The effect of mass transfer on the temperature gradient of a crystal growing from melt

The change in the temperature gradient on the crystal side while the rate of crystal growth from melt is varied has long been debated. Abe and Takahashi have recently reported an unambiguous experimental demonstration that the temperature gradient is a decreasing function of the growth rate, which is different from previous theories, experimental results, and widely held notion of other researchers. The present paper provides a theoretical basis for this seemingly peculiar effect of the growth rate on the temperature gradient. The essential matter is the effect of mass transfer, the role of which had been commonly disregarded in old studies. Although the rate of mass transfer is not large compared to that of heat conduction, it is proven that the temperature gradient is subjected to the mass transfer in a definite manner. Our analysis shows that the effect becomes significant when the crystal diameter is large, which is consistent with the experimental observation. Another effect of the mass transfer is the change in the shape of melt/crystal interface. In old studies, the temperature gradient was determined by Stefan's equation; however, this treatment confuses the cause and effect. The temperature gradient should be determined by the fundamental equation of heat conduction. When the gradient is determined in this way, the shape of the melt/crystal interface spontaneously adjusts to satisfy Stefan's equation.     

The migration of gas-filled brine inclusions in rock salt under a temperature gradient

In natural halite crystals two sorts of inclusions will move if there exists a temperature gradient. The direction of moving brine inclusions is orientated towards the heat source. Brine inclusions which additionally contain more than 10% gas move towards the cold end of a specimen. This model is well known but detailed information about the migration mechanism of these so-called SORBY inclusions have been lacking in literature so far. In this paper it will be demonstrated that SORBY inclusions having a diameter of up to 20 micrometers can move undisturbed through the crystal. SORBY inclusions with a diameter of more than 20 micrometers are fixed and form droplets with their tips directed towards the cold side of the specimen. Later when the tips have grown the inclusions will emit a new daughter inclusion which can move through the crystal. The velocity of migration depends on the generation of daughters. Extended kinds of SORBY inclusions are stable for a long time. However, these can decay into many individuals which will move through the crystal like the others.     

Simulation of temperature and flow fields in an inductively heated melt growth system

The goal of the research presented here is to apply a global analysis of an inductively heated Czochralski furnace for a real sapphire crystal growth system and predict the characteristics of the temperature and flow fields in the system. To do it, for the beginning stage of a sapphire growth process, influence of melt and gas convection combined with radiative heat transfer on the temperature field of the system and the crystal‐melt interface have been studied numerically using the steady state two‐dimensional finite element method. For radiative heat transfer, internal radiation through the grown crystal and surface to surface radiation for the exposed surfaces have been taken into account. The numerical results demonstrate that there are a powerful vortex which arises from the natural convection in the melt and a strong and large vortex that flows upwards along the afterheater side wall and downwards along the seed and crystal sides in the gas part. In addition, a wavy shape has been observed for the crystal‐melt interface with a deflection towards the melt. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Control of multi-zone resistive heater in low temperature gradient BGO Czochralski growth with a weighing feedback,based on the global dynamic heat transfer model

The global heat transfer in a crystallization setup has been optimized to develop a strategy of control over a three-zone heater in the BGO Czochralski process, in order to provide invariable thermal conditions near the solid–liquid interface in the stage of a constant-diameter crystal growth. The functional related to the exactness of the heat balance condition at the crystallization front, i.e., the Stefan problem, was chosen as the target function. The optimization yielded unexpected results. The temperature of the lower heater should be lowered, relative to that of the middle heater, with increasing crystal length, whereas the temperature of the upper heater is to be raised. These recommendations were incorporated into a dynamic model of the oxide Czochralski process with a weighing control and into the control loop of the temperature regulators of a crystallization setup. A comparison of results of the time-dependent simulation with the real growth process confirmed that the new control strategy minimizes the deviation of the solid–liquid interface from the prescribed one, significantly decreases variations of interface shape during the process, and enables growth of high-quality crystals.     

Crystallization of a germanium melt in an external electric field

Data are presented on experimental studies of the influence of an external electric field on crystallization of a germanium melt under the layer of a B₂O₃ flux. It has been found out that with the field supercoolings of the melt sharply change. This effect is due to the change of the number of active nucleation centres at the germanium – B₂O₃ flux interface. The maximum supercoolings of the germanium melt ΔT⁻ = 190 K were obtained when a negative potential was connected to germanium. The dependences of supercooling on preliminary melt overheating were measured.     

Morphology of sic epitaxial layers grown by temperature gradient zone melting (I). Dependence of the crystallization boundary smoothness on the epitaxial layers growth conditions

The dependence of the smoothness of the crystallization boundary on the temperature gradient zone melting conditions is investigated. The observed depth of the crystallization boundary is compared with the depth, calculated by the method proposed by D. E. TEMKIN.     

Morphology of SiC epitaxial layers grown by temperature gradient zone melting (II). The dependence of the structural properties of the epitaxial layers on the growth conditions

In the present paper the relationships between the structural perfection of the layer, represented by the Tb average integral concentration (which is a criterion for the second phase quantity), the rocking curve half-width (a criterion for the general structural perfection of the layer) and the layer growth conditions, represented by the quantity, which is the most important characteristic of the growth process, namely the supersaturation are discussed. The considered model allows to conclude, that a optimal value of the supersaturation exists, at which the structural perfection is maximal.     

Instability of the melt flow in VGF growth with a traveling magnetic field

The linear instability of a thermally stratified melt flow in the VGF configuration driven by a traveling magnetic field (TMF) is considered numerically and experimentally. The dependency of the instability threshold on the governing parameters is found for several cuts through the parameter space covering a wide range of possible applications. In a first approximation the linear instability occurs when the dimensionless TMF forcing parameter reaches the magnitude of the Grashof number. This is particularly true in a medium-sized crucible where the first instability is axisymmetric and sub-critical. As the Grashof number increases the flow develops self-similar boundary layers and the instability becomes three-dimensional. The instability originates in the bottom boundary layer where the convection tends to suppress the imposed temperature gradient in the central part of the melt zone. It is shown that the TMF may serve as a tool to control the phase interface shape without causing flow instationarity when the crucible diameter exceeds a certain value. This value is estimated to be around 6 cm for GaAs. The flow stays stable if the TMF is used for a reversal of the meridional flow with the aim to remove a possible dopant concentration peak on the axis.     

The electric field gradient in a random packing model of amorphous ionic materials

The electronic field gradient distribution at both the cation and anion sites has been computed for a dense random packing model of amorphous FeF₃ and analysed with particular reference to the sign of the principal component q. For the (large sphere) anion components twice as many sites are found with q>0 as with q<0 and the distribution of asymmetry parameter η is quite anomalous for the sites with positive q. These unusual features, and their essential absence at the (small sphere) cation sites, can be understood in terms of the local coordinations of the two types of ionic constituent and are likely to remain at least qualitatively valid for majority anions and minority cations in a wider context of amorphous ionic materials.     

Intermediate asymptotic regime of coalescence in a homogeneous supersaturated solution and change in kinetic indexes

New coalescence regimes, in which the asymptotic behavior of the grain-size distribution function differs significantly from the classical Lifshitz-Slyozov distribution, are found within the approach taking into account the finiteness of the maximum grain size. The cases are considered where the grain-growth kinetics is controlled by either the processes at phase boundaries or the diffusion of monomers. Time dependences are found for the critical and maximum grain radii and the time evolution of the grain-size distribution function in the cases of positive and negative initial supersaturation is described. It is established that a change in the dominant mechanism of grain growth may lead to an intermediate asymptotic coalescence regime, passing in the final stage to the diffusion mode. This change manifests itself in the change in the power exponents in the time dependence of the grain size.     

New approach to simulation of radiative-conductive heat transfer in semi-transparent crystals being pulled from a melt

A method is suggested for the solution of multi-dimensional radiative heat transfer problems arising in growing crystals. The basic idea of the approach lies in the construction of a special division of the unit sphere into a set of solid angles (cells) and in the approximation of the radiation intensity in each solid angle by the P₁ approximation. The radiant transport equation is satisfied in the mean over each elementary cell and the system of partial differential equations of the second order relative to the local zeroth-moments of radiation intensity are obtained. It is shown that the solid angle subdivision can be carried out in different ways with respect to specific features of the heat transfer problem under consideration. As a result even a very rough partition permits satisfactory accuracy of the numerical solutions. One of the main advantages of the method consists in using solid angle subdivisions which can be varied from point to point of the spatial domain. The latter gave possibility to simulate the radiative heat transfer in a circular cylinder of finite length with specular side surface. On this basis the calculation of the temperature field in a cylindrical sapphire crystal being pulled from the melt has been carried out without any restriction on the size of the crystal     

Simulation of temperature and gas density field distribution in diamond films growth on silicon wafer by hot filament CVD

In the present study, the temperature and gas density field inside the hot filament chemical vapor deposition (HFCVD) reactor, which play a determinate role on the growth rate and quality of as-deposited diamond films, are simulated using the finite volume method, and the influence of the size and arrangement of filaments and inlets are investigated. Firstly, the correctness of the simulation model is verified by comparing the temperature data obtained from the simulation with that measured in an actual depositing process, and the results show that the error between them is less than 3%. Thereafter, the deposition parameters are optimized using this model as N(filament number)=6, r(filament radius)=0.4 mm, D(filament separation)=16–18 mm, H(substrate–filament distance)=8–9 mm, and 25 inlets. Finally, diamond films are deposited on silicon (100) wafers using above parameters and the results of characterization by SEM and Raman spectrum exhibit that the deposited diamond films appear homogeneous surface with fine-faceted crystals.     

Synthesis of chalcogenide and pnictide crystals in salt melts using a steady-state temperature gradient

Some examples of growing crystals of metals, alloys, chalcogenides, and pnictides in melts of halides of alkali metals and aluminum at a steady-state temperature gradient are described. Transport media are chosen to be salt melts of eutectic composition with the participation of LiCl, NaCl, KCl, RbCl, CsCl, AlCl₃, AlBr₃, KBr, and KI in a temperature range of 850–150°C. Some crystals have been synthesized only using a conducting contour. This technique of crystal growth is similar to the electrochemical method. In some cases, to exclude mutual influence, some elements have been isolated and forced to migrate to the crystal growth region through independent channels. As a result, crystals of desired quality have been obtained using no special equipment and with sizes sufficient for study under laboratory conditions.     

The influence of heat-dissipation and temperature fluctuations on SbSI crystallization in thin layers

Single crystal films of SbSI 5 to 100 μ in thickness have been obtained by crystallization from melts in a close spacing. The films crystallized under conditions under conditions of direct heat -dissipation and periodical fluctuations of temperature near the melting point. The phase transition in the films was revealed by means of capacity measurements at temperatures of ∼ 20 °C.     

Heat and mass transfer problems in solution growth of GaP crystals by the travelling solvent method (TSM)

The influence of the natural convection on the heat and mass transfer process during growth of GaP crystals from the solution is considered. The two-dimensional quasi-stationary thermodiffusive hydrodynamic problem for the GaP growth system by travelling solvent method (TSM), as a model, has been solved. Computation is given for the temperature and concentration field distribution in the solution. The picture of vortex configuration for different lengths of the liquid zone, the shape of the growing and dissolving interfaces and also the boundary layers thickness are obtained. The experimental dependence of the growth rate on the convection intensity observed mostly confirmed the calculation results.     

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.     

Remarks on the separation of a solid solution transported by evaporation-condensation at a small temperature difference

The nearly congruent transport of a solid solution by incongruent solid-vapour and vapour-solid phase transitions in a closed, almost isothermal system is considered–in particular referring to the crystal growth of pseudobinary A^IVB^VI solid solutions. The fact is interpreted that the small temperature difference required for the creation of the mass driving force of the process causes composition variations smaller than often assumed.     

The transportation of brine inclusions in rock salt in a temperature field of a heat source

There are three kinds of brine inclusions in a natural crystal of halite, as follows: a) inclusion totally filled with brine; b) inclusions partially filled with brine and gas (SORBY inclusions) and c) inclusions totally filled with gas. Type a) and b) migrate in the crystal under the influence of a temperature gradient. Type c) inclusions do not move. This paper deals with the question whether the migration causes tracks in the crystal or not. In general, no tracks are caused directly by the motion of inclusions. However, there are some phenomena which can be explained as tracks. The reasons of these phenomena are examined and described.     

In situ high temperature 27Al NMR study of structure and dynamics in a calcium aluminosilicate glass and melt

The temperature dependence (25–1400 °C) of ²⁷Al NMR spectra and spin–lattice relaxation time constants T₁ have been studied for a calcium aluminosilicate (43.1CaO–12.5Al₂O₃–44.4SiO₂) glass and melt using an in situ high temperature probe, and the glass has been characterized by ambient temperature, high field MAS NMR. The peak positions and the line widths show a consistent behavior as motional averaging of the quadrupolar satellites increases with increasing temperature. The rate of decrease with temperature of T₁ drastically increases near the glass transition temperature T_g, which suggests a change in NMR relaxation process from vibrational to translational motions. Above the T₁ minimum (≈1200 °C), NMR correlation times obtained from T₁ are in good agreement with shear relaxation times estimated from viscosity, suggesting that microscopic nuclear spin relaxation is controlled by the same dynamics as macroscopic structural relaxation, and thus that atomic-scale motion is closely related to macroscopic viscous flow.     

Influence of a high vertical magnetic field on Te dopant segregation in InSb grown by the vertical gradient freeze method

A vertical gradient freeze apparatus was set up to investigate the influence of a vertical magnetc field on Te dopant segregation in InSb. Te-doped InSb crystals were grown in the presence and absence of an 80.0 kG magnetic field. The axial profile of the Te concentration in the crystal grown in the magnetic field was observed to be more uniform than that grown without magnetic field, which was attributed to the influence of the high magnetic field on Te dopant segregation by reducing convection in the melt.