Computation of the axial temperature distribution for the travelling heater method

A theoretical model for the computation of the axial temperature distribution for the THM arrangement is described considering the heat flow in radial direction. The calculated temperature distribution is compared with the measured one. The correspondence is sufficient. By means of this model, it is possible to estimate the effect of a change of important growth parameters prior to the experiment. The model also permits a calculation of temperature distributions of other crystal growth methods (e.g. Bridgman, zone levelling, zone melting) by changing the boundary conditions only.     

数值模拟自然对流对直拉单晶硅的影响

在直拉单晶硅生长的过程中,自然对流对晶体界面的形状、温度场及应力分布影响很大。本文采用二维模型对熔体内自然对流对单晶硅的影响作了数值模拟,在低雷诺数时采用层流模型,高雷诺数时采用紊流模型,Gr的变化范围从3×106到3×1010,这样涵盖了从小尺寸到大尺寸的直拉单晶硅生长系统。数值结果表明熔体的流动状态不仅与熔体的Gr有关,还与熔体高度和坩埚半径的比值密切相关。当Gr>108时,熔体内确实存在紊流现象,层流模型不再适合,随着Gr的增大,紊流现象加剧,轴心处的等温线变得更为陡峭,不利于晶体生长。     

Three-dimensional thermocapillary and buoyancy convections and interface shape in horizontal Bridgman crystal growth

Computer simulation is conducted to study three-dimensional (3D) thermocapillary and buoyancy convections and their effects on the growth interface for horizontal Bridgman crystal growth. The free-boundary model is based on a finite volume approximation of continuity, momentum, and energy equations on a collocated grid. Crystal growth of GaAs is used as an example. From calculated results, it is observed that the effect of buoyancy convection on the growth interface is significant. With the thermocapillary effect, the 3D flow structures are not changed much, but its effect on the growth interface is not trivial. Due to the convections, the growth interface is always concave, and its deflection is affected significantly by the growth rate and thermal environment. A simple strategy of interface control is illustrated. Furthermore, slight crucible tilting can also affect the 3D flows leading to an asymmetric growth interface.     

Influence of phosphine flow rate on Si growth rate in gas source molecular beam epitaxy

As reported by other authors, we have also observed that the Si growth rate decreases with increasing phosphine (PH₃) flow rate in gas source Si molecular beam epitaxy using phosphorous (P) as a n-type dopant. Why small quantity PH₃ can affect Si growth rate? Up to now, the quantitative characterization of PH₃ flow influence on Si growth rate is little known. In this letter, the PH₃ influence will be analyzed in detail and a model considering strong P surface segregation and its absorption of hydrogen will be proposed to characterize the effect.     

Numerical simulation and validation of the Peltier pulse marking of solid/liquid interfaces

We describe a numerical approach of the solidification of binary alloys to study the motion of a crystal/melt interface submitted to current pulses involving a modification of the dopant concentration field. For the thermal aspect, the Thomson effect, the Peltier effect and Joule heating have been included in the heat flow. For the solutal segregation, our model is based on mass transports which occur in the liquid phase, namely diffusion and convection. Numerical computations are validated by comparison with experimental data and thus could find applications in the prediction of the effects of Peltier pulse marking in crystal growth.     

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.     

一个实用的生产用Ⅲ-Ⅴ族化合物半导体材料Turbo-Disc MOCVD生长模型

在MOCVD质量控制生长模式下,通过分析Ⅲ-Ⅴ族化合物半导体材料在衬底表面的反应过程,建立了一个实用的生长模型.此模型是基于分子动力学、化学反应热力学理论分析之上的.针对Turbo-Disc 反应体系,分析了Turbo-Disc 的传热以及质量传送模式后, 建立了Turbo-Disc的生长模型.在此模型中建立了输入反应室的参数(IPs)和边界层的生长参数的关系.在对组分匹配的GaInP/GaAs 三组分生长体系进行分析时,发现此模型是非常有效的,理论计算的结果与实验得到的结果非常吻合.应用此模型在实际生产中可以迅速地得到匹配的多组分外延层.     

Columnar grain growth pattern with fluid flowing in molten pool

A coupled model was used to simulate columnar grain growth in TIG (tungsten inert‐gas) molten pool of nickel base alloy. The cellular automaton algorithm for dendritic growth is incorporated with solute transport model to take fluid flow into consideration. The results indicate that shear flow changes the solute distribution at the S/L (Solid/Liquid) interface, leading to asymmetrical growth of columnar grains. The dendrite arms on the upstream side grow fast, while the growth of dendrite arms on the downstream side is much delayed. However, dendrite arms on both sides are not as well‐developed as the grain growth without flow. With inlet flow velocity increasing, the phenomenon becomes more obvious. In addition, shear flow also results in more severe coring segregation. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CFD modelling of single crystal growth of potassium dihydrogen phosphate (KDP) from binary water solution at 30 °C

Crystal growth rate depends on both diffusion and surface reaction. In industrial crystallizers, there exist conditions for diffusion-controlled growth and surface reaction-controlled growth. Using mathematical modelling and experimental information obtained from growth studies of single crystals, it is possible to separate these phenomena and study how they are affected by concentration, slip velocities of particles, temperature and finally estimate the parameters for crystal growth models.In this study, a power-law growth model using activity-based driving force is created. Computational fluid dynamics (CFD) was used to evaluate the thickness of a diffusion layer around the crystal. Parameters of the crystal growth model were estimated using a non-linear optimization package KINFIT. Experimental data on growth rate of the (1 0 1) face of a potassium dihydrogen phosphate (KDP) single crystal and simulated data on the thickness of a diffusion layer at the same crystal face were used in parameter estimation. The new surface reaction model was implemented into the CFD code. The model was used to study the effect of flow direction on growth rate of the whole crystal with various slip velocities and solute concentrations.The developed method itself is valid in general but the parameters of crystal growth model are dependent on the system. In this study, the model parameters were estimated and verified for KDP crystal growth from binary water solution.     

Surface chemistry and transport effects in GaN hydride vapor phase epitaxy

A simple quasi-thermodynamic model of surface chemistry in GaN hydride vapor phase epitaxy (HVPE) is presented. The model is coupled with the detailed 3D simulations of species transport in a horizontal-tube reactor and validated by the comparison with the data on the GaN growth rate obtained by laser reflectometry. Parametric study of the growth rate as a function of temperature and species flow rates has been performed over a wide range of growth conditions. The important role of species transport in an HVPE reactor is demonstrated. In particular, a strong effect of the natural concentration convection resulting in the formation of recirculation zones and in a non-uniform vapor composition is revealed by modeling. The impact of these effects on the GaN growth rate and V/III ratio on the growth surface is discussed in detail.     

Growth of equiaxed dendritic crystals settling in an undercooled melt,Part 1: Tip kinetics

Experiments are conducted to measure the dendrite tip growth velocities of equiaxed crystals of the transparent model alloy succinonitrile–acetone that are settling in an undercooled melt. The tip velocities are measured as a function of the crystal settling speed and the Eulerian angle between the dendrite arms and the flow direction relative to the crystal. The ratio of the settling speed (or flow velocity) to the tip growth velocity ranges from 62 to 572. The ratio of the measured tip velocity to that predicted from a standard diffusion theory for free dendritic growth ranges from almost zero for dendrite tips growing in the wake of the crystal, about unity for dendrite tips with an orientation close to normal to the flow direction, and up to two for dendrite tips growing into the flow. Despite the relatively strong flow relative to the crystal, the average tip growth velocity of the six primary dendrite arms of an equiaxed crystal is found to be in excellent agreement with the standard diffusion theory result. The individual tip velocities are correlated using a boundary layer model of free dendritic growth in the presence of melt flow that is modified to account for the flow angle dependence. Using the same dendrite tip selection parameter, σ^*, as established previously under purely diffusive conditions (0.02), good agreement is achieved between the measured and predicted tip velocities. The model is also found to predict well the variations in the tip velocity that occur during settling due to crystal rotation and settling speed changes.     

AlInN MOVPE: growth chemistry and analysis of trends

Comprehensive model of AlInN Metal-Organic Vapor Phase Epitaxy (MOVPE) accounting for the gas-phase and surface chemistry including parasitic reactions/particle formation is developed. Experimental data and modeling results suggest that as V/III ratio increases from several tens (growth of pure AlN) to several thousands (growth of AlInN), the partial AlN growth rate decreases even in the absence of strong particle formation. This effect is associated with the formation of heavy molecular weight/low diffusivity gas-phase dimer species at high ammonia concentration. At elevated pressures growth rate decreases with pressure at a weakly changing composition, which is related to the gas-phase losses of In- and Al-containing species due to reaction with AlN particles. Model allows the prediction of both the AlInN growth rate and composition versus group-III flow rates, temperature, and pressure.     

Theoretical consideration of the growth kinetics for GaAs and GaSb

An extended MOMBE growth kinetics model is proposed, based on the Robertson model, to explain both the GaAs growth rate variation and modulated beam mass spectroscopy data reported by Martin and Whitehouse. In this model, we assume that (1) MEGa molecules react with ethyl-radicals to form DEGa, (2) excessive group-V molecules on the surface suppress the decomposition of DEGa and enhance the desorption of DEGa, (3) reaction of DEGa with ethyl-radicals to form TEGa is negligible, and (4) effective surface coverage of excessive group-V atoms during growth is determined by the double layer adsorption model including desorption parameters for group-V molecules. The first assumption (1) is found to be a dominant process to explain the behaviour of DEGa desorption at high temperatures. This model can reproduce the dependences of both growth rate and desorbing rate of Ga alkyls on substrate temperature during GaAs MOMBE growth. The use of Sb instead of As produces a significant change in the growth rate variation with substrate temperature and group-V flux for the growth of GaSb, in spite of the use of the same TEGa flow rate. This can be rationalized by the difference in the desorption parameters for Sb and As.     

Effects of susceptor rotation speed and total flow rate on selectivity in metalorganic chemical vapor deposition growth techniques

We investigate the effect of using a high-speed rotating susceptor on selectivity of InGaAs growth by low-pressure metalorganic chemical vapor deposition (MOCVD), and compare this with the effect of the total hydrogen flow rate at 450°C. It is found that selectivity is greatly improved with increased rotation speed, as previously reported, and is also affected by the total flow rate. It is confirmed that an increase in the flow rate has a similar effect on selectivity as an increase in rotation speed. The improved selectivity in both cases can be explained by a higher gas velocity in the growth chamber. It is also found that large variation in selectivity at higher rotation speeds might be caused by the recirculation flow on the substrate when the total flow rate is much less than the matching flow rate.     

Selection criterion for the growing dendritic tip in a non-isothermal binary system under forced convective flow

A free dendrite growth during solidification into external forced flow is analyzed using a sharp interface model. A criterion for selection of the stable growth mode is derived for the axisymmetric dendrite growing into non-isothermal binary system under convective flow. The criterion obtained rallies analytic results for dendrite growth under forced convection in a pure system [Ph. Bouissou, P. Pelce, Phys. Rev. A 40 (1989) 6673] and dendrite growth in a stagnant binary system [M. Ben Amar, P. Pelce, Phys. Rev. A 39 (1989) 4263].     

Application of rotating magnetic fields in Czochralski crystal growth

The physical principles of electromagnetic stirring with a rotating magnetic field are explained and a mathematical model to calculate the electromagnetic volume force, the fluid flow and the transport of heat and solutes is outlined. For the electromagnetic volume force and for the order of magnitude of the flow velocities approximative analytical expressions are given. A high flexibility in configuring the volume force in order to achieve a desired flow distribution is obtained by multi-frequency stirring that is by superposition of two or several magnetic fields with different frequencies and/or sense of rotation. Results of experimental investigation and mathematical simulation of multi-frequency stirring are given. Numerical simulation of the fluid flow, the temperature and the oxygen distribution in a Czochralski process crucible was performed including the effect of single mode and multi-frequency stirring. The results indicate that electromagnetic stirring should offer large potentials for the optimization of the flow configuration in a Czochralski process crucible. Finally examples from literature of practical application of rotating magnetic fields in crystal growth are presented.     

Analysis of SiC crystal sublimation growth by fully coupled compressible multi-phase flow simulation

A fully coupled compressible multi-phase flow solver was developed to effectively design a large furnace for producing large-size SiC crystals. Compressible effect, convection and buoyancy effects, flow coupling between argon gas and species, and the Stefan effect are included. A small and experimental furnace is used to validate the solver. First, the essentiality of 2D flow calculation and the significance of incorporating buoyancy effect and gas convection, the Stefan effect, and flow interaction between argon gas and species were investigated by numerical results. Then the effects of argon gas on deposition rate, growth rate, graphitization on the powder source, and supersaturation and stoichiometry on the seed were analyzed. Finally, the advantages of an extra chamber design were explained, and improvement of growth rate was validated by the present solver.     

The impact of pressure and temperature on growth rate and layer uniformity in the sublimation growth of AlN crystals

To effectively design a large furnace for producing large-size AlN crystals, a fully coupled compressible flow solver was developed to study the sublimation and mass transport processes in AlN crystal growth. Compressible effect, buoyancy effects, flow coupling between aluminum gas and nitrogen gas, and Stefan effect are included. Two sets of experimental data were used to validate the present solver. Simulation results showed that the distributions of Al and N₂ partial pressures are opposite along the axial direction due to constant total pressure and Stefan effect, with the Al and nitrogen partial pressures being highest at the source and seed crystals positions, respectively. The distributions of species inside the growth chamber are obviously two-dimensional, which can curve a flat crystal surface. Simulation results also showed that AlN crystal growth rate can be increased by reducing total pressure or by increasing seed temperature or by increasing source-seed temperature difference. High nitrogen pressure causes decrease in growth rate, but it is beneficial for obtaining uniform growth rate in the radial direction. Results of simulation also showed that there is an optimized temperature difference (40 °C) in the present furnace for obtaining good homogeneity of growth rate.     

Homoepitaxial growth of 6H–SiC thin films by metal-organic chemical vapor deposition using bis-trimethylsilylmethane precursor

Homoepitaxial silicon carbide (SiC) films were grown on 3.5° off-oriented (0 0 0 1) 6H–SiC by metal-organic chemical vapor deposition (MOCVD) using bis-trimethylsilylmethane (BTMSM, C₇H₂₀Si₂). A pronounced effect of the growth conditions such as source flow rate and growth temperature on the polytype formation and structural imperfection of the epilayer was observed. The growth behavior was explained by a step controlled epitaxy model. It was demonstrated by high-resolution X-ray diffractometry and transmission electron microscopy that high-quality 6H–SiC thin films were successfully grown at the optimized growth condition of substrate temperature 1440°C with the carrier gas flow rate of 10 sccm.