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)     

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)     

Combined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growth

In order to understand the influence of crucible geometry combined with natural convection and Marangoni convection on melt flow pattern, temperature and pressure fields in silicon Czochralski crystal growth process, a set of numerical simulations was conducted. We carry out calculation enable us to determine temperature, pressure and velocity fields in function of Grashof and Marangoni numbers. The essential results show that the hemispherical geometry of crucible seems to be adapted for the growth of a good quality crystal and the pressure field is strongly affected by natural and Marangoni convection and it is more sensitive than temperature. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global simulation of a Czochralski furnace for silicon crystal growth against the assumed thermophysical properties

In order to understand the effects of the thermophysical properties of the melt on the transport phenomena in the Czochralski (Cz) furnace for the single crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnace (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) was carried out using the finite‐element method. The global analysis assumed a pseudosteady axisymmetric state with laminar flow. The results show that different thermophysical properties will bring different variations of the heater power, the deflection of the melt/crystal interface, the axial temperature gradient in the crystal on the center of the melt/crystal interface and the average oxygen concentration along the melt/crystal interface. The application of the axial magnetic field is insensitive to this effect. This analysis reveals the importance of the determination of the thermophysical property in numerical simulation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 carbon and silicon carbide contamination during the melting process of the Czochralski silicon crystal growth

Carbon contamination in single crystalline silicon is detrimental to the minority carrier lifetime, one of the critical parameters for electronic wafers. In order to study the generation and accumulation of carbon contamination, transient global modeling of heat and mass transport was performed for the melting process of the Czochralski silicon crystal growth. Carbon contamination, caused by the presence of carbon monoxide in argon gas and silicon carbide in the silicon feedstock, was predicted by the fully coupled chemical model; the model included six reactions taking place in the chamber. A simplified model for silicon carbide generation by the reaction between carbon monoxide and solid silicon was proposed using the closest packing assumption for the blocky silicon feedstock. The accumulation of carbon in the melted silicon feedstock during the melting and stabilization stages was predicted. Owing to this initial carbon content in the melt, controlling carbon contamination before the growth stage becomes crucial for reducing the carbon incorporation in a growing crystal.     

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.     

The Czochralski Method ‐ where we are 90 years after Jan Czochralski’s invention

The Czochralski method, i.e. pulling a crystal from the melt, became the most important technology for the production of large semiconductor (Si, GaAs, InP, GaP …) and optical crystals (oxides, CaF₂ …). The present status is achieved by a profound analysis of the mechanisms of heat and species transport which are relevant for the stability of the Czochralski growth process and the performance of the growing crystal. It was clearly demonstrated in the last few years that modeling by numerical simulation is an indispensable tool to analyze the Czochralski process and to understand the governing mechanisms. The contribution presents examples of this kind of modeling the Czochralski technique in correlation with experimental investigations in order to illustrate the present status of understanding relevant processing phenomena. Furthermore, it is shown what problems need still to be solved in the future in order to further improve the yield and quality of Czochralski‐grown crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global simulation of coupled carbon and oxygen transport in a Czochralski furnace for silicon crystal growth

For accurate prediction of carbon and oxygen impurities in a single crystal produced by the Czochralski method, global simulation of coupled oxygen and carbon transport in the whole furnace was implemented. Both gas-phase transportation and liquid-phase transportation of oxygen and carbon were considered. With five chemical reactions considered, SiO and CO concentrations in gas and C and O atom concentrations in silicon melt were solved simultaneously. The simulation results show good agreement with experimental data.     

Characterization of a Czochralski grown silicon crystal doped with 1020 cm‐3 germanium

A dislocation‐free silicon single crystal doped with 10²⁰ cm^‐3 germanium (Ge) has been grown using the Czochralski (CZ) growth technique. The Ge concentration in the seed‐end and tang‐end of the crystal was 8×10¹⁹cm^‐3and 1.6×10²⁰ cm^‐3, respectively. The effective segregation coefficient of Ge, the distribution of flow pattern defects (FPDs) and the wafer warpage have been characterized. Both the effective segregation coefficient and the equilibrium segregation coefficient of Ge in silicon were evaluated. Then, the density of FPDs was traced from seed‐end to tang‐end of the ingot, a suppression of FPDs by Ge doping was shown. That is probably because the Ge atoms consume free vacancies and thus a higher density of smaller voids is formed. Furthermore, the mechanical strength of wafers has also been characterized by batch warpage analysis. The warpage in the seed‐end was larger than that in the tang‐end of the ingot, showing that the mechanical strength of wafers is enhanced by Ge doping. Such improvement is interpreted by an enhanced dislocation pinning effect associated with the enhanced nucleation of grown‐in oxygen precipitates in the Ge‐doped silicon wafers. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

提拉法制备铜单晶研究

采用提拉法生长出大尺寸(111)铜单晶,晶体尺寸为ф(12～19)mm×85 mm.通过XRD、金相显微分析讨论了铜单晶的晶体结构与生长缺陷,并采用双臂电桥测定(111)铜单晶的电阻率.结果表明:晶体具有(111)取向、强度高,表明晶体取向良好;蚀坑呈典型三角锥形,位错密度在105～106 cm-2之间;在室温下,(111)铜单晶电阻率为1.289×10-8Ω·m.     

钼酸铅单晶生长及其缺陷研究

本文通过CZ法生长钼酸铅单晶,讨论了温度梯度、拉速、转速等生长参数对晶体质量的影响,分析了晶体开裂、包裹物等宏观缺陷以及位错等微观缺陷的形成机理,并从晶体形态、包裹体和位错密度变化方面探讨了晶体生长参数与晶体缺陷之间的内在关系,从而优化温度梯度等生长参数.温度梯度为20～25℃/cm,晶体转速为28r/min,拉速为1.6mm/h时,生长出的晶体形态完整,无开裂现象,晶体中无气泡包裹体,位错密度明显减小,晶体尺寸达φ40mm×70mm,无散射颗粒,在波长0.42～5.5μm范围内,平均透光率为72.6;.     

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.     

Intrinsic gettering in germanium-doped Czochralski crystal silicon crystals

The intrinsic gettering (IG) of germanium-doped Czochralski (GCZ) silicon with different concentrations of germanium has been investigated in this paper. The conventional Czochralski (CZ) and the GCZ silicon samples were annealed using a one-step high temperature process followed by a sequence of low–high temperature annealing cycles. It was found that the good defect-free denude zones in the near surface of the GCZ silicon could be achieved using simply a one-step high temperature annealing process. Furthermore, the density of bulk microdefects as IG sites was higher than that in the CZ silicon, as a result of germanium enhancing oxygen precipitation during three-step annealing. Meanwhile, the experimental results showed that germanium also enhanced the out-diffusion of oxygen. Furthermore, it is believed that germanium doping can increase the ability of IG in CZ silicon wafers.     

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.     

Boron segregation control in silicon crystal ingots grown in Czochralski process

Boron-doped silicon single crystals of 207 mm diameter with various growing conditions are grown from a large amount of the melt in the cusp-magnetic Czochralski method, and the effects of growing parameters on dopant concentrations in the crystals are experimentally investigated. Equilibrium distribution coefficient of boron calculated by BPS model is 0.716. With the crystal rotation (ω) of 13 rpm and the crucible rotation of , the effective distribution coefficient (k_e) is 0.751 in zero magnetic strength and increases up to 0.78 in the magnetic strength of 640 G. For , there is no significant influence of ω on k_e. With , k_e is almost unity. The experimental results are compared with theory.     

提拉法晶体生长数值模拟研究进展

数值模拟方法是了解晶体生长过程中各种物理现象和问题的重要手段,可以为晶体生长工艺参数的设定、温场设计等提供参考.本文介绍了最近几十年来数值模拟技术对提拉法生长晶体过程中物理问题的研究进展,同时对晶体生长过程中界面形状、液流、速度场、温度场、各种输运过程以及工艺条件和参数对晶体生长的影响等的数值模拟进行了介绍.     

Nd:YVO4 crystal growth by Czochralski technique with a submerged plate

This paper is to investigate the growth of Nd:YVO₄ (yttrium vanadate) crystal by the modified Czochralski technique with a submerged plate. Numerical studies are performed to examine melt convection and heat transfer during Nd:YVO₄ growth. The attention is paid to study the effects of initial elevation of the submerged plate, crystal diameter, and melt level on melt inclusions. It is found that the increase in crystal rotation rate and crystal diameter, and the decrease in melt level will increase the axial temperature gradient at the edge and in the center of the crystal, and change the interface shape from convex to flat. The experiments are also carried out to confirm the feasibility of the proposed new technique for controlling melt inclusions in Nd:YVO₄ crystal growth.     

Czochralski growth of Lu1‐xScxBO3:Ce solid solution crystals

Single crystals of Lu_1‐xSc_xBO₃:Ce (x=0.2, 0.3, 0.5, 0.7) were grown by Czochralski method. Continuous solid solution with calcite structure and a linear compositional dependency of crystal lattice parameter in the system Lu_1‐xSc_xBO₃:Ce are formed and their symmetry belong to hexagonal system with R3c space group checked by X‐ray powder diffraction. The electron probe micro‐analysis measurements show that the main inclusions in Lu_1‐xSc_xBO₃:Ce crystals are in the form of Sc rich oxide and Ce rich oxide. The ICP‐AES tests show that the more Sc ion content in Lu_1‐xSc_xBO₃:Ce, the smaller effective segregation coefficient of Ce in crystal will be. The X‐ray excited luminescence spectra of Lu_1‐xSc_xBO₃:Ce crystals all present a double peaked emission band with maxima round 370 and 400 nm corresponding to Ce³⁺ emission and a self trapped excitons (STE) band peaking at 269 nm. In addition, due to high density, high relative light yield, fast decay time and no‐hygroscopic property, Lu_0.8Sc_0.2BO₃:1 at%Ce crystal could be a good candidate material for scintillation application by improving the crystal quality and cerium concentration. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)