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.     

Melt Convection in a Czochralski Crucible

2d-axisymmetric of natural and forced convection in the melt of a Czochralski equipment has been performed. The influence of the flow on the shape of the interface has been studied.     

直拉单晶硅生长时空洞演化的相场模拟

为研究大直径直拉硅生长时空洞的演化规律,建立了与有限元模型所模拟的晶体生长温度场相结合的空洞演化相场模型,并应用该模型模拟研究了空洞形貌及其分布状态的变化过程以及不同初始点缺陷浓度对空洞演化的影响规律.结果表明:直拉硅单晶生长过程中,空洞的演化经历了孕育-形核-长大-稳定四个阶段,其形貌和分布状态亦由孤立的球形向偏聚的串珠形转变;与较低的点缺陷浓度相比,初始点缺陷浓度较高时,空洞的数目、平均尺寸、面积分数普遍较大,孕育阶段缩短、形核和长大阶段延长;空洞的偏聚及合并、长大的现象显著;当温度低于980 K时,大直径的空洞数目不再增加.     

Heat and Mass Transport Computation at the Sublimation Growth of SiC

Steady‐state heat and mass transport at the SiC growth process are computed by the general‐purpose finite‐element package FIDAP^TM. Specific features are the radiation exchange in several cavities at temperatures up to 2700 K and concentration dependent Stefan velocities resulting from sublimation/condensation at the vapour‐solid interfaces. The article describes the computational procedure in order to achieve convergence of the temperature and velocity field. The transport rate of the SiC building species meets the range of experimental results.     

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)     

Experimental Study of Interface Inversion of Tb3ScxAl5‐xO12 Single Crystals Grown by the Czochralski Method

Thermal conditions and rotation rate were examined experimentally for obtaining a flat interface growth of high melting‐point oxide (Tb₃Sc_xAl_5‐xO₁₂ ‐ TSAG) by the Czochralski method. The critical crystal rotation rate can be significantly reduced, of about twice at low and very low temperature gradients comparing to medium temperature gradients in the melt and surroundings of the crystal. The interface shape of TSAG crystals is not very sensitive on crystal rotation rate at small rotations and becomes very sensitive at higher rotations, when the interface transition takes place. The range of crystal rotation rates during the interface transition from convex to concave decreases with a decrease of temperature gradients. At low temperature gradients interface inversion crystals takes place in very narrow range of rotation rates, which does not allow one to growth such crystals with the flat interface. Even changing crystal rotation rate during the growth process in a suitable manner did not prevent the interface inversion from convex to concave and thus did not allow to obtain and maintain the flat interface.     

Three‐dimensional numerical investigation of the effects of an open window on the convective heat transfer of an oxide Czochralski system

A three‐dimensional numerical analysis was carried out for a real Czochralski crystal growth furnace containing only gas and without any melt and crystal in order to investigate the effects of a small observation window on the temperature and flow field of the system. For this approach, the induction heating equations, the Navier‐Stokes equation with Boussinesq approximation, the continuity and energy equations have been solved in cylindrical coordinates using the finite element method. It has been found that the flow and thermal fields in the system are obviously three‐dimensional and non‐axisymmetric. The gas enters the system through the window is directed towards the opposite side wall where it is divided into two parts of vertical direction as well as expands in horizontal direction. Consequently, there is a spiral gas flow in the crucible and afterheater which rotates upwards in azimuthal direction along the walls. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of Free Convection on Solid/Liquid Interface in the Czochralski Crystal Growth Method

This paper regards the interaction of free and forced convection in the Czochralski configuration. A relationship between the crystal rotation rate and growth parameters at which the crystallization front remains flat, at which the crystallization front remains almost flat, has been studied. This relationship is compared with experimental data.     

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)     

基于数值模拟的CZSi单晶收尾控制参数研究

采用理论分析和有限元数值模拟相结合的方法研究了晶体收尾过程中的温度分布与热量传递.解释了"倒草帽"形收尾(收尾前段晶体直径猛然收缩)的成因,指出了改进收尾形状的方法,研究结果对于合理设定直拉硅单晶收尾工艺参数具有一定的参考意义.通过对比试验,仿真计算结果与单晶炉实验测试结果相吻合.     

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 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)     

Analysis of Fluid Flow and Heat Transfer in a Gas Phase Crystal Growth Furnace

Steady-state simulations of fluid flow and temperature field are presented for an equipment that is used to grow Zinc Selenide single crystals from the gaseous phases via physical (PVT) or chemical vapour transport (CVT). Due to the horizontal arrangement of the air-filled furnace pipe calculating the natural convection in the air requires a 3D (three-dimensional) treatment of the problem. The simulations have been done by applying the commercial finite-element package FIDAP. The Navier-Stokes equation is solved with the Boussinesq approximation. The heat transfer analysis comprises also internal radiation wall-to-wall exchange. Due to the presence of the ampoule in the pipe, the development of vortices with higher velocities is restrained, so that the maximum velocity is roughly 1/4 of that in the case without an ampoule.     

Growth of KCl crystal by Czochralski method and influence of nanodiamond impurity on its hardness and optical properties

KCl alkali halide crystal with different nanodiamond impurity was grown by Czochralski method. X‐Ray diffraction of the outcome samples reveals that they are still single crystal. Also crystal hardness observation reveals that the hardness of KCl single crystal has been increased by adding different percentage of nanodiamond impurity. In addition, the study of FTIR spectrums of the pure and doped crystals represents that the KCl optical properties has not changed.     

Phase‐field simulation of dendrite growth under forced flow conditions in an Al–Cu welding molten pool

A quantitative phase‐field model for directional solidification is applied to study dendrite growth under forced flow conditions in an Al‐Cu Gas Tungsten Arc (GTA) welding molten pool. Evolution of the dendrite morphology and the solute field under forced flow conditions is simulated. Growth of columnar grains goes through three periods, including the initial instability period, the competitive growth period and the relatively stable period. The solute segregation, the solute redistribution and the solute concentration in the liquid side of the interface are investigated, respectively. For the given conditions, simulation results are in good agreement with experimental findings.     

Experiments on the oscillatory convection of low Prandtl number liquid in Czochralski configuration for crystal growth with cusp magnetic field

This paper presents results of experiments on the oscillatory convection of mercury in a Czochralski configuration with cusp magnetic field. Temperature fluctuation measurements are carried out to determine the critical Rayleigh number for the onset of time dependent natural convection. The effects of a cusp magnetic field on the supercritical natural convection coupled with rotation of crystal disk are investigated. In the presence of a rotating flow it is found that a cusp magnetic field can induce a new long wave instability and can amplify the temperature fluctuation depending on the magnitude of the relevant flow similarity parameters and the melt aspect ratios. A flow regime diagram for the amplification and damping of the temperature fluctuations is presented to provide an experimental data base for finding optimum growth conditions in the cusp magnetic field Czochralski process.     

Time-dependent simulation of the growth of large silicon crystals by the Czochralski technique using a turbulent model for melt convection

A numerical model is developed to perform the dynamic and global simulation of Czochralski growth. The effect of melt convection is taken into account by means of an eddy viscosity flow model, which can represent the mixing effect of flow oscillations on the heat transfer. Our method is used to investigate the dynamics of the growth of a 40 cm silicon crystal.     

Numerical Simulation of the Flow Field and Solute Segregation in Edge‐Defined Film‐Fed Growth

The purpose of this study is to clarify the effect of hydrodynamics and mass transport on the bubble generation in sapphire shaped crystals. The basic idea is that nucleation of bubbles can be anticipated in places were the gas chemical composition is maximum. Finite elements numerical simulation (FIDAP^TM software) is used in order to solve the momentum, mass and chemical species conservation equations in the liquid enclosed in the capillary channel and in the liquid meniscus. A parametric study is performed and the effect of the die geometry and of the physical parameters are clarified. It is shown that the main effect is related to the rejection of the gas at the solid‐liquid interface and that forced and thermo‐capillary convection can explain the experimental observation of the concentration of microbubbles very close to the outer crystal surface in certain cases.