Control of crystal growth in bridgman furnace

Control of crystal quality during crystal growth requires accurate implementation of thermal boundary conditions. We identify this problem as the furnace temperature control problem. The thermal boundary conditions, in turn, dictate the interface shape between the solid and the liquid region of the material. Determination of the boundary conditions for a given desired interface shape is considered as the material temperature control problem in this paper. We outline the current efforts for the solution of the furnace temperature control and the material temperature control problems. We restrict our review to Bridgman growth control techniques.     

Influence of temperature conditions in horizontal Bridgman furnace on crystal growth of GaAs

The experimental investigation of the boat shape and boat position in the furnace in the case of unseeded horizontal Bridgman growth of GaAs single crystals was carried out. The relation between axial and radial temperature gradients in the furnace was also studied. On the basis of experimental results the optimum conditions for the growth of low dislocation density GaAs single crystals were derived.     

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)     

Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth

For the seeding process of oxide Czochralski crystal growth, influence of the crucible bottom shape on the heat generation, temperature and flow field of the system and the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and 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 generation in the crucible wall as a source the fluid flow and temperature field of the entire system as well as the seed‐melt interface shape were determined. We have considered two cases, flat and rounded crucible bottom shape. It was observed that using a crucible with a rounded bottom has several advantages such as: (i) The position of the heat generation maximum at the crucible side wall moves upwards, compared to the flat bottom shape. (ii) The location of the temperature maximum at the crucible side wall rises and as a result the temperature gradient along the melt surface increases. (iii) The streamlines of the melt flow are parallel to the crucible bottom and have a curved shape which is similar to the rounded bottom shape. These important features lead to increasing thermal convection in the system and influence the velocity field in the melt and gas domain which help preventing some serious growth problems such as spiral growth. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Charge dissolution and heat and mass transfer during hydrothermal crystal growth with heat field rotation

Crystallography Reports - Analytical modeling of laminar thermal gravitational convection in a vertical porous cylinder of radius R and height H (R is much smaller than H) with a low-compressed...     

Influence of the flow velocity,supersaturation and temperature on the crystal growth from solutions

This paper is a review of our experimental research on the influence of the supersaturation, flow velocity and temperature on the linear crystallization rate of different faces of model crystal systems. The obtained experimental results are discussed in the light of the new theoretical treatments on crystal growth from low temperature solutions.     

Global heat loss and thermal stress analysis in Czochralski crystal growth

Based on our invention of an energy‐efficient Czochalski crystal growth furnace, a 2D‐axisymmetric numerical simulation model of LiNbO₃ crystal growth is developed. The heat transfer, melt and gas flow, radiation and the interface deflection have been examined. Heat losses in the furnace and the insulator, as well as the heating power and thermal stress distribution at three stages of crystal growth are calculated in detail. It is found that a large proportion of heat dissipates through the water‐cooling system, and at the steel shell of the furnace, gas convection heat transfer is the major cooling mechanism. Less heat dissipation by radiation and more heat flux by gas convection to the crystal sidewall results in a larger concentrated thermal stress, which may induce large crystal cracks in the growth process. The simulation results of heating power are in coincidence with the actual power of our furnace, which verifies the feasibility of our model. The detailed information with respect to the device obtained from simulation can help to optimize the energy‐saving design and growth process.     

Thermochemical analysis of native point defects and substitutional carbon and boron in GaAs crystal growth

The phase extent of GaAs has been analyzed and compared with published phase diagrams as related to total and partial point defect equilibria including charged and uncharged Frenkel, Schottky, antisite defects and substitutional carbon and boron on both sublattices. The well-known transition between semiconducting and semi-insulating behaviour at 300 K as a function of melt stoichiometry in LEC crystals can be reproduced in our model in which complete equilibrium exists above, only electronic equilibrium below a freeze-in temperature of 1100 K. The corresponding model standard enthalpy of formation of neutral Schottky defects is 4.0 eV, of a pair of neutral uncorrelated antisite defects 3.8 eV, of neutral Ga Frenkel defects 4.1 eV and of neutral As Frenkel defects 3.6 eV. Defect reactions in cooling processes after crystal growth are discussed and shown to be quite different for crystals with high or low dislocation density. Semi-insulating behaviour requires the existence of carbon acceptors if dislocations provide internal sources and sinks for point defects. For ideal crystals carbon would not be necessary. The possible site distribution of C and B is analyzed in its dependence on temperature and chemical potential of As. Constitutional supercooling is negligible in LEC growth. Macrosegregation is severe if the As fraction in the melt deviates more than ±0.02 from the stoichiometric value 0.5.     

Purification and crystal growth of TlBr for application as a radiation detector

Thallium bromide is a semiconductor compound with high atomic number and density. It has a CsCl‐type simple cubic crystal structure and it is non‐hygroscopics. The TlBr crystals are relatively soft with a knoop hardness number of 12. In this work, the TlBr commercial powder was purified by zone refining and the purest material section was used for crystal growth by Bridgman method. Efforts have been concentrated on the purification of the TlBr. The purification efficiency has been evaluated (NAA and ICP‐MS) by impurities reduction results after zone refining passes. The crystalline quality was evaluated by X‐ray diffraction. The characterized TlBr crystal as a detector has shown good response to gamma radiation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of crystallization conditions on the mechanism and rate of crystal growth of potassium sulphate

Growth rate of potassium sulfate crystals was studied in a fluidized bed crystallizer. Higher growth rates were observed at larger bed heights. Larger crystals grow faster than smaller size crystals due to the changed fluid dynamics. The growth rate was found to be very sensitive to the pH value of the solution. The growth rate increases with increasing the pH value and the increase of growth in the acidic medium is faster than in the basic medium. The presence of small amounts of Cr³⁺ ions reduces the growth rate of potassium sulfate dramatically. The presence of Cr³⁺ ions lowers the saturation temperature and increases the width of the metastable zone, i.e. shifts the metastability of the solution to be at lower level of supersaturation.     

Influence of gravitation on the processes of heat and mass transfer in solution crystal growth by the travelling heater method (THM) (III)

The effect of the natural and thermocapillary convection on the vortex configuration in solution during growth of PbTe crystal by the travelling heater method is considered. The estimation of the parameters of growth process (i. e. axial temperature gradients, gravitational acceleration, degree of the solution's surface contact with ampoule), when the vortex configuration undergoes qualitative variation, is given. In terms of the one-dimensional thermodiffusive problem solution the effect produced by the convective stirring on the position of growing and dissolving interfaces is described.     

Influence of initial growth parameters on the structural and optical properties of GaAs on (001) Si

The structural and optical properties of GaAs on (001) Si substrates were investigated by transmission electron microscopy (TEM) and low-temperature photoluminescence (PL). It was found that the success of the two-step growth technique is controlled by the quality (morphology and defect density) of the low-temperature grown AlGaAs nucleation layer. GaAs epilayers grown on low V/III ratio AlGaAs nucleation layers exhibit improved surface morphologies and structural properties. These results were confirmed by optical measurements where it was shown that the best PL response was obtained from GaAs epilayers in which the initial AlGaAs nucleation layers were deposited at a low V/III ratio.     

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.     

Characteristic temperature fields of crystal growth calculated with the aid of heat flow potentials

In order to grow monocrystals of larger and larger diameters, more detailed knowledge about the steady state temperature field and its effects on the growing crystal is needed. It can be acquired from experimental data only by means of a subtilized numerical analysis. A mathematical model based on closed-form solutions for the steady state cylindrical case is given. Using the so called “heat flow potential” defined in KIRCHHOFFS sense, any temperature dependence of the heat conductivity k can exactly be taken into account. It can be shown that the problem treated is linear and is generally of the Laplace type. So, the temperature field T(r, z) in cylindrical coordinates r, z can be calculated if the surface temperature function T(r₀, z), the shape of the growth interface and the temperature-dependent heat conductivity k(T) are known. Numerical examples of temperature fields of silicon crystal growth processes are presented.     

Numerical simulation of MHD rotator action on hydrodynamics and heat transfer in single crystal growth processes

The article presents the results of the mathematical and physical simulations of the influence of a rotating magnetic field (RMF) on the hydrodynamics and heat transfer in processes of large semiconductor single crystal growth in ampoules. Different versions of the RMF are considered, in particular, for symmetric and asymmetric positions of a RMF inductor with regard to the melt in the ampoule, for two counter-rotating magnetic fields, for different geometrical ratios in the “RMF inductor - liquid melt” system, and for different electrical conductivities of the hard walls at their contact with the melt. The interconnection between the distribution of the electromagnetic forces in the liquid volume and the formed velocity patterns, temperature distribution and shape of the solidification front is studied. An original method for the definition of the electromagnetic forces, which considers finite dimensions of the RMF inductor and melt, was used to calculate real conditions of the RMF influence on growth processes. The numerical results obtained are compared to the data of model experiments. Their satisfactory agreement permits us to propose this calculation method for the definition of the optimal parameters of a growth process under specific conditions and to select the most rational type of RMF influence.     

Influence of growth related thickness fluctuations on the spectral and lateral luminescence intensity distribution in GaAs quantum wells

The effect of low energy exciton sinks on the spectral and spatial luminescence intensity distribution has been investigated in a single quantum well (QW) and a multiple QW structure prepared by growth interrupted molecular beam epitaxy (MBE). Both samples contain growth-related lateral variations of the exciton confinement energy on the order of the exciton diffusion length, which cause a lateral and spectral intensity distribution in cathodoluminescence images.     

Influence of the revolution number of the stirrer in viscous liquid on the crystal mass growth rate

The relative velocity between crystal and viscous solution has significant influence on the crystal mass growth rate. In this article a horizontal crystallizer with a stirrer is considered. It appears that in the case of laminar flow of viscous liquid, the relative velocity between crystal and solution doesn't depend on the revolution number of the stirrer and is approximately equal to the settling velocity of the crystal.     

Influence of Coriolis force on thermal convection and impurity segregation during crystal growth under microgravity

In contrast with the generally accepted viewpoint, it is shown that the Coriolis force caused by rotation of an orbital station can appreciably affect natural convection and impurity distribution during the growth of crystals from a melt in orbital flight conditions. 2D and 3D steady and oscillatory convection in a rectangular enclosure is considered. The resonance phenomenon arising due to the interaction of the Coriolis force and harmonic oscillations of the gravity force is demonstrated. It is shown that for moderate values of the Ekman number the Coriolis force suppresses convection in one direction and amplifies it in the other, which in turn results in deformation of the impurity distribution over the cross-section of the crystal.