ACRT forced convection and its effects on solute segregation and heat and mass transfer during single crystal growth

A numerical simulation study was carried out for CdZnTe vertical Bridgman method crystal growth with the accelerated crucible rotation technique (ACRT). The convection, heat and mass transfer in front of the solid‐liquid interface, and their effects on the solute segregation of the grown crystal can be characterized with the following. ACRT brings about a periodic forced convection in the melt, of which the intensity and the incidence are far above the ones of the natural convection without ACRT. This forced convection is of multiformity due to the changes of the ACRT parameters. It can result in the increases of both the solid‐liquid interface concavity and the temperature gradient of the melt in front of the solid‐liquid interface, of which magnitudes vary from a little to many times as the ACRT wave parameters change. It also enhances the mass transfer in the melt in a great deal, almost results in the complete uniformity of the solute distribution in the melt. With suitable wave parameters, ACRT forced convection decreases the radial solute segregation of the crystal in a great deal, even makes it disappear completely. However, it increases both the axial solute segregation and the radial one notably with bad wave parameters. An excellent single crystal could be gotten, of which the most part is with no segregation, by adjusting both the ACRT wave parameters and the crystal growth control parameters, e.g. the initial temperature of the melt, the temperature gradient, and the crucible withdrawal rate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

碲锌镉垂直布里奇曼法晶体生长过程固液界面的演化

计算模拟了半导体材料碲锌镉垂直布里奇曼法单晶体生长过程,以等温线图展示了固液界面形状的演化,分析了温度梯度和坩埚移动速率对固液界面形状以及晶体内组分偏析的影响.计算结果表明在凝固的初始段,固液界面的凹陷深度较大,随后有较大幅度的减小.整个凝固过程中固液界面的凹陷深度值有一定的波动性.提高温度梯度、降低坩埚移动速率均能有效地减小固液界面的凹陷,改善晶体的径向组分偏析.     

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)     

半导体单晶生长过程中的位错研究

阐述了现有的半导体单晶位错模型,即临界切应力模型和粘塑性模型的基本理论及应用状况.分析了熔体法单晶生长过程中影响位错产生、增殖的各种因素,以及抑制位错增殖的措施.与熔体不润湿、与晶体热膨胀系数相近的坩埚材料,低位错密度的籽晶可有效地抑制生长晶体的位错密度;固液界面的形状及晶体内的温度梯度是降低位错密度的关键控制因素,而两因素又受到炉膛温度梯度、长晶速率、气体和熔体对流等晶体生长工艺参数的影响.最后,对熔体单晶生长过程的位错研究进行了展望.     

Optimization of thermal environment during crystal growth of large‐sized Nd:YAG by Temperature Gradient Technique

A finite‐element model is employed to analysis the thermal environments in Temperature Gradient Technique (TGT) furnace during the growth of large‐sized Nd:YAG crystal. The obtained results show that when the crucible is located at the lower position inside of the heater, a flatter solid‐liquid interface is established, which makes it easier to obtain the core‐free Nd:YAG crystal. Meanwhile, the lower crucible position can induce higher axial temperature gradient, which is beneficial to the release of latent heat. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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)     

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.     

Numerical study of radial temperature distribution in the AlN sublimation growth system

A large radial temperature gradient in the AlN sublimation growth system would lead to non‐uniform growth rate along the radial direction and introduce thermal stress in the as grown crystal. In this paper, we have numerically studied the radial thermal uniformity in the crucible of a AlN sublimation growth system. The temperature difference on the source top surface is insignificant while the radial temperature gradient on the lid surface is too large to be neglected. The simulation results showed that the crucible material with a large thermal conductivity is beneficial to obtain a uniform temperature distribution on the lid surface. Moreover, it was found that the temperature gradient on the lid surface decreases with increased lid thickness and decreased top window size.     

3D simulation of the effects of growth parameters on the growth of sapphire crystals using heat exchanger method

3D simulations using the commercial CFDRC and FIDAP code, which are based on finite element techniques, were performed to investigate the effects of anisotropic conductivity on the convexity of the melt–crystal interface and the hot spots of sapphire crystal in a heat‐exchanger‐method crystal growth system. The convection boundary conditions of both the energy input to the crucible by the radiation as well as convection inside the furnace and the energy output through the heat exchanger are modeled. The cross‐sectional flow pattern and the shape of the melt–crystal interface are confirmed by comparing the 3‐D modeling results with previous 2D simulation results. In the 3D model, the “hot spots” in the corners of the crucible are donut shaped, and the shape changes with the value of the conductivity of anisotropic crystal. The outline of the crystal becomes more convex as the conductivity in the z direction (k_sz) increases. The outline of melt–crystal interface is elliptical when the anisotropic conductivity is moving in the radial direction (k_sx and k_sy). The portion at the outline touching the bottom of the crucible is smaller than the maximum outline of the crystal, meaning that the shape at the “hot spot”, changes with the value of the conductivities of anisotropic crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of Nd:Sr3Ga2Ge4O14 crystals by a modified Bridgman method

Bridgman growth of Nd:SGG (Sr₃Ga₂Ge₄O₁₄) crystals has been investigated for the first time. Pt crucible of ∅︁25mm×250mm with a seed well of ∅︁10mm×80 mm is used, and seed is SGG crystal of ∅︁10mm×50mm grown by Bridgman method in advance. The growth parameters are optimized as the furnace temperature is set to 1450∼1500°C, temperature gradient in the crystal‐melt interface is less than 25 K/cm and growth rate is less than 0.5mm/h. The Nd:SGG crystals with 25mm in diameter and 60mm in length are grown successfully from 1.5 to 8at% Nd³⁺ doped stoichiometric Sr₃Ga₂Ge₄O₁₄ melt. The distribution coefficient and concentration of Nd³⁺ in Nd:SGG crystals are obviously higher than those of Nd:YAG crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of the diameteral response of a czochralski crystal II. The melt temperature — furnace temperature relation

The paper is the second in a series which presentes results on the small-signal diametral response of a Czochralski crystal grown in a resistively heated furnace to variations in heater temperature and pull rate. Here it is shown that the small-signal bulk melt temperature variation is related to the small-signal furnace temperature variation via a first order linear differential equation.     

Radiative Heat Transfer in a Resistance Heated Floating Zone Furnace: A Numerical Study with FIDAPTM

This paper presents a numerical study of radiative heat transfer in a floating zone (FZ) furnace which was performed by using the commercial finite element program FIDAP^TM. This resistance furnace should provide a temperature higher than the melting temperature of silicon (i.e. T_max ≈ 1500 °C) and a variable temperature gradient at the liquid/solid interface (≥ 25 K/cm). Due to the high working temperatures, heat radiation plays the dominant role for the heat transfer in the furnace. For this reason, the quality of view factors used in the wall‐to‐wall model was carefully inspected with energy‐balance checks. A numerical model with two control parameters is applied to study the influence of material and geometrical parameters on the temperature field. In addition, this model allows us to estimate the internal thermal conditions which were used as thermal boundary conditions for partial 3D simulations. The influences of an optical lens system on the radial symmetry of the temperature field were examined with these partial 3D simulations. Furthermore, we used the inverse modeling method to achieve maximum possible temperature gradients at the liquid/solid interface according to the limitation of maximum available power and the maximum stable height of a melt zone.     

Sensitivity Analysis on Indium Phosphide Liquid Encapsulated Czochralski Growth

The optimization of the InP liquid encapsulated Czochralski systems is usually difficult, time consuming and very expensive. Here, the relative importance of the different growth parameters (e.g., pull rate, system temperatures and geometry) on the growth interface deflection, the temperature gradients within the melt and the crystal and the dislocation density has been investigated through a sensitivity analysis. The sensitivity coefficients have been calculated by means of a mathematical model, previously validated, based on the thermoelastic theory for the dislocation formation and on the thermal capillary theory for the temperature field within the system. The crucible temperature profile has been selected as the more important parameter to control the crystal quality during the growth.     

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.     

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)     

12英寸硅单晶生长过程中熔液面位置控制方法研究

集成电路用12英寸硅单晶生长过程中,为满足晶体生长界面附近温度梯度的要求,需要测量并控制晶体生长过程中硅熔体液面位置.传统的设定坩埚上升速度和激光测距的方法有时不能适应直拉硅单晶生长技术的发展.本文提出并实现了一种采用CCD图像捕捉和测量液面位置的方法,结合调节坩埚上升速度来控制液面高度,最终可以满足生长集成电路用12英寸硅单晶的需要.     

Numerical investigation of the effect of heat shield shape on the oxygen impurity distribution at the crystal–melt interface during the process of Czochralski silicon crystal growth

In this study, a numerical simulation is performed to investigate the effect of the shape of the heat shield on the oxygen concentration in the melt. The results show that the oxygen concentration in the melt can be significantly decreased by increasing the speed of the argon gas near the crucible wall. This can be achieved by enlarging the horizontal length of the heat shield. The oxygen concentration at the melt–crystal interface varies with the length of the crystal growth. In the initial stage, there is a significant decrease in the oxygen concentration as the growth length increases. There is also a significant reduction in the emission of oxygen from the crucible wall due to the lower melt depth and crucible temperature. The transportation of oxygen impurity towards the melt–crystal interface is suppressed by the vortex motion in the melt. When the crystal exceeds a certain length, the oxygen concentration in the melt–crystal interface starts to increase with increasing crystal length, due to the drop in vortex motion in the melt.     

Directional Solidification and Melting of Eutectic GaIn

Eutectic gallium-indium is studied in a horizontal Bridgman furnace geometry. Differential temperature gradients are applied to solidify and melt the alloy while observing in-situ the interface morphology and the chemical segregation in the melt and in the solid as well. Upon cooling, a wedge-type indium-rich mushy zone develops at the cold wall. The melt is initially stirred by convective flow. After solidification starts the roll cell recedes to be replaced by a chemically layered conductive melt that eventually solidifies with rather uniform eutectic structure. Upon re-melting, the morphology of the interface adopts a profile that is predetermined by the original solid structure. Those patterns, as well as the flow, are different from single element solid melting experiments and have yet to be modeled. Under high thermal gradient the convective flow mixes the binary melt and the visualized density pattern eventually becomes that of a homogeneous melt.     

Modeling analysis of liquid encapsulated Czochralski growth of GaAs and InP crystals

The results of three‐dimensional unsteady modeling of melt turbulent convection with prediction of the crystallization front geometry in liquid encapsulated Czochralski growth of InP bulk crystals and vapor pressure controlled Czochralski growth of GaAs bulk crystals are presented. The three‐dimensional model is combined with axisymmetric calculations of heat and mass transfer in the entire furnace. A comprehensive numerical analysis using various two‐dimensional steady and three‐dimensional unsteady models is also performed to explore their possibilities in predicting the melt/crystal interface geometry. The results obtained with different numerical approaches are analyzed and compared with available experimental data. It has been found that three‐dimensional unsteady consideration of heat and mass transfer in the crystallization zone provides a good reproduction of the solidification front geometry for both GaAs and InP crystal growth.