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)     

Numerical simulation of thermal and mass transport during Czochralski crystal growth of sapphire

The thermal and flow transport in an inductively heated Czochralski crystal growth furnace during a crystal growth process is investigated numerically. The temperature and flow fields inside the furnace, coupled with the heat generation in the iridium crucible induced by the electromagnetic field generated by the RF coil, are computed. The results indicate that for an RF coil fixed in position during the growth process, although the maximum value of the magnetic, temperature and velocity fields decrease, the convexity of the crystal‐melt interface increases for longer crystal growth lengths. The convexity of the crystal‐melt interface and the power consumption can be reduced by adjusting the relative position between the crucible and the induction coil during growth. (© 2010 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 influence of substrate temperature on the growth of sexiphenyl on mica(001)

Sexiphenyl thin films were grown by Hot Wall Epitaxy on air‐cleaved mica (001) surfaces at substrate temperatures between 293 K and 440 K. For the entire temperature range, organic thin films show nano‐needle like morphology. The nano‐needles grown at low substrate temperature (293 K) are shortest, and their growth is accompanied by a simultaneous formation of flat islands which disturbs the growth of nano‐needles. On the contrary, unusually long nano‐needles with typical lengths up to the mm range evolve during the growth at a substrate temperature close to the material's thermal desorption temperature at about 440 K. X‐ray diffraction reveals two different crystalline orientations for nano‐needles in the entire temperature range. At low substrate temperatures dominantly the (11 ) plane of the β‐phase is formed parallel to the mica (001) surface. At elevated temperatures another strong texture becomes dominant which is close to the (11 ) crystal orientation. In contrast to this, crystallites with the preferred orientation (001) parallel to the surface of the substrate are formed at low substrate temperature (293 K). This crystal orientation can be associated with flat islands observed in the early growth stage. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On chemical kinetics of silicon deposition from silane (III). LPCVD poly silicon formation in the temperature range 900–950 K

LPCVD poly Silicon deposition form silane has been investigated for limited conditions regarding temperature, silane input and pumping speed. It has been found that layer growth is controlled by a chemical reaction of 0.5^th-order in consequence of which growth rate linearly decays along the axis of an open isothermal reactor tube. The slope of that decay is determined not only by the reaction rate constant but also by linear gas velocity within the tube and that part of total substrate surface area that is effectively exposed to silane at each wafer position. In conseqence growth rate decay is the steeper not only the higher temperature will be chosen but also the slower gas velocity is adjusted and the smaller wafers are separated to each other. The kind of how axial layer growth rate distribution is effected by changing wafer spacing is a proof for the heterogeneous reaction mechanism. The silicon forming reaction is characterised by an activation energy of about 52 kcal/mole.     

Numerical design of Metal‐Organic Vapour Phase Epitaxy process for gallium nitride epitaxial growth

The paper presents the results of numerical simulations and experimental measurements of the epitaxial growth of gallium nitride in Metal Organic Vapor Phase Epitaxy within a AIX‐200/4RF‐S reactor. The aim was to develop optimal process conditions for obtaining the most homogeneous crystal layer. Since there are many factors influencing the chemical reactions on the crystal growth area such as: temperature, pressure, gas composition or reactor geometry, it is difficult to design an optimal process. In this study various process pressures and hydrogen volumetric flow rates have been considered. Due to the fact that it is not economically viable to test every combination of possible process conditions experimentally, detailed 3D modeling has been used to get an overview of the influence of process parameters. Numerical simulations increased the understanding of the epitaxial process by calculating the heat and mass transfer distribution during the growth of gallium nitride. Appropriate chemical reactions were included in the numerical model which allowed for the calculation of the growth rate of the substrate. The results obtained have been applied to optimize homogeneity of GaN film thickness and its growth rate.     

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)     

The numerical simulation of heat and mass transfer during growth of a binary system by the travelling heater method

The influence of convection and heat and mass transfer on the shape and position of melt/solid interfaces and on radial composition segregation is analysed numerically for the travelling heater method growth of a binary alloy in a vertical transparent ampoule. Results are presented for crystal and melt with thermophysical properties similar to Cd_xHg_1−xTe with the assumption that the pseudobinary CdTe-HgTe phase diagram is true. The two-dimensional axisymmetric heat transfer equation, hydrodynamical equation and convective diffusion equation are included in the mathematical model. The rates of crystal growth and dissolution are supposed to be proportional to the compositional supercooling in the melt near the interfaces. It is shown for the conditions when convection is absent that the interfaces are asymmetrically positioned respectively to the heater centre line. Intensive convection makes their position more symmetrical but the length of the liquid zone greater. The flow pattern in the melt appears to be greatly influenced by solutal gravitational convection. The nonlinear dependence of the melt density on the temperature and composition are used in the model. The cases when speed of the heater is antiparallel (stable density stratification) or parallel (unstable stratification) to the vector of gravitational acceleration are considered.     

Reaction kinetics for the CBE growth of GaAs from triethylgallium; computer modelling studies incorporating recent surface spectroscopic data

A new model for the decomposition of triethylgallium on GaAs(100), with kinetic parameters derived from the results of surface science experiments, is presented. Deficiencies of early models are corrected by including surface coverage and site blocking effects, and lateral interactions between absorbed DEG species are included. The model successfully predicts variations in the rate of CBE growth of GaAs with substrate temperature, and addresses effects induced by variations in arsenic overpressure. This dependence of growth rate on the arsenic flux is modelled by computing the steady state concentrations of absorbed arsenic as a function of temperature and As₂ and TEG flux. Excess arsenic is shown to inhibit GaAs growth by blocking sites for TEG absorption.     

Theoretical consideration of the growth kinetics for GaAs and GaSb

An extended MOMBE growth kinetics model is proposed, based on the Robertson model, to explain both the GaAs growth rate variation and modulated beam mass spectroscopy data reported by Martin and Whitehouse. In this model, we assume that (1) MEGa molecules react with ethyl-radicals to form DEGa, (2) excessive group-V molecules on the surface suppress the decomposition of DEGa and enhance the desorption of DEGa, (3) reaction of DEGa with ethyl-radicals to form TEGa is negligible, and (4) effective surface coverage of excessive group-V atoms during growth is determined by the double layer adsorption model including desorption parameters for group-V molecules. The first assumption (1) is found to be a dominant process to explain the behaviour of DEGa desorption at high temperatures. This model can reproduce the dependences of both growth rate and desorbing rate of Ga alkyls on substrate temperature during GaAs MOMBE growth. The use of Sb instead of As produces a significant change in the growth rate variation with substrate temperature and group-V flux for the growth of GaSb, in spite of the use of the same TEGa flow rate. This can be rationalized by the difference in the desorption parameters for Sb and As.     

Transport phenomena analysis for boron CVD in a horizontal cold-wall reactor

The transport phenomena in a horizontal cold-walled semicircular reactor are analyzed for the CVD of boron from BCl₃ and H₂. The mixed problem of energy, momentum, and mass conservations is solved by a simple finite difference method. The concentration of the B-reactant on the deposition surface is substituted by the sum of equilibrium mole fractions of the B-containing gas species. The profiles of temperature, velocity, and reactant concentrations in the CVD reactor are illustrated, and the boron deposition rate profile along the substrate is predicted. The effect of the reactant input composition on the deposition rate is calculated, and compared with the experimental data.     

The influence of natural convection on the mass transfer kinetics in LPE growth

The simplified scheme has been suggested for quantitative estimation of the effect of natural convection on the LPE layers thickness while growing from a finite solution with parallel horizontal and vertical substrates. The convective-diffusive mass transfer model is being developed on the base of boundary layer approximation. In the case of horizontal growth the layer thickness is determined by effective solution thickness which is distinguished for an upper and lower substrate and depends on convection intensity. For the vertical growth system the expression describing the variation of layer thickness along the substrate has been obtained and the vertical temperature gradient necessary for eliminating a wedge shaped growth in this case is calculated. The experimental investigations of LPE growth of GaP layers from finite solution with horizontal and vertical substrates are carried out. The thickness and shape of LPE layers obtained in both cases coincide well with results of calculation.     

PVT法生长大直径6H-SiC晶体感应加热对系统的影响

采用有限元分析法系统地研究了大尺寸6H-SiC晶体PVT法生长装置中感应加热线圈的不同高度和匝间距对生长腔、粉源以及晶体生长温度场的影响;分析比较了线圈不同高度和匝间距时晶体生长面径向温度梯度的变化.结果表明:在中频电源的输出功率和频率固定,盲孔内径不变的情况下,通过调整线圈匝间距和高度可以减小晶体生长面径向温度梯度,改善晶体的质量,同时又有较高的生长速率.     

Vapour-phase epitaxial growth of ZnS on GaP

Single crystal layers of ZnS about 100 μm thick were grown epitaxially on GaP substrates in an open tube system using source ZnS powder and a flowing hydrogen atmosphere. The growth rate for different substrate temperatures increases with increasing hydrogen flow rate, but the growth rate profiles resemble each other in shape. The profile shifts towards the low temperature side as the source temperature is decreased. The (111)B substrate orientation is found to be preferable to the (111)A or the (100) with respect to surface morphology and crystal quality. X-ray diffraction investigations and luminescent properties show that the (111)B grown layers are of high quality. All ZnS layers grown on GaP substrates are craked on cooling, which may be due to the thermal expansion mismatch between the layer and the substrate. Heat-treatment of the grown layer does not reduce the resistivity, but increases the photoluminescence intensity markedly. Selective vapour-phase epitaxial growth has been successfully applied resulting in crack-free ZnS layers on GaP substrates.     

分子束外延生长过程中GaAs(001)表面铝液滴的扩散成核过程

量子点的性质主要由其密度及尺寸参数控制,而原子在衬底上的成核运动又决定了量子点的密度、直径、高度等参数,因此研究原子的扩散成核过程对自组装制备量子点具有重要意义.本文通过分子束外延生长技术研究了GaAs(001)表面金属铝液滴的成核过程,发现衬底温度和金属铝沉积速率的变化直接影响了液滴的尺寸、密度以及形状等特征.根据经...     

Large eddy simulation of Marangoni convection in Czochralski crystal growth

Large eddy simulation model is used to simulate the fluid flow and heat transfer in an industrial Czochralski crystal growth system. The influence of Marangoni convection on the growth process is discussed. The simulation results agree well with experiment, which indicates that large eddy simulation is capable of capturing the temperature fluctuations in the melt. As the Marangoni number increases, the radial velocity along the free surface is strengthened, which makes the flow pattern shift from circumferential to spiral. At the same time, the surface tension reinforces the natural convection and forces the isotherms to curve downwards. It can also be seen from the simulation that a secondary vortex and the Ekman layer are generated. All these physical phenomena induced by Marangoni convection have great impacts on the shape of the growth interface and thus the quality of the crystal. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

外加氩气流下脉冲激光烧蚀制备纳米硅晶粒成核生长动力学研究

为研究纳米硅晶粒成核生长动力学过程,采用脉冲激光烧蚀(PLA)技术,在室温,50～200 Pa的氩气氛围中,通过引入垂直于烧蚀羽辉轴线的外加气流,在水平放置的衬底上沉积了一系列纳米Si晶薄膜.扫描电子显微镜( SEM)、拉曼(Raman)散射和X射线衍射(XRD)检测结果表明,未引入气流时,衬底上相同位置处晶粒尺寸随气体压强的增大逐渐减小;在距靶1 ～2cm范围内引入气流后,尺寸变化规律与未引入气流时相反.通过分析晶粒尺寸及其在衬底上的位置分布特点,结合流体力学模型和热动力学方程,分析得出在激光能量密度一定的条件下,环境气体压强、烧蚀粒子温度和密度共同影响着纳米晶粒的成核生长.     

Numerical study of radial temperature distribution in the AlN sublimation growth system

A large radial temperature gradient in the AlN sublimation growth system would lead to non‐uniform growth rate along the radial direction and introduce thermal stress in the as grown crystal. In this paper, we have numerically studied the radial thermal uniformity in the crucible of a AlN sublimation growth system. The temperature difference on the source top surface is insignificant while the radial temperature gradient on the lid surface is too large to be neglected. The simulation results showed that the crucible material with a large thermal conductivity is beneficial to obtain a uniform temperature distribution on the lid surface. Moreover, it was found that the temperature gradient on the lid surface decreases with increased lid thickness and decreased top window size.     

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Kyropoulos (Ky) method is the most suitable technique for the growth of high‐quality sapphire single crystal for substrate applications. Cracks are often observed in the grown ingot that significantly reduces industrial productivity. In the paper, cracking causes are analyzed by examining crystal shape, thermal stress and three‐dimensional effects during the stable growth of sapphire crystal. It is found that locally induced thermal stress around the shoulder of the crystal is the largest. However, thermal stress is not fully responsible for the cracks, since the predicted stress level is lower than a critical value regarding crystal cracking. Polycrystalline growth or/and other crystal defects must be another factor that degrades the critical value and makes the crystal more fragile. Simulation results further show that crystal shape has less effect on the thermal stress level, although experiments have shown that crack‐free crystals usually have smooth surfaces. The initial cracking position in the ingot predicted in simulation agrees well with experimental observation after considering crystal defects in a qualitative discussion. From the view of three‐dimensional simulation, the variation of heating condition during growth may result in high thermal stress locally that leads to the cracks at one side of the crystal. Additionally, three‐dimensionally unexpected temperature drop of the heater may be responsible for the sticking‐to‐crucible phenomenon at the shoulder region of the grown crystal.     

Clathrate-hydrate film growth along water/hydrate-former phase boundaries—numerical heat-transfer study

This paper describes two analytic models for the heat-transfer-controlled lateral growth of a clathrate-hydrate film along a planar interface between liquid water and an immiscible hydrate-forming fluid (or guest fluid), such as methane or carbon dioxide. The two models are different from each other only regarding the assumption of the film-front geometry. Either model assumes the film to be uniform and constant in thickness, ignoring possible changes in the thickness on a time scale relevant to its lateral growth. Another fundamental assumption employed in the model is that the film's hydrate-forming front is maintained at the hydrate/guest/water three-phase equilibrium temperature, thereby forming a two-dimensional temperature distribution in the surrounding three-phase space. Based on these assumptions, the transient, two-dimensional conductive heat transfer from the film front into the three phases is formulated and numerically solved to give the instantaneous rate of lateral film growth (i.e., the linear speed of the film-front) along the water/guest-fluid interface, while the film thickness is arbitrarily assumed as a fitting parameter. By comparing the predicted rates of film growth with the corresponding experimental data obtained with methane or carbon dioxide as the guest fluid, we estimated the film thickness to be about 10–20 μm for the methane hydrate at a pressure of 9.06 MPa and about 0.5 μm for the carbon-dioxide hydrate at a pressure of 5 MPa.