Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

In this paper, the role of seed rotation on the characteristics of the two‐dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two‐dimensional quasi‐steady state numerical simulations were carried out to analyze the seed‐melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ω_seed = 5‐30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed‐melt interface during the seeding process. The seed‐melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed‐melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed‐melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ω_seed) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamics of layer growth and consequences for protein crystal perfection

In situ high-resolution optical interferometry of lysozyme crystal growth reveals that under steady external conditions, the local growth rate R, vicinal slope p and step velocity are not steady but fluctuate by several times their average values. The variations in p, which is proportional to the local step density, indicate that these fluctuations occur through the dynamic formation of step bunches. Our previous work with unstirred solutions has shown that the fluctuation amplitude of R increases with supersaturation and crystal size (Vekilov et al., Phys. Rev. E 54 (1996) 6650). Based on scaling arguments and numerical simulations, we have argued that the fluctuations are the response of the coupled bulk transport and nonlinear interface kinetics to finite amplitude perturbations provided by the intrinsically unsteady step generation. In this paper, we emphasize the recently discovered spatio-temporal correlation between the sequence of moving step bunches and striations (compositional variations) in the crystal, visualized by polarized-light microscopy. Hence, these unsteady kinetics have detrimental effects on the perfection of the crystals, and means to reduce and eliminate them should be sought. To this end, based on the above conclusion as to the mechanism of the kinetic unsteadiness, we accelerated the bulk transport towards the interface by forced solution flow. We found that this results in lower fluctuation amplitudes. This observation confirms that the system-dependent kinetic Peclet number, Pe_k, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe_k can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities. Interestingly, on further increase of the solution flow velocities >500 μm/s, the fluctuation amplitudes in R increased again, while the average growth rate decreased. At low supersaturations, this leads to growth cessation. The growth instability, deceleration and cessation were immediately reversible upon reduction of the flow velocity. When solutions, intentionally contaminated with ∼1% of covalent lysozyme dimer were used, these undesirable phenomena occurred at about half the flow rates required in pure solutions. Thus, we conclude that enhanced convective supply of impurities to the interface causes an increase in step-bunching related defects, growth deceleration and, in some cases, cessation. Finally, we correlate the “slow protein crystal growth” to step bunch formation. We show that in the absence of significant step density variations, the kinetic coefficient for step propagation is as high as 4×10⁻³ cm/s, which is 1–2 orders of magnitude higher than the previously determined, apparent values for any protein.     

Production of sapphire tubes for high-pressure sodium lamps using the stepanov method at high rates of growth

The process of the Stepanov growth of sapphire tubes is studied at the growth rates up to 20 mm · min⁻¹ in a Mo crucible with graphite succeptor. It is established that the main factor preventing the production of high-quality samples is contamination of the melt due to the gas transport reactions the growth chamber atmosphere and formation of oversaturated carbon solid solution in the Al₂O₃ matrix. The decomposition of this solid solution gives rise to the second-phase-particle precipitations. The production of highquality sapphire tubes at the growth rates up to 20 mm · min⁻¹ is possible with a careful elimination of water vapours and oxygen from the growth chamber atmosphere.     

Effect of ultrasound on the growth striation and electrical properties of Ga<Subscript>0.03</Subscript>In<Subscript>0.97</Subscript>Sb single crystals

The growth striation of impurity segregation and electrical properties of Ga_0.03In_0.97Sb single crystals grown by the Czochralski method in an ultrasonic field have been investigated. It is established that ultrasonic irradiation of the melt during growth significantly decreases the growth striation (in particular, it eliminates striations spaced at a distance of more than 14 μm). The Ga_0.03In_0.97Sb single crystals grown in an ultrasonic field had a higher charge-carrier mobility and thermoelectric power in comparison with the single crystals grown without ultrasound.     

Effect of NH3 flow rate on m-plane GaN growth on m-plane SiC by metalorganic chemical vapor deposition

This paper reports a study of the effect of NH₃ flow rate on m-plane GaN growth on m-plane SiC with an AlN buffer layer. It is found that a reduced NH₃ flow rate during m-plane GaN growth can greatly improve the recovery of in situ optical reflectance and the surface morphology, and narrow down the on-axis (1 0 1¯ 0) X-ray rocking curve (XRC) measured along the in-plane a-axis. The surface striation along the in-plane a-axis, a result of GaN island coalescence along the in-plane c-axis, strongly depends on the NH₃ flow rate, an observation consistent with our recent study of kinetic Wulff plots. The pronounced broadening of the (1 0 1¯ 0) XRC measured along the c-axis is attributed to the limited lateral coherence length of GaN domains along the c-axis, due to the presence of a high density of basal-plane stacking faults, most of which are formed at the GaN/AlN interface, according to transmission electron microscopy.     

The Characteristics of GaP Window Layer Grown by Indium‐added Liquid Phase Epitaxy

The effects of added Indium on the growth characteristics of GaP were systematically studied using conventional liquid phase epitaxy technique with Ga‐rich GaP source melt. The GaP growth rate uniformly increase with the source melt of increasing Indium addition against Gallium solvent. These epilayers have mirror‐like surface morphology examined by optical microscope except several grown films with large amount of Indium addition meet a terrible interface. The surface morphologies examined by AFM showed the ripples in samples of R_0.05 and R_0.4 and distinct islands with elliptical base shape in the sample of R_0.7 (R‐In ratio). The epitaxial layer with incorporation of Indium addition during growth had good performance on the carrier concentrations and resistivity. The composition of compound semiconductor become to InGaP at higher amount of In addition to Ga was examined by double‐crystal X‐ray diffraction and the distribution of Indium examined by SIMS also provided the evidences in sample of R_0.7.     

LPE growth of YLaTm and YLaEu garnet films

The growth of films of the composition Y_3?(x+yLa_xR_yFe_5?zGa_zO₁₂, where R = Tm or Eu, on GGG substrates by liquid phase epitaxy from a PbO-B₂O₃ fluxed melt is described. Highly uniform, low defect density films have been grown by means of horizontal dipping using intermittent substrate rotation in conjunction with a novel substrate holder. A furnace with three separate temperature zones was used to optimize the vertical temperature profile. Incorporation of La into the films allows compositions containing Tm to be made whose lattice parameters are matched to GGG and compositions which contain Eu to be made with smaller Eu concentrations than were previously possible. The compositions grown, which contain only trivalent cations, exhibit growth induced anisotropy, high mobility, low coercivity, and sufficient magnetostriction to allow ion implantation to effectively suppress hard bubble formation. Detailed measurements of saturation temperature as a function of oxide concentration show that the La ion contributes differently to the garnet phase than do other commonly used rare earth cations. The kinetics of melt equilibration have been studied and procedures to equilibrate the melt to ensure reproducible film growth are described. Electron microprobe analysis has been used to determine the La distribution coefficient as a function of La concentration, the growth rate of the film, and the melt temperature.     

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

Heat 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)     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1: non‐rotating seed

For the seeding process of oxide Czochralski crystal growth, the flow and temperature field of the system as well as the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used initially in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and non‐rotating seed crystal. At first the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF coil was calculated. Using this heat source the fluid flow and temperature field were determined in the whole system. We have considered two cases with respect to the seed position: (1) before and (2) after seed touch with the melt. It was observed that in the case of no seed rotation (ω_seed = 0), the flow pattern in the bulk melt consists of a single circulation of a slow moving fluid. In the gas domain, there are different types of flow motion related to different positions of the seed crystal. In the case of touched seed, the seed‐melt interface has a deep conic shape towards the melt. It was shown that an active afterheater and its location with respect to the crucible, influences markedly the temperature and flow field of the gas phase in the system and partly in the melt. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of Solid and Liquid Inclusions on Morphology of Crystallization Front

The interaction between crystallization front and solid particles was studied for substances characterized by the normal growth mechanism (continuous growth). It has been measured the critical velocity below which the particle of radius R is repulsed by moving interface and above it is captured. It has been shown that critical velocity is proportional to R⁻(1.4–1.8) what satisfactorily agrees with Chernov-Temkin's theory. Data have been received about change of interface morphology at capture of solid particles for growth from pure and impurity-contained melt. The dendrites have been found to split at interaction with particles and concentration inhomogeneities. Taking for example Al-Cu alloy, possibility has been shown to disperse the dendritic structure by formation concentration inhomogeneities in the melt.     

Effective convection coefficient for porous interface and solute segregation

Convective heat and mass transfer coefficients are used to calculate the rate at which convection sweeps heat and mass away from the interface. Convection in melt growth is driven by various forces, and the resulting convoluted flows are laminar or turbulent. Furthermore, cross-flow through the “porous” interface has a profound effect on convection. Thus, a general effective coefficient (h_eff ), which accounts for: (i) uniform flow “suction” through the porous interface, (ii) forced and/or natural convection, (iii) laminar or turbulent flow, and (iv) finite Schmidt numbers, is derived. Focusing next on solute segregation, mass conservation is used to derive a simple equation for k_eff (effective segregation coefficient) as a function of h_eff. Here, h_eff is an input, which provides the rate at which convection sweeps the rejected solute away from the interface.From the general expression, even simpler expressions are developed for restricted range of conditions, e.g., Czochralski growth under forced laminar convection (no natural convection or turbulence). h_eff utilizes numerous established correlations, all developed for impermeable solids.     

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 (Tb₃Sc_xAl_5‐xO₁₂ ‐ 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.     

Characterization of large‐sized Nd:YAG single crystals grown by horizontal directional solidification

Nd³⁺‐doped Y₃Al₅O₁₂ single crystals have been grown by the horizontal directional solidification (HDS) method in different thermal zone. The Grashof (G_r), Prandtl (P_r), Marangoni (M_a) and Rayleigh (R_a) numbers of melt in HDS system have been discussed for our experimental system to understand the mechanism of melt flow patterns and concentration gradient of dopant. The concentration gradient of Nd³⁺ ions was explained with melt flow processes during crystal growth in different thermal zone, and results indicated that high growth temperature will be helpful for uniformity of dopant in HDS‐grown single crystal. The main microscopic growth defects such as bubbles and irregular inclusions in HDS‐grown Nd:YAG crystals were observed, and the causes were discussed as well. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigations of the crystal growth of PbMoO4 by the Czochralski method

The thermal conditions at the liquid/solid interface are characterized by temperature measurements in the melt and on the growing crystal with 〈001〉-seed orientation. The thermal boundary layer was determined, from which the relation of effective thermal conductivity of the liquid and solid phase was found to be λ_l,eff/λ_s,eff = 0.25. The liquid/solid interface is extremly convex towards the melt and has a conical shape. When the crystal diameter reaches a certain value the cone was truncated with the formation of a facet in the centre. This typical interface shape is mainly the result of a difference between the effective thermal conductivity of melt and crystal.     

Effect of small copper additives on the growth of gallium crystals from a melt

It is shown in the present work that copper additives influence substantially the growth of Ga crystals from a melt which is expressed in different ways, depending on the impurity concentration. With rising copper concentrations we observed a substantial retarding in the growth rates as compared with deformed pure Ga crystals, and a change of the mechanism of growth. The results can be explained by a rejection of the impurity by the growing crystal which causes retarding of the growth and with the impurity inclusion like CuGa₂ particles, which gives rise to dislocations, intersecting the growing faces.     

Interfacial stability and grain diameter of the metal phase of directionally solidified Al-Si-type eutectics

The morphology of the solid-liquid interface and the metal phase grain diameter of Al—Si-type eutectics (Al—Si, Ag—Si, Ag—Ge, Zn—Ge) were investigated in the range of a growth rate R = 0.2 … 20 mm/h and of a temperature gradient at the solid-liquid interface G = 2 … 25 K/mm. Three types of interfacial morphologies depending on the G/R ratios were found out. The G/R ratio of the transition from a planar to a nonplanar solid-liquid interface corresponds to the critical G/R|_c ratio, which can be calculated by the criterion of the constitutional undercooling. The grain diameter of the metal phase depends on growth parameters as follows: d_K ∼ R^—rG^—g with r = 0.33 … 0.43 and g = −0.37 … 0.03.     

Interface Dynamics during Indium Antimonide Crystal Growth

Experiments with a stoichiometric InSb compound were first performed at small temperature gradient across the crystal/melt interface of 3 °C/cm and furnace translation velocity, V_frn, of 2 μ/sec. Known growth requirements for quality crystals were confirmed. They are, (1) the interface temperature must be close to the congruent melting temperature and, (2) the interface must be located within the adiabatic zone. These requirements can be obtained only through specific settings of the heater temperatures. An X-ray radioscopic system has been modified to accommodate real-time visualization of the crystal/melt interface during vertical Bridgman-Stockbarger growth of InSb. It is shown that asymmetric temperature settings of the heaters can be advantageously used to minimize defect formation. The interface temperature was assessed indirectly with calibrated outside thermocouples. Optical microscopy and electron microprobe analyses provided feedback on crystalline homogeneity.     

Pattern formation mechanism of a periodically faceted interface during crystallization ofSi

We investigated the pattern formation mechanism of a periodically faceted crystal–melt interface during the crystallization of Si by in situ observation. It was directly proved that spacing between the reentrants of adjacent zigzag facets increases with the unification of adjacent facets when a facet with a higher growth velocity catches up with the one with a lower growth velocity. The spacing becomes stable after unification, and the stable spacing was found to increase with increase in growth velocity. The experimental results was discussed by taking the negative temperature gradient in front of the growth interface into account.     

The mechanism of crystal growth in glass forming systems

A critical survey on experimental results on the mode of growth in simple glass forming melts is given, attention being mainly concentrated to data obtained at small undercoolings. Dissolution rates, change of interfacial conditions at constant undercooling as well as detailed structural determinations are considered as experimental evidences, complementary to a thorough analysis of growth-temperature dependences. For network glass formers (SiO₂, GeO₂, P₂O₅, Na₂B₄O₇) with melt structures, similar to those of the corresponding crystals, the normal mode of growth is typical. For a number of simple glass forming substances in which the crystallization is connected with a process of molecular reconstruction (NaPO₃, LiPO₃), spiral growth could be proved. Dislocation-free crystals of high entropy of melting glass forming substances (Na₂S₂O₃ · 5 H₂O, thymol) are obtained after prolonged annealing and growth in thin bored capillaries. Two-dimensional growth is verified for the resulting perfect crystals.     

Numerical Simulation of Temperature and Flow Field in the Melt for the Vapour‐pressure‐ controlled Czochralski Growth of GaAs

The influence of the melt flow on the temperature field and interface during the vapour‐pressure‐controlled growth of GaAs was studied numerically with the commercial general‐purpose program FIDAP^TM. The thermal boundary conditions for the domain of seed, crystal, boron oxide and crucible were taken from a global calculation for an equipment used at the IKZ to grow 6″ crystals. Due to the large melt volume the buoyancy forces become rather strong and have to be counteracted by reasonable rotation rates. Preliminary results have been obtained for iso‐ and counter‐rotation showing that the flow field exhibits structures on small scales. High rotation rates are needed to counteract the buoyancy flow efficiently and to achieve a smooth flat interface. Even if the the flow structure is not resolved in detail, the interface shape can be deduced form the calculations.