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.     

Modulating dopant segregation in floating-zone silicon growth in magnetic fields using rotation

The feasibility of modulating dopant segregation using rotation for floating-zone silicon growth in axisymmetric magnetic fields is investigated through computer simulation. In the model, heat and mass transfer, fluid flow, magnetic fields, melt/solid interfaces, and the free surface are solved globally by a robust finte-volume/Newton's method. Different rotation modes, single- and counter-rotations, are applied to the growth under both axial and cusp magnetic fields. Under the magnetic fields, it is observed that dopant mixing is poor in the quiescent core region of the molten zone, and the weak convection there is responsible for the segregation. Under an axial magnetic field, moderate counter-rotation or crystal rotation improves dopant uniformity. However, excess counter-rotation or feed rotation alone results in more complicated flow structures, and thus induces larger radial segregation. For the cusp fields, rotation can enhance more easily the dopant mixing in the core melt and thus improve dopant uniformity.     

Dopant transport during semiconductor crystal growth: Axial versus transverse magnetic fields

The present study investigates the effects of magnetic field orientation, magnetic field strength and growth rate on the dopant segregation in semiconductor crystals, and presents results of dopant composition in the crystal and in the melt at several different times during growth for several combinations of process parameters. The crystal's lateral segregation depends on the magnetic field's orientation and strength while the axial segregation depends on the magnetic field's strength and the growth rate. If either convective or diffusive transport truly dominates, then the crystal's dopant distribution is laterally uniform. The axial distribution in the crystal approaches the well-mixed limit if the melt motion is strong and the growth rate is slow, and the distribution approaches the diffusion-controlled limit if the melt motion is slow and the growth rate is fast. The deviations of the dopant distribution in the crystal from lateral uniformity and from the classical limits are quantified for several combinations of process parameters.     

Simulation of dopant zone-leveling for variable distribution coefficient in KCl: EuCl2 system

Experimental data of Eu²⁺ distribution in EuCl₂-doped KCl ingots are analyzed. After settling the relation between variable distribution coefficient and the dopant concentration in the melt, the simulation of the dopant zone-leveling for various molten zone widths is performed. It is shown that owing to the decrease of the distribution coefficient caused by increasing dopant concentration in the molten zone, the number of the zone passes after which the dopant concentration levels off undergoes significant reduction.     

ø300 mm直拉硅单晶生长过程中的变晶现象及其影响因素

直拉法生长直径300 mm硅单晶过程中,直径均匀是获得高品质硅单晶的关键。在生产实践中发现,当硅晶体进入等径生长阶段,过高的提拉速度会引起晶体发生扭晶现象,导致晶线断裂随即变晶,对等径生长不利。本文采用数值模拟和理论相结合的方法分析了ø300 mm硅单晶生长过程中扭晶现象的成因,建立了不同提拉速度下晶体直径与熔体温度分布的关系,分析了晶体发生扭晶的影响因素。结果表明,随着提拉速度的增加,熔体自由表面产生过冷区且该过冷区随提拉速度的增加不断扩大,过冷区的产生是导致晶体发生扭晶的主要原因。提出了一种基于有限元热场数值模拟的最大稳定提拉速度的判别方法,并给出了通过改变晶体旋转速度来改善熔体自由表面温度分布的工艺措施建议,从而避免晶体扭晶现象的发生。研究结果对设计大尺寸硅单晶生长热场具有一定的指导作用。     

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.     

Validation of strong magnetic field asymptotic models for dopant transport during semiconductor crystal growth

This paper presents a numerical solution for the unsteady transport of a dopant during the growth of a semiconductor crystal from a melt with an externally applied magnetic field. This solution confirms the results of an asymptotic model. Both solutions show that at every time during the growth of the crystal, the dopant distribution (1) is very nonuniform throughout the melt, and (2) is far from the instantaneous steady state. The present numerical solution for an arbitrary mass Péclet number Pe_m and an arbitrary Hartmann number Ha predicts a dopant distribution in the crystal, which agrees remarkably well with the dopant distribution predicted by the asymptotic solution for Pe_m 1 and Ha 1. The maximum difference between the crystal compositions predicted by these two different approaches is less than 4% for the range of magnetic field strengths considered.     

Simulation of dopant zone-leveling in a solid ingot

Simple simulation procedure permitting to perform accurate calculations of the dopant distribution in an ingot after desired number of passes of the molten zone is presented. The results obtained for various distribution coefficients and various widths of the molten zone are discussed. It is shown that the number of passes indispensable for the dopant concentration leveling drastically decreases with the width of the molten zone even for the most disadvantageous range of the distribution coefficients.     

Characterization of large‐sized Nd:YAG single crystals grown by horizontal directional solidification

Nd³⁺‐doped Y₃Al₅O₁₂ single crystals have been grown by the horizontal directional solidification (HDS) method in different thermal zone. The Grashof (G_r), Prandtl (P_r), Marangoni (M_a) and Rayleigh (R_a) numbers of melt in HDS system have been discussed for our experimental system to understand the mechanism of melt flow patterns and concentration gradient of dopant. The concentration gradient of Nd³⁺ ions was explained with melt flow processes during crystal growth in different thermal zone, and results indicated that high growth temperature will be helpful for uniformity of dopant in HDS‐grown single crystal. The main microscopic growth defects such as bubbles and irregular inclusions in HDS‐grown Nd:YAG crystals were observed, and the causes were discussed as well. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of Zn‐doped Germanium under Microgravity

The doping of germanium with zinc from a remote, temperature‐stabilized source was studied under microgravity. A nominally undoped Ge‐crystal was grown by the Gradient‐Freeze technique with the melt surface being in permanent contact with a gaseous atmosphere of zinc. The dopant and carrier concentrations in the solidified Germanium were measured by SIMS, Hall and resistance measurements and compared with the results of a terrestrial reference experiment as well as with concentration profiles calculated on the basis of the thermodynamics of the growth system. The results prove the possibility of vapour phase doping under microgravity. Moreover, the Zn‐concentration at the initial phase boundary even agrees well with the equilibrium value, strongly indicating a nearly homogeneous distribution of the dopant within the melt before the crystallization.     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1: non‐rotating seed

For the seeding process of oxide Czochralski crystal growth, the flow and temperature field of the system as well as the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used initially in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and non‐rotating 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 source the fluid flow and temperature field were determined in the whole system. We have considered two cases with respect to the seed position: (1) before and (2) after seed touch with the melt. It was observed that in the case of no seed rotation (ω_seed = 0), the flow pattern in the bulk melt consists of a single circulation of a slow moving fluid. In the gas domain, there are different types of flow motion related to different positions of the seed crystal. In the case of touched seed, the seed‐melt interface has a deep conic shape towards the melt. It was shown that an active afterheater and its location with respect to the crucible, influences markedly the temperature and flow field of the gas phase in the system and partly in the melt. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A modified zone growth method for an InGaAs single crystal

We have been developing a zone growth method for an In_xGa_1−xAs single crystal with a uniform InAs composition, using an InGaAs source, InGaAs melt and InGaAs seed charged in a crucible. This time, we modified the zone growth method to increase the length of an InGaAs zone crystal. A gap created between the wall around the InGaAs source and the inner wall of the crucible effectively prevents the interruption in normal zone growth because it changes the directions of heat current in the source. In addition, we found that it is very important for single crystal growth that no rotation of the crucible takes place during zone growth, because the degree of mixing caused by melt convection is reduced. The zone growth region of the obtained InGaAs crystal is almost exclusively of single-crystal-type, and it is about 26 mm long, which is 1.5 times the region length of the zone single crystal reported previously. We believe that a longer growth period could have further increased the length of our zone crystal, because some of the source remained. The InAs composition (x) of the zone crystal is greater than 0.3, and the crystal diameter is 15 mm.     

红外LED用GaAs单晶的垂直梯度凝固制备研究

GaAs单晶是当前光电子器件的主要衬底材料之一,在红外LED中有着重要应用。但杂质浓度高、迁移率低等缺点会严重影响红外LED器件性能。为生产出低杂质浓度、高迁移率、载流子分布均匀、高利用率的红外LED用掺硅垂直梯度凝固(VGF)法GaAs单晶,本文研究了热场分布、合成舟和炉膛材质、工艺参数对单晶的成晶质量、杂质浓度、迁移率、载流子分布的影响。利用CGSim软件对单晶生长热场系统进行数值模拟研究,温区一至温区六长度比例为8∶12∶9∶5∶5∶7时,恒温区达到最长,位错密度达到1 000 cm^-2以下,成晶率达到85%。采用打毛石英合成舟进行GaAs合成,用莫来石炉膛替代石英炉膛,可以获得迁移率整体高于3 000 cm²/(V·s)的GaAs单晶,满足红外LED使用要求。对单晶生长工艺参数展开研究,采用提高头部生长速度、降低尾部生长速度的方式提高单晶轴向载流子浓度均匀性,头尾部载流子浓度差降低33%,尾部迁移率从2 900 cm²/(V·s)提高到3 560 cm²/(V·s)。单晶有效利用长度提高33...     

Resistivity distribution of silicon single crystals using codoping

Numerous studies including continuous Czochralski method and double crucible technique have been reported on the control of macroscopic axial resistivity distribution in bulk crystal growth. The simple codoping method for improving the productivity of silicon single-crystal growth by controlling axial specific resistivity distribution was proposed by Wang [Jpn. J. Appl. Phys. 43 (2004) 4079]. Wang [J. Crystal Growth 275 (2005) e73] demonstrated using numerical analysis and by experimental results that the axial specific resistivity distribution can be modified in melt growth of silicon crystals and relatively uniform profile is possible by B–P codoping method. In this work, the basic characteristic of 8 in silicon single crystal grown using codoping method is studied and whether proposed method has advantage for the silicon crystal growth is discussed.     

旋转磁场对空间浮区内流场及浓度场的影响

采用全浮区模型数值研究了旋转磁场作用下熔区内热毛细对流流动特性,分析了磁场强度对流场及浓度场的影响.研究发现,无磁场时,熔体内杂质浓度场和流场呈现三涡胞对称振荡特征;温度场主要由扩散作用决定,呈对称分布.旋转磁场作用下,Ma数基本保持不变.当磁场强度B0≤1 mT时,熔体内杂质浓度场和流场与无磁场时结构类似,但旋转磁场的搅拌作用使得熔体内周期性振荡提前出现,且当旋转磁场产生的洛伦兹力相对较大时,表面张力产生的三维振荡对流得到很好地抑制.B0=5 mT时,周向波动被完全抑制,熔区内流场和浓度场呈二维轴对称分布.旋转磁场对熔体流动产生的轴向抑制作用和周向搅拌作用,都有助于熔体流动的稳定性、浓度分布以及温度分布的均匀性,从而有利于高质量晶体的生长.     

Automated growing of large single crystals controlled by melt level sensor

The process of single crystal pulling is considered with simultaneous starting material make-up into the melt and heater temperature control in response to a signal generated by the electronic contact melt level sensor, viz.: (i) conditions ensuring the radial broadening steadiness; (ii) effect of melt level displacement, melt temperature changes, changes of solid/liquid interface shape, melt evaporation on the growing crystal diameter; (iii) conditions of crystal purification from impurities and uniform distribution of dopant.     

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.     

Connection of the Thermocapillary Flow Characteristics and the Impurity Distribution Pattern in Floating Zone Molten Molybdenum Single Crystals

The results of the impurity distribution in W-doped Molybdenum single crystals grown by electron beam floating zone melting are related to the characteristics of computed steady thermocapillary flow and impurity distribution within the molten zone. Particularly the influence of the number and the strength of eddies in the molten zone on the impurity distribution pattern in the grown crystal for different aspect ratios is considered.     

Rotating magnetic fields: Fluid flow and crystal growth applications

Rotating or alternating magnetic fields are widely used in the industrial steel casting process or in metallurgical manufacturing. For the growth of single crystals, these techniques attracted a rapidly increasing attention within the last years: a well defined melt flow leads to a more homogeneous temperature and concentration distribution in the melt and consequently improves the growth process. Rotating magnetic fields (RMF) might be used instead of crucible and/or crystal rotation avoiding mechanically induced disturbances or might be added to conventional rotation mechanisms to gain a further flow control parameter. Compared to static magnetic fields, rotating ones are distinguished by a much lower energy consumption and technical effort. Furthermore, there are no reports on detrimental effects such as the generation of thermoelectromagnetic convection or coring effects in the grown crystals. One advantage of rotating magnetic fields is the possibility to apply them even to melts with a rather low electrical conductivity like e.g. aqueous solutions. High flow velocities are already generated with moderate fields. Therefore the field strength has to be adjusted with care because otherwise undesirable Taylor vortices might be induced. In the last years, the potential of rotating magnetic fields for crystal growth processes was demonstrated for model arrangements using e.g. gallium or mercury as a test liquid as well as for a variety of growth techniques like Float Zone, Czochralski, Bridgman, or Travelling Heater Methods: Fluctuations of the heat transport due to time-dependent natural convection have could be reduced by more than an order of magnitude or the mass transport could be improved with respect to the a better radial symmetry and/or a more homogeneous microscopic segregation.     

Fe3+对KDP晶体生长影响的研究

金属离子对KDP晶体的影响是多方面的.本文采用不同的过饱和度,在不同的Fe3+掺杂浓度的生长溶液中生长KDP晶体,定量地研究了Fe3+对KDP晶体生长的影响.实验发现,无论是在高过饱和度还是在低过饱和度下生长KDP晶体,在一定的浓度范围内,Fe3+的掺入既可以增加生长溶液的稳定性,又可以有效抑制晶体柱面的扩展,而且晶体基本不楔化,同时,对晶体光学性能的影响也不大.