Molecular dynamics simulations of the crystal–melt interface mobility in HCP Mg and BCC Fe

The temperature profile around the moving solid–liquid interface during non-equilibrium molecular dynamics (MD) simulations of crystallization and melting is examined for HCP Mg and BCC Fe. An evident spike (valley) is found around the solid–liquid interface during solidification (melting). Considering the effect of a non-uniform temperature distribution, it is found that, if the actual interface temperature is adopted to compute the interface mobility, rather than the thermostat temperature (or the mean temperature of the whole system), the kinetic coefficient is approximately a factor of two larger than previous estimates. Although the magnitude of the kinetic coefficient is larger than the previous estimates, the crystalline anisotropies derived in the current work are consistent with earlier calculations.     

Optimisation of the VGF growth process by inverse modelling

Numerical and experimental results on the thermal optimisation of vertical gradient freeze crystal growth are presented. An inverse modelling approach is described aimed at solidification with a constant growth rate and planar solid–liquid interface. As a result of modelling an optimised growth process characterised by a modified ampoule configuration and thermal regime was established. For experimental confirmation Ga-doped germanium single crystals were grown with the optimised process. In good agreement with the numerical results, solidification with an almost constant growth rate was achieved with the interface deflection being significantly lower than in conventionally grown crystals.     

Numerical study of induction heating in melt growth systems—Frequency selection

A set of 2D finite element numerical simulation of induction heating process for an oxide Czochralski crystal growth system has been made for a range of f=1–100 kHz applied frequency of driving current. It was shown that the frequency selection has a marked effect in all basic induction phenomena, including electromagnetic field distribution, skin depth, coil efficiency, and intensity and structure of heating in the growth setup.     

Influence of crucible geometry and position on the induction heating process in crystal growth systems

A series of 2D finite element numerical simulations of induction heating process for an oxide Czochralski crystal growth system has been done for different shapes and locations of a metal crucible. Comparison between the computational results shows the importance of crucible shape, geometry and its position with respect to the RF-coil on the electromagnetic field and heat generation distribution in the growth setup.     

Reactions at the liquid silicon/silica glass interface

Experiments have been carried out to determine the nature and origin of the spots growing on silica glass surfaces in contact with liquid silicon during CZ–Si crystal growth. Silica glass ampoules were filled with silicon and tempered between 5 min and 40 h at a temperature (1693 K) slightly above the melting point of silicon. Cross sections of the ampoules with solidified silicon have been examined by scanning electron microscopy and optical polarization microscopy. In addition cross sections from commercial silica glass crucibles used in the Czochralski process or dipped into the silicon melt were investigated with the same methods. At the silicon/silica glass interface different reaction zone morphologies were detected. A solution-precipitation mechanism is suggested for the fast lateral growth of the reaction zone, which is proposed to consist of small cristobalite crystals embedded in a silica glass matrix.     

Nd:YVO4 crystal growth by Czochralski technique with a submerged plate

This paper is to investigate the growth of Nd:YVO₄ (yttrium vanadate) crystal by the modified Czochralski technique with a submerged plate. Numerical studies are performed to examine melt convection and heat transfer during Nd:YVO₄ growth. The attention is paid to study the effects of initial elevation of the submerged plate, crystal diameter, and melt level on melt inclusions. It is found that the increase in crystal rotation rate and crystal diameter, and the decrease in melt level will increase the axial temperature gradient at the edge and in the center of the crystal, and change the interface shape from convex to flat. The experiments are also carried out to confirm the feasibility of the proposed new technique for controlling melt inclusions in Nd:YVO₄ crystal growth.     

Ionic impurity transport and partitioning at the solid–liquid interface during growth of lithium niobate under an external electric field by electric current injection

Transport of ionic species in the melt and their partitioning at the solid–liquid interface during growth of lithium niobate was studied under the influence of intrinsic and external electric fields. A Mn-doped lithium niobate (Mn:LiNbO₃) single crystal was grown via the micro-pulling-down (μ-PD) method with electric current injection at the interface. Mn ions were accumulated or depleted at the interface, depending on the sign of the injected current. The electric current injection induced an interface electric field as well as a Coulomb force between the interface and Mn ions. The electric field modified the transportation of Mn ions and their partitioning into the crystal, while the Coulomb force led to adsorption or rejection of Mn ions at the interface in addition to Mn concentration change due to the electric field. Effect of the Coulomb force was often observed to be larger on Mn concentration at the interface than that of the induced electric field, and dominated the redistribution of Mn in the solid. It has been experimentally and analytically shown that Mn concentration partitioned into the crystal can be obtained by multiplying Mn concentration at the interface by a field-modified partition coefficient, k_E0, instead of the conventional equilibrium partition coefficient, k₀.     

Heat transfer and convection in Czochralski growth of large BGO Crystals

In the present work, numerical modeling has been performed to analyze heat transfer and melt convection during bismuth germanate Bi₄Ge₃O₁₂ (BGO) crystal growth by the Czochralski growth method. In addition to global heat-transfer modeling, the suggested model accounts for the radiative heat exchange in the crystal and melt convection together with the crystallization front formation. The model helped to analyze the modification of the growth setup made by including additional heater. The numerical predictions obtained with CGSim software agree well with available experimental data.     

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.     

Mixed-phase solidification of thin Si films on SiO2

Mixed-phase solidification (MPS) is a new beam-induced solidification method that can produce large-grained and highly (1 0 0)-surface textured polycrystalline Si films on SiO₂. The grains resulting from this mixed-phase solidification (MPS) method, which was conceived based on a well-known phenomenon of coexisting solid–liquid regions in radiatively melted Si films, are found to be essentially devoid of various intragrain defects that always plague, and subsequently degrade the utility of large-grained Si films previously obtained using other crystallization techniques. It is experimentally shown that multiple exposures are required in order to generate such a polycrystalline microstructure from an initial amorphous precursor. The observed trends are conceptually explained in terms of the melt being initiated primarily at grain boundaries in polycrystalline films, and melting and solidification subsequently proceeding laterally at interface-location specific rates as determined by the local thermodynamic factors, which include the anisotropic surface and interfacial energies of the grains, and the unusual local thermal profile—all transpiring within a near-equilibrium but nonisothermal and dynamic environment that needs to address the thermal and stability requirements associated with the coexisting solid–liquid regions.     

Unidirectional seeded single crystal growth from solution of benzophenone

A novel crystal growth method has been established for the growth of single crystal with selective orientation at room temperature. Using volatile solvent, the saturated solution containing the material to be crystallized was taken in an ampoule and allowed to crystallize by slow solvent evaporation assisted with a ring heater. The orientation of the growing crystal was imposed by means of a seed fixed at the bottom of the ampoule. By selecting a suitable ring heater voltage and by controlling the ring heater voltage, nucleation and the growth rate of the crystal were controlled more effectively. By employing this novel method, benzophenone single crystal ingots of diameters 10 and 20 mm and length more than 50 mm were successfully grown using xylene as solvent. The ease in scaling up of diameter from 10 to 20 mm shows the vital advantage of this technique. It was possible to achieve solute–crystal conversion efficiency of 100 percent. The grown benzophenone crystal was characterized by FTIR, TG and DTA, powder X-ray diffraction, X-ray rocking curve, optical transmission study and powder SHG measurement. The results show that the crystal quality is at least as good as the quality of the crystal grown by other known methods. Also, microbial growth was naturally avoided in this method, as the fresh solution is constantly made available for the growing crystal.     

Study of batch maltitol (4-O-α-d-glucopyranosyl-d-glucitol) crystallization by cooling and water evaporation

It is obvious that maltitol, like other disaccharides, owes some of its functional properties to structural features such as the flexibility of the glycosidic bond and hydrogen bonding and to its aqueous solution physicochemical properties, especially solubility and metastable zone width. This is particularly the case for molecular arrangements, which take place before and during crystallization process. We have previously used FTIR spectra to study structural properties of the maltitol molecule in concentrated solution like molecular associations or changes in conformation [1]. To complement these molecular properties, the different maltitol solution physicochemical properties having a relationship with maltitol–water or maltitol–maltitol interactions like solubility, metastable zone width, viscosity, and density were determined [2]. In this work we used these physicochemical results to optimize maltitol crystallization both by reducing the process duration and by improving the obtained crystal quality. Two strategies have been tested: the optimization of the time/temperature profile during the classical cooling crystallization and the application to maltitol of evaporative crystallization, a process usually used for sucrose preparation. The obtained results mainly showed remarkable difference in crystal mean size and crystal size distribution when the cooling profile was modified. On the other hand, evaporative crystallization was shown to make it possible to lower considerably the crystallization time compared to the cooling process but crystal morphological properties seem to be considerably modified by evaporation.     

Growth and interface study of 2 in diameter CdZnTe by THM technique

Growth interface of large diameter CdZnTe ingots grown from Te solution by travelling heater method have been studied. Both macroscopic and microscopic investigations were carried out. The results indicated that the shape of the interface strongly governs the grain growth on the ingot, while the microscopic morphology of the growth interface is responsible for Te inclusions in the grown crystal.     

Growth of SiGe bulk crystals with uniform composition by utilizing feedback control system of the crystal–melt interface position for precise control of the growth temperature

We developed an automatic feedback control system of the crystal–melt interface position to keep the temperature at the interface constant during growth, and demonstrate its successful application to grow Ge-rich SiGe bulk crystals with uniform composition. In this system, the position of the crystal–melt interface was automatically detected by analyzing the images captured using in situ monitoring system based on charge-coupled-devices camera, and the pulling rate of the crucible was corrected at every 1 min. The system was found to be effective to keep the crystal–melt interface position during growth even when the variation of the growth rate is quite large. Especially, the interface position was kept for 470 h during growth of Ge-rich SiGe bulk crystal when we started with a long growth melt of 80 mm. As a result, a 23 mm-long Si_0.22Ge_0.78 bulk crystal with uniform composition was obtained thanks to the constancy of the growth temperature during growth through the control of the interface position. Our technique opens a possibility to put multicomponent bulk crystal in a practical use.     

A new thermal assembly design for the directional solidification of transparent alloys

A modified design of the thermal assembly is presented for the directional solidification of transparent alloys that eliminates the radial temperature gradient and minimizes the curvature of the interface. An additional booster heater is designed, and the position of the heater is shown to be critical in obtaining a flat interface. A full-scale numerical calculation, carried out for succinonitrile-0.5 wt% Salol, shows that the interface concavity can be reduced gradually by placing the booster heater just above the cold end and by adjusting the temperature of the booster heater while keeping the hot and cold zone temperatures fixed. Experimental measurements of temperatures at the wall and at the center have been carried out systematically by using two calibrated thermocouples, and the observed thermal profiles have been shown to strongly support the numerical prediction. When a macroscopically flat interface is obtained, it is shown that columnar growth away from the ampoule wall can be observed and photographed. The effects of thermal gradient and the temperature setting of the booster heater on the planarity of the interface are discussed.     

Impact of amorphous Ge thin layer at the amorphous Si/Al interface on Al-induced crystallization

We investigated the impact of an amorphous Ge (a-Ge) thin layer inserted at the amorphous Si (a-Si)/Al interface on Al-induced crystallization. In situ observation of the growth process clarified that the nucleation rate is drastically reduced by insertion of a-Ge, which led to increase in the average size of crystal grains. This was interpreted as resulting from decrease in the driving force of crystallization, mainly due to the larger solubility of Ge in Al than that of Si in Al. The obtained films were SiGe alloys with lateral distribution of Ge content, and its origin is discussed based on the two-step nucleation process.     

Modeling analysis of liquid encapsulated Czochralski growth of GaAs and InP crystals

The results of three‐dimensional unsteady modeling of melt turbulent convection with prediction of the crystallization front geometry in liquid encapsulated Czochralski growth of InP bulk crystals and vapor pressure controlled Czochralski growth of GaAs bulk crystals are presented. The three‐dimensional model is combined with axisymmetric calculations of heat and mass transfer in the entire furnace. A comprehensive numerical analysis using various two‐dimensional steady and three‐dimensional unsteady models is also performed to explore their possibilities in predicting the melt/crystal interface geometry. The results obtained with different numerical approaches are analyzed and compared with available experimental data. It has been found that three‐dimensional unsteady consideration of heat and mass transfer in the crystallization zone provides a good reproduction of the solidification front geometry for both GaAs and InP crystal growth.     

Applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field

To examine the applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic fields, LES calculations with Smagorinsky–Lilly turbulence model and van Driest damping at the solid walls are carried out. The program package for the calculations was developed on the basis of the open-source code library OpenFOAM^®${\mathrm{OpenFOAM}}^{\circledR }$. A previously published laboratory model with low temperature melt InGaSn, a 20” crucible, and process parameters corresponding to industrial Czochralski silicon systems is considered. Flow regimes with two crystal and crucible rotation rates and with different strengths of the traveling magnetic field “down” are analyzed. The calculated distributions of averaged temperature and standard temperature deviations are compared with measured ones in the laboratory system, and a relatively good agreement between them is shown. The influence of chosen time steps and grid sizes is analyzed by comparing Fourier spectra of temperature time-autocorrelation functions and temperature spatial distributions, and it is shown that the used moderate meshes of few hundred thousand cells can be applied for practical calculations.     

The influence of indium on the growth of GaN from solution under high pressure

The influence of significant fraction (10–50 mole%) indium in liquid gallium on GaN crystallization from a ternary Ga–In–N solution was analyzed. Crystallization experiments of GaN on GaN-sapphire templates from Ga–In solutions, at 1350–1450 °C, with prior to the growth seed wetting at 1500 °C, and 1.0 GPa N₂ pressure, without solid GaN source showed faster growth of GaN on the seed (by a factor of 1.5–2) than using pure gallium solvent. Nevertheless the new grown crystals were morphologically unstable. The instability was reduced by decrease of the wetting temperature down to 1100 °C or by omitting the wetting procedure entirely, which indicated that GaN dissolves much faster in Ga–In melt than in pure Ga and that the unstable growth was caused most likely by complete dissolution of GaN template before the growth. It was observed that the crystals grown on bulk GaN substrates did not show morphological instability observed for GaN-sapphire templates. The influence of indium on thermodynamic and thermal properties of the investigated system is discussed.     

Resistivity distribution of silicon single crystals using codoping

Numerous studies including continuous Czochralski method and double crucible technique have been reported on the control of macroscopic axial resistivity distribution in bulk crystal growth. The simple codoping method for improving the productivity of silicon single-crystal growth by controlling axial specific resistivity distribution was proposed by Wang [Jpn. J. Appl. Phys. 43 (2004) 4079]. Wang [J. Crystal Growth 275 (2005) e73] demonstrated using numerical analysis and by experimental results that the axial specific resistivity distribution can be modified in melt growth of silicon crystals and relatively uniform profile is possible by B–P codoping method. In this work, the basic characteristic of 8 in silicon single crystal grown using codoping method is studied and whether proposed method has advantage for the silicon crystal growth is discussed.