Crucible Rotation Research Articles

Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.

Growth of nickel single crystals with a diameter of 8 in. using the Czochralski method

We grew large single crystals of metal nickel with a maximum diameter of 8 in. using the Czochralski (CZ) method. Characteristics of the metal material, namely, the seed elongation and intense cooling radiation at high temperatures during crystal growth, are the main challenges when growing ingots with large diameters. These problems were resolved by optimizing the parameters related to crystal growth, such as reduction of crucible and ingot rotation speed, and adjustment of shoulder formation angle of ingot shape. The produced ingots were confirmed to be single crystals by the Laue back-reflection method. Wafers were cut from single crystal ingots using a multi-wire saw with diamond abrasive grains. A smooth, mirror-like surface was obtained on the wafers by using an ordinary mechanical polishing method. The full width at half maximum values of the X-ray rocking curve of the metal nickel crystal surface significantly depends on the surface treatment method. It was found that ordinary mechanical mirror polishing introduces strain on the surface and non-uniformity of the crystal orientation.

Effect of cusp magnetic field on the turbulent melt flow and crystal/melt interface during large-size Czochralski silicon crystal growth

The influences of cusp magnetic field on the turbulent melt flow and the crystal/melt interface are studied by three-dimensional unsteady simulations for 300 mm industrial Czochralski silicon crystal growth. Detailed comparisons are implemented for the melt flow pattern, temperature and velocity oscillations as well as the crystal/melt interface with and without magnetic field. It is found that the melt flow is complex and irregular in this system, accompanied with rich flow structures and large temperature and velocity fluctuations. Under the application of cusp magnetic field, the turbulent melt flow is significantly inhibited with the simple flow structure as well as the periodic temperature and velocity fluctuations. The anticlockwise periodical flow in the melt induced by cusp magnetic field can help to reduce the impurity in the crystal and suppress the crystal/melt interface deformation. In particular, the thermal waves on the melt free surface are firstly observed with cusp magnetic field for large-size Czochralski silicon crystal growth, traveling in the direction of crucible rotation.

Numerical study of ACRT in the THM growth of CdZnTe crystals

The accelerated crucible rotation technique (ACRT) is a widely used method for the optimization of crystal growth. However, the interactions between the original natural convection in the traveling heater method (THM) and forced convection by ACRT make the flow behavior complicated and also hard to be predicted. With the help of numerical simulation, the effects of different ACRT regimes on flow patterns, growth interface, and temperature gradient during the THM growth are discussed. The simulation results show that there are two kinds of hydrodynamics mechanisms during ACRT, i.e. Ekman flow and centrifugal-force-induced vortex. When a small-rotation ACRT of 2.5 RPM as recommended by classical Ekman flow theory is used, the Ekman flow is too weak to affect the initial natural convection. A counter-rotating vortex arising from the uneven distribution of centrifugal force will be periodically formed in the center, causing a large transient growth rate and a fluctuating temperature gradient. Increasing the rotation rate to 15 RPM, the centrifugal-force-induced vortex disappears and the flow structure is greatly changed under the combined effects of Ekman flow and natural convection. A convex interface is obtained and the transient growth rate is also reduced. Finally, the effect of a large-rotation ACRT of 40 RPM is also discussed.

Effects of different cusp magnetic ratios and crucible rotation conditions on oxygen transport and point defect formation during Cz silicon crystal growth

The effects of different crucible counter- and iso-rotation rates and cusp magnetic ratios (MRs) on the melt flow, temperature, oxygen content, and point defect formation during the growth of a 5-inch diameter silicon crystal are discussed numerically. In cases without a cusp magnetic field (CMF), the oxygen content gets smaller at a low crucible rotation speed than at a high one, for both counter- and iso-rotation conditions. This trend is reversed under a CMF. The flow field is controlled by the crucible rotation rate, the rotation direction between the crucible and the crystal, and the MR. Since the melt flow motion is retarded by the Lorentz force at a high MR, diffusion has a greater effect on oxygen transport in the bulk melt. It promotes the transport of oxygen atoms from the crucible wall towards the melt surface and the growth interface. The point defect density is quite dependent on the thermal field arising from changes in the growth interface shape. Microdefects in the silicon crystal can be reduced in density and enhanced in the radial uniformity using a high crucible iso-rotation rate and high unbalanced MR. A flatter shape of growth interface can be obtained under these growth conditions.

Effect of crucible rotation on the temperature and oxygen distributions in Czochralski grown silicon for photovoltaic applications

Oxygen concentration is sensitive to changes in the rotation rate for Czochralski grown silicon crystals.

Effect of the pulling, crystal and crucible rotation rate on the thermal stress and the melt–crystal interface in the Czochralski growth of germanium crystals

The effect of the pulling rate on the melt–crystal interface shape and melt streamline is investigated.

The influence of crucible and crystal rotation on the hydrodynamics of a melt with a Prandtl number 16 and on heat transfer in the Czochralski method

The effect of crucible rotation on the evolution of the melt flow structure at a Prandtl number 16 on the temperature and velocity fields and on convective heat transfer in the Czochralski method is simulated numerically in the mixed convection regimes at a given crystal rotation rate. The ranges of similarity parameters corresponding to stationary and unsteady melt flows and heat transfer regimes, as well as regimes with the most uniform radial distributions of local heat fluxes are determined. In the initial regime Reynolds, Grashof and Marangoni numbers are set to ReK = 95, Gr = 4870 and Ma = 5835.

Numerical Investigation of Effect of Temperature Profile Imposed on the Crucible Surface on Oxygen Incorporated at the Crystal Melt Interface for 450 mm Diameter Silicon Single Crystal Growth in Presence of CUSP Magnetic Field Using Czochralski Technique

Numerical investigation has been carried out to study the effect of thermal boundary condition on turbulent melt flow and oxygen transfer inside a crucible used to grow 450 mm diameter silicon single crystal using Czochralski method. Two types of thermal boundary conditions, namely, isothermal crucible surface and experimentally measured temperatures on the crucible surface have been imposed on the crucible wall and crucible bottom. Melt motion owing to buoyancy, surface tension variation at the free melt surface as well as crystal and crucible rotation has been considered. Effect of CUSP magnetic field has also been investigated. Melt having aspect ratio of 1 and 0.5, representing high and moderate level of melt inside the crucible have been considered. K-epsilon turbulent model with low Reynolds number formulation has been used for turbulence modelling. Melt motion governed by natural convection, Marangoni convection and crystal as well as crucible rotation shows higher oxygen concentration at melt crystal interface for aspect ratio of 1, when experimental temperature profile is imposed at the crucible wall. For melt aspect ratio of 0.5, natural convection and Marangoni convection dependent melt show higher oxygen concentration for isothermal crucible wall boundary condition. Marangoni convection in absence of rotation of crystal and crucible leads to low oxygen concentration zone near the crystal outer surface, the size of which is larger for melt aspect ratio of 0.5. Maximum turbulent viscosity values for aspect ratio of 1, in case of experimental temperature at the crucible are higher compared to isothermal case, which is just the opposite of the trend for aspect ratio of 0.5. Imposing a CUSP magnetic field leads to similar distribution of turbulent viscosity for both types of thermal boundary conditions, irrespective of the type of thermal boundary condition. Oxygen concentration at the melt crystal interface is found to be higher in presence of CUSP magnetic field. Value of maximum turbulent viscosity for the two boundary condition are similar for melt aspect ratio of 1.0. Crucible surface temperature profile for aspect ratio of 1, on actual melt aspect ratio of 0.5 predicts lower oxygen concentration at melt crystal interface. Values and distribution of turbulent viscosity is however the same for both temperature profiles.

Optimization of the melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process using an artificial neural network and a genetic algorithm

The melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process significantly influence the crystal quality. In this paper, an optimization system with the combination of an artificial neural network and a genetic algorithm is proposed to optimize the growth parameters during the growth process. Flattening the melt/crystal interface and reducing the oxygen concentration along the interface were chosen as the optimization targets. Two important growth parameters, the crystal rotation rate and crucible rotation rate, were chosen as optimization variables. First, a global heat and mass transfer model was developed to simulate the crystal growth process and then tested with experimental data. The verified heat and mass transfer model was then used to train an artificial neural network with the aim of rapidly assessing the complex nonlinear dependence of the interface shape and oxygen concentration on the growth parameters. The trained neural network combined with a genetic algorithm was then used to obtain the optimal growth parameters. Both deflection of the melt/crystal interface and the oxygen concentration along the interface decreased after optimization. Finally, the optimal growth parameters were checked in the heat and mass transfer model to evaluate the performance of the optimization system. The proposed method will also be useful for optimization of other crystal growth processes.

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.

Growth and characterization of room temperature radiation detection material Cd0.95Mg0.05Te

Recently, researchers were interesting in exploring alternative materials for well-studied CdZnTe which was the key material of radiation detection. Cadmium Magnesium Telluride (Cd1-xMgxTe) crystal was regarded as promising one for room temperature X-ray and gamma-ray detectors due to some potential advantages. In this paper, two large-size Cd0.95Mg0.05Te ingots with 30 mm diameter and over 100 mm length were successfully grown by a modified vertical Bridgman method. Two modifications, including Cd excess or Te-rich condition and the accelerated crucible rotation technique (ACRT), were applied in growing process to decrease defects, enhance resistivity and homogenize component distribution. The results indicated that both ingots had a cubic zinc-blende structure. The distribution of Mg element in the ingots along axial direction was very homogeneous. The energy band gap of Cd0.95Mg0.05Te was close to Cd0.9Zn0.1Te. Low density of Te inclusions (103 cm−3 order of magnitudes) and high IR transmittance (over 60%) showed the good crystal quality. Raman scattering spectroscopy also showed a good crystal quality for Cd0.95Mg0.05Te crystals. Thus, Cd0.95Mg0.05Te crystals could be a promising radiation detector material.

Growth of Single-Crystal Cd0.9Zn0.1Te Ingots Using Pressure Controlled Bridgman Method

We report growth of single-crystal Cd0.9Zn0.1Te ingots while using the pressure-controlled Bridgman method. The Cd pressure was controlled during growth to suppress its evaporation from the melt and reduce the size of Te inclusions in the as-grown crystals. The accelerated crucible rotation technique (ACRT) was used to suppress constitutional supercooling. The fast accelerating and slow decelerating rotation speeds were optimized. Two-inch Cd0.9Zn0.1Te single-crystal ingots without grain boundaries or twins were grown reproducibly. Glow discharge mass spectrometry results indicate the effective segregation coefficients of Zn and In dopants are 1.24 and 0.18, respectively. The full width half maximum (FWHM) of X-ray rocking curve was approximately 22.5 ″, and the IR transmittance was approximately 61%, indicating high crystallinity. The mean size of the Te inclusions was approximately 13.4 μm. Single-crystal wafers were cut into 5 × 5 × 2 mm3 slices and then used to fabricate gamma ray detectors. The energy resolution and peak-to-valley ratio maps were constructed while using 59.5 keV gamma ray measurements, which proved the high uniformity of detection performance.

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

This work presented a series of three-dimensional unsteady numerical simulations on the characteristics of the mixed oscillation flows of binary mixture in a Czochralski crystal growth model. The silicon-germanium melt is investigated and the capillary ratio is minus one. The simulation results showed that, for the special capillary ratio, the thermal and solutocapillary forces are imposed in opposite directions and counteract each other. With the effect of buoyancy, the balance between the capillary forces is disturbed. Mixed with the forced convection driven by rotation, the capillary-buoyancy convection is complex. The basic mixed flow streamlines are presented as various rolling cells. The directions of the rolls are dependent on the combinations of surface and body forces. With the increase of temperature gradient, the basic flow stability is broken, and the oscillations occur. The crucible rotation has an effective influence on the stability enhancement. However, affected by the crystal rotation, the critical condition experiences an increase to a turning point, and then undergoes a sharp reduction to zero. Once the instability is incubated, the surface oscillations are analyzed. For the three-dimensional steady flow, only spatial oscillations are observed circumferentially, and the surface patterns of spokes, rosebud, and pulsating ring are obtained. For the unsteady oscillation flow, the spiral hydrosoultal waves, rotating waves, and superimposition of spirals and spokes are observed, and the oscillation behaviors are also discussed.

Improved Nd distribution in Czochralski grown YAG crystals by implementation of the accelerated crucible rotation technique

Nd:YAG is a well-known laser material typically grown from the melt using the Czochralski (CZ) method, and like many other doped materials grown from the melt, it suffers from dopant segregation, giving an average Nd concentration in the crystal (Nd%) far less than that in the melt, with Nd variation along the growth axis. Here, the Nd segregation issue is addressed by the successful implementation of the Accelerated Crucible Rotation Technique (ACRT) with CZ. Compared to conventional CZ, ACRT provided improved Nd uniformity, higher Nd incorporation, and control of Nd% along the growth axis, even achieving higher Nd% in the crystal than the initial Nd from the overall melt. ACRT also affects the solid/liquid interface shape and thus the radial segregation. It is thus shown that ACRT and the mixing it provides is promising for achieving unconventional dopant profiles in CZ crystals.

Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method

Effect of different crucible rotations on the silicon melt surface in Czochralski furnace is studied using an image-based measurement system. The mathematical model on the relationship between the target feature in the image and the melt level is discussed. A new improved approach based on Otsu method is applied to segment the feature area from the imperfect image due to uneven illumination. The calibration experiment indicates that the measurement system has resolution of 0.00371 mm. The effectiveness experiment shows that system measurements are very accurate. The surfaces of silicon melt with different crucible rotation rates are measured and analyzed. The result reveals that the melt surface becomes a paraboloid shape with crucible rotation. Moreover, crucible rotations cause more fluctuation on the melt surface under less silicon melt mass. This work may provide us with an effective method to monitor the melt surface change during crystal growth.

Формирование анодной области плазменной дуги на вращающемся графитовом тигле

Formation of anode spots on rotating graphite crucible in the plasma arc furnace was investigated. The size and temperatures of the spots were determined by means of photographs and optical pyrometer. Composition of the plasma in anode spot region has been calculated. Cylindrical crucible of 100 mm in diameter with an axial hole of 40 mm in diameter and 28 mm in depth was rotated with the speed of ~100 rpm. Cylindrical cathode of 50 mm in diameter had an axial channel of 24 mm in diameter. Argon was fed through the channel as plasma forming gas. Crucible and cathode were located in the steel water cooled chamber with a volume of 150 liters. The arc was several centimeters long, arc current was 560-630 A. It was shown experimentally that 23-25 kW argon plasma arc can forms contracted or diffuse anode spot. The current density of contracted spot is 1800 A/cm2, while that of diffuse spot is ~250 A/cm2. Contracted spot formation occurs on a cold crucible and accompanied by intensive evaporation of graphite in a spot region. The carbon vapor decreased ionization potential of plasma near the anode and promoted contraction. A uniform heating of the hole in crucible up to 2700 K is needed for transformation of the contracted spot into diffuse one. Such heating was attained by rotation of crucible. Thermal isolation of crucible also promotes diffuse spot formation. Poisson’s equation was solved, and the voltage falls in space charge zones were calculated for contracted and diffuse spots as 10.7 and 1.5 V respectively. It was assumed that the lesser voltage fall promotes the diffuse spot formation.

Numerical simulation and global heat transfer computations of thermoelastic stress in Cz silicon crystal

AbstractGlobal heat transfer computations were performed for the investigation of thermal stress in a Czochralski silicon crystal. The temperature distribution, thermal stress properties including maximum shear stress and von Mises stress distributions at two different axial crystal positions have been investigated with the help of heat transfer simulations. By analyzing the obtained results, the thermal stress maxima during the Czochralski growth process can be controlled by applying optimal crystal rotation of 8 rpm and counter crucible rotations of 5 and 15 rpm for a crystal position of 100 mm and 300 mm. This shows that by applying optimal crystal and counter crucible rotations throughout the growth process, the thermal stress maxima of a growing crystal can be reduced.

Effect of crucible rotation on the distribution of carbon, oxygen and nitrogen impurities in multi-crystalline silicon grown by directional solidification process – a numerical simulation analysis

Simulation analysis is done to understand the effect of crucible rotation on the distribution of carbon, nitrogen and oxygen impurities in directionally solidified mc-silicon ingot. Based on their segregation coefficient and solubility, these non-metallic impurities get incorporated into mc-silicon ingot from feedstock and different parts of the furnace. The temperature gradient in silicon melt causes irregular melt convection and that is minimized by applying rotation on the crucible. In the present work, we have applied spin up crucible rotation with different rotation rates such as 3, 6, 9, 12 and 15 rpm from beginning to the end of the growth and distribution of impurities was analyzed. Also, the segregation, axial and radial distribution of non-metallic impurities in silicon ingot for different rpm was investigated.

The influence mechanism of melt flow instability on the temperature fluctuation on the crystal/melt interface during Czochralski silicon crystal growth

The temperature fluctuation on the crystal/melt interface during Czochralski silicon crystal growth is firstly investigated with LES method based on the relationship between kinetic undercooling and growth rate. The effects of crystal and crucible rotation on the temperature fluctuation are analyzed. The results show that when crystal counter-rotates with crucible, the temperature fluctuations on the interface and that in the melt close to crystal are more intense compared with co-rotation. The characteristic frequencies of temperature fluctuations on the interface and that in the melt are identical for counter-rotation. However, this consistency of the characteristic frequencies is not obvious for co-rotation. In particular, the temperature fluctuations on the interface are about 0.4 K and 0.7 K for co-rotation and counter-rotation, respectively. Importantly, the influence mechanism of melt flow instability on temperature fluctuation is clarified by the analyses of cross-correlation and local convective heat transport.