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)     

Liquid phase epitaxy set‐up designed for in situ X‐ray study of SiGe island growth on (001) Si substrates

In situ X‐ray examination at a synchrotron beamline of the solution growth of self‐assembled SiGe structures on silicon (001) substrates through the backside has been realized by a specific heating equipment and a suitable growth assembly. The furnace allows heating of the growth assembly up to 600 °C. The temperature field and the gas flow in the furnace have been numerically modeled. In this way a meaningful estimate about the power consumption and the thermal gradient across the sample has been reached. Despite its low heat capacity and, thus, fast heating and cooling ability the furnace can be stabilized to ± 0.1 K by a high‐performance temperature controller. The growth assembly has been prepared within three separate stages carried out in conventional slideboat liquid phase epitaxy equipment. Such growth assembly allows carrying out then intended experiments without H₂ as normally used in liquid phase epitaxy in favor of N₂, meeting the demand of minimized risks at beamlines. The equipment ensures an easy handling of the growth assembly. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Design of Double‐Ellipsoid Mirror Furnace and its Thermal Characteristics for Floating‐Zone Growth of SrxBa1‐xTiO3 Single Crystals

We have designed a double ellipsoid mirror furnace for floating‐zone crystal growth using lamps with rectangular filaments. Its thermal characteristics were studied using an alumina tube for several system configurations. A simple comparison with a commercial furnace that used cylinder lamps for the heating profile was also conducted. By adjusting lamp orientation and positions, one could modify heating profiles easily. In general, the thermal characteristics of the furnace were consistent with the model's prediction [J. Crystal Growth 173 (1997) 561]. The effects of growth chamber and heat pipe were further illustrated. Furthermore, a suitable system configuration leading to better heating uniformity and lower thermal gradients near the growth interface was found for the floating‐zone growth of Sr_xBa_1‐xTiO₃ single crystals.     

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.     

热屏下降式单晶炉设计与研究

光伏发电以绿色、可再生、能源质量高和不受资源分布地域的限制等优点被广泛使用,单晶硅又以低衰减率和高转换效率等优点渐渐超过了多晶硅光伏电池在市场中的份额,但成本问题和产能问题一直束缚着单晶硅太阳能产业的发展。本文提出了一种在晶体生长过程中随硅液面下降而下降的直拉单晶炉热屏结构,来解决在拉晶过程中坩埚上升所造成的拉晶速度和稳定性降低以及拉晶能耗增加的问题,并以CL120-97单晶炉热场为研究对象,利用有限元仿真对单晶炉优化前后晶体和熔体的热场以及氩气流场进行分析。分析仿真结果表明,优化后单晶炉不仅可以提高单晶炉拉晶的速度和质量,而且还能有效降低单晶炉拉晶的能耗。     

直拉法单晶炉随动式加热器设计

单晶炉是一种在以高纯氩气为主的惰性气体环境中,用石墨热场加热,将多晶硅材料加以熔化,用直拉法生长单晶硅的设备,在太阳能单晶硅拉制的过程中,如何提高拉晶的速度和质量以及降低设备的能耗一直是单晶硅厂家永恒的追求。本文从机械结构的角度分析了坩埚上升在单晶炉拉晶过程中所造成的拉晶速度下降和额外能耗问题,在此问题的基础上提出了一种加热器随坩埚在拉晶过程中上升的单晶炉结构优化方法,并通过有限元仿真对单晶炉优化前后晶体和熔体的热场以及拉晶过程中加热器功率进行分析。结果表明,改进后的单晶炉不仅可以提高拉晶过程的稳定性和拉晶速度,从而进一步提高单晶炉的拉晶质量和产量,而且还能有效降低单晶炉拉晶的能耗。     

Macro-segregation, dynamics of interface and stresses in high pressure LEC grown crystals

High dislocation density and strong dopant inhomogeneities have been found in high pressure liquid-encapsulated Czochralski (HPLEC) grown crystals. The origin and underlying mechanisms of these defects are attributed to the complex nature of transport phenomena in the HPLEC system. Our integrated computer model (MASTRAPP) can simulate this process by calculating the flow and heat transfer in both the melt and the gas, and thermal-elastic stress in the crystal. In this work, this model has been further extended to investigate the development of thermal stress in the growing crystal and the redistribution of dopant in the melt. The results for InP growth show complex gas flow and heat transfer pattern in the system. Two large stress spots are predicted by the model, one at the edge of the crystal just above the encapsulant layer and the other in the top corner of the crystal. Although the stress always remains largest at the first location, its value decreases as the crystal grows, due to the enhanced cooling of the crystal. A curved crystal/melt interface is also found to introduce high thermal stresses in its vicinity, which may be dangerous because of a high temperature at the interface and thus a low strength of the crystal. The model also predicts both radial and longitudinal dopant segregation in the growing crystal, and shows that the dopant redistribution in the melt is caused by the complex flow pattern in the melt. This is the first time, that a strong radial dopant segregation has been predicted based on a comprehensive flow model for a HPLEC growth.     

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)     

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)     

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)     

半导体单晶生长过程中的位错研究

阐述了现有的半导体单晶位错模型,即临界切应力模型和粘塑性模型的基本理论及应用状况.分析了熔体法单晶生长过程中影响位错产生、增殖的各种因素,以及抑制位错增殖的措施.与熔体不润湿、与晶体热膨胀系数相近的坩埚材料,低位错密度的籽晶可有效地抑制生长晶体的位错密度;固液界面的形状及晶体内的温度梯度是降低位错密度的关键控制因素,而两因素又受到炉膛温度梯度、长晶速率、气体和熔体对流等晶体生长工艺参数的影响.最后,对熔体单晶生长过程的位错研究进行了展望.     

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)     

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.     

Numerical and experimental studies on crack formation in LiNbO3 single crystal

A global analysis of heat transfer was carried out in an inductively heated Czochralski (CZ) furnace which was actually used to grow LiNbO₃ single crystals, and then the temperature profiles obtained were used to calculate the three-dimensional thermal stress field in the crystal. By comparing the numerical results with the experimental ones, it was found that controlling the thermal environment in the CZ furnace so that the thermal stresses at the crystal surface might not exceed a certain value is important to realize the cracking free growth operation. In this study, this was accomplished through some modifications in the furnace design such as insertion of an after-heater into the furnace. These findings were verified by additional numerical simulations and crystal growth experiments for some growth conditions.     

热屏结构对泡生法蓝宝石单晶炉功率影响研究

蓝宝石晶体因优异的综合性能被广泛用于航空航天等高性能要求领域.泡生法是目前生产大直径蓝宝石单晶的主要方法,热场对生产工艺、产品质量和单晶炉功率具有重要影响;并将影响生产成本.本文对氧化锆及钼金属组合式热屏中氧化锆材料内置、外置及材料不同组合方式对泡生法蓝宝石单晶炉功率的影响进行研究,得到合理的热场结构;并与实际生产结果进行验证.结果表明:相比于传统的15层钼保温结构,加入氧化锆保温层会明显降低单晶炉能耗,其中氧化锆内置的热场结构对单晶炉能耗降低影响更为明显;随着氧化锆层由0增加至15层,单晶炉能耗显著降低,相比传统15层钼保温结构,15层氧化锆保温结构炉体功率降低了38;.     

大尺寸电阻加热式碳化硅晶体生长热场设计与优化

大尺寸低缺陷碳化硅(SiC)单晶体是功率器件和射频(RF)器件的重要基础材料,物理气相传输(physical vapor transport, PVT)法是目前生长大尺寸SiC单晶体的主要方法。获得大尺寸高品质晶体的核心是通过调节组分、温度、压力实现气相组分在晶体生长界面均匀定向结晶,同时尽可能减小晶体的热应力。本文对电阻加热式8英寸(1英寸=2.54 cm)碳化硅大尺寸晶体生长系统展开热场设计研究。首先建立描述碳化硅原料受热分解热质输运及其多孔结构演变、系统热输运的物理和数学模型,进而使用数值模拟方法研究加热器位置、加热器功率和辐射孔径对温度分布的影响及其规律,并优化热场结构。数值模拟结果显示,通过优化散热孔形状、保温棉的结构等设计参数,电阻加热式大尺寸晶体生长系统在晶锭厚度变化、多孔介质原料消耗的情况下均能达到较低的晶体横向温度梯度和较高的纵向温度梯度。     

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.     

Thermal simulation of the Czochralski silicon growth process by three different models and comparison with experimental results

Temperatures were measured within an industrial Czochralski silicon puller and compared with simulation results. The temperatures were measured by thermocouples in the crystal along the axis as well as inside the lateral and bottom insulations. The temperature distribution of the furnace was computed using three different software codes. It could be demonstrated that today's simulation methods are capable of handling such a complex heat transfer simulation task as that encountered in the case of Czochralski silicon growth furnaces, with the exception of the melt convection problem, which has not yet been satisfactorily solved.     

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.     

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)