Heat and Momentum Transfer Numerical Analysis in a Vertical Bridgman Growth System

In this work the momentum and heat transfer on a Bridgman system for the growth of GaSb has been studied. The main objective was to obtain some information about the role of the different processes like conduction, radiation and convective effects both in the melted material and the surrounding environment. These simulations are based on a 2D axi‐symmetrical model using a finite element method based code. The simulations have been carried out both in steady and transient states. It has been demonstrated that the consideration of a moving environment is important in the distribution of temperatures. The effects of the variations of thermal conductivities and emisivities on the thermal and velocity fields have been investigated. The results show that the key parameters are the thermal conductivities of the different materials present in the system, which produce significant changes in the convective flows inside the melt.     

Axial Solute Transport during Bridgman Growth of BiSbTe3‐Mixed Crystals ‐ a comparison of analytical and numerical results

2D/3D‐transient finite‐element computer simulations of heat and mass transport including convection have been performed for a Bridgman configuration close to real growth conditions. The results for the axial distribution of the excessive tellurium in BiSbTe₃ semiconductor crystals grown from the melt are compared with the predictions of analytical segregation models.It is shown that Favier's model can be successfully applied for quantitatively estimating model parameters of segregation. Finally, the transition from normal gravity to microgravity conditions is discussed.     

The role of inner and internal radiation on the melt growth of sapphire crystal

In this paper, for an inductively heated Czochralski furnace used to grow sapphire single crystal, influence of the inner (wall‐to‐wall) and crystal internal (bulk) radiation on the characteristics of the growth process such as temperature and flow fields, structure of heat transfer and crystal‐melt interface has been studied numerically using the 2D quasi‐steady state finite element method. The obtained results of global analysis demonstrate a strong dependence of thermal field, heat transport structure and crystal‐melt interface on both types of radiative heat transfer within the growth furnace.     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

In this paper, the role of seed rotation on the characteristics of the two‐dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two‐dimensional quasi‐steady state numerical simulations were carried out to analyze the seed‐melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ω_seed = 5‐30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed‐melt interface during the seeding process. The seed‐melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed‐melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed‐melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ω_seed) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three‐dimensional numerical investigation of the effects of an open window on the convective heat transfer of an oxide Czochralski system

A three‐dimensional numerical analysis was carried out for a real Czochralski crystal growth furnace containing only gas and without any melt and crystal in order to investigate the effects of a small observation window on the temperature and flow field of the system. For this approach, the induction heating equations, the Navier‐Stokes equation with Boussinesq approximation, the continuity and energy equations have been solved in cylindrical coordinates using the finite element method. It has been found that the flow and thermal fields in the system are obviously three‐dimensional and non‐axisymmetric. The gas enters the system through the window is directed towards the opposite side wall where it is divided into two parts of vertical direction as well as expands in horizontal direction. Consequently, there is a spiral gas flow in the crucible and afterheater which rotates upwards in azimuthal direction along the walls. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Modification of Fluid Flow and Heat Transport in Vertical Bridgman Configurations by Rotating Magnetic Fields

Applying a rotating magnetic field to an electrically conducting liquid, a Lorentz force is induced which generates a melt rotation of a certain angular velocity. A cylindrical gallium melt (aspect ratio 2.5) has been used as a model liquid. The melt has been heated from the bottom (Ra = 10⁶) or from the top (Ra = −10⁶) and the resulting temperature fluctuations in the melt have been measured in dependence on the rotating field strength (B_max = 30 mT). In the case of the unstable gradient 0.8 mT are sufficient to dominate the buoyancy driven convection and to reduce the amplitude of the buoyancy caused temperature oscillations for more than one order of magnitude. At the same time, the fluctuation frequency increases with the field strength. In the case of the stabilizing temperature gradient, low amplitude/high frequency temperature fluctuations are generated by the rotating magnetic field, indicating the transition to a time-dependent flow. In both cases we see an increase of the convective heat transport for magnetic inductions higher than approximately 5 m T. Applying the rotating magnetic field to the Bridgman growth of gallium doped germanium, the same behavior can be seen: Growing with a top-seeded arrangement, the intensity of the dopant striations is decreased and their frequency is increased. Growing with a bottom-seeded arrangement, the interface curvature changes from concave to convex and the flow becomes time-dependent.     

Silicon transport under rotating and combined magnetic fields in liquid phase diffusion growth of SiGe

The effect of applied rotating and combined (rotating and static) magnetic fields on silicon transport during the liquid phase diffusion growth of SiGe was experimentally studied. 72‐hour growth periods produced some single crystal sections. Single and polycrystalline sections of the processed samples were examined for silicon composition. Results show that the application of a rotating magnetic field enhances silicon transport in the melt. It also has a slight positive effect on flattening the initial growth interface. For comparison, growth experiments were also conducted under combined (rotating and static) magnetic fields. The processed samples revealed that the addition of static field altered the thermal characteristics of the system significantly and led to a complete melt back of the germanium seed. Silicon transport in the melt was also enhanced under combined fields compared with experiments with no magnetic field. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

In order to understand the nature of surface spoke patterns on silicon melt in industrial Czochralski furnaces, a series of unsteady three‐dimensional numerical simulations were conducted for thermocapillary‐buoyancy flow of silicon melt in annular pool (inner radius r_i = 15 mm, outer radius r_o = 50 mm, depth d = 3 mm). The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll‐cell thermocapillary‐buoyancy flow. With large temperature difference, the simulation can predict three‐dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux (3 W/cm²) does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of BiSbTe3 -Mixed Crystals using a Bridgman Configuration of the TITUS Furnace - Numerical Simulation of Convection and Segregation

A standard Bridgman configuration of the TITUS facility was used to grow BiSbTe ₃ -mixed crystals at normal and at reduced gravity. The growth experiments in space, including a dynamical registration of the temperature distribution of the furnace, were performed during the MIR'97 mission. The transient temperature profiles have been analysed to get thermal boundary conditions for numerical simulations of convection and segregation with the FEM package FIDAP. The calculations have been done within the frame of a 3D model close to the real growth conditions. The aim of the paper is to discuss the resulting Buoyancy driven flow configuration in the melt and its influence on the radial and axial segregation depending on the gravity level.     

Existence,stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity

A thermocapillary model is used to study the existence, stability, and nonlinear dynamics of detached melt crystal growth in a vertical Bridgman system under zero gravity conditions. The model incorporates time-dependent heat, mass, and momentum transport, and accounts for temperature-dependent surface tension effects at the menisci bounding the melt. The positions of the menisci and phase-change boundary are computed to satisfy the conservation laws rigorously. A rich bifurcation structure in gap width versus pressure difference is uncovered, demarcating conditions under which growth with a stable gap is feasible. Thermal effects shift the bifurcation diagram to a slightly different pressure range, but do not alter its general structure. Necking and freeze-off are shown to be two different manifestations of the same instability mechanism. Supercooling of melt at the meniscus and low thermal gradients in the melt ahead of the crystal–melt–gas triple phase line, either of which may be destabilizing, are both observed under some conditions. The role of wetting and growth angles in dynamic shape stability is clarified.     

Effect of the Temperature Fluctuation of the Melt on β‐BaB2O4 (BBO) Crystal Growth

In this paper the effect of the growth temperature fluctuation, for instance, the transient furnace temperature variation due to a short‐term electric power supply interruption on BBO crystal growth was investigated based on the theory of temperature wave transmitting in melt and the boundary layer theory of melt. It was found that the critical width of the temperature pulse to avoid the temperature wave penetrating through the boundary layer and reaching to the growth interface at a constant rotation speed (9∼4 r/min) is 69∼150 s and the corresponding amplitude of the temperature pulse is high more than 60 °C due to the large thickness of the velocity boundary layer of the melt. This result indicates that a small transient temperature fluctuation has no significant effect on the crystal quality, and therefore implies that not only transport processes but interface growth kinetics, a two‐dimensional nucleation growth mode at the interface may also dominate the crystal growth.     

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.     

Simulation of temperature and flow fields in an inductively heated melt growth system

The goal of the research presented here is to apply a global analysis of an inductively heated Czochralski furnace for a real sapphire crystal growth system and predict the characteristics of the temperature and flow fields in the system. To do it, for the beginning stage of a sapphire growth process, influence of melt and gas convection combined with radiative heat transfer on the temperature field of the system and the crystal‐melt interface have been studied numerically using the steady state two‐dimensional finite element method. For radiative heat transfer, internal radiation through the grown crystal and surface to surface radiation for the exposed surfaces have been taken into account. The numerical results demonstrate that there are a powerful vortex which arises from the natural convection in the melt and a strong and large vortex that flows upwards along the afterheater side wall and downwards along the seed and crystal sides in the gas part. In addition, a wavy shape has been observed for the crystal‐melt interface with a deflection towards the melt. (© 2010 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)     

Compositional Effects on Solidification of Congruently Melting InSb

In vertical Bridgman and Czochralski growth of stoichiometric electronic materials such as InSb, GaSb, and GaAs, growth from stoichiometric melts is commonly desired to achieve high quality. Off-stoichiometric growth is considered significant in the quest to understand transport phenomena leading to the observed sporadic inclusions. Here we apply radiographic interface visualization and calibrated interface temperature measurements to study growth of InSb from off-stoichiometric melts. The crystals are analyzed for structure and chemical segregation. Results indicate concentration boundary layer formation in the melt ahead of the interface. Evidence is presented for heterogeneous nucleation sites within αInSb. Analysis indicates that these nucleation sites develop ahead of the interface in the off-stoichiometric melt phase as the melt temperature at the interface drops below the congruent melting temperature of αInSb.     

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)     

Bridgman growth of CdxHg1−xTe— A review

Recent developments in the bulk Bridgman growth method for Cd_xHg_1−xTe are reviewed. Both melt mixing and heat flow control techniques have been applied in attempts to produce more uniform material in terms of composition. In the U.K. work has concentrated on application of the Accelerated Crucible Rotation Technique (ACRT) to achieve the required uniformity improvements. Elsewhere, various means to control isotherm shape have been used with the same aim. The ultimate use of the material is in infra-red detectors and Bridgman grown Cd_xHg_1−xTe has produced these successfully for both photoconductive and photovoltaic applications.     

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)