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.     

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.     

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)     

Effect of the Temperature Fluctuation of the Melt on β‐BaB2O4 (BBO) Crystal Growth

In this paper the effect of the growth temperature fluctuation, for instance, the transient furnace temperature variation due to a short‐term electric power supply interruption on BBO crystal growth was investigated based on the theory of temperature wave transmitting in melt and the boundary layer theory of melt. It was found that the critical width of the temperature pulse to avoid the temperature wave penetrating through the boundary layer and reaching to the growth interface at a constant rotation speed (9∼4 r/min) is 69∼150 s and the corresponding amplitude of the temperature pulse is high more than 60 °C due to the large thickness of the velocity boundary layer of the melt. This result indicates that a small transient temperature fluctuation has no significant effect on the crystal quality, and therefore implies that not only transport processes but interface growth kinetics, a two‐dimensional nucleation growth mode at the interface may also dominate the crystal growth.     

Evolution of real structure in Ge‐Si mosaic crystals

The structure and properties of Czochralski (Cz)‐grown Ge_1‐xSi_x mosaic crystals were investigated using optical microscopy, atomic force microscopy, X‐ray diffraction analysis, microprobe analysis, FTIR and transmission electron microscopy. The role of segregation, form of solid‐liquid interface and dislocation generation in the development of mosaic structure were analyzed and used for optimization of growth parameters such as Si concentration and growth rate. The dislocation density estimated experimentally was compared with the calculated data. Composition fluctuations caused by formation of cellular structure at the interface lead to a local lattice misorientation that is one of the reasons for crystal mosaicity. Model of mosaic structure generation in terms of dislocation density and composition variations is presented.     

Numerical investigation of crystal growth process of bulk Si and nitrides – a review

Heat and mass transfer during crystal growth of bulk Si and nitrides by using numerical analysis was studied. A three‐dimensional analysis was carried out to investigate temperature distribution and solid‐liquid interface shape of silicon for large‐scale integrated circuits and photovoltaic silicon. The analysis enables prediction of the solid‐liquid interface shape of silicon crystals. The result shows that the interface shape became bevel like structure in the case without crystal rotation. We also carried out analysis of nitrogen transfer in gallium melt during crystal growth of gallium nitride using liquid‐phase epitaxy. The result shows that the growth rate at the center was smaller than that at the center. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

梯度掺杂的YVO4-Nd∶YVO4复合晶体

利用改进的提拉法生长了一种新型YVO₄-Nd∶YVO₄ 复合晶体,在晶体中部实现了Nd³⁺的0.10%~0.25%(原子数分数)浓度梯度掺杂。晶体中, Nd³⁺掺杂区的弱吸收系数较未掺杂区大,表现出界面吸收现象。观测了复合晶体对泵浦光的吸收和温度分布,发现晶体沿轴向的泵浦吸收相对均匀,温度梯度相对较小。未镀膜的复合晶体样品在1 064 nm波段显示了良好的连续激光性能,光-光转换效率为37.0%,斜效率为40.9%。     

Growth and characterization of L‐valine ‐ a nonlinear optical crystal

The growth of a new nonlinear optical material L‐valine by solvent evaporation method is reported here. To grow good quality crystals pH value of growth solution has been optimized and solubility of L‐valine in different solvents and different pH values was determined. The grown crystals were characterized by IR, single crystal XRD, DTA and TGA, optical transmission and second harmonic generation (SHG) efficiency measurement. SHG efficiency of L‐valine was found equivalent to KDP and its transmission is 75%‐80% from ultraviolet to near IR region. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Growth and characterization of Bis Thiourea Zinc Acetate (BTZA)

Single crystals of BTZA have been grown by low temperature solution growth method using slow cooling process at an optimized pH of 3.5. The grown crystals have been examined under an optical microscope to study its surface morphology. The morphological studies show that the growth takes place by spreading of growth layers. Formation of rectangular shaped etch pit on the as‐grown crystal has been explained in relation to the growth conditions. Single crystal X‐ray diffraction analysis has been carried out to confirm the monoclinic system. Transmission spectrum reveals that the crystal has a low UV cut off of 434.5 nm and has a transmittance of 100%. Dependence of micro hardness on load has been studied. Powder X‐ray Diffraction and FT‐IR have been carried out to characterize the grown crystals. BTZA forms metal – sulfur bond and has good optical transmission in the entire visible region, which is the essential requirement for a non‐linear crystal. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Distribution coefficient of boron in Si crystal ingots grown in cusp-magnetic Czochralski process

Silicon single crystals are grown by the Czochralski method with various growing conditions. Effective segregation coefficient of boron is found to depend on the magnetic field in cusp-magnetic Cz method. Effects of zero-Gauss plane (ZGP), ZGP shape and magnetic intensity (MI) on the dopant concentration and its distribution in the crystal are experimentally investigated. The shape of ZGP is not only flat but also parabolic due to the magnetic ratio (MR), which is the ratio of the lower to upper electric-current densities in the configurations of the cusp-magnetic field. Equilibrium distribution coefficient of boron calculated by BPS model is 0.698. With the crystal rotation (w) of 16 rpm and the crucible rotation of ?0.5 rpm, the effective distribution coefficient (k_e) is 0.728 in zero magnetic intensity and increases up to 0.8093 in the parabolic ZGP shape. Although the magnetic strength near the crystal–melt interface decreases with increasing MR, it increases in the bulk melt, and hence k_e increases. Flow stability in the bulk melt influences k_e. At the magnetic field and growing conditions, k_e increases with increasing initial charge size of the silicon melt. There is no significant influence of ZGP on the radial distribution of the boron concentration. Simulation results of melt flow in the presence of a parabolic ZGP are outlined, and the segregation results in the experiments are compared with published experimental data.     

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)     

紊流模型模拟分析旋转对提拉大直径单晶硅的影响

本文采用紊流模型对提拉大直径单晶硅时,对晶体旋转、坩埚旋转及二者共同作用三种情况下,熔体内的流线、等温线、氧的浓度分布、紊流粘性系数、紊动能等作了数值模拟,发现晶体的旋转能提高氧的径向均匀性,紊流粘性系数和紊动能随着坩埚转速的提高先增加后下降.晶体坩埚同时旋转时并不能有效降低紊流粘性系数,但能使子午面上的流动受到抑制,等温线更为平坦,有利于晶体生长.     

System of Mathematical Models for the Analysis of Industrial FZ-Si-Crystal Growth Processes

A system of coupled mathematical models and the corresponding program package is developed to study the interface shape, heat transfer, thermal stresses, fluid flow as well as the transient dopant segregation in the floating zone (FZ) growth of large silicon crystals (diameter more than 100mm) grown by the needle-eye technique. The floating zone method with needle-eye technique is used to produce high-purity silicon single crystals for semiconductor devices to overcome the problems resulting from the use of crucibles. The high frequency electric current induced by the pancake induction coil, the temperature gradients and the feed/crystal rotation determine the free surface shape of the molten zone and cause the fluid motion. The quality of the growing crystal depends on the shape of the growth interface, the temperature gradients and corresponding thermal stresses in the single crystal, the fluid flow, and especially on the dopant segregation near the growth interface. From the calculated transient dopant concentration fields in the molten zone the macroscopic and microscopic resistivity distribution in the single crystal is derived. The numerical results of the resistivity distributions are compared with the resistivity distributions measured in the grown crystal.     

热屏优化对大直径单晶硅生长影响的数值模拟

通过对28英寸热场生长300 mm硅单晶过程中结晶速率、固液界面形状、晶体中热应力及晶体中氧含量的数值计算提出了在该热场条件下热屏的优化方案。数值计算结果表明:对热屏底端与晶体表面和熔体自由液面的距离以及热屏材料(优化前热屏使用单一石墨材料,优化后采用辐射率较高的内壁材料结合反射率较高的外壁材料组成复合式热屏)的优化可以减少主加热器对晶体的热辐射使得固液界面更加平坦,藉此增加结晶速率,减小晶体内热应力和熔体中氧含量。     

Movable partition designed for the seed‐assisted silicon ingot casting in directional solidification process

For the seed‐assisted casting process for silicon ingots, different partition blocks were designed in the directional solidification (DS) furnaces to preserve the seed crystals and optimize the thermal field in the hot‐zone. A transient global model was established to investigate the effects of different partition blocks during the solidification process. The simulation results showed that the partition blocks can significantly influence the temperature distributions and the melt flow fields. From the designed partition blocks, the movable partition block was more favorable for the seed‐assisted DS process. A suitable temperature gradient and a flat seed‐melt (s‐m) interface were obtained, which facilitated the preservation of seed crystals effectively, and an optimized crystal‐melt (c‐m) interface was achieved as well. One of the designs of the movable partition blocks was implemented in quasi‐mono crystalline silicon casting experiments and it has been confirmed that the designed movable partition block was helpful for the improvement of the single crystal area.     

相场方法及其在晶体生长中的应用

相场方法已被发掘出用于直接求解时的自由边界问题－著名的斯特藩方程。该方法作为晶体生长过程中模拟复杂图形成图的计算工具，已呈现出强有力的生命力。目前的研究在于努力发展精巧的计算技术，以便于晶体生长和金属凝固过程进行了理论模拟，而这些技术将有可能方法地应用于工业流程。相场方法之所以具有吸引力，基于如下事实：在计算机模拟过程中，即可避免对于边界实时追踪，又不需要反复判别是否满足显式边界条件。在过去的10年中，它已逐步被用于研究晶体生长的基础课题。诸如；热质输运，晶体生长动力学，二维和三维枝晶生长，图形选择，生长形态和显微结构等。本文对相场方法进行评述，同时给出其最新应用结果。     

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)     

A stability diagram for crystal growth from the vapor – a review

Stability of the solid‐vapor interface is investigated. Surface roughening and evolution of flat faces at the growth interface is considered in terms of relation between gradient of temperature in the crystal and gradient of concentration in the vapor. Stability diagram is proposed, based on experimental data. The diagram summarizes the various forms and structures, which can be obtained using a typical system for growth from the vapor. The critical lines for constitutional supersaturation and appearance of low and high index faces were plotted. This attempt to the problem of stability of the growth interface differs from the former investigations mainly in looking for dependence between temperature field and concentration field rather than between more absolute parameters like temperature and supersaturation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于神经网络和遗传算法的铸锭晶体硅质量控制及工艺优化

铸锭晶体硅是太阳能级晶硅材料的重要来源之一,为了进一步降低硅片成本,需要在保证晶体质量的同时发展大尺寸铸锭晶硅。影响铸造晶体硅质量的热场控制核心参数包括晶体生长速度与生长界面温度梯度之比V/G、壁面热流q、生长界面高度差Δh和硅熔体内部温差ΔT等。针对铸锭晶体硅生长过程中的质量控制问题,本研究基于人工神经网络(ANN)模型对晶体生长过程建立了工艺控制优化方法,利用实验测量数据和数值仿真模拟结果构建铸锭晶体硅生长过程的工艺控制数据集,以底部隔热笼开口和侧、顶加热器功率比作为主要工艺控制参数,V/G、|q|、|Δh|和ΔT为优化目标,建立用于研究晶体生长工艺控制参数和热场参数之间映射关系的神经网络模型。使用训练完成的模型分析底部隔热笼开口及侧、顶加热器功率比对晶体生长过程热场的影响规律,并采用遗传算法(GA)对铸锭晶体硅生长过程的工艺控制参数以提高晶体质量为目标进行优化,最后结合实际生产中的检测图像讨论了V/G对晶体质量的影响。研究表明晶体生长中期的V/G沿横向变化较平缓,对应缺陷较少且分布均匀,因此增大V/G在横向上的均匀度也是提高晶体质量的一个重要因素。