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.     

降温速率对升级冶金硅定向凝固生长多晶硅少子寿命的影响

对经过前期提纯的冶金级硅料进行一次性定向凝固生长多晶硅铸锭,研究了长晶阶段降温速率对多晶硅少子寿命的影响。结果显示降温速率越低,获得多晶硅少子寿命越高,但降温速率低到一定程度时,少子寿命反而会降低。通过测试生长多晶硅硅锭曲率半径、晶体结构等数据,分析了该现象的产生原因。这将有助于升级冶金硅一次性定向凝固生长多晶硅铸锭的生产应用。     

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.     

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.     

Growth of semiconductor silicon crystals

This paper focuses on the recent developments in Czochralski (CZ) crystal growth of silicon for large-scale integrated circuits (LSIs) and multi-crystalline silicon growth using a directional solidification method for solar cells. Growth of silicon crystals by the CZ method currently allows the growth of high-quality crystals that satisfy the device requirements of LSIs or power devices for electric cars. This paper covers how to obtain high-quality crystals with low impurity content and few point defects. It also covers the directional solidification method, which yields crystals with medium conversion efficiency for photovoltaic applications. We discuss the defects and impurities that degrade the efficiency and the steps to overcome these problems.     

An enhanced cooling design in directional solidification for high quality multi-crystalline solar silicon

An enhanced cooling design for nucleation was proposed for directional solidification based on the enhanced heat transfer through gas flow, and the effects of initial cooling conditions during directional solidification on the quality of multi-crystalline silicon for solar cells were studied. The properties of the grown grains under different initial cooling conditions were measured. The grain size, grain orientations, and the percentage of twin boundaries, as well as minority lifetime and defect density, were affected significantly by the initial cooling. The implementation of this design to a commercial furnace was also discussed, and promising results were obtained.     

The effects of argon gas flow rate and furnace pressure on oxygen concentration in Czochralski silicon single crystals grown in a transverse magnetic field

The effects of the argon gas flow rate and furnace pressure on the oxygen concentration in a transverse magnetic field applied Czochralski (TMCZ) silicon single crystals were examined through experimental crystal growth. A gas controller which had been proposed by Zulehner was used for this series of experiments. In the TMCZ gas-controlled crystals, a decrease in the oxygen concentration with a decrease in furnace pressure was found. A clear relationship between the oxygen concentration and the argon gas flow rate was not obtained due to the limited experimental conditions. The relationships between the oxygen concentration and the furnace pressure and the argon gas flow rate previously observed for Czochralski (CZ) crystals by a similar gas controller were confirmed by the present gas controller. The oxygen concentration changes in the TMCZ and the CZ crystals were analyzed in terms of the calculated flow velocity of the argon gas between the gas controller and the silicon melt surface. In contrast with the CZ gas-controlled crystals, the oxygen concentration was decreased with an increase in the flow velocity of argon gas in the TMCZ gas-controlled crystals. The surface temperature model and the melt flow pattern model which had been proposed in the previous report are discussed again in light of the present experimental results.     

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。     

Influence of solidification of binary eutectic lamellar systems on surface tension driven convection in zero gravity conditions

The effect of solidification of the lamellar binary eutectic system on the onset of surface tension driven convection (so-called Marangoni instability) is studied in a zero gravity environment. Some main general conclusions concerning the possibility for onset of the Marangoni convection within the melt can be drawn from the analysis, viz., the curvature of the free surface has a destabilizing effect on the onset of the flow; the increased perturbed heat transfer rate from the system stabilizes the melt; the onset of the solutal Marangoni convection closely depends on the ratio of the lamellae half-widths and the solutal Marangoni instability is more sensitive against the perturbations than the temperature Marangoni one.     

Silicon ingot casting by gas assisted solidification

Gas Assisted Solidification (GAS) is a casting method to provide low cost silicon materials for the fabrication of solar cells. In this paper, a detailed study on the mode of solidification is made according to the operational variables. The most appropriate soaking temperature is about 40 °C above the melting point of silicon, with an optimum soaking period of 4.5 hr. A slow temperature decreasing rate of about 1–2 °C/min is to ensure the formation of large grains. A triggering time of gas flow close to the end of the soaking period is most desirable. With a steep increment of gas flow rate, a large gas flow rate of about 300 1/min in the steady state period is to set for the conditions of growing elongated grains. The grown ingots were subjected to chemical and physical characterization, and some preliminary data will also be presented for their correlation.     

大晶粒多晶硅铸锭生长的热场设计与模拟

为了生长大晶粒的多晶硅铸锭,晶体从形核到后续生长的热场环境控制至关重要.本文首先在侧加热器与散热块之间加一可移动的隔热环.通过向上移动隔热环,并在底部喷射氩气冷却,对生长工艺进行优化控制.然后利用数值模拟,对改进后的生长界面形状、晶体和熔体中的等温线、晶体和熔体的轴向温度分布以及冷却量对生长环境的影响进行分析.模拟结果表明:冷却速率的最佳值在5 ～ 15 W/m2之间,且优化后的晶体和熔体中等温线更平坦,晶体轴向温度梯度增大约1.72 K/cm,从而可有效地避免侧壁形核,促进大晶粒的生长,同时提高了生长速率.     

Numerical investigation of magnetic field effect on pressure in cylindrical and hemispherical silicon CZ crystal growth

The effect of axial magnetic field of different intensities on pressure in silicon Czochralski crystal growth is investigated in cylindrical and hemispherical geometries with rotating crystal and crucible and thermocapillary convection. As one important thermodynamic variable, the pressure is found to be more sensitive than temperature to magnetic field with strong dependence upon the vorticity field. The pressure at the triple point is proposed as a convenient parameter to control the homogeneity of the grown crystal. With a gradual increase of the magnetic field intensity the convection effect can be reduced without thermal fluctuations in the silicon melt. An evaluation of the magnetic interaction parameter critical value corresponding to flow, pressure and temperature homogenization leads to the important result that a relatively low axial magnetic field is required for the spherical system comparatively to the cylindrical one.     

Pattern transition of temperature distribution at Czochralski silicon melt surface

The melt surface temperature in Czochralski silicon growth was studied by CCD camera observation. The thermal radiation energy from the melt surface was converted into temperature by the blackbody calibration method and was recorded with a VCR as two-dimensional color images. The experimental results without a crystal revealed that the temperature distribution at the melt surface can change in four patterns depending on the crucible rotation rate: axisymmetric spoke pattern at low rotation rates, n-folded and island patterns at medium rotation rates, and cellular patterns at high rotation rates. To predict the fluid motion from the experimental observations, three-dimensional time-dependent numerical simulations of the silicon melt flow were executed. As a result, a qualitative transition model for the temperature distribution and the Czochralski silicon melt flow was derived.     

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.     

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Heat transfer and fluid flow in HEM crystal growth of silicon in cylindrical cavity is studied numerically. The walls of the crucible are heated to a fixed temperature. The exchanger that causes and induces natural convection is seated at the middle‐bottom of the crucible. The finite‐volume method is employed to solve the governing equations with proper boundary conditions. The effects of transport mechanism on the temperature distribution, melt flow, pressure and stream function are presented. We focus our work on the pressure field which has not yet been studied in HEM crucible. Also, we extend our work on a wide range Grashof number and for large numbers until 10¹² not yet studied in HEM furnace. It is found that the onset of flow fluctuations appears at Gr = 10¹⁰. Uniform temperature is observed in the entire melt at high Grashof number with development of a thermal boundary layer close to the exchanger. The thermal boundary layer thickness is calculated for strong buoyancy regime. Besides, for very high Gr number, buoyancy has less effect on temperature and then on melt‐crystal interface shape. During enlarging Gr, pressure evolution is related to temperature variation more than flow pattern.     

Melting and solidification behavior of laser-crystallized silicon thin-films studied by transient conductance measurements

In this paper we report on transient conductance measurements during melting and solidification of thin silicon films on foreign substrates, which were irradiated with an excimer laser. The silicon films were deposited on borosilicate float glass or single crystal silicon wafers that were coated with different intermediate layers. Our results show that the laser fluence required to melt the entire Si layer is mainly determined by the silicon–substrate interfacial thermal resistance and not by the heat conductivity of the bulk substrate. The solidification velocity, on the other hand, is strongly influenced by the heat conductivity of the bulk substrate and reaches a maximum value of 0.95 m/s for c-Si compared to 2.19 m/s for borosilicate float glass.     

Numerical optimization of thermal field in CdTe crystal growth by travelling heater method

Cadmium telluride (CdTe) and his compounds play a leading role in X‐ray and γ‐ray detector technology. One of the most used methods for growing these crystals is the travelling heater method (THM). The ingots obtained by using this technique show excellent composition uniformity, but the structural quality is affected by the presence of large grains which appear because of large curvatures of the solid‐liquid interface during the solidification process. This numerical work investigate the thermal field and melt convection in CdTe processing by THM in order to elucidate the mechanism of growing these crystals. The influence of the furnace geometry on the interface shape and temperature gradient in liquid is analyzed for samples with small (1 cm) and large (5 cm) diameters. The computations include flow effects on thermal field in the melted zone. The thermal conditions are optimized for THM growth of CdTe crystals at high solidification temperatures. A new multi‐zone furnace configuration for growing crystals of large diameter and flattened interface is proposed in this work.     

分离结晶垂直Bridgman法生长CdZnTe晶体的全局数值模拟

采用FLUENT软件对分离结晶Bridgman法生长CdZnTe晶体进行了全局数值模拟.模拟对象为:熔体上部边界条件分别为固壁和自由表面时两种晶体生长系统.重点考虑坩埚和晶体之间狭缝宽度e和重力对分离结晶过程的影响.在计算中分别取e=0 mm、0.5 mm和1 mm三种狭缝宽度,得到了在微重力和常重力条件下的温度分布、结晶界面形状以及流函数分布图.结果表明:在微重力条件下,当熔体上部为固壁时,随着狭缝宽度的增大,热毛细力作用增强,流动强度增强;当熔体上部为自由表面时,则与之相反.在常重力条件下,由于浮力-热毛细对流的共同作用,随着狭缝宽度的增加,流动强度逐渐减弱,有助于提高晶体生长质量.     

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.     

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.