Influence of furnace design on the thermal stress during directional solidification of multicrystalline silicon

Directional solidification is one of the most popular techniques for massive production of multicrystalline silicon (mc-Si). Dislocation is one of the major defects that significantly affect the photovoltaic performance. For the analysis and optimization of stress-induced dislocation, a computational tool has been developed to investigate thermal stress distribution during directional solidification process of multicrystalline silicon. Temperature distribution in the furnace, S/L interface shape and melt flow are simulated. Parametric studies are further conducted to evaluate the effect of furnace design on the interface shape and on the maximum von Mises stress in the growing ingot. To consider the effects of the crucible geometry qualitatively, three-dimensional modeling of the thermal stress is performed with or without the constraint of the crucible. The regions of dislocation multiplication are evaluated by comparing von Mises stress to critical resolved shear stress (CRSS). The results imply that the dislocation in the growing ingot can be reduced by optimizing the design of the directional solidification furnace.     

Numerical simulation of a new SiC growth system by the dual-directional sublimation method

A new SiC growth system using the dual-directional sublimation method was investigated in this study. Induction heating and thermal conditions were computed and analyzed by using a global simulation model, and then the values of growth rate and shear stress in a growing crystal were calculated and compared with those in a conventional system. The results showed that the growth rate of SiC single crystals can be increased by twofold by using the dual-directional sublimation method with little increase in electrical power consumption and that thermal stresses can be reduced due to no constraint of the crucible lid and low temperature gradient in crystals.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Nitride bonded silicon nitride as a reusable crucible material for directional solidification of silicon

Nitride bonded silicon nitride (NBSN) has the potential of a reusable crucible material for directional solidification of silicon. This is demonstrated in this work by reusing a NBSN crucible six times for the directional solidification of undoped multicrystalline (mc) silicon ingots. The progress of the ingot contamination at subsequent use of the NBSN crucible was studied systematically. Minority carrier lifetime, electrical resistivity as well as impurity content were analyzed after each solidification run. The results were compared to those obtained from ingots which were crystallized by using identical directional solidification process parameters in standard fused silica crucibles with silicon nitride coating. The impurity content of the ingots can be clearly correlated to the impurity content of the NBSN crucible. The main impurity is the acceptor B. Its concentration in the ingots decreases from about 10¹⁷ atoms/cm³ to 10¹⁶ atoms/cm³ with continued reuse. The contamination mechanism is most likely due to outdiffusion from the crucible wall into the Si melt.     

Applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field

To examine the applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic fields, LES calculations with Smagorinsky–Lilly turbulence model and van Driest damping at the solid walls are carried out. The program package for the calculations was developed on the basis of the open-source code library OpenFOAM^®${\mathrm{OpenFOAM}}^{\circledR }$. A previously published laboratory model with low temperature melt InGaSn, a 20” crucible, and process parameters corresponding to industrial Czochralski silicon systems is considered. Flow regimes with two crystal and crucible rotation rates and with different strengths of the traveling magnetic field “down” are analyzed. The calculated distributions of averaged temperature and standard temperature deviations are compared with measured ones in the laboratory system, and a relatively good agreement between them is shown. The influence of chosen time steps and grid sizes is analyzed by comparing Fourier spectra of temperature time-autocorrelation functions and temperature spatial distributions, and it is shown that the used moderate meshes of few hundred thousand cells can be applied for practical calculations.     

Solid mechanics and material strength studies on the melt growth of bulk single crystals

Microdefects such as dislocations and macrocracking should be controlled during the crystal growth process to obtain high-quality bulk single crystals. Solid mechanics and material strength studies on the single crystals are of importance to solve the problems related to the generation and multiplication of dislocations and the cracking of single crystals. The present paper reviews such research activities that comprise the thermal stress analysis during crystal growth process, the dislocation density estimation during crystal growth process, and the cracking of single crystal due to thermal stress.     

Transient analysis of the cooling process and influence of bottom insulation on the stress in the multicrystalline silicon ingot

Directional solidification is one of the most popular techniques for massive production of multicrystalline silicon. After growth and annealing, the ingot is cooled down by a designed cooling process, which is initialized by descending bottom insulation, and then is controlled both by power ramp‐down rate and by motion of the bottom insulation. Thermal stress is piled up during cooling, and associated crystal defects, such as dislocation and micro‐cracks, may generate and propagate in the ingot. In the paper, transient modeling is applied to study the effect of bottom insulation on the cooling process. Temperature, velocity and thermal stress fields are obtained with linear, parabolic and sinusoidal motions of the insulation. The measured and predicted temperatures at two points of the ingot are found consistent. Distributions of von Mises stress in the ingot at different cooling time are obtained, and the maximum von Mises stresses are presented as a function of the cooling time. Specifically, dislocation‐free regions, evaluated by the critical resolved shear stress model, at certain cooling time, and area fractions of the regions as a function of the cooling time are proposed. The linear motion is further discussed with different moving rates, considering its wide applications in the current industry and convenient realization in control.     

Optimisation of the VGF growth process by inverse modelling

Numerical and experimental results on the thermal optimisation of vertical gradient freeze crystal growth are presented. An inverse modelling approach is described aimed at solidification with a constant growth rate and planar solid–liquid interface. As a result of modelling an optimised growth process characterised by a modified ampoule configuration and thermal regime was established. For experimental confirmation Ga-doped germanium single crystals were grown with the optimised process. In good agreement with the numerical results, solidification with an almost constant growth rate was achieved with the interface deflection being significantly lower than in conventionally grown crystals.     

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。     

Validation of a 3D multi-physics model for unidirectional silicon solidification

A model for transient movements of solidification fronts has been added to X-stream, an existing multi-physics simulation program for high temperature processes with flow and chemical reactions. The implementation uses an enthalpy formulation and works on fixed grids. First we show the results of a 2D tin solidification benchmark case, which allows a comparison of X-stream to two other codes and to measurements. Second, a complete 3D solar silicon Heat Exchange Method (HEM) furnace, as built by PVA TePla is modeled. Here, it was necessary to model the complete geometry including the quartz crucible, radiative heaters, bottom cooling, inert flushing gas, etc. For one specific recipe of the transient heater power steering, PVA TePla conducted dip-rod measurements of the silicon solidification front position as function of time. This yields a validation of the model when applied to a real life industrial crystallization process. The results indicate that melt convection does influence the energy distribution up to the start of crystallization at the crucible bottom. But from that point on, the release of latent heat seems to dominate the solidification process, and convection in the melt does not significantly influence the transient front shape.     

Impurity segregation in directional solidified multi-crystalline silicon

In this paper numerical results on the impurity segregation in directional solidified multi-crystalline silicon are presented and compared with experimental results. A solute transport model has been established to predict the final segregation pattern of impurities in the ingot. The segregation is analyzed experimentally on the basis of Fourier transform infrared (FTIR) spectroscopy and glow-discharge mass spectrometry (GDMS). Precipitates were located by IR-transmission microscopy (IRM). Qualitative agreement between simulation and experiment is found. It is demonstrated how the flow pattern can influence the final solute distribution. The simulation also shows that the solubility limit of carbon and nitrogen is reached locally in the ingot and SiC and Si₃N₄ precipitates are likely to form.     

Role of marangoni tension effects on the melt convection in directional solidification process for multi-crystalline silicon ingots

We carried out global simulations to investigate the marangoni tension effect on the thermal and flow fields in the silicon melt of the directional solidification process for multi-crystalline silicon ingots. The argon flow rate was varied to provide different solidification conditions and to change the relative values between the argon shear stress and the marangoni tension at the melt free surface. We found that the marangoni tension together with the shear stress mainly influences the upper layer melt convection while the thermal buoyancy force dominates the bulk flow of the melt. At low argon flow rates, the argon shear stress can be neglected and the marangoni tension alone enhances the melt convection intensity near the gas–melt–crucible triple junction point. The marangoni tension is so weak that it cannot modify the melt flow pattern in this case. For medium flow rate, the marangoni tension can significantly weaken the shear stress effect at the outer part of the melt free surface, leading to a distinctive flow pattern in the silicon melt. With further increase in argon flow rate, the shear stress sharply increases and dominates the upper layer melt flow, limiting the marangoni tension effect to the triple point. The numerical results are helpful for better understanding and controlling of the directional solidification process for high quality multi-crystalline silicon ingots.     

The effects of annealing on non-polar (1 1 2¯ 0) a-plane GaN films

Non-polar a-plane (1 1 2¯ 0) GaN films were grown on r-plane sapphire by metal–organic vapor phase epitaxy and were subsequently annealed for 90 min at 1070 °C. Most dislocations were partial dislocations, which terminated basal plane stacking faults. Prior to annealing, these dislocations were randomly distributed. After annealing, these dislocations moved into arrays oriented along the [0 0 0 1] direction and aligned perpendicular to the film–substrate interface throughout their length, although the total dislocation density remained unchanged. These changes were accompanied by broadening of the symmetric X-ray diffraction 1 1 2¯ 0 ω-scan widths. The mechanism of movement was identified as dislocation glide, occurring due to highly anisotropic stresses (confirmed by X-ray diffraction lattice parameter measurements) and evidenced by macroscopic slip bands observed on the sample surface. There was also an increase in the density of unintentionally n-type doped electrically conductive inclined features present at the film–substrate interface (as observed in cross-section using scanning capacitance microscopy), suggesting out-diffusion of impurities from the substrate along with prismatic stacking faults. These data suggest that annealing processes performed close to film growth temperatures can affect both the microstructure and the electrical properties of non-polar GaN films.     

Mixed-phase solidification of thin Si films on SiO2

Mixed-phase solidification (MPS) is a new beam-induced solidification method that can produce large-grained and highly (1 0 0)-surface textured polycrystalline Si films on SiO₂. The grains resulting from this mixed-phase solidification (MPS) method, which was conceived based on a well-known phenomenon of coexisting solid–liquid regions in radiatively melted Si films, are found to be essentially devoid of various intragrain defects that always plague, and subsequently degrade the utility of large-grained Si films previously obtained using other crystallization techniques. It is experimentally shown that multiple exposures are required in order to generate such a polycrystalline microstructure from an initial amorphous precursor. The observed trends are conceptually explained in terms of the melt being initiated primarily at grain boundaries in polycrystalline films, and melting and solidification subsequently proceeding laterally at interface-location specific rates as determined by the local thermodynamic factors, which include the anisotropic surface and interfacial energies of the grains, and the unusual local thermal profile—all transpiring within a near-equilibrium but nonisothermal and dynamic environment that needs to address the thermal and stability requirements associated with the coexisting solid–liquid regions.     

Elasto-plastic simulation of stress evolution during grain growth using a phase field model

Coupling effects among phase transformation, temperature and stress/strain are formulated based on thermodynamics using a phase field model. The elasto-plastic constitutive relationship is applied for stress analysis considering thermal expansion, transformation dilatation, and the effect of stress on phase transformation is included in the formulation. Subsequently, equations are numerically solved using a finite element method and stress evolution due to phase transformation and residual stress distribution are simulated. The results obtained show that large stresses are generated around phase interfaces. The high-stress regions move as grains grow, and finally residual stress distribution is observed along grain boundaries. The distribution and values at the grain boundaries are revealed to depend on the timing of collision and positioning of nuclei.     

Influence of thermal stabilization on the solute concentration of the melt in directional solidification

Experiments on Al–25 at%Ni peritectic alloy consisting of melting followed by thermal stabilization ranging from 0 to 2 h were carried out in a Bridgman-type furnace. Temperature distribution, microstructure evolution and solute concentration in the mushy zone are characterized. An analytical model is proposed to evaluate the Ni concentration of the melt after thermal stabilization. Effect of temperature gradient and volume fraction of liquid phase in the mushy zone on the Ni concentration of the melt is discussed. The steady state Ni concentration of the melt is inappropriately below the initial Ni concentration of the sample. The deviation increases with decreasing temperature gradient. Finally, the influence of thermal stabilization on the solute concentration of the melt is discussed based on a comparison of Al–Ni peritectic alloys with Al–Ni hyper-eutectic alloys and Al–Cu hypo-eutectic alloys.     

On favorable thermal fields for detached Bridgman growth

The thermal fields of two Bridgman-like configurations, representative of real systems used in prior experiments for the detached growth of CdTe and Ge crystals, are studied. These detailed heat transfer computations are performed using the CrysMAS code and expand upon our previous analysis [C. Stelian, A. Yeckel, J.J. Derby, Influence of thermal phenomena on crystal reattachment during the dewetted Bridgman growth, J. Cryst. Growth, in press] that posited a new mechanism involving the thermal field and meniscus position to explain stable conditions for dewetted Bridgman growth. Computational results indicate that heat transfer conditions that led to successful detached growth in both of these systems are in accordance with our prior assertion, namely that the prevention of crystal reattachment to the crucible wall requires the avoidance of any undercooling of the melt meniscus during the growth run. Significantly, relatively simple process modifications that promote favorable thermal conditions for detached growth may overcome detrimental factors associated with meniscus shape and crucible wetting. Thus, these ideas may be important to advance the practice of detached growth for many materials.     

基于迁移学习的大尺寸铸锭晶体硅热场设计

不同尺寸的铸锭晶体硅生长过程具有相似性,小尺寸晶体的生长规律可以迁移至大尺寸。本文采用迁移学习(TL)对G8型铸锭炉进行热场设计,设计对象为侧、顶加热器位置及体积、侧隔热笼分区块高度,主要设计目标为减少晶体内部的位错缺陷、抑制硅锭边缘多晶且使晶体生长界面微凸。首先使用神经网络对已有的G7铸锭炉建立热场几何参数与热场评价参数间的映射模型,然后将该模型迁移至G8铸锭炉,对比不同模型结构对迁移过程的影响,采用Dropout分析模型是否存在过拟合,并使用遗传算法(GA)结合聚类算法(CA)对热场几何参数进行优化,以上为G8热场设计过程。最后对优化结果采用数值模拟方法研究其在晶体生长过程中的温度分布、固液界面形状等,最终选定的优化方案能够实现较高质量的长晶。将该方案同时应用于G7和G8热场并进行对比,结果表明G8在硅熔体和硅晶体中的轴向温度梯度均小于G7,在晶体生长界面沿径向的温度梯度也小于G7,这有利于减小晶体内部的热应力。     

Control of multi-zone resistive heater in low temperature gradient BGO Czochralski growth with a weighing feedback,based on the global dynamic heat transfer model

The global heat transfer in a crystallization setup has been optimized to develop a strategy of control over a three-zone heater in the BGO Czochralski process, in order to provide invariable thermal conditions near the solid–liquid interface in the stage of a constant-diameter crystal growth. The functional related to the exactness of the heat balance condition at the crystallization front, i.e., the Stefan problem, was chosen as the target function. The optimization yielded unexpected results. The temperature of the lower heater should be lowered, relative to that of the middle heater, with increasing crystal length, whereas the temperature of the upper heater is to be raised. These recommendations were incorporated into a dynamic model of the oxide Czochralski process with a weighing control and into the control loop of the temperature regulators of a crystallization setup. A comparison of results of the time-dependent simulation with the real growth process confirmed that the new control strategy minimizes the deviation of the solid–liquid interface from the prescribed one, significantly decreases variations of interface shape during the process, and enables growth of high-quality crystals.     

Centrifugal separation of primary silicon crystal in solvent refining of silicon using Al‐30% Si alloy

This study describes the formation of a primary silicon network during separation of an Al‐30% Si melt and the process conditions to make bigger primary silicon crystals. As the crucible rotates in the centrifugal separation, the unfrozen aluminum‐rich phase and small silicon particles are pushed outside through the openings in the silicon network. As a result, primary silicon crystals are separated in the form of a foam after centrifugation. The recovery of the silicon ranged from 13 to 18% depending on the location in the crucible. The size of the primary silicon achieved by changing the cooling rate and quenching temperature during solidification is also measured using a quenching furnace. Primary silicon particles exhibit a coarse, plate‐like morphology, although small star‐like silicon particles are also found in the aluminum‐rich matrix. The fraction of plate silicon decreases, while the fraction of small globular silicon increases with an increasing cooling rate. The thickness of the primary silicon plate also decreases with an increasing cooling rate in the samples quenched at various temperatures during solidification.