [ 0 0 0 1 ] growth, ( 1 0 1 ̄ 0 ) and ( 0 0 0 1 ) facets were formed at the solid–liquid interface. The former often causes an alteration growth in its conical part, and the latter generate a core dislocation that deteriorates the crystal homogeneity. We were able to reduce these crystal defects by controlling the growth conditions, such as the temperature gradient at the melt surface along the radial direction ( T g) or the crystal-rotation rate ( R c). When T g became higher, the alteration caused by nucleation in a super-cooling melt in contact with a ( 1 0 1 ̄ 0 ) facet was reduced. Controlling R c enabled core dislocations to be reduced.

Experimental Study of Interface Inversion of Tb3ScxAl5-xO12 Single Crystals Grown by the Czochralski Method

Thermal conditions and rotation rate were examined experimentally for obtaining a flat interface growth of high melting-point oxide (Tb 3 Sc x Al 5-x O 12 - TSAG) by the Czochralski method. The critical crystal rotation rate can be significantly reduced, of about twice at low and very low temperature gradients comparing to medium temperature gradients in the melt and surroundings of the crystal. The interface shape of TSAG crystals is not very sensitive on crystal rotation rate at small rotations and becomes very sensitive at higher rotations, when the interface transition takes place. The range of crystal rotation rates during the interface transition from convex to concave decreases with a decrease of temperature gradients. At low temperature gradients interface inversion crystals takes place in very narrow range of rotation rates, which does not allow one to growth such crystals with the flat interface. Even changing crystal rotation rate during the growth process in a suitable manner did not prevent the interface inversion from convex to concave and thus did not allow to obtain and maintain the flat interface.

Controlling transport phenomena in the Czochralski crystal growth process

A mathematical formulation and computational techniques are presented to describe optimal control and design strategies for the suppression of turbulent motions in the melt and the minimization of temperature gradients in the crystal in Czochralski crystal growth processes. The methodologies developed can be used to test control mechanisms, design parameters, and optimization objectives to determine their effectiveness in improving the processes. They can also be used to effect such improvements by systematically determining optimal values of the design parameters. The controls or design parameters considered include applied magnetic fields, temperature gradients along the side wall of the crucible, and crucible and crystal rotation rates. The results show that applied magnetic fields can be very effective in reducing velocity perturbations in the melt, while side wall temperature gradients are less effective and crucible and crystal rotation rates are ineffective. The results also show that applied magnetic field and crucible and rotation rates are ineffective in reducing temperature gradients in the crystal or in the melt.

Crystal growth and optical assessment of Nd 3+ : GdAl 3(BO 3) 4 crystal

This paper reports the high-temperature top-seeded solution growth (TSSG) of large single crystal of Nd 3+-doped GdAl 3(BO 3) 4 from a K 2Mo 3O 10-LiF flux cooled at a rate of 2 K/day and using a crystal rotation rate of 4.5 rpm. The polarized optical absorption and fluorescence spectra of Nd 3+ : GdAl 3(BO 3) 4 crystal have been investigated. Polarized absorption cross sections are 4.3×10 −20 and 2.6×10 −20 cm 2 with band widths of 8.7 and 6.1 nm for σ- and π-polarization, respectively. The emission cross sections are 6.3×10 −19 and 6.0×10 −19 cm 2 for σ- and π-polarization, respectively, at 1062 nm corresponding to the 4F 3/2→ 4I 11/2 transition. The fluorescence lifetime is 54.3 and 57 μs at 300 and 20 K, respectively.

Effect of crystal rotation on the three-dimensional mixed convection in the oxide melt for Czochralski growth

The three-dimensional flow field in the melt has significant effect on the quality and stability of the growing oxide single crystal by the Czochralski method. The flow field exhibits different characteristics in terms of periodic and non-periodic three-dimensional nature depending on the process parameters. In this paper, the role of crystal rotation rate on the characteristics of the three-dimensional turbulent flow field in the oxide melt has been studied. Based on a block-structured finite-volume Navier–Stokes solver, quasi-direct numerical simulations were carried out to analyze the flow field in a crucible with different crystal rotation rates from 0.0 to 6.0 rpm. The crystal rotation rate has been found to be a sensitive parameter and has a significant effect on the characteristics of the flow field. While the flow field with a crystal rotation rate of 4.0 rpm (Gr/Re 2=343) attains a non-periodic state from the initial periodic state, the flow field with a crystal rotation rate of 6.0 rpm (Gr/Re 2=192) remains always periodic. It was shown that the criterion of (Gr/Re 2<235) as recently proposed by the authors [S. Enger, B. Basu, M. Breuer, F. Durst, J. Crystal Growth 219 (2000) 144] could be used to ensure periodic thermal and flow field in the melt during the growth of oxide crystals.

Numerical 3D study of FZ growth: dependence on growth parameters and melt instability

Three-dimensional modelling of the floating zone (needle-eye) crystal growth process is carried out to analyse numerically the stability of the melt flow and the influence of the crystal rotation rate and inductor slit width on the 3D flow field and on the grown crystal resistivity. The unsteadiness of the melt is simulated and it is found that for the considered growth parameters a steady-state flow can be a reasonable approximation to the unsteady melt motion. The parametric studies have shown that increasing the rotation rate essentially changes the flow pattern and weakens the rotational striations, while the inductor slit width has a more local influence on these characteristics.

F208 小型シリコンCZ炉の総合解析(オーガナイズドセッション17 : 材料およびデバイス製造の熱工学)

The influence of crystal and crucible rotation on the silicon melt flow and oxygen transport in a small Czochralski (Cz) furnace is investigated by global numerical simulation for crystal rotation rates from 0 to 20rpm and for crucible counter-rotation rates from 0 to 2.5rpm. Results show that the rotations give significant effects on melt flow and oxygen transport. Effects of rotation rates on oxygen concentration distribution on the melt/crystal and melt/gas interfaces are examined.

Growth of βII-Li3VO4 single crystals by the heater-in-zone zone-melting method using a traveling solvent of LiVO3

Low-form (βII-) Li3VO4 single crystals have successfully been grown by the heater-in-zone zone-melting method using a traveling solvent of LiVO3. The as-grown crystals are transparent and have no cracks or bubble inclusions. To prevent the crystals from cracking, the temperature of the heater is set to below 700°C. The growth rate must be less than 0.25mm/h and the crystal rotation rate more than 30rpm in order to eliminate bubble formation. The formation of low-angle grain boundaries is effectively suppressed by growing the crystals along the [001] direction. The emission of green light from the as-grown βII-Li3VO4 single crystal is observed by irradiation with a Nd:YAG laser.

Temperature field simulation and correlation to the structural quality of semi-insulating GaAs crystals grown by the vapour pressure controlled Czochralski method (VCz)

Recent results of global thermal field modelling using the software programs CrysVUN++ and STHAMAS are presented for 3- and 4-inch VCz SI GaAs growth assemblies. For the first time global simulations including the gas and melt convection in a VCz arrangement are shown. In contrast to conventional LEC the impact of gas convection on the temperature distribution in the growing crystal is not dominant in the VCz case. Contrary to that melt convection cannot be neglected and needs to be controlled by crucible and crystal rotation rates. Simulations were used to optimise the temperature fields in the VCz arrangements and thus, to reduce the von Mises stress within the growing crystal. Doing this, the EPD could be reduced by approximately one order of magnitude compared to conventional LEC. Minimum EPD's were found to be in the range of some 10 3 cm −2 for 4″ crystals. The observed nearly flat (slightly convex) interfaces are in agreement with the simulations. The achieved good radial uniformity of the carbon incorporation and electrical parameters is due to the improved thermal boundary conditions.

Growth of a 3″ langasite crystal with clear faceting

A macrodefect-free langasite (La 3Ga 5SiO 14) crystal 3" in diameter was grown along its Z-axis by the Czochralski technique. The grown crystal showed clear faceting on (0 0 0 1) and (0 1 1̄ 0) faces, forming a hexagonal column shape, and it had minor faceting on (0 1 1̄ 1) in the conical part, making a stepped hexagonal pyramid. Thermal treatment of the melt and uniform interface shape are important to the growth of langasite with stable facet development. Interface instability occurred during the formation of the conical portion of the crystal under a high crystal rotation rate. The homogeneity in composition was investigated two dimensionally by the X-ray Bond diffraction method. The congruent melt composition for langasite is also discussed relative to the stoichiometric composition.

非線形光学結晶CsB3O5の育成と評価

Single crystal of nonlinear optical crystal CsB3O5 (CBO) which has good properties for deep ultra-violet (UV) generation was investigated, and some optical properties were measured for the first time. In this report, the growth conditions were experimentally established. Single crystals with good optical homogeneity were obtained when the rotation rate of crystal was faster than 30 rpm. This phenomenon was explained by considering growth phenomena of segregation effect. Large single crystals were grown by a top seeded solution growth with the established conditions. The size of one of these was a×b×c=45×41×44mm3. Optical absorption edges at UV and IR regions were measured quantitatively to be 168 nm and 3400 nm.

Effect of internal radiative heat transfer on transition of flow modes in CZ oxide melt

A numerical study was carried out to investigate the effect of internal radiative heat transfer on the transition of flow modes in an axisymmetric Czochralski oxide melt. Results were obtained over a wide range of absorption coefficients of the melt and the crystal rotation rates for two different Marangoni numbers, 0 and 2.82×10 4. As a result, it was found that melt convection with only the steady flow mode exists in the optically thicker melt, while a transition from the steady flow mode to the axisymmetric oscillatory one occurs in the opaque and optically thinner melt as the crystal rotation rate increases. This flow transition is also affected by the Marangoni effect in the melt.

The Effect of Free Convection on Solid/Liquid Interface in the Czochralski Crystal Growth Method

This paper regards the interaction of free and forced convection in the Czochralski configuration. A relationship between the crystal rotation rate and growth parameters at which the crystallization front remains flat, at which the crystallization front remains almost flat, has been studied. This relationship is compared with experimental data.