Numerical investigation of induction heating and heat transfer in a SiC growth system

A global simulation model is applied for a silicon carbide growth system heated by induction coils. A finite‐volume method (FVM) and a global model are applied to solve the equations for electromagnetic field, conductive and radiative heat transfer. The growth rate is predicted by Hertz‐Knudsen equation and one‐dimensional mass transfer equation. Further, simulations for five different coil positions are carried out to investigate the effects of coil position on temperature distribution in the furnace. The numerical results reveal that the variation of temperature in the radial direction along the substrate surface and the temperature difference between the powder and substrate are greatly affected by the coil position. The predicted growth rate along the substrate surface for five coil positions is also studied. Finally, a reasonable range of coil positions maintaining a balance between large‐diameter crystal, high growth rate, temperature limitation of material and lower electrical power consumption is obtained. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of active afterheater on the induction heating process in oxide Czochralski systems

Different shapes and orientations of an active afterheater for oxide Czochralski crystal growth systems are considered and corresponding results of electromagnetic field and volumetric heat generation have been computed using a finite element method (Flex‐PDE package). For the calculations, the eddy current in the induction coil (i.e. the self‐inductance effect) has been taken into account. The calculation results show the importance of an active afterheater, its shape as well as its geometry and position with respect to the crucible on the heat generation distribution in a CZ growth system. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of a new SiC growth system by the dual-directional sublimation method

A new SiC growth system using the dual-directional sublimation method was investigated in this study. Induction heating and thermal conditions were computed and analyzed by using a global simulation model, and then the values of growth rate and shear stress in a growing crystal were calculated and compared with those in a conventional system. The results showed that the growth rate of SiC single crystals can be increased by twofold by using the dual-directional sublimation method with little increase in electrical power consumption and that thermal stresses can be reduced due to no constraint of the crucible lid and low temperature gradient in crystals.     

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.     

Two and three‐dimensional numerical modeling of induction heating in oxide Czochralski systems

In this article we report on a set of two‐dimensional and three‐dimensional numerical calculations for three different oxide Czochralski configurations in order to compare the results of the electromagnetic fields and the heat generation distribution. Two configurations without and with a gap between the crucible and active afterheater have axisymmetric conditions while the configuration with an open observation window in the afterheater is characterized by a non‐axisymmetric geometry. It has been found that in the non‐axisymmetric configuration under the influence of the observation window is located at the crucible side wall after a short distance behind the window cut out. Besides this influence the volumetric distribution of heat generation in the system is about symmetric. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nucleation of AlN on SiC substrates by seeded sublimation growth

The nucleation of aluminum nitride (AlN) on silicon carbide (SiC) seed by sublimation growth was investigated. Silicon-face, 8 off-axis 4H-SiC (0 0 0 1) and on-axis 6H-SiC (0 0 0 1) were employed as seeds. Initial growth for 15 min and extended growth for 2 h suggested that 1850 °C was the optimum temperature of AlN crystal growth: on an 8 off-axis substrate, AlN grew laterally forming a continuous layer with regular “step” features; on the on-axis substrate, AlN grew vertically as well as laterally, generating an epilayer with hexagonal sub-grains of different sizes. The layer's c-lattice constant was larger than pure AlN, which was caused by the compression of the AlN film and impurities (Si, C) incorporation. Polarity sensitive and defect selective etchings were performed to examine the surface polarity and dislocation density. All the samples had an Al-polar surface and no N-polar inversion domains were observed. Threading dislocations were present regardless of the substrate misorientation. Basal plane dislocations (BPDs) were revealed only on the AlN films on the 8 off-axis substrates. The total dislocation density was in the order of when the film was 20– thick.     

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)     

Numerical investigation of carbon and silicon carbide contamination during the melting process of the Czochralski silicon crystal growth

Carbon contamination in single crystalline silicon is detrimental to the minority carrier lifetime, one of the critical parameters for electronic wafers. In order to study the generation and accumulation of carbon contamination, transient global modeling of heat and mass transport was performed for the melting process of the Czochralski silicon crystal growth. Carbon contamination, caused by the presence of carbon monoxide in argon gas and silicon carbide in the silicon feedstock, was predicted by the fully coupled chemical model; the model included six reactions taking place in the chamber. A simplified model for silicon carbide generation by the reaction between carbon monoxide and solid silicon was proposed using the closest packing assumption for the blocky silicon feedstock. The accumulation of carbon in the melted silicon feedstock during the melting and stabilization stages was predicted. Owing to this initial carbon content in the melt, controlling carbon contamination before the growth stage becomes crucial for reducing the carbon incorporation in a growing crystal.     

Systematic study of epitaxy growth uniformity in a specific MOCVD reactor

Gallium nitride (GaN) is a direct bandgap semiconductor widely used in bright light‐emitting diodes (LEDs). Thin‐film GaN is grown by metal‐organic chemical vapour deposition (MOCVD) technique. Reliability, efficiency and durability of LEDs are influenced critically by the quality of GaN films. In this report, a systematic study has been performed to investigate and optimize the growth process. Fluid flow, heat transfer and chemical reactions are calculated for a specific close‐coupled showerhead (CCS) MOCVD reactor. Influences of reactor dimensions and growth parameters have been examined after introducing the new conceptions of growth uniformity and growth efficiency. It is found that GaN growth rate is mainly affected by the concentration of (CH3)3Ga:NH3 on the susceptor, while growth uniformity is mainly influenced by the recirculating flows above the susceptor caused by natural convection. Effect of gas inlet temperature and the susceptor temperature over the growth rate can be explained by two competing mechanisms. High growth efficiency can be achieved by optimizing the reactor design.     

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.     

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)     

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 modelling of instability and supercritical oscillatory states in a Czochralski model system of oxide melts

The motivation for this study is the need for accurate numerical models of melt flow instabilities during Czochralski growth of oxides. Such instabilities can lead to undesirable spiralling shapes of the bulk crystals produced by the growing process. The oxide melts are characterized by Prandtl numbers in the range 5<Pr <20, which makes the oxide melt flow qualitatively different from the intensively studied flows of semiconductors characterized by smaller Prandtl numbers Pr <0.1. At the same time, these flows can be modelled experimentally by many transparent test fluids (e.g. water, silicon oils, salt melts), which have similar Prandtl numbers, but allow one to avoid the extremely high melting‐point temperatures of the oxide materials. Most previous studies of melt instabilities for Prandtl numbers larger than unity suffer from a lack of accuracy that is caused by the use of coarse grids. Recent convergence studies made for a series of simplified problems and for a hydrodynamic model of Czochralski growth showed that for a second order finite volume method reliable stability results can be obtained on grids having at least 100 nodes in the shortest spatial direction. The obvious numerical difficulties call for an extensive benchmark exercise, which is proposed here on the basis of recently published experimental and numerical data, as well as some preliminary results of this study. The calculations presented are performed by two independent numerical approaches, which are based on second‐order finite volume and finite element discretizations. We start our comparison from the steady states, whose parametric dependencies sometimes exhibit turning points and multiplicity. We then compare the critical temperature differences corresponding to the onset of instability, and finally compare calculated supercritical oscillatory states and phase plots. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Understanding the cubic AlN growth plane from first principles

The structure of clean and reconstructed cubic AlN (0 0 1) surfaces has been investigated from first principles. In the nitrogen rich part of the phase diagram, a nitrogen termination has been found to be favored. Under aluminum-rich conditions, a contracted adlayer of Al-atoms on top of an Al-termination is favored.     

Numerical study for diffusion processes in dissolution and growth of heterostructures formed by LPE. Part II. Effect of programmed temperature changes

The paper presents the numerical study of mass transfer in growth and dissolution of CdHgTe compounds in LPE systems that are subjected to temperature changes. Effect of solid-state diffusion on heterostructure formation is analyzed in the wide range of operating parameters.     

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.     

Numerical study of induction heating in melt growth systems—Frequency selection

A set of 2D finite element numerical simulation of induction heating process for an oxide Czochralski crystal growth system has been made for a range of f=1–100 kHz applied frequency of driving current. It was shown that the frequency selection has a marked effect in all basic induction phenomena, including electromagnetic field distribution, skin depth, coil efficiency, and intensity and structure of heating in the growth setup.     

A method to model the transient performance of high frequency vibration in crystal growth

A general method to quantitatively study the transient fluctuation related to the high frequency vibration in crystal growth is developed. An example during the Czochralski crystal growth has been simulated, and the simulation coincides with the experimental date. On basis of the model, the influence of vibration frequency on the transient fluctuations for temperature and velocity are elucidated. Then an available approach to control the vibration effect is proposed.     

Effect of AlN doping on the growth morphology of SiC

AlN doped SiC films were deposited on on‐axis Si‐face 4H‐SiC (0001) substrates by the physical vapor transport (PVT) method. Thick film in the range of 20 μm range was grown and morphology was characterized. Films were grown by physical vapor deposition (PVD) in a vertical geometry in the nitrogen atmosphere. We observed that nucleation occurred in the form of discs and growth occurred in hexagonal geometry. The X‐ray studies showed (001) orientation and full width of half maxima (FWHM) was less than 0.1° indicating good crystallinity. We also observed that film deposited on the carbon crucible had long needles with anisotropic growth very similar to that of pure AlN. Some of the needles grew up to sizes of 200 μm in length and 40 to 50 μm in width. It is clear that annealing of SiC‐AlN powder or high temperature physical vapor deposition produces similar crystal structure for producing AlN‐SiC solid solution. SEM studies indicated that facetted hexagons grew on the top of each other and coarsened and merged to form cm size grains on the substrate. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of the in-situ sublimation in the growth of HgI2 platelets from vapour

The Quality of HgI₂ platelets grown from the vapour phase has been studied, varying different growth parameters, i.e. starting material, addition of polyethylene, source/crystallisation temperature, in-situ sublimation. It has been found that the in-situ sublimation at high temperature is the essential factor for the production of HgI₂ platelets. This in-situ sublimation was made in the same growth ampoule at temperatures over 200 °C and prior to the growth process. All the other growth parameters studied in this work influenced the quality of the platelets although they did not affect their production. Finally, the grown platelets have been characterised by optical observation and by differential scanning calorimetry.