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.     

Two and three‐dimensional numerical modeling of induction heating in oxide Czochralski systems

In this article we report on a set of two‐dimensional and three‐dimensional numerical calculations for three different oxide Czochralski configurations in order to compare the results of the electromagnetic fields and the heat generation distribution. Two configurations without and with a gap between the crucible and active afterheater have axisymmetric conditions while the configuration with an open observation window in the afterheater is characterized by a non‐axisymmetric geometry. It has been found that in the non‐axisymmetric configuration under the influence of the observation window is located at the crucible side wall after a short distance behind the window cut out. Besides this influence the volumetric distribution of heat generation in the system is about symmetric. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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.     

Three‐dimensional study of the pressure field and advantages of hemispherical crucible in silicon Czochralski crystal growth

The effects of several growth parameters in cylindrical and spherical Czochralski crystal process are studied numerically and particularly, we focus on the influence of the pressure field. We present a set of three‐dimensional computational simulations using the finite volume package Fluent in two different geometries, a new geometry as cylindro‐spherical and the traditional configuration as cylindro‐cylindrical. We found that the evolution of pressure which is has not been studied before; this important function is strongly related to the vorticity in the bulk flow, the free surface and the growth interface. It seems that the pressure is more sensitive to the breaking of symmetry than the other properties that characterize the crystal growth as temperature or velocity fields. (© 2010 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)     

Uniformity analysis of temperature distribution in an industrial MOCVD reactor

Three‐dimensional models, coupling fluid flow and heat transfer, have been adopted to analyze influences of the process parameters on the temperature uniformity in an industrial MOCVD reactor. Important factors, such as the inlet gas flow, the susceptor rotation, the heater power, the distance between the heat shield and the susceptor (d₁), as well as the distance between the heater and the susceptor (d₂), have been investigated carefully. The system heating condition is characterized by temperature uniformity denoted as the standard deviation of temperature, and by thermal efficiency expressed as a combination parameter of the dissipated energy. The results reveal that decrease of the gas flow and the rotation rate, as well as increase of the distance d₁, could monotonically enhance the temperature uniformity. The results also show that decrease of the above three parameters could improve the thermal efficiency. Furthermore, increase of the distance d₂ enhances the temperature uniformity, and reduces the thermal efficiency slightly. The influences of the parameters on the uniformity vary at the different locations of the susceptor as divided into Zone A, Zone B and Zone C. The conclusions help the growth engineer optimize the system design and process conditions of the reactor.     

Growth of ZnO single crystals by an induced nucleation from a high temperature solution of the ZnO‐PbF2 system

To grow ZnO single crystals from a high temperature solution of the ZnO‐PbF₂ system, a gas cooling system was assembled at the bottom of the crucible to induce nucleation in the initial growth stage. The growth experiments were carried out in a homemade vertical Bridgman furnace and Pt crucible of 28 mm in diameter was used. The furnace temperature was set to 1100°C and the flow rate of the oxygen gas was optimized as 3.0 l/min. ZnO crystal up to 5∼8mm in the thickness was obtained with the lowering rate of 0.3 mm/h. XRD patterns showed that the as‐grown crystal was pure ZnO Wurtzite phase. The impurity ions were analyzed by the glow discharge mass spectroscopy (GDMS) as 390.0 ppm and 40.0 ppm for Pb²⁺ and F^‐, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three‐dimensional thermoelastic stresses in off‐axis oriented single crystals with hexagonal symmetry

A three‐dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off‐axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle ϕ of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite‐element method. In our example, the off‐axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non‐zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 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)     

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)     

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)     

Effect of different solvents on the habit of meta‐nitroaniline single crystals

The habit of the organic non‐linear optical material meta‐nitroaniline (mNA) crystallized from different organic solvents such as acetone, benzene, ethyl acetate, n‐hexane, methanol and toluene were studied. Solubility of mNA in these solvents at various temperatures in the range between 288 and 323 K was determined by gravimetric method. Crystals were grown by restricted evaporation of solvents method. Solutions with different solvents having different chemical nature and polarity yielded crystals with different habits: one‐dimensional needles, two‐dimensional rhombic platelets and three‐dimensional octahedral. In addition, the mNA crystals show unidirectional growth behaviour along its polar [001] direction irrespective of the solvents used. All the grown crystals were found to be orthorhombic system with point group mm2 and space group Pbc2₁ which was confirmed by powder X‐ray diffraction study. Optical transmittance study showed that the grown mNA single crystals have optical transparency in the wavelength range between 430 and 1550 nm. SHG efficiency of the grown mNA crystal was 3 times grater than KDP. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental investigation of different configurations for the seeded growth of SiC crystals via a VLS mechanism

The growth of SiC crystals or epilayers from the liquid phase has already been reported for many years. Even if the resulting material can be of very high structural quality and the possibility to close micropipes was demonstrated, handling the liquid phase still is a challenge. Moreover, it is highly difficult to stabilize the C dissolution front and then to stabilize the growth front over a long growth time. Based on the Vapour‐Liquid‐Solid (VLS) mechanism, we present a new configuration for the growth of SiC single crystal which should allow first to simplify the liquid handling at high temperature and second to precisely control the crystal growth front. The process consists in a modified top and bottom seeded solution growth method, in which the liquid is held under electromagnetic levitation and fed from the gas phase. 3C‐SiC crystals exhibiting well‐faceted morphology were successfully obtained at 1100‐1200 °C with exceptional growth rates, varying from 1 to 1.5 mm/h in Ti‐Si melt. It was shown that the nucleation density decreases simultaneously with increasing propane partial pressure. At 1200‐1400 °C, thick homoepitaxial 6H‐SiC layers were successfully obtained in Co‐Si and Ti‐Si melts, with growth rate up to 200 µm/h. Large terraces with smooth surfaces are observed suggesting a layer by layer growth mode, and the influence of the system pressure was demonstrated. It was shown that the terrace size decrease simultaneously with increasing propane partial pressure which suggests the beginning of a two dimensional to three dimensional growth mode transition. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Measurement of three‐dimensional concentration gradients around a crystal growing from its aqueous solution using laser schlieren

Schlieren measurements of the gradients of the concentration field around a KDP crystal growing from its aqueous solution are reported. The measurement of the concentration gradient field is important for crystal growth because it controls the rate of solute transport from the bulk of the solution to the crystal surface. In the crystal vicinity, the concentration gradients have a three dimensional distribution. The concentration gradient field has been imaged using monochrome schlieren technique. Four view angles, namely 0, 45, 90 and 135° have been utilized. By interpreting the schlieren images as projection data of solute concentration gradient, the three‐dimensional concentration gradient field around the crystal has been determined using an algebraic reconstruction technique. At low supersaturation levels, the growth process is accompanied by weak fluid movement during which diffusion effects are significant. At higher levels of supersaturation and large crystal size, a well‐defined convective plume around the growing crystal is observed. Reconstruction of concentration gradients around the crystal explains the preferential growth rates of various faces of the crystal. The non‐circular shape of the crystal is seen to affect the symmetry of the distribution of concentration gradients in its vicinity. The effect of crystal morphology on the orientation of convection currents rising from the crystal surface has also been brought out on the basis of the reconstructed concentration gradients distribution in the growth chamber. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of induction heating and heat transfer in a SiC growth system

A global simulation model is applied for a silicon carbide growth system heated by induction coils. A finite‐volume method (FVM) and a global model are applied to solve the equations for electromagnetic field, conductive and radiative heat transfer. The growth rate is predicted by Hertz‐Knudsen equation and one‐dimensional mass transfer equation. Further, simulations for five different coil positions are carried out to investigate the effects of coil position on temperature distribution in the furnace. The numerical results reveal that the variation of temperature in the radial direction along the substrate surface and the temperature difference between the powder and substrate are greatly affected by the coil position. The predicted growth rate along the substrate surface for five coil positions is also studied. Finally, a reasonable range of coil positions maintaining a balance between large‐diameter crystal, high growth rate, temperature limitation of material and lower electrical power consumption is obtained. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D simulation of the effects of growth parameters on the growth of sapphire crystals using heat exchanger method

3D simulations using the commercial CFDRC and FIDAP code, which are based on finite element techniques, were performed to investigate the effects of anisotropic conductivity on the convexity of the melt–crystal interface and the hot spots of sapphire crystal in a heat‐exchanger‐method crystal growth system. The convection boundary conditions of both the energy input to the crucible by the radiation as well as convection inside the furnace and the energy output through the heat exchanger are modeled. The cross‐sectional flow pattern and the shape of the melt–crystal interface are confirmed by comparing the 3‐D modeling results with previous 2D simulation results. In the 3D model, the “hot spots” in the corners of the crucible are donut shaped, and the shape changes with the value of the conductivity of anisotropic crystal. The outline of the crystal becomes more convex as the conductivity in the z direction (k_sz) increases. The outline of melt–crystal interface is elliptical when the anisotropic conductivity is moving in the radial direction (k_sx and k_sy). The portion at the outline touching the bottom of the crucible is smaller than the maximum outline of the crystal, meaning that the shape at the “hot spot”, changes with the value of the conductivities of anisotropic crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropy of the optical absorption in layered single crystals of MoRe0.001Se1.999

Energy gap of MoRe_0.001Se_1.999 single crystal has been determined by fundamental absorption methods. The incident light was polarized along c‐axis of the crystals. The interpretion of the data is given within frameworks of two and three dimensional models. Both direct and indirect transitions are involved in the absorption process. The indirect transition was found to be allowed with two phonons participating in the process. The three dimensional model could be used to describe the optical properties of the single crystal. The energy gaps depend upon the amount of the intercalating Re material, which show the anisotropy of the chemical bonds. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

KDP single crystal growth via three‐dimensional motion growth method

A novel system for rapid crystal growth, namely three‐dimensional motion growth method (“3D MGM”) was proposed. Using this system, a potassium dihydrogen phosphate (KDP) seed was grown to a single crystal with a final size of 50×55×85 mm³. The KDP crystal was characterized by Raman spectroscopy, UV‐vis‐NIR spectroscopy, extinction ratio, laser damage threshold, and etching studies. Raman spectrum shows KDP crystal grown by “3D MGM” maintains good crystallinity as that grown by rotating‐crystal method (“RCM”). The “3D MGM” grown KDP crystal has much better transmittance, higher extinction ratio, higher damage threshold and less dislocation density, compared to “RCM” grown crystal.