Influence of Local Magnetic Fields on P-Doped Si Floating Zone Melting Crystal Growth in Microgravity

A two-dimensional axisymmetric numerical model is presented to study the influence of local magnetic fields on P-doped Si floating zone melting crystal growth in microgravity. The model is developed based on the finite difference method in a boundary-fitted curvilinear coordinate system. Extensive numerical simulations are carried out, and parameters studied include the curved growth interface shape and the magnetic field configurations. Computed results show that the local magnetic field is more effective in reducing the impurity concentration nonuniformity at the growth interface in comparison with the longitudinal magnetic field. Moreover, the curved growth interface causes more serious impurity concentration nonuniformity at the growth interface than the case with a planar growth interface.

Effect of non-uniform magnetic field on crystal growth by floating-zone method in microgravity

The magnetic damping effect of the non-uniform magnetic field on the floating-zone crystal growth process in microgravity is studied by numerical simulation. The results show that the non-uniform magnetic field with designed configuration can effectively reduce the flow near the free surface and then in the melt zone. At the same time, the designed magnetic field can improve the impurity concentration non-uniformity along the solidification interface. The primary principles of the magnetic field configuration design are also discussed.

Magnetic field design for floating zone crystal growth

The magnetic fields produced by electrical coils are designed for P-doped Si crystal growth in a floating full zone in microgravity environment. The fields are designed specially to reduce the how near the free surface and then in the melt zone by adjusting the coil positions near the melt zone. The effects of the designed magnetic fields on reducing the Row velocity and the non-uniformity of the concentration distribution in the melt zone are better than those of the case of a uniform longitudinal magnetic field, obtained by numerical simulation. It is expected to improve the radial macro-segregation and reduce the convection in the crystal growth at the same time by using the designed magnetic field.

Influence of convections on dopant segregation in floating-zone crystal-growth system

The steady and axisymmetric crystal growth process of floating zone model was studied numerically to concern with the influence of convection and phase change on effective segregation. An iteration method of numerical simulation considering both thermocapillary and buoyancy effects for GaAs crystal growth gave the effective segregation coefficient, which was compared with the space experiment of GaAs on board the Chinese recoverable satellite. The calculated segregation coefficient of a two-dimensional model was found to be smaller than the one suggested by space experiment with the simplified assumption of an one-dimensional model.

Influence of low-gravity level on crystal-growth in floating-zone

The influence of low gravity level on crystal growth in the floating zone, which involves thermocapillary convection, phase change convection, thermal and solutal diffusion, is investigated numerically by a finite element method for the silicon crystal growth process. The velocity, temperature, concentration fields and phase change interfaces depending on heating temperature and growth rates are analyzed. The influence of low gravity level on the concentration is studied especially. The results show that the non-uniformities of concentration are about 10(-3) for growth rate nu(p) = 5.12 x 10(-8) m/s, 10(-2) for nu(p) = 5.12 x 10(-7) m/s and relatively larger for larger growth rate in the gravity level g = 0-9.8 m/s2. The thermocapillary effect is strong in comparison with the Bridgman system, and the level of low gravity is relatively insensitive for lower growth rates.

Crystal-growth in floating zone with phase-change and thermosolutal convections

Floating zone crystal growth in microgravity environment is investigated numerically by a finite element method for semiconductor growth processing, which involves thermocapillary convection, phase change convection, thermal diffusion and solutal diffusion. The configurations of phase change interfaces and distributions of velocity, temperature and concentration fields are analyzed for typical conditions of pulling rates and segregation coefficients. The influence of phase change convection on the distribution of concentration is studied in detail. The results show that the thermocapillary convection plays an important role in mixing up the melt with dopant. The deformations of phase change interfaces by thermal convection-diffusion and pulling rods make larger variation of concentration field in comparison with the case of plane interfaces.

Hydrostatic instabilities in floating zone cristal growth process

If only Fluid Mechanics aspects are considered, the configuration appearing in the floating zone technique for crystal growth can be modelled as a mass of liquid spanning between two solid rods. Besides, if now the influence of temperature gradients and heat flow are not considered, the simplest fluid model consists of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart: the so called liquid bridge. As it is well known, if both supporting disks were parallel, coaxial and of the same diameter, 2R, the volume of liquid, V, were equal to that of a cylinder of the same L and R (V=KR~L) and no body forces were acting on the liquid column, the fluid configuration (under these conditions of cylindrical shape) will become unstable when the distance between the disks equals the length of the circumference of the supporting disks (L=2KR, the so-called Rayleigh stability limit). One should be aware that the Rayleigh stability limit can be dramatically modified when the geometry differs from the above described cylinder (due to having non-coaxial disks, different diameter disks, liquid volume different from the cylindrical one, etc) or when other external effects like accelerations either axial or lateral are considered. In this paper the stability limits of liquid bridges considering different types of perturbations are reviewed.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .1. Experiments

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was experimentally studied, and discussions were concentrated on the influence of liquid bridge volume on the onset of oscillation. Distributions of critical applied temperature difference and frequency depending on the volume of the liquid bridge were obtained, and there was a gap range of liquid volume which separated the curve of marginal stability into two parts for fixed rod diameter and aspect ratio. The results imply that the volume of the liquid bridge is a sensitive critical parameter for the onset of oscillation. The implication on the instability is also discussed in the present paper.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .2. Numerical-simulation

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was studied numerically for an unsteady and two-dimensional model, and studies were concentrated on the influence of liquid bridge volume on the onset of oscillation in comparison with the experimental results in the Paper I. The numerical results agree with the experimental ones presented in the previous paper, in which the distributions of critical applied temperature difference depending on the volume of liquid bridge and a gap range of liquid volume in marginal stability curve were obtained.

Coupling of melting-solidification phase-change convection with floating-zone convection under microgravity

A finite element algorithm is used to analyze the process of floating zone crystal growth under microgravity. The effect of phase change convection coupled with surface tension convection is considered. The results show that the rate of crystal growth is very important. The single-crystal-melt interface is steeper than the feed-melt interface during the process of crystal growth. When the rate exceeds a critical value, the Marangoni vortex near the feed-melt interface will become so large that a secondary vortex will exist.

Floating zone convection

The microgravity research, as a branch of the advanced sciences and a spe- cialized field of high technology, has been made in China since the late 1980's. The research group investigating microgravity fluid physics consisted of our col- leagues and the authors in the Institute of Mechanics of the Chinese Academy of Sciences (CAS), and we pay special attention to the floating zone convection as our first research priority. Now, the research group has expanded and is a part of the National Microgravity Laboratory of the CAS, and the research fields have been extended to include more subjects related to microgravity science. Howev- er, the floating zone convection is still an important topic that greatly holds our research interests.

Microstructural and mechanical study of AL2O3/Er3Al5O12 eutectic rods grown by the laser floating zone method

Eutectic rods of Al2O3–Er3Al5O12 were grown by directional solidification using the laser-heated floating zone method at rates in the range 25–1500 mm/h. Their microstructure and mechanical properties (hardness, toughness and strength) were investigated as a function of the growth rate. A homogeneous and interpenetrated microstructure was found in most cases, and interphase spacing decreased with growth rate following the Hunt–Jackson law. Hardness increased slightly as the interphase spacing decreased while toughness was low and independent of the microstructure. The rods presented very high bending strength as a result of the homogeneous microstructure, and their strength increased rapidly as the interphase spacing decreased, reaching a maximum of 2.7 GPa for the rods grown at 750 mm/h. The bending strength remained constant up to 1300 K and decreased above this temperature. The relationship between the microstructure and the mechanical properties was established from the analysis of the microstructure and of the fracture mechanisms

On the structure of the floating zone in melting

Floating zone melting is used in crystal growth and purification of high melting materials. The use of a reduced gravity environment will remove the constraint imposed on the length of the zone by the hydrostatic pressure. The equilibrium of the fioatmg zone may involve, (1)Hydrostatic forces, when the zone rotates as a whole. (2)Convective driving forces, when the zone is stationary but fluid property gradients appear.(3) Hydrodynamic forces, when some parts of the zone are set into motion with respect to others. The last effects are considered in this paper. The flow pattern of a floating zone held between two discs in relative motion is complicated, and thence the solution of the problem is difficult even assuming a constant property-newtonian liquid Nevertheless, when a small parameter appears m the problem, the complete flow field can be split into zones where simple solutions are found. To illustrate this approach, the spin up from rest of an initially cylindrical floating zone is considered with detail. Here the small parameter is the time elapsed from the impulsive starting of motion. Since the problem which has been considered, as well as some others which can be tackled by use of similar methods, concern the viscous layer close to either plate, they can be simulated experimentally in the ground laboratory with short floating zones. Procedures to produce these zones are indicated.

Mechanical properties up to 1900 K of Al2O3/Er3Al5O12/ZrO2 eutectic ceramics grown by the laser floating zone method

Directionally solidified Al2O3–Er3Al5O12–ZrO2 eutectic rods were processed using the laser floating zone method at growth rates of 25, 350and 750 mm/h to obtain microstructures with different domain size. The mechanical properties were investigated as a function of the processing rate. The hardness, 15.6 GPa, and the fracture toughness, 4 MPa m1/2, obtained from Vickers indentation at room temperature were practically independent of the size of the eutectic phases. However, the flexural strength increased as the domain size decreased, reaching outstanding strength values close to 3 GPa in the samples grown at 750 mm/h. A high retention of the flexural strength was observed up to 1500 K in the materials processed at 25 and 350 mm/h, while superplastic behaviour was observed at 1700 K in the eutectic rods solidified at the highest rate of 750 mm/h

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection III. Three-dimensional model

An unsteady and three-dimensional model of the floating-half-zone convection on the ground is studied by the direct numerical simulation for the medium of 10 cSt silicon oil, and the influence of the liquid bridge volume on the critical applied temperature difference is especially discussed. The marginal curves for the onset of oscillation are separated into two branches related, respectively, to the slender liquid bridge and the fat liquid bridge. The oscillatory features of the floating-half-zone convection are also discussed.