Effect of surface tension‐driven flow on BaB2O4 crystal growth from high temperature melt‐solution

The surface tension driven‐flow in BaB₂O₄ (BBO) melt‐solution is visualized by differential interference microscope coupled with Schlieren technique, and the streamline of the steady thermocapillary convection is found to be in form of an axially symmetric pattern. Based on the observation of BBO crystal rotation caused by the convective vortex, the widths of interfacial concentration, heat and momentum boundary layer are calculated. The effect of thermocapillary convection on boundary layer thickness is also investigated. Results show that the width of boundary layer decreases linearly with the increasing of dimensionless Marangoni number. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

In order to understand the nature of surface spoke patterns on silicon melt in industrial Czochralski furnaces, a series of unsteady three‐dimensional numerical simulations were conducted for thermocapillary‐buoyancy flow of silicon melt in annular pool (inner radius r_i = 15 mm, outer radius r_o = 50 mm, depth d = 3 mm). The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll‐cell thermocapillary‐buoyancy flow. With large temperature difference, the simulation can predict three‐dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux (3 W/cm²) does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three‐dimensional unsteady thermocapillary flow under rotating magnetic field

Under a rotating magnetic filed (RMF), the instability of thermocapillary flow and its evolution with increasing Marangoni number (Ma) for semiconductor melt (Pr = 0.01) in a floating liquid bridge model (As = 1) are investigated numerically. Under 5 mT RMF, the thermocapillary flow is steady and axisymmetric with Ma < Ma_c, and the critical Marangoni number Ma_c for convection instability is 29.5, which is obtained by the direct numerical simulation. When the Ma is a little bit beyond the Ma_c, the thermocapillary flow loses stability to become a three‐dimensional rotating oscillatory convection, and a periodic oscillation is confirmed by the fast Fourier transform analysis, the oscillatory main frequency decays with increasing Ma. Under 1 mT–6 mT RMF, the Ma_c increases roughly with the magnetic strength except the Ma_c at 4 mT, where the corresponding change of flow mode after the instability is observed. The oscillatory convection occurs with a smaller Ma in the RMF than that without magnetic field. In addition, no instability toward a three‐dimensional steady convection, which is the state of thermocapillary flow without magnetic field after the first instability, is observed under the RMF.     

Effect of the Temperature Fluctuation of the Melt on β‐BaB2O4 (BBO) Crystal Growth

In this paper the effect of the growth temperature fluctuation, for instance, the transient furnace temperature variation due to a short‐term electric power supply interruption on BBO crystal growth was investigated based on the theory of temperature wave transmitting in melt and the boundary layer theory of melt. It was found that the critical width of the temperature pulse to avoid the temperature wave penetrating through the boundary layer and reaching to the growth interface at a constant rotation speed (9∼4 r/min) is 69∼150 s and the corresponding amplitude of the temperature pulse is high more than 60 °C due to the large thickness of the velocity boundary layer of the melt. This result indicates that a small transient temperature fluctuation has no significant effect on the crystal quality, and therefore implies that not only transport processes but interface growth kinetics, a two‐dimensional nucleation growth mode at the interface may also dominate the crystal growth.     

Solutocapillary convection in germanium‐silicon melts

Surface tension gradients in free crystal growth melts give rise to convective flow. If these gradients are due to thermal gradients, the well known thermocapillary (Marangoni) convection ensues. Concentration gradients due to segregation at the interface during growth can lead to additional solutocapillary convection. A system with large solutocapillary convection is Ge‐Si due to the pronounced segregation and the strong difference in surface tension; solutal buoyancy convection is also present due to the large density difference between Ge and Si. Solutocapillary convection will oppose thermocapillary convection in the Ge‐Si system since Si, having the higher surface tension, is preferentially incorporated into the crystal. A set of experiments directly proving and partially quantifying the effect has been conducted under microgravity during a parabolic flight campaign by recrystallizing Ge‐Si mixtures of different compositions, between 3% and 9% Si, in a crucible with tracers to visualize the movement. Solutocapillary flow with initial flow rates in excess of 5.5 cm/s at the onset of crystallization was measured. A slight dependence of the flow velocity on the initial Si content has been found. Experiments on the ground showed the same effect but with overall smaller speeds; this difference can be explained by the additional action of solutal buoyancy convection. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three‐dimensional flow in a thin annular layer of silicon melt with bidirectional temperature gradients

Bidirectional temperature gradients coexist virtually in surface tension driven flows. However, the simulations have been performed to the flow with only one temperature gradient. A series of 3 D numerical simulations are conducted to investigate the Marangoni‐thermocapillary flow of silicon melt in a thin annular layer with bidirectional temperature gradients. The temperature gradients are produced by the temperature difference ΔT between walls and the constant heat flux q on the bottom, respectively. When changing q, the melt presents different state evolutions at different ΔT. Furthermore, two critical q are found, one makes the minimum melt temperature higher than the crystallization temperature and the other makes the flow unsteady. Both of the critical heat fluxes decrease with increasing ΔT. q contributes more to the elevation of the melt temperature, while ΔT contributes more to the enhancement of the melt instability. In addition, the melt on the free surface flows mainly along the radial direction.     

Existence,stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity

A thermocapillary model is used to study the existence, stability, and nonlinear dynamics of detached melt crystal growth in a vertical Bridgman system under zero gravity conditions. The model incorporates time-dependent heat, mass, and momentum transport, and accounts for temperature-dependent surface tension effects at the menisci bounding the melt. The positions of the menisci and phase-change boundary are computed to satisfy the conservation laws rigorously. A rich bifurcation structure in gap width versus pressure difference is uncovered, demarcating conditions under which growth with a stable gap is feasible. Thermal effects shift the bifurcation diagram to a slightly different pressure range, but do not alter its general structure. Necking and freeze-off are shown to be two different manifestations of the same instability mechanism. Supercooling of melt at the meniscus and low thermal gradients in the melt ahead of the crystal–melt–gas triple phase line, either of which may be destabilizing, are both observed under some conditions. The role of wetting and growth angles in dynamic shape stability is clarified.     

Direct melt crystal growth of isotactic polybutene‐1 trigonal phase

The morphology, crystalline structure and crystal growth kinetics of melt‐crystallized thin isotactic polybutene‐1 films have been studied with transmission electron microscopy, electron diffraction and optical microscopy. It is demonstrated that a bypass of tetragonal phase crystallization and direct melt crystal growth of the trigonal phase can be achieved via self‐seeding at atmospheric pressure using solution‐grown trigonal crystals as nuclei. Electron microscopy and optical microscopy observations show that melt‐crystallized isotactic polybutene‐1 single crystals of the trigonal phase have rounded or hexagonal morphologies around 75°C. The growth rate of trigonal crystals in the melt has been obtained by in‐situ optical microscopy. The growth rate of trigonal crystals in the melt is 1/100 and 1/1000 that of tetragonal crystals in the melt around 70 and 90°C, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Axial Solute Transport during Bridgman Growth of BiSbTe3‐Mixed Crystals ‐ a comparison of analytical and numerical results

2D/3D‐transient finite‐element computer simulations of heat and mass transport including convection have been performed for a Bridgman configuration close to real growth conditions. The results for the axial distribution of the excessive tellurium in BiSbTe₃ semiconductor crystals grown from the melt are compared with the predictions of analytical segregation models.It is shown that Favier's model can be successfully applied for quantitatively estimating model parameters of segregation. Finally, the transition from normal gravity to microgravity conditions is discussed.     

Modelling of the Transport Processes in Bridgman grown Gallium Antimonide

In this work the thermal, velocity and species fields in the melt during the crystal growth by the vertical Bridgman method, has been studied. The simulations were focused on the special case of GaSb, which is a semiconductor of high technological importance. The simulations have been carried out both in 2 and 3‐D. In both cases the momentum (Navier‐Stockes), energy and mass transport equations were solved. The wall‐to‐wall radiation has also been included. In the two‐dimensional case an axisymmetric global model was developed taking into account the different elements present inside the real Bridgman growth system. In order to study the transport processes in the whole system during a complete growth process, the time dependence has also been considered. In the three‐dimensional case, the mathematical domain is restricted to the melt. These simulations were developed in order to study the influence of the ampoule tilting on the dopant distribution in the melt.     

Growth of Zn‐doped Germanium under Microgravity

The doping of germanium with zinc from a remote, temperature‐stabilized source was studied under microgravity. A nominally undoped Ge‐crystal was grown by the Gradient‐Freeze technique with the melt surface being in permanent contact with a gaseous atmosphere of zinc. The dopant and carrier concentrations in the solidified Germanium were measured by SIMS, Hall and resistance measurements and compared with the results of a terrestrial reference experiment as well as with concentration profiles calculated on the basis of the thermodynamics of the growth system. The results prove the possibility of vapour phase doping under microgravity. Moreover, the Zn‐concentration at the initial phase boundary even agrees well with the equilibrium value, strongly indicating a nearly homogeneous distribution of the dopant within the melt before the crystallization.     

Inversion of conductivity type of III‐V compound layers in experiments with LPE growth from rare‐earth containing melts

Rare‐earth (RE) elements present in the growth melt of the LPE process are known to have a purifying effect on the grown layers of III‐V compounds. The RE atoms exhibit high chemical affinity preferentially to shallow donors, forming insoluble aggregates that remain in the melt and do not, ordinarily, enter the solid phase. The aim of the paper is to simulate the situation, sometimes observed experimentally, where the gradual gettering of donor impurity, consequent upon increasing the RE content in the melt, leads to an inversion of the electrical conductivity type of the grown layer from n to p. Usefulness of the approach is demonstrated by interpreting results of an experimental work. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Silicon transport under rotating and combined magnetic fields in liquid phase diffusion growth of SiGe

The effect of applied rotating and combined (rotating and static) magnetic fields on silicon transport during the liquid phase diffusion growth of SiGe was experimentally studied. 72‐hour growth periods produced some single crystal sections. Single and polycrystalline sections of the processed samples were examined for silicon composition. Results show that the application of a rotating magnetic field enhances silicon transport in the melt. It also has a slight positive effect on flattening the initial growth interface. For comparison, growth experiments were also conducted under combined (rotating and static) magnetic fields. The processed samples revealed that the addition of static field altered the thermal characteristics of the system significantly and led to a complete melt back of the germanium seed. Silicon transport in the melt was also enhanced under combined fields compared with experiments with no magnetic field. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

The role of inner and internal radiation on the melt growth of sapphire crystal

In this paper, for an inductively heated Czochralski furnace used to grow sapphire single crystal, influence of the inner (wall‐to‐wall) and crystal internal (bulk) radiation on the characteristics of the growth process such as temperature and flow fields, structure of heat transfer and crystal‐melt interface has been studied numerically using the 2D quasi‐steady state finite element method. The obtained results of global analysis demonstrate a strong dependence of thermal field, heat transport structure and crystal‐melt interface on both types of radiative heat transfer within the growth furnace.     

Synthesis and characterization of 4,4′‐dihydroxy‐α‐methylstilbene crystal

4,4′‐dihydroxy‐α‐methylstilbene (DHAMS) was synthesized by condensation reaction with chloroacetone and phenol in the presence of concentrated sulfuric acid, and has been successfully grown by solution growth technique. This is the first report in the literature on the crystallization of DHAMS and exhibited the birefringent melt (liquid crystal property) of the optical properties. FTIR and FTNMR studies are in accordance with the structure. Good quality crystals were grown by slow evaporation technique by acetone as solvent. A transmission spectrum of the crystal was obtained in the region of 285 nm. The structural and optical properties were studied. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using a Phase‐field‐like Approach for the Calculation of Melt Flow and Interface Shape during Czochralski Growth

A phase‐field‐like approach is introduced into the commercial general‐purpose program FIDAP^TM to calculate the melt‐crystal interface for a quasi‐stationary approach of the Czochralski growth. Temperature and flow field are solved using the segregated solver of the FIDAP^TM software.     

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.     

The Czochralski Method ‐ where we are 90 years after Jan Czochralski’s invention

The Czochralski method, i.e. pulling a crystal from the melt, became the most important technology for the production of large semiconductor (Si, GaAs, InP, GaP …) and optical crystals (oxides, CaF₂ …). The present status is achieved by a profound analysis of the mechanisms of heat and species transport which are relevant for the stability of the Czochralski growth process and the performance of the growing crystal. It was clearly demonstrated in the last few years that modeling by numerical simulation is an indispensable tool to analyze the Czochralski process and to understand the governing mechanisms. The contribution presents examples of this kind of modeling the Czochralski technique in correlation with experimental investigations in order to illustrate the present status of understanding relevant processing phenomena. Furthermore, it is shown what problems need still to be solved in the future in order to further improve the yield and quality of Czochralski‐grown crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of LaBGeO5 crystal fibers by the micro‐pulling down technique

The LaBGeO₅ compound (LBGO) was prepared by solid state reaction at 1050°C and characterized by XRD and DTA analysis. The direct growth of LBGO fibers from the melt using micro‐pulling down technique was unsuccessful because of its high viscosity. The study of the LBGO‐LiF phase diagram showed that LiF could be considered as a convenient flux to reduce viscosity of the melt during the growth process. Several crystal fibers were then grown and characterized by Raman spectroscopy. To decrease the high volatility of LiF, B₂O₃ was added to the melt. A white cloudy fiber was obtained from LiF‐B₂O₃ flux and checked by Raman spectroscopy and scanning electron microscopy.