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LEC- and VGF-growth of SI GaAs single crystals - Recent developments and current issues
Abstract
The paper reviews the progress made in crystal growth of semi-insulating GaAs by liquid encapsulation Czochralski and vertical gradient freeze techniques during the last few years under the continuous need for cost reduction of the production process.
... The other main techniques for growing GaAs single crystals are the liquid-encapsulation Czochralski (LEC) and the vapor-pressure-controlled Czochralski method (VCz). In the LEC method, large temperature gradients around 100 K/cm allow an efficient heat removal from the interface and therefore larger growth velocities, typically around 7-10 mm/h for crystals larger than 3" [Shi93,Jur05]. Typical growth parameters for the VCz of GaAs are gradients of 20-40 K/cm and growth rates of 3-5 mm/h [Neu01]. ...
... State-of-the-art VGF growth of GaAs is characterized by etch pit densities (EPD) below 500 cm ≠2 for 4"-GaAs:Si and around 1300 cm ≠2 for undoped 4"-GaAs [Bir03,Bue01]. This is about one order of magnitude smaller compared to LEC growth [Jur05]. Additionally, diameter control is not necessary due to the predetermined crucible form in VGF growth. ...
... Such a setup is characterized by a reduced complexity and superior upscaling potential [Bir03]. It is therefore in particular suitable for industrial production [Jur05]. ...
Im Rahmen der vorliegenden Arbeit wurden Si-dotierte und undotierte 4” VGF-GaAs Einkristalle unter dem Einfluss von Wandermagnetfeldern (TMF) gezüchtet. Die für den Prozess benötigte Wärme und das Wandermagnetfeld wurden simultan mithilfe der kombinierten Regelung von Gleich- und Wechselströmen in einem KRISTMAG Heizer-Magnet-Modul (HMM) erzeugt. Alle Züchtungsexperimente wurden in einer kommerziellen VGF-Anlage mit eingebautem Eintiegel-HMM und in einer neu entwickelten VGF-Anlage mit Multitiegel-HMM durchgeführt. Der Einfluss der durch die Lorentzkräfte angetriebenen Schmelze auf die Form der fest-flüssig Phasengrenze wurde innerhalb einer TMF-Parameterstudie analysiert. Im Vergleich mit Referenzkristallen, welche ohne TMF gezüchtet wurden, zeigte sich, dass die Durchbiegung der Phasengrenze durch die Anwendung eines geeigneten Doppelfrequenz-TMF um etwa 30% verringert und der Kontaktwinkel am Tiegel um etwa 10% vergrößert werden kann. Zudem wurden Synergieeffekte von TMF-Anwendung und den Ansätzen zur Prozessintensivierung - Scale-Up, Speed-Up und Numbering-Up - für die Verbesserung der Prozesseffizienz erfolgreichnachgewiesen. Es wurden gleichzeitig zwei 4” VGF-GaAs:Si Einkristalle unter dem Einfluss eines TMF in einer Multitiegel-Anlage gezüchtet. In Kristallen, welche ohne oder mit zu starkem TMF gezüchtet wurden, waren Wachstumsstreifen sichtbar. Wurde die magnetische Flussdichte des TMF an den Kristallisationsverlauf angepasst, konnten nahezu keine Mikroinhomogenitäten detektiert werden. Die Länge der Kristallfacetten stabilisierte sich durch den Einsatz der Wandermagnetfelder. Zusätzlich konnten die Versetzungsdichten innerhalb der Kristalle durch Optimierung des thermischen Aufbaus und der Phasengrenzform signifikant reduziert werden. Mithilfe eines dem Züchtungsverlaufes angepassten Doppelfrequenz-TMF sowie der Nutzung eines BN-Suszeptors, wurde eine durchschnittliche EPD von 100 cm-2 in einem GaAs:Si Kristall erzielt.
... T HE vertical gradient freeze (VGF) process is the most important technology for the production of bulk compound semiconductor crystals, such as gallium arsenide (GaAs) or indium phosphide (InP) [1], which are needed for high-power and high-frequency electronics and infrared lightemitting and laser diodes. For these purposes, the crystals have to meet high requirements with respect to their purity and structural perfection. ...
... Herein, the derivatives y (α 1 ) from (16) depends on these variables and, thus, can be solved for them. 1 Finally, recovering the original state x(t) by using the map (15) and γ (t) = y 2 (t), the approximate system output in flat coordinates can be stated in terms of (5) ...
In this contribution, tracking control designs using output feedback are presented for a two-phase Stefan problem (SP) arising in the modeling of the vertical gradient freeze process. The two-phase SP, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying spatial extent of the solid and liquid domains during growth. After discussing the special needs of the process, collocated and flatness-based state feedback designs are carried out. The quality of the provided approximations and the performance and robustness against parameter uncertainties of the open- and closed-loop control setups are analyzed in several simulations.
... The Vertical Gradient Freeze (VGF) process is the most important technology for the production of bulk compound semiconductor crystals like Gallium-Arsenide (GaAs) or Indium-Phosphide (InP) [1] which are especially used for manufacturing high-power and high-frequency electronics as well as infrared light-emitting and laser diodes. For these purposes the crystals have to meet high requirements with respect to their purity and structural perfection. ...
... Appendix A. 1 ...
In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying extent of the solid and liquid domains during growth. After discussing the special needs of the process, collocated as well as flatness-based state feedback designs are carried out. To render the setup complete, an observer design is performed, using a flatness-based approximation of the original distributed parameter system. The quality of the provided approximations as well as the performance of the open and closed loop control setups is analysed in several simulations.
... The liquid encapsulated Czochralski (LEC) method was originally used to grow InP, but this method cannot applied to produce InP wafers for current market specifications due to high temperature gradient and high amount of dislocations [3,4]. Recently, the VGF process has been used to grow high-quality InP [5][6][7][8][9][10]. The VGF process has many advantages such as a low temperature gradient, low dislocation density, and no need for diameter control due to a predefined crucible [11]. ...
To scale up Indium phosphide (InP) crystal growth to industrial scale, there is a need to increase the growth rate and crystal length while maintaining high quality. Here, melt-conditioned vertical gradient freeze (MCVGF) is investigated. In this method, a pyrolytic boron nitride (PBN) rotor with special shape rotates inside the melt at a slow speed. It consequently enhances the melt movement and latent heat removal from the crystal front. In this study, a full 3-dimensional model is presented for both original and proposed VGF process including an energy equation, Navier–Stokes equations, moving mesh theory, and thermal stress equations. The growth speed is set to about 7 mm/h. Melt flow, temperature gradient, crystal front, and thermal stress were calculated and compared between these two cases. Crystal growth with acceptable quality is impossible during the original VGF process, but the MCVGF shows very good potential to overcome the limitations. The crystal front is found to be flat with small concavity at high growth rates, which is perfect for crystal growth. The thermal stress was checked for MCVGF: It reduces by 50% in comparison with original process under critical value. The simulation proved that MCVGF is feasible for the crystal growth process and is a perfect method for industrial crystal growers to increase production speed and crystal structural perfection.
... Unlike the more common Czochralski (CZ) process (Friedrich et al., 2015) in which crystals are grown from the melt in an upside-down configuration, the Vertical Gradient Freeze (VGF) technique uses an upward growth direction which is more beneficial in terms of the heat flow in the crystal. Therefore, it can be used for the bulk production of high quality compound semiconductor single crystals (Jurisch et al., 2005) like Gallium-Arsenide (GaAs) or Indium-Phosphide that are hard to grow in a CZ setup. ...
This contribution presents the application of nonlinear model predictive control to the Vertical Gradient Freeze crystal growth process. Due to the time-varying spatial extent of the crystal and melt during growth, this process is characterised by two coupled free boundary problems that form a so called two-phase Stefan problem which is of nonlinear nature. To apply model predictive control to this process, a simplified, spatially distributed representation of the system is derived and transferred into a spatially lumped form by means of the finite element method. For this model, a nonlinear control problem is formulated, that takes process limitations into account and tries to satisfy different quality objectives by formulating demands on the systems spatiotemproal temperature distribution. This provides the foundation for the presented predictive control design. Finally, the approximated model and the controller are verified for different real-world scenarios that include model errors and parameter uncertainties.
... The Vertical Gradient Freeze (VGF) crystal growth process is used for the production of high efficiency bulk compound semiconductor single crystals like Gallium-Arsenide (GaAs) or Indium-Phosphide (InP) (Jurisch et al., 2005). The process basically works as follows: A seed crystal is placed at the bottom of a rotationally symmetric crucible which is later filled with solid semiconductor chunks. ...
This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of two coupled free boundary problems and is a vital part of many crystal growth processes due to the time-varying extent of crystal and melt during growth. In addition, a different approach for the numerical approximation of the backstepping transformations kernel is presented.
... The ToT values 30 of the peaks, converted to μs, versus photon energy are shown in Figure 8. ToT( ) = × + − − , and non-linear part of is clearly visible at the same energy as shown in [Jak11]. ...
Nowadays, X-ray imaging methods have found their way into manifold applications in everyday life and scientific fields. Besides classical X-ray detector systems, semiconductor pixel detectors have gained increasing attention during the last years. In so-called hybrid detectors, a pixelated readout electronics, which processes the charge signal created in the sensor and provides analyzable data, is connected to a suitable sensor material via small solder bumps. Thus, besides the ongoing development of the readout electronics itself (e.g. in the framework of the Medipix-collaborations based at CERN), the growth and characterization of suitable semiconductor sensor materials is one of the main research activities in this field. Silicon, despite showing an excellent material homogeneity and being available in large wafers at low cost, cannot be used efficiently for photon energies above 20 keV due to its low absorption coefficient. Hence, especially for medical applications and material testing, which take place at higher X-ray energies, there is a need for alternative sensor materials to ensure high absorption efficiencies. For this purpose, so-called high-Z materials like germanium (Ge), cadmium telluride (CdTe) and gallium arsenide (GaAs) are promising candidates. While Ge needs cooling and CdTe and semi-insulating GaAs have been in the center of attention since many years, there is considerably less work on chromium compensated, high resistivity GaAs, which was introduced by a group at the Tomsk State University already in 2001 and shows very promising material properties.
The aim of this work was thus to provide a detailed characterization of this material as sensor for pixelated X-ray detectors based on photon counting readout electronics of the Medipix chip family.
It could be shown that from the electron charge transport parameters, high resistivity (HR) GaAs is very well suited to be applied in semiconductor pixel detectors. The presence of intrinsic material inhomogeneities mainly caused by dislocations typical of GaAs grown from the melt was revealed by synchrotron white beam topography and was found to result in local X-ray sensitivity variations. However, it could be shown that these structures remain stable in time even under high flux conditions and could be easily corrected for by a simple flatfield correction, leading to a very good image quality with high signal-to-noise ratios. Further, the limiting factor for the detector performance was rather found to be the readout electronics than the sensor material. Count rate variations of the detector assemblies during long term measurements could be attributed to variations in the supply voltage of the readout chips. In addition, measurements performed at the ANKA synchrotron at KIT showed that the high flux behavior of the sensor material was limited by the pulse processing dead time of the pixel electronics, although the performance at high fluxes could be improved by optimized chip settings. By doing so, fluxes > 10^10 (s*mm²)^-1 could be tolerated over a long period, thus enabling these detectors to be used at synchrotron beamlines. The spatial resolution of the detectors, which was determined by MTF measurements, as well as the spectroscopic performance was found to be limited by the small pixel size of the Medipix chips (55×55 µm²) in combination with a sensor thickness of 500 µm, causing them to suffer from charge sharing and from the presence of characteristic X-rays. In this regard it could be shown that the charge summing mode implemented in the most recently developed Medipix chip can overcome many of these limitations and considerably improves the spectroscopic performance as well as the quantum efficiency. The ability to discriminate contrast agents in CT measurements makes these detectors suitable for future applications in imaging methods like spectroscopic X-ray imaging/CT in medical diagnostics and non-destructive material testing.
... The severe requirements imposed on the wafer with regard to the homogeneity of dislocation density, the high thermal stability of the structural defects, and the high mechanical strength should suppress degradation of produced devices. 1,2 In comparison to other industrially applied bulk growth methods such as liquid encapsulation Czochralski (LEC), vaporpressure-controlled Czochralski (VCz), and vertical Bridgman (VB), VGF is characterized by low investment and operating costs but also by low productivity. 2 The reason for the latter lies mainly in different growth velocities; i.e., in the LEC process, the crystals can be grown fairly rapidly at 7−10 mm/h, while in the VGF process, crystal growth is considerably slower (∼3 mm/h). 2 Since the first attempts of Gault et al. in the 1980s to grow GaAs by the VGF method, 3 this process has matured remarkably, particularly because of the systematic optimization of the furnace setup by numerical modeling. ...
The GaAs vertical gradient freeze (VGF) crystal growth process can be intensified in various ways, e.g., utilizing external fields, scaling up, numbering up the crucibles, etc. Successful application of traveling magnetic fields (TMFs) in 4 in. VGF GaAs growth for the flow control and process acceleration encouraged us to search for synergistic conceptions. Pros and cons
of process scale up and numbering up under TMFs were addressed using threedimensional
numerical simulations. The comparison of concepts was focused on the control of solid/liquid interface morphology and energy balance. A novel multicrucible furnace design was proposed and compared with a single-crucible design, both based on KRISTMAG technology. The simulation results showed the clear superiority of the numbering-up concept; e.g., the total energy consumption per run with equal yield was reduced to 32% of the value for the standard process. Moreover, a beneficial interface morphology was achievable without a trade-off with
growth rates.
The vertical gradient freeze (VGF) process needs to regulate the temperature field more accurately to ensure the successful seed crystal introduction and good crystal growth condition compared to the vertical Bridgman method, such as a suitable solid–liquid interface temperature gradient. This work presents a method for regulation of the temperature field via temperature control of six heaters during VGF growth of InP crystal with numerical simulation, and shows the involution for both the melt convection and the solid–liquid interface temperature gradient. Two of the six heaters were in the heating zone, two in the gradient zone, and the others in the cooling zone. Firstly, three temperature settings for the six heaters were selected through many trial calculations to ensure the success of seed crystal introduction. Secondly, their effects on the temperature field in the crucible and the convection in the melt were investigated. The results show that the axial temperature gradient in the melt increases with an increase in the heating zone temperature or a decrease in the cooling zone temperature, of which the maximum for each simulation experiment almost always appears at the solid–liquid interface and decreases continuously with the crystal growth process. Moreover, the maximum temperature gradient in the melt for all the simulations is well below 10 K/cm due to the shouldering stage 2, which cannot improve significantly even if the heating zone temperature increases and the cooling zone temperature decreases to room temperature. The temperature setting of the heaters has no significant influence on the convection pattern in the melt, which is nearly the same for all three settings. However, the maximum velocity of the convection field increases significantly with the axial temperature gradient increase. The number of convective vortices in the melt decreases from four at the initial seeding stage to one at the end of the equal-diameter growth for every simulation, but the maximum flow velocity decreases very slowly from the shouldering stage.Graphical Abstract
GaAs crystals are important III–V compound semiconductor materials and the bandgap and quantum efficiency can be optimized by doping. However, the doping may bring some problems to the crystal growth. In this paper, Si‐doped GaAs crystals are grown by the modified vertical Bridgman method and the influence of Si doping on dislocations and mechanical properties are discussed. It is found that a proper amount of Si doping significantly reduces the dislocation density of GaAs crystals. The mechanical properties of (100), (110), (111), and (511) planes are measured, and the results show that the mechanical properties of Si‐doped GaAs crystals have obvious anisotropy. The (111) plane has the strongest mechanical properties among them. The Vickers hardness, fracture toughness, nanoindentation hardness, and elastic modulus of the (111) plane are 6.05 GPa, 0.69 MPa m1/2, 10.82 GPa, 138.7 GPa, respectively. Moreover, Si doping can improve the mechanical properties of GaAs crystals. In this paper, 2 in. Si‐doped GaAs crystal is grown by the modified vertical Bridgman method and the influence of Si doping on dislocations and mechanical properties are discussed. In addition, the mechanical properties of Si‐doped GaAs crystal in different planes are also measured, which confirms the anisotropy of Si‐doped GaAs crystals.
This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of two coupled free boundary problems and is a vital part of many crystal growth processes due to the time-varying extent of crystal and melt during growth. In addition, a different approach for the numerical approximation of the backstepping transformations kernel is presented.
Molecular-like carbon-nitrogen complexes in GaAs are investigated both experimentally and theoretically. Two characteristic high-frequency stretching modes at \num{1973} and \SI{2060}{cm^{-1}}, detected by Fourier transform infrared absorption (FTIR) spectroscopy, appear in carbon- and nitrogen-implanted and annealed layers. From isotopic substitution it is deduced that the chemical composition of the underlying complexes is CN$_2$ and C$_2$N, respectively. Piezospectroscopic FTIR measurements reveal that both centers have tetragonal symmetry. For density functional theory (DFT) calculations linear entities are substituted for the As anion, with the axis oriented along the \hkl<100> direction, in accordance with the experimentally ascertained symmetry. The DFT calculations support the stability of linear N-C-N and C-C-N complexes in the GaAs host crystal in the charge states ranging from $+3$ to $-3$. The valence bonds of the complexes are analyzed using molecular-like orbitals from DFT. It turns out that internal bonds and bonds to the lattice are essentially independent of the charge state. The calculated vibrational mode frequencies are close to the experimental values and reproduce precisely the isotopic mass splitting from FTIR experiments. Finally, the formation energies show that under thermodynamic equilibrium CN$_2$ is more stable than C$_2$N.
In this wok, a novel multi-crucible Bridgman method is developed to produce the Ø 2 inch Si-doped GaAs crystals. Five placements are designed in the furnace means five ingots could be produced at the same time. Twinning and high dislocation density are the main growth defects that often take place in the crystals. After the solid-liquid interface and crystal cooling rate are optimized, the Si-doped GaAs crystals with favorable single crystalline yield are successfully obtained. The average etching pits density (EPD) of optimized GaAs crystals is <1500/cm2. Full width at half maximum (FWHM) are tested all less than 60″ that indicates GaAs crystals have high crystalline quality. The carrier concentration near the bottom and tail parts of ingots is in range of (4.5-5.9) × 1017 /cm3 and (1.2-2.1) × 1018 /cm3 due to segregation of Si element in GaAs crystals. Accordingly, the mobility is decreased from 2128–2651 cm2/v.s to 1581–1854 cm2/v.s. The result proves such multi-crucible Bridgman method is a feasible way for industrial growth of Si-doped GaAs crystals for opto-electronic application.
Defect Formation during Crystal Growth from the Melt
This chapter gives an overview of the important defect types and their origins during the bulk crystal growth from the melt. The main thermodynamic and kinetic principles are considered as driving forces of defect generation and incorporation, respectively. Results of modelling and practical in situ control are presented. Strong emphasis is given to semiconductor crystal growth since it is from this class of materials that most has been first learned, the resulting knowledge then having been applied to other classes of material.
The treatment starts with zero-dimensional defect types, i.e. native and extrinsic point defects. Their generation and incorporation mechanisms are discussed. Micro- and macro-segregation phenomena - striations and the effect of constitutional supercooling - are added. The control of dopants by using non-conservative growth principle is considered. One-dimensional structural disturbances - dislocations and their patterning - are discussed next. The role of high-temperature dislocation dynamics for collective interactions, like cell structuring and bunching, is shown. In a further section second phase precipitation and inclusion trapping are discussed. The importance of in situ stoichiometry control is underlined. Finally two special defect types are treated - faceting and twinning. First the interplay between facets and inhomogeneous dopant incorporation, then main factors of twinning including melt structure are outlined.
Using hybrid density functional calculations, we address the structural properties, formation energies, and charge transition levels of a variety of oxygen defects in GaAs. The set of considered defects comprises the bridging O atom in a As-O-Ga configuration, interstitial O atoms in tetrahedral sites, and O atoms substitutional to either Ga (OGa) or As atoms (OAs). In addition, we consider an As vacancy containing two O atoms, for which the most stable configurations are found through the use of molecular dynamics simulations, and defect complexes involving a OAs defect bound to either one or two AsGa antisites, denoted AsGa−OAs and (AsGa)2−OAs, respectively. We find that the bridging O defect and the AsGa−OAs and (AsGa)2−OAs complexes are the most stable oxygen defects in GaAs. The actual occurrence of these defects is examined against two criteria. The first criterion concerns the stability against O dissociation and is evaluated via the calculation of dissociation energies. The second criterion involves the defect formation at thermodynamic equilibrium and is inferred from the comparison between the formation energy of the oxygen defect and that of its O-related dissociation product (bridging O defect). Both the AsGa−OAs and (AsGa)2−OAs complexes satisfy these criteria and are stable against O dissociation. Further analysis in cooled-down conditions leads us to dismiss the AsGa−OAs defect due to the more favorable bonding of two rather than one AsGa antisites. The conclusion that only the bridging O defect and the (AsGa)2−OAs complex are expected to occur is in accord with experimental observations.
Charge collection mechanisms are investigated in surface channel GaAs MOSFETs under broadbeam heavy ion irradiation and pulsed two-photon-absorption laser irradiation. The large barrier between the gate dielectric and GaAs eliminates gate conduction current, but there is significant gate displacement current. Charge enhancement occurs because radiation-generated holes accumulate in the substrate, which increases the local electrostatic potential. The increased potential enhances the source-to-drain current, resulting in excess collected charge. The collected charge increases significantly with gate bias, due to the long tails of the charge waveforms that occur for higher gate bias. The collected charge increases with increasing drain bias.
The growth of GaAs crystal that for solar cell was studied by Bridgman method. The results indicate the carrier concentration would fullfill the requirement for solar cell application as the doped Si concentration is up to 0.05%. Twinning is the major defect that often happenned during crystal growth process. GaAs crystal with φ2 in×140 mm and nearly 100% crystallization was obtained after the growth rate and thermal environment is optimized. The average etching pit density of the as-grown crystal is <1000/cm2, and the carrier concentration is in the range of 1.4-2.1×1018/cm3.
Yield improvement and advanced defect control can be identified as the driving forces for modeling of industrial bulk crystal growth. Yield improvement is mainly achieved by upscaling of the whole crystal growth apparatus and increased processing windows with more tolerances for parameter variations. Advanced defect control means on one hand a reduction of the number of deficient crystal defects and on the other hand the formation of beneficial crystal defects with a uniform distribution and well defined concentrations in the whole crystal. This 'defect engineering' relates to the whole crystal growth process as well as the following cooling and optional annealing processes respectively. These topics were illustrated by examples of modeling and experimental results of bulk growth of silicon (Si), gallium arsenide (GaAs), indium phosphide (InP) and calcium fluoride (CaF2). These examples also involve the state of the art of modeling of the most important melt growth techniques, crystal pulling (Czochralski methods) and vertical gradient freezing (Bridgman-type methods).
Exposure to Radiation Energy: The materials existing on Earth are exposed to both natural and man-made radiation. Natural background radiation comes from three primary sources: cosmic radiation, external terrestrial radiation, and radon radiation. In addition to these radiations, there are man-made radiations that come from medical X-rays, gamma rays, nuclear medicine, (radionuclides/isotopes), and consumer products [1]. A schematic of the sources of radiation exposure that all the living and the nonliving materials are exposed to is listed below in Fig. 2.1.
Mankind from the prehistoric age has admired crystals. However, the significance of that beauty for the engineers and the scientists is on the basis of structural symmetry, simplicity, and purity. These characteristics endow crystals with unique physical and chemical properties, which have been used to cause a major transformation of the electronic industry. The systematic growth of synthetic crystals might be viewed as an art rather than science and has been described by some experts in this field as a new agriculture. The list of the synthetic crystals grown in the laboratory is far from exhaustive, but it shows how several old substances develop unique properties when they have the form of crystals. Figure 6.1 shows the many facets cut in a synthetic diamond crystal—a highly refractive, colorless crystalline allotrope of carbon.
Gallium has been labeled as a critical metal due to rapidly growing consumption, importance for low-carbon technologies such as solid state lighting and photovoltaics, and being produced only as a by-product of other metals (mainly aluminum). The global system of primary production, manufacturing, use and recycling has not yet been described or quantified in the literature. This prevents predictions of future demand, supply and possibilities for efficiency improvements on a system level. We present a description of the global anthropogenic gallium system and quantify the system using a combination of statistical data and technical parameters. We estimated that gallium was produced from 8-21% of alumina plants in 2011. The most important applications of gallium are NdFeB permanent magnets, integrated circuits and GaAs/GaP-based light-emitting diodes, demanding 22-37%, 16-27% and 11-21% of primary metal production respectively. GaN-based light-emitting diodes and photovoltaics are less important, both with 2-6%. We estimated that 120-170 tons, corresponding to 40-60% of primary production, ended up in production wastes that were either disposed of or stored. While demand for gallium is expected to rise in the future, our results indicated that it is possible to increase primary production substantially with conventional technology, as well as improve the system-wide material efficiency.
Fourier transform infrared absorption measurements have been carried out on GaAs crystals doped or implanted with carbon, nitrogen and oxygen. In the presence of carbon and nitrogen, thermally stable defects occur with strong molecular-like bonding giving rise to absorption bands of vibrational character in the mid-infrared. By implantation of the nitrogen isotopes 14N and 15N, a complex of the chemical composition CN2 is identified. This defect is the origin for the mode at 2060 cm−1 previously attributed to a (C, O)-complex. A further absorption band at 1973 cm−1 is tentatively attributed to the stretching mode of a CN entity.
The crack behavior of Si-doped GaAs crystals produced by a novel pulling-down method was investigated. Some cracks were observed in the crystal tail part and no twins or polycrystals were observed. The cracking mechanism was discussed considering the growth parameters, such as the pulling-down rate, annealing time and cooling speed of the furnace. The crystal was easily broken if the cooling rate was too fast. To avoid cracking, the temperature profile and the growth parameters had been optimized. The cleavage property of the GaAs crystal was strongly related to its atomic arrangement and corresponding electron density map. Ultrasonic vibration or mechanical machine would make the crystal cleaved along (110) plane. GaAs crystal displayed a strong anisotropic crack property under the force of microindentation test.
The challenge in the future fabrication of semiconductor bulk crystals is the improvement of the crystal quality with a simultaneous increase of the yield. For that, a proper control of mass transfer within the fluid phase is required. Besides the damping of violent convective fluctuations, the thickness of the diffusion boundary layer, causing morphological instability, has to be decreased. The influence of ultrasound in molten Germanium was analyzed by numerical simulations. The simulations were provided by applying commercial software packages ANSYS® and FLUENT®. ANSYS® was used to model the ultrasonic wave propagation in the whole growth system consisting of melt and crystal, crucible and surrounding media. As a result the sound pressure distribution in every point of the melt and the displacement in every point of the solid have been obtained. The melt flow and the temperature distribution were simulated with the help of FLUENT®. The main focus was the analysis of Schlichting streams that occur at the crystallization front which affect the diffusion boundary layer. It was shown that ultrasonic treatment can help to reduce the harmful diffusion boundary layer very effectively. (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Many concepts of external magnetic field applications in crystal growth processes have been developed to control melt convection, impurity content and growing interface shape. Especially, travelling magnetic fields (TMF) are of certain advantages. However, strong shielding effects appear when the TMF coils are placed outside the growth vessel. To achieve a solution of industrial relevance within the framework of the project inner heater-magnet modules(HMM) for simultaneous generation of temperature and magnetic field have been developed. At the same time, as the temperature is controlled as usual, e.g. by DC, the characteristics of the magnetic field can be adjusted via frequency, phase shift of the alternating current (AC) and by changing the amplitude via the AC/DC ratio. Global modelling and dummy measurements were used to optimize and validate the HMM configuration and process parameters. GaAs and Ge single crystals with improved parameters were grown in HMM-equipped industrial liquid encapsulated Czochralski (LEC) puller and commercial vertical gradient freeze (VGF) furnace, respectively. The vapour pressure controlled Czochralski (VCz) variant without boric oxide encapsulation was used to study the movement of floating particles by the TMF-driven vortices.
A carbon-oxygen complex occurring in gallium arsenide crystals after annealing at around 700 °C is studied. Fourier transform infrared absorption measurements on the associated vibrational band at 2060 cm-1 under uniaxial stress reveal that the center has tetragonal symmetry. From the intensity of the 18O-related satellite band it is concluded that four oxygen atoms are involved. Ab initio local density calculations show that a tetragonal CO4 molecule forms a stable entity in the gallium arsenide lattice.
Infrared absorption measurements have been carried out on a carbon–oxygen complex in gallium arsenide. The stretching mode at 2059.6 cm−1 has been investigated at low temperatures with polarized light under uniaxial stress in the 〈100〉, 〈111〉, and 〈110〉 crystallographic directions. The splitting behavior due to lifting of orientational degeneracy shows that the center has tetragonal symmetry. The intensity of the isotope shifted satellite band caused by the naturally abundant 18O isotope is not in agreement with the identification as a simple CO-molecule. The number of incorporated oxygen atoms is 3 ± 1. The assignment of the defect to a CO2 molecule is in agreement with the experimental data available so far.
Transition between turbulent flow regimes is studied experimentally in a cylinder of liquid mercury heated from below under the influence of a rotating magnetic field. The latter creates a rotating flow which almost completely suppresses the temperature fluctuation near horizontal boundaries at a much lower angular velocity than a simple mechanical rotation. Our experiment confirms that this effect persists in the deep turbulent range to Grashof numbers as high as about 109. An intermediate range is observed for Gr > 2 × 108 with the temperature fluctuation suppressed in the core but near the sidewall. This is explained by turbulent friction replacing the Coriolis force as the leading retarding force. The linear instability of a simplified model is studied numerically. The model considers a base flow consisting of a uniform rotation and a formally independent uniform meridional flow in a cylinder with an adverse vertical temperature gradient. The model shows that the bulk meridional flow being itself much slower than the rotation is able to delay the Rayleigh-Bénard instability.
Accelerated VGF-growth of 4 in. GaAs ingots by downwards traveling magnetic fields (TMFs) was investigated numerically. The focus was led on the feasibility of control of s/l interface shape by Lorentz forces in the range of crystal growth rates from 3 to 9 mm/h. Particularly, the aim of this study was to derive a method for a prediction of electro-magnetic parameters of TMF such as frequency, phase shift and AC amplitude that provide maximal improvement of interface deflection towards convex morphology during the fast growth.A typical VGF furnace equipped with a KRISTMAG® internal heater-magnet module was used for the simultaneous generation of heat and TMF.The revealed deflections were correlated with dimensionless numbers: Grashof Gr, Stephan Ste and Forcing number F. With an increase of F while holding Gr and Ste numbers constant, transition through the point of maximal positive deflection was marked by a lift of the stream function vortex from the region of triple point upwards.
For the first time 4-in. Ge single crystals were grown using the vertical gradient freeze technique (VGF) in a traveling magnetic field (TMF) generated in a heater-magnet module (HMM). The HMM was placed closely around the growth container inside the chamber of the industrial Bridgman equipment “Kronos”. The HMM generates heat and a TMF together. It has a coil-shaped design and replaces the standard meander-type heater. Direct current (DC) for heat production and out-of-phase-accelerated currents (AC) for TMF generation were simultaneously delivered to three equally spaced coil segments connected by star-type wiring. In order to achieve a nearly flat and slightly convex growing interface the AC amplitude, frequency and phase shift have been optimized numerically by using the 3D CrysMAS code and validated by striation analysis on as-grown crystals. Low-field frequencies in the range f=20–50 Hz proved to be of most suitable condition. TMF programming is required to obtain constant interface morphology over the whole growth run. First Ge single crystals grown under nearly optimal conditions show reduced macro- and micro-inhomogeneities, relatively low dislocation density of (3–10)×102 cm−2, and high carrier mobility of μp=2800 cm2 V−1 s−1.
The magnetic susceptibility χ of n-type GaAs was determined for a wide variety of dopants and carrier concentrations n ranging from 3.0 × 106 cm−3 to 3.6 × 1018 cm−3 over a temperature range from 9 to 300 K. A constant χ is found for n up to ≈2 × 1017 cm−3 (at 300 K). For higher n, the diamagnetic susceptibility increases linearly with n1/3 in accordance with the Landau–Peierls term. This behavior is independent of the type of dopant. In contrast to χ, the rate of change dχ/dT depends on n in a more complex, non-monotonic way.
We review the progress of silicon carbide (SiC) bulk growth by the sublimation method, highlighting recent advances at Dow Corning, which resulted in the commercial release of 100mm n-type 4H-SiC wafers with median micropipe densities (MPD) in production wafers 0.1cm−2 and the demonstration of micropipe free material over a full 100mm diameter. Investigations by Synchrotron White Beam X-ray Topography (SWBXRT) and molten KOH etch pit analysis of 100mm wafers demonstrate threading screw dislocation densities 500cm−2. Additional results indicate the positive impact of maintaining thermo-mechanical stress levels in the growing crystal below the critical resolved shear stress on reducing basal plane dislocation densities to values as low as ∼300–400cm−2 in 100mm crystals. We summarize the steps of systematic quality improvements on increasing wafer diameter, utilizing numerical simulations of the SiC growth system as a critical tool to guide this process. For the economical production of SiC epitaxy, a 10×100mm wafer platform has been established in a warm-wall planetary chemical vapor deposition (CVD) reactor. The combined improvements in the epitaxy process, pre-epi wafer surface preparation and the underlying substrate quality itself have led to a reduction of the device killer defect density from 8cm−2 to 1.5cm−2 on a volume product like 100mm 4° off-axis 6.5μm epi-wafers. Dow Corning production epi-wafers routinely show Schottky diode yields above 90% at a die size of 2mm×2mm. Additionally, 50–100μm thick epitaxy on 76mm 4° off-axis wafers with morphological defect densities of 2–6cm−2, a surface roughness (RMS) ≤1nm as measured by atomic force microscopy (AFM), and carrier lifetimes consistently in the range of 2–3μs has been demonstrated.
The present paper introduces a new numerical method for predicting the characteristics of thermocapillary turbulent convection in a differentially-heated rectangular cavity with two superposed and immiscible fluid layers. The unsteady Reynolds form of the Navier–Stokes equations and energy equation are solved by using the control volume approach on a staggered grid system using SIMPLE algorithm. The turbulence quantities are predicted by applying the standard k–ε turbulence model. The level set formulation is applied for predicting the topological changes of the interface separating the two fluid layers and to provide an accurate and robust modeling of the interfacial normal and tangential stresses. The computational results obtained showed good agreement when compared with the previous experimental, numerical and analytical benchmark data for different validation cases in both laminar and turbulent regimes. The present numerical method is then applied to predict the velocity and temperature distribution in two immiscible liquid layers with undeformable interface for a wide range of Marangoni numbers. The laminar-turbulent transition is demonstrated by obtaining the turbulence features at high interfacial temperature gradient which is characterized by high Marangoni number. The effect of increasing Marangoni number on the interface dynamics in turbulent regime is also investigated.
The steady laminar two-dimensional thermocapillary convection in the thin annular two superposed horizontal liquid layers with one free surface, one liquid/liquid interface subjected to a radial temperature gradient was investigated using asymptotical analysis. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the lower layer thickness to the gap width, goes to zero. The numerical experiments are also carried out to compare with the asymptotic solution of the steady two-dimensional thermocapillary convection. The asymptotic results indicate that the expressions of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio.
The steady laminar two-dimensional thermocapillary convection of two superposed horizontal liquid layers in a shallow annular
cavity was investigated using asymptotical analysis. The liquids were supposed to be immiscible with a nondeformable interface.
The cavity was heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces were rigid and
adiabatic. Asymptotic solutions were obtained in the core region in the limit as the aspect ratio, which was defined as the
ratio of the lower layer thickness to the gap width, and trended to zero. The numerical experiments were also carried out
to compare with the asymptotic solution of the steady two-dimensional thermocapillary convection. It is found that the expressions
of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio.
For the first time semi-insulating (SI) GaAs single crystals were grown by the liquid encapsulated Czochralski (LEC) method using a traveling magnetic field (TMF) system generated in a heater–magnet module (HMM). The system was developed within the framework of the KRISTMAG˜® project. The HMM, that generates heat and TMF simultaneously, was placed closely around the crucible inside the chamber of the industrial CI 358 puller. Before the growth experiments the induced vertical Lorentz force density FLz was evaluated by the weight force response of a dummy. First growth experiments at various f/ϕ ratios (f—frequency and ϕ—phase shift) were carried out. Interface morphology and temperature fluctuation strengths were analyzed by a striation technique. Etch pit density, carbon, residual impurity and EL2° contents as well as electrical properties of the as-grown TMF–LEC GaAs crystals were measured. A preliminary correlation between crystal qualities and field frequency has been noticed.
The challenge of increasing and maintaining a high yield for 6″ GaAs crystal growth is of utmost importance for meeting the price requirements dictated by today's requirements for semi-insulating GaAs substrates. For maintaining a low dislocation density in the grown ingots, the growth process time is typically long and, sometimes, the final ingots may exhibit twins and poly-crystalline formation. These defects may occur at the beginning of the cylindrical part of the ingot, or even at the conical part of pBN crucible so the whole ingot is rejected. On the other hand, these defects may appear further away from the seed and the location of the onset of these defects will determine the extent of the useful (production worthy) crystal length, also known as “yield”. The reasons for the onset of these defects are, however, not fully understood [M. Jurisch, F. Borner, Th. Bunger, St. Eichler, T. Flade, U. Kretser, A. Kohler, J. Stenzenberger, B. Weinert. J. Crystal Growth 275 (2005) 283].In this study, we conducted numerical simulation using the transient two-dimensional mathematical model of the GaAs crystal growth by vertical gradient freeze method (VGF-method). We defined a new parameter “A” that is equal to the scatter of heat fluxes at m/c interface. Our study showed that some correlation exists between the defect appearance and A-value at m/c interface close to crucible wall. We have found that the frequency of a totally bad crystal length is higher if the A-value exceeds a certain value. Close to the crystal tail the scatter must be less than a defined A-value at the beginning of crystallization. Reduction in A-value was found to occur due to anomalies in the melt flow close to the m/c interface and crucible wall leading to the higher frequency of defects close to the crystal tail.Based on the correlation found, we developed a new technology regime that results in crystals grown with a lower frequency of defect occurrence at crucible wall.
Three-dimensional (3D) electromagnetic computer modeling is used to analyze the effects of asymmetry at the crystal growth by the vertical gradient freeze (VGF) and liquid encapsulation Czochralski (LEC) methods under traveling magnetic fields (TMF). Based on the results a heater-magnet module (HMM), combining the generation of heat and induction of magnetic field, was developed and optimized. It will be shown that asymmetry effects are caused by the designs of the heater-magnet coils and bus bars. They are enforced when a TMF of higher frequencies is used. It can be concluded that for VGF arrangements without container rotation the module design must be modified. Compared to that in case of LEC the effect of asymmetry can be effectively graduated by crucible and crystal rotations.
Unintentionally doped GaAs crystals grown from Ga-rich melts without B2O3 encapsulation by the modified vapour pressure controlled Czochralski (VCz) method are analysed. The influence of this growth technique on dislocation density and distribution is presented. The concentration of As precipitates in dependence on the melt composition is shown. Finally, the contents of residual impurities and their influence on some characteristic electrical parameters are discussed. The attention is focused on the feasibility of in situ controlled near-stoichiometric semi-insulating (SI) GaAs crystals with minimized content of As precipitates.
This chapter gives a general overview of the defect types and their origins at the bulk crystal
growth. The role of thermodynamics, kinetics, convection, segregation, thermomechanical stress and non‐stoichiometry are considered. The possible influence of the structure of the fluid phase is implied. Results of modelling and practical measures of in situ defect control are presented. Strong emphasis is given to semiconductor crystal growth from melt. The defects are treated in the classical manner: 0‐, 1‐, 2‐ and 3‐dimensional ones, i.e. point defects, impurity and dopant distributions, dislocations,
cell
structures and second phase particles. After the generation and incorporation mechanisms of point defects are discussed micro‐ and macrosegregation phenomena, i.e. striation formation and the effect of constitutional supercooling are added. Then the formation and multiplication of dislocations and their collective interactions, leading to cell
structuring, are shown. The importance of temperature field engineering is underlined. Selected two‐dimensional defects like facets and twins are delineated next. Finally, second phase precipitation and inclusion trapping are discussed. The importance of in situ stoichiometry control is accentuated.
This chapter gives an overview of the important defect types and their origins during bulk crystal growth from the melt. The main thermodynamic and kinetic principles are considered as driving forces of defect generation and incorporation, respectively. Results of modeling and practical in situ control are presented. Strong emphasis is given to semiconductor crystal growth since it is from this class of materials that most has been first learned, the resulting knowledge then having been applied to other classes of material.
The treatment starts with zero-dimensional defect types, i.e., native and extrinsic point defects. Their generation and incorporation mechanisms are discussed. Micro- and macrosegregation phenomena – striations and the effect of constitutional supercooling – are added. The control of dopants by using the nonconservative growth principle is considered. One-dimensional structural disturbances – dislocations and their patterning – are discussed next. The role of high-temperature dislocation dynamics for collective interactions, such as cell structuring and bunching, is shown. In a further section second-phase precipitation and inclusion trapping are discussed. The importance of in situ stoichiometry control is underlined. Finally two special defect types are treated – faceting and twinning. First the interplay between facets and inhomogeneous dopant incorporation, then main factors of twinning including melt structure are outlined.
Selected fundamentals of transport processes and their importance for crystal growth are given. First, principal parameters and equations of heat and mass transfer, like thermal flux, radiation and diffusion are introduced. The heat‐ and mass‐ balanced melt‐solid and solution‐solid interface velocities are derived, respectively. The today’s significance of global numeric simulation for analysis of thermo‐mechanical stress and related dislocation dynamics within the growing crystal is shown. The relation between diffusion and kinetic regime is discussed. Then, thermal and solutal buoyancy‐driven and Marangoni convections are introduced. Their important interplay with the diffusion boundary layer, component and particle incorporation as well as morphological interface stability is demonstrated. Non‐steady crystallization phenomena (striations) caused by convective fluctuations are considered. Selected results of global 3D numeric modeling are shown. Finally, advanced methods to control heat and mass transfer by external forces, such as accelerated container rotation, ultrasonic vibration and magnetic fields are discussed.
Results on the experimental and numerical modelling of the melt flow typically observed in vertical gradient freeze (VGF) crystal growth with a travelling magnetic field (TMF) are presented. Particular attention is paid on the transition from a laminar to a time-dependent flow, which represents a crucial problem in VGF growth. Low-temperature model experiments at around 80 °C were performed using a GaInSn melt in a resistance furnace with concentric, separately adjustable heating zones. The TMF was created by an external coil system, and the flow velocity was measured by means of the ultrasonic Doppler velocimetry (UDV). The melt flow was simulated numerically using a finite volume code based on the open source code library OpenFOAM. As a criterion for the stability of the flow the turbulent kinetic energy was calculated under the influence of the TMF and thermal buoyancy. The results obtained are compared to isothermal TMF flow modelling at ambient temperature. The stability limit of the melt flow is found to be significantly influenced by the mutual interaction of buoyant and TMF-driven flows. Both experimental and numerical results show the stabilizing effect of natural, VGF-type buoyancy on the TMF-induced flow.
The present paper investigates the correlations between the cell dimension d of characteristic dislocation cell patterns and acting thermo-elastic stress τ at the growth of 6-inch semi-insulating VCz and VGF GaAs crystals. Whereas the dislocation density and cells are analysed experimentally the history of the elastic stress, responsible for the cell formation, is obtained by global numeric calculation. At stresses below 1 MPa diffusion-controlled creep is the dominant mechanism of dislocation motion. Different d (τ) - proportionalities in VCz and VGF crystals are determined. This is due to the varying thermal conditions and stay times of the growing crystal at high temperatures. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
GaAs crystals have been grown without B2O3 encapsulation by the vapour-pressure controlled Czochralski (VCz) method to reduce undesired boron incorporation and to enable in situ control of the Ga/As ratio in the melt. With increasing Ga content of the melt the omnipresent As precipitate concentration decreases in as-grown GaAs crystals. Semiinsulating (SI) GaAs crystals could been obtained even from melts with a composition of 46 at.% As. Comparative cathodoluminescence (CL) measurements on those crystals and on boron-contaminated GaAs show that the luminescence bands at 1.316 eV and at 1.441 eV are related to BAs. Reduced concentrations of boron and EL2 result in significant lower near-band edge absorption, mainly caused by the photoionization cross section of As antisites in SI GaAs. These VCz GaAs crystals possess improved optical properties. Semi-conducting (SC) GaAs:Si crystals were grown from near-stoichiometric melts. Positron annihilation lifetime spectroscopy measurements show that the low boron concentration in our SC VCz GaAs results always in 3 times higher Ga vacancy concentrations compared to standard SC GaAs. CL bands due to optical transitions at 0.95 eV and 1.15 eV are related to auto-compensating (VGaSiGa)2- and (SiGaVGaSiGa)– complexes, respectively, and depend on the doping level. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
IntroductionSelected FundamentalsTMF Generation in Heater-Magnet ModulesThe HMM DesignNumerical ModelingDummy MeasurementsGrowth Results under TMFConclusions and OutlookAcknowledgmentReferences
IntroductionPrinciples of Thermal ModelingVerification of Numerical ModelsYield Enhancement by Defect ControlConclusions
AcknowledgementsReferences
IntroductionRetrospectionCrystal Growth without B2O3 EncapsulantInclusions, Precipitates and DislocationsResidual Impurities and Special Defect StudiesElectrical and Optical Properties in SI GaAsBoron in SC GaAsOutlook on TMF-VCzConclusions
AcknowledgmentsReferences
It has been demonstrated that 200 mm diameter semi-insulating (SI) GaAs single crystals can be grown by an upscaled proprietary VGF method successfully used for commercial crystal growth up to 150 mm in the past. First results of structural and electrical characterization of wafers made from these crystals will be presented. They are similar to those known for state-of-the-art 150 mm SI GaAs VGF/VB crystals.
Growth of GaAs crystals by the vertical Bridgman technique has several advantages over LEC — material with lower dislocation density, lower elastic stresses and higher homogeneity can be grown. Most importantly, it also promises lower production costs. However, the method has been hampered by a low single crystal yield due to poly growth and twin formation. During the last few years our group has developed the technical prerequisites to overcome this problem. In the first part of this report we shall present two new furnace concepts and some growth results. In the second part we will discuss the technical developments of crucibles.
A numerical modeling algorithm is developed which is able to calculate the powers of an arbitrary number of heaters in a crystal growth configuration in order to obtain a prescribed temperature distribution in a growing crystal. Such a mathematical procedure is called inverse modeling. The algorithm is implemented in our software system CrysVUN++ for global thermal simulation of crystal growth processes. The efficiency of this new strategy of inverse modeling is demonstrated by applying it to an industrial vertical gradient freeze (VGF) process for the growth of GaAs crystals with 3″ diameter. As a result we obtain optimized growth conditions which will be discussed in comparison to the state of the art of VGF technology.
6″ SI GaAs single crystals are grown by the standard LEC-process in a new-generation multi-heater puller designed for charges up to 50kg and crucibles up to 12″, applying the carbon controlled growth technology. It is demonstrated that the increasing requirements of device manufacturers with regard to macroscopic and mesoscopic homogeneity of electrical properties, mechanical strength, flatness and cleanliness of the wafers can be fully met by LEC grown 6″ crystals.
Citation
H. C. RAMSPERGER and EUGENE H. MELVIN, "THE PREPARATION OF LARGE SINGLE CRYSTALS," J. Opt. Soc. Am. 15, 359-359 (1927)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-15-6-359
The ChemSage code [Eriksson and Hack, Metall. Trans. B 12 (1990) 1013] to minimize the total Gibbs free energy was used to calculate phase equilibria in the complex thermochemical system representing LEC GaAs crystal growth which comprises the growth atmosphere, the liquid boron oxide, the GaAs melt and solid phases including the GaAs crystal. The behaviour of C, B, O, N and H in the crystal growth melt at 1509.42 K is investigated in dependence on relevant technological parameters.
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.
An extensive computer program called ChemSage, based upon the SOLGASMIX Gibbs energy minimizer, is presented together with
several examples which illustrate its use. ChemSage was designed to perform three types of thermochemical calculations in
complex systems involving phases exhibiting nonideal mixing properties. These are the calculation of thermodynamic functions,
heterogeneous phase equilibria, and steady-state conditions for the simulation of simple multistage reactors. The thermodynamic
functions module calculates specific heat, enthalpy, entropy, and Gibbs energy with respect to a chosen reference state for
a given phase and, if this phase is a mixture, the partial properties of its components. Chemical equilibrium calculations
can be made for a system which has been uniquely defined with respect to temperature, pressure (or volume), and composition.
One of these quantities may also be replaced by an extensive property or phase target,e.g., for the calculation of adiabatic and liquidus temperatures, respectively.
The present paper gives a review on fundamentals, modelling, growth, structural and electrical properties of semi-insulating GaAs single crystals, grown in low temperature gradients by the Vapour Pressure Controlled Czochralski Method (VCz), with diameters from 75 up to 150 mm. Special attention is drawn to the investigation of the temperature-fields inside the growing crystals (and thus thermoelastic stress). Additionally, the influence of convective transport of heat within meit and inert gas is investigated by both experiment and modelling. Thermodynamic aspects of arsenic pressure control within the inner VCz chamber as well as the special experimental and technological challenges are discussed. High quality 100 mm (4-inch) crystals with EPD < 104 cm−2 and low as-grown residual strain are presented. Very low carbon concentrations of ≈1014 cm−3 were obtained for the first time in VCz crystals. This material, as one of the challengers to conventional LEC material, is able to meet similar electrical specifications whilst showing improved structural quality and better parameter homogeneity even in the as-grown state. Initial studies of a VCz crystal grown without boric oxide encapsulant is presented.
This paper presents first results of 200 mm diameter semi-insulating (SI) GaAs crystal growth experiments. The LEC method was used on condition that temperature gradients in critical regions can be controlled adequately. For furnace design and process parameter evaluation, powerful numerical simulation was indispensable. The structural and electrical properties of crystals grown by this temperature gradient controlled LEC method are similar to those known for state-of-the-art 150 mm SI GaAs crystals.
Thermodynamic equilibrium in gallium arsenide crystal growth systems with the components Ga–As–C–B–N–Si–O has been analysed by using a Gibbs energy minimisation computer package. Emphasis is placed on graphical representations to describe the behaviour of C, B, Si and O in the crystal growth melt at 1513 K. The various experimentally observed correlations between solute elements in the liquid and the encapsulant are rationalised. Additionally, guidance is provided for improvements in the design of crystal growth operations. Instead of relying on the current procedure of maintaining purity control on the input materials and standardised operating conditions, it is suggested that the flow of wet CO or H2/CO2 input gas flow mixtures be used to fix C and O activities and, thereby, reduce the thermodynamic degrees of freedom of the system to zero.
The quality of arsenic and of GaAs polymaterial influences the substrate properties and their reproducibility. Interactions and correlations are investigated. The purification process of arsenic and the process parameters of the two-step synthesis were optimized. The impurity concentration and the stoichiometry variations in GaAs boules have been significantly decreased. As a result, the substrate mobilities have increased and the reproducible adjustment of resistivities in a range of 5 × 106 to 8 × 107 Ω cm within a narrow gap has been achieved.
The segregation behavior of carbon during the GaAs LEC process is described by a combined carbon and oxygen transport model. For this attempt the well-known Scheil formalism was extended by consideration of the incorporation and extraction of carbon via CO transport through the encapsulating boron oxide. The influence of the changing oxygen potential was included in order to describe the experimental data, especially for low carbon levels. The model is helpful for the adjustment of growth parameters relevant for carbon doping in order to achieve a homogeneous carbon distribution at any specified level.
A quantitative prediction of the thermal field and of the location of the interface in the Czochralski process requires a precise knowledge of the heat transfer taking place in the entire furnace. The problem is highly complex, since it involves radiation, heat conduction, heating elements and convection-diffusion in the melt. These features are taken into account in our model while outer control parameters - such as power dissipated in the heater and convective losses on the enclosure - are used as input instead of arbitrary boundary conditions. Each constituent such as the heater, the crucible, the melt and the crystal is covered by a finite element mesh. The radiative exchanges within each enclosure are calculated with the assumption of the diffuse-gray surfaces and with the use of a viewed and hidden part algorithm together with a Galerkin discretization. The model allows one to investigate the sensitivity of the temperature field with respect to the geometry of the furnace, the presence of a heat shield and the material properties of the constituents.
The influence of the inert gas pressure on the growth of 4 GaAs crystals by the liquid encapsulated Czochralski method (LEC) process is studied for a range of the Ar gas pressure up to 10 bar by using our finite-volume computer code STHAMAS. Up to the pressure of 0.6 bar we are considering laminar convection. For the pressure range from 5 to 10 bar we are using the buoyancy extended standard k-ϵ turbulence model with wall functions to simulate the gas flow. The numerical results show that the Argon gas pressure has a strong influence on the consumption of heater power in qualitative agreement with our experimental results. The convex curvature of the growth interface and the maximum thermal stress (von Mises criterion) are found to increase with increasing gas pressure both in the laminar and turbulent evaluations.
In the present paper, the flow and temperature fields in a 20 kg silicon Czochralski melt were studied by 3D, time-dependent numerical simulation using the real melt geometry and realistic thermal boundary conditions for different types of magnetic fields. The numerical results are compared directly with temperature distributions obtained experimentally for the same parameter as in the numerical simulations. It is found that the main characteristics of the experimentally observed temperature distributions are fairly well reproduced by the 3D simulations, although there still exist some quantitative discrepancies.
A modified liquid encapsulated Czochralski (LEC) process has been
developed which yields completely single crystals 22 kg in weight, 110
mm diameter and 435 mm parallel length. These crystals will yield up to
375 wafer/ingot compared with the 50-80 wafers typical of the current 8
kg process. This process moves the production of GaAs substrates from a
research and development operation to a genuine production process with
significant improvements in economy, for both substrate and device
manufacturers. The key to the process is the control of melt/solid
interface shape by modification of the thermal geometry of the MRSL
15/25 puller, using a simple single heater system. Uniformity of
electrical properties was maintained over the length of these long
crystals
This paper presents prospects for the future market, availability and cost of 6 in. diam. GaAs substrates from a substrate supplier's point of view. Outlining the challenges to the substrate supplier, we discuss the current issues and the future potential of production technologies (crystal growth, annealing, and wafer processing) for 6 in. diam. GaAs substrates, and mention current issues for 3 in. diam. InP substrates. In addition, we introduce 6 in. diam. GaAs and 3 in. diam. InP crystals grown by the VCZ method, which is a promising technology for the production of large substrates for multimedia devices