Three-dimensional global analysis of thermal stress and dislocations in a silicon ingot during a unidirectional solidification process with a square crucible

A three-dimensional global model was used to obtain the solution of a thermal field within the entire furnace during a unidirectional solidification process of multicrystalline silicon with a square crucible. Then the thermal stress distribution in the silicon ingot was solved. Based on the solution of thermal stress, relaxation of stress and multiplication of dislocations were performed by using the Haasen–Alexander–Sumino model (HAS model). The influence of crucible constraint on stress levels and dislocations was investigated. It was found that the crucible constraint had significant influence on the thermal stresses and dislocations in the ingot. The results indicated that it is important to reduce the crucible constraint in order to relax thermal stresses and reduce dislocations in a silicon ingot during the solidification process.     

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.     

Optimisation of the VGF growth process by inverse modelling

Numerical and experimental results on the thermal optimisation of vertical gradient freeze crystal growth are presented. An inverse modelling approach is described aimed at solidification with a constant growth rate and planar solid–liquid interface. As a result of modelling an optimised growth process characterised by a modified ampoule configuration and thermal regime was established. For experimental confirmation Ga-doped germanium single crystals were grown with the optimised process. In good agreement with the numerical results, solidification with an almost constant growth rate was achieved with the interface deflection being significantly lower than in conventionally grown crystals.     

The influences of supersaturation on LPE growth of GaN single crystals using the Na flux method

The dependency of LPE growth rate and dislocation density on supersaturation in the growth of GaN single crystals in the Na flux was investigated. When the growth rate was low during the growth of GaN at a small value of supersaturation, the dislocation density was much lower compared with that of a substrate grown by the Metal Organic Chemical Vapor Deposition method (MOCVD). In contrast, when the growth rate of GaN was high at a large value of supersaturation, the crystal was hopper including a large number of dislocations. The relationship between the growth conditions and the crystal color in GaN single crystals grown in Na flux was also investigated. When at 800 °C the nitrogen concentration in Na–Ga melt was low, the grown crystals were always tinted black. When the nitrogen concentration at 850 °C was high, transparent crystals could be grown.     

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Kyropoulos (Ky) method is the most suitable technique for the growth of high‐quality sapphire single crystal for substrate applications. Cracks are often observed in the grown ingot that significantly reduces industrial productivity. In the paper, cracking causes are analyzed by examining crystal shape, thermal stress and three‐dimensional effects during the stable growth of sapphire crystal. It is found that locally induced thermal stress around the shoulder of the crystal is the largest. However, thermal stress is not fully responsible for the cracks, since the predicted stress level is lower than a critical value regarding crystal cracking. Polycrystalline growth or/and other crystal defects must be another factor that degrades the critical value and makes the crystal more fragile. Simulation results further show that crystal shape has less effect on the thermal stress level, although experiments have shown that crack‐free crystals usually have smooth surfaces. The initial cracking position in the ingot predicted in simulation agrees well with experimental observation after considering crystal defects in a qualitative discussion. From the view of three‐dimensional simulation, the variation of heating condition during growth may result in high thermal stress locally that leads to the cracks at one side of the crystal. Additionally, three‐dimensionally unexpected temperature drop of the heater may be responsible for the sticking‐to‐crucible phenomenon at the shoulder region of the grown crystal.     

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.     

Propagation behavior of threading dislocations during physical vapor transport growth of silicon carbide (SiC) single crystals

The dislocation formation and propagation processes in physical vapor transport (PVT) grown 4H silicon carbide (4H–SiC) single crystals have been investigated using defect selective etching and transmission electron microscopy (TEM). It was found that while the growth initiation process generally increased the density of threading dislocations in the grown crystal, for certain areas of the crystal, threading dislocations were terminated at the growth initiation. Foreign polytype inclusions also introduced a high density of dislocations at the polytype boundary. In the polytype-transformed areas of the crystal, almost no medium size hexagonal etch pits due to threading screw dislocations were observed, indicating that the foreign polytype inclusions had ceased the propagation of threading screw dislocations. Based on these results, we argued the formation and propagation of the threading dislocations in PVT grown SiC crystals, and proposed the dislocation conversion process as a plausible cause of the density reduction of threading dislocations during the PVT growth of SiC single crystals.     

Role of non-stoichiometry in the cracking of oxide crystals

The cracking and stoichiometric deviations frequently observed in crystals of mixed oxides have generally been perceived to be unrelated phenomena. The present study pertains to the cracking in Czochralski grown crystals of three different materials, viz. CdWO₄, PbWO₄ and ZnWO₄. The results obtained on the single-crystal growth as well as on the thermal stability of melts of these materials and of their constituent oxides demonstrate, for the first time, that stoichiometric deviations manifest as cracks in the crystals. An important outcome of this investigation is that materials exhibiting a small degree of super-cooling with stable melting and solidification temperatures should be less prone to cracking.     

Gel growth of α and γ glycine and their characterization

The microbial free single crystals of α and γ glycine were grown from gel at room temperature in a new chemical route. These crystals showed a superior quality than the solution grown crystals. The metastable α-form and the stable γ-form of glycine were crystallized in silica gel by solubility reduction method. The form of crystallization is confirmed by single crystal and powder X-ray diffraction analyses. The crystals of α and γ glycine were found to crystallize in monoclinic and hexagonal crystal systems, respectively. For analyzing the functional group and thermal stability of α and γ glycine crystals, spectroscopic and thermal analyses have been carried out. The dielectric studies were performed to find the dielectric constant of the grown crystals and the results are discussed. Second harmonic generation efficiency of the crystal was measured by Kurtz’s powder method using Nd:YAG laser and it was found to be 2.68 times that of potassium dihydrogen phosphate crystals.     

Control of multi-zone resistive heater in low temperature gradient BGO Czochralski growth with a weighing feedback,based on the global dynamic heat transfer model

The global heat transfer in a crystallization setup has been optimized to develop a strategy of control over a three-zone heater in the BGO Czochralski process, in order to provide invariable thermal conditions near the solid–liquid interface in the stage of a constant-diameter crystal growth. The functional related to the exactness of the heat balance condition at the crystallization front, i.e., the Stefan problem, was chosen as the target function. The optimization yielded unexpected results. The temperature of the lower heater should be lowered, relative to that of the middle heater, with increasing crystal length, whereas the temperature of the upper heater is to be raised. These recommendations were incorporated into a dynamic model of the oxide Czochralski process with a weighing control and into the control loop of the temperature regulators of a crystallization setup. A comparison of results of the time-dependent simulation with the real growth process confirmed that the new control strategy minimizes the deviation of the solid–liquid interface from the prescribed one, significantly decreases variations of interface shape during the process, and enables growth of high-quality crystals.     

Numerical and experimental studies on crack formation in LiNbO3 single crystal

A global analysis of heat transfer was carried out in an inductively heated Czochralski (CZ) furnace which was actually used to grow LiNbO₃ single crystals, and then the temperature profiles obtained were used to calculate the three-dimensional thermal stress field in the crystal. By comparing the numerical results with the experimental ones, it was found that controlling the thermal environment in the CZ furnace so that the thermal stresses at the crystal surface might not exceed a certain value is important to realize the cracking free growth operation. In this study, this was accomplished through some modifications in the furnace design such as insertion of an after-heater into the furnace. These findings were verified by additional numerical simulations and crystal growth experiments for some growth conditions.     

Preparation, characterization and non-linear optical properties of pristine m-nitroaniline (m-NA) and its recycled polystyrene (Re-PS) coated single crystals

Meta-nitroaniline (m-NA) is one of the organic single crystals extensively studied due to its high non-linear effect. m-NA is also known to exhibit comparable or even better non-linear optical (NLO) properties than known inorganic materials. In this paper, we report development of m-NA single crystals by solution growth technique using different solvent systems. The size of the single crystal varies depending on solvent. The highest average crystal size acquired was 10 mm×5 mm×5 mm using methyl ethyl ketone and acetone as solvent. These single crystals were characterized using various physico-chemical techniques such as XRD and scanning electron microscopy (SEM). The developed crystals were subsequently coated with recycled polystyrene (Re-PS) (1, 2, 5 and 10 wt% concentrations) to study the effect of polymer coating on the second harmonic generation (SHG) properties of the single crystals. The purpose of polymer coating on m-NA single crystal is to improve surface morphology of crystal (i.e. it makes surface smooth) and to enhance power handling capacity for pulse laser of a crystal which, in turn, improves the SHG intensity. The optimum percentage of coating was determined for the m-NA single crystals obtained from different solvent systems. Furthermore, the polymer coating also plays key role in preventing the degradation of the m-NA crystal (well-known as highly sublime material) and ultimately increasing the shelf life of the crystal for its device application.     

The crystal growth and perfection of 2,4,6-trinitrotoluene

Large crystals of TNT were grown from ethyl acetate solution by both temperature lowering and solvent evaporation. The perfection of crystals grown from seeds under carefully controlled conditions was generally higher than those prepared by uncontrolled solvent evaporation. Examination by X-ray topography revealed the crystals to have a characteristic growth induced defect structure comprising growth sectors and boundaries, growth banding, solvent inclusions and dislocations. Twins and stacking faults (SF) were also observed. Many of the defects noted in the topographs can be attributed to impurities. The influence of the highly anisotropic crystal structure on the nature of growth defects is discussed. A structural model proposed to explain twinning and SF formation is partially supported by topographic evidence.     

Low-angle boundary investigation in silicon single crystals

Low-angle boundaries in Si single crystals grown from the melt in [111], [100], [112], [110], [118] and [115] directions were investigated by chemical etching, copper decoration technique and X-ray topography. — LAB of four types were found in planes parallel to the crystal growth axes. Rearrangement of dislocations from slip bands into LAB was observed in heavily-doped Si crystals. The origin of LAB in melt grown Si crystals is discussed. It is shown that these boundaries are well interpreted in terms of dislocation alignment formation in the thermal stress field of the growing crystal.     

Finite element analysis of dislocation density during bulk single crystal growth (effect of doping atoms in InP single crystal)

A computer code for simulation of dislocation density in a bulk single crystal during liquid encapsulated Czochralski (LEC) or Czochralski (CZ) growth process. In this computer code, the shape of crystal–melt interface and the temperature in a crystal at an arbitrary time were determined by linear interpolation of the results that were discretely obtained by heat conduction analysis of a CZ single crystal growth system. A dislocation kinetics model called Haasen–Sumino model was used as a constitutive equation. In this model, creep strain rate is related to dislocation density, and this model extended to multiaxial stress state was incorporated into a finite element elastic creep analysis program for axisymmetric bodies. Dislocation density simulations were performed using this computer code for InP bulk single crystals with about 8″ in diameter. In the analysis, the effect of dopant atoms on the dislocation density was examined. In the case of a low doped InP single crystal, dislocations are distributed in the whole of the crystal. On the other hand, in the case of a highly doped InP single crystal, dislocations are localized at both the central and peripheral regions of the crystal.     

Surface growth mechanisms and structural faulting in the growth of large single and spherulitic titanosilicate ETS-4 crystals

Morphological, surface and crystallographic analyses of titanosilicate ETS-4 products, with diverse habits ranging from spherulitic particles composed of submicron crystallites to large single crystals, are presented. Pole figures revealed that crystal surfaces with a-, b- and c- axes corresponded to 110, 010 and 001 directions, respectively. Thus, technologically important 8-membered ring pores and titania chains in ETS-4 run along the b-axis of single crystals and terminate at the smallest crystal face. Height of the spiral growth steps observed on 1 0 0 and 0 0 1 surfaces corresponded to the interplanar spacings associated with their crystallographic orientation, and is equivalent to the thickness of building units that form the ETS-4 framework. Data suggest that the more viscous synthesis mixtures, with a large driving force for growth, increased the two- and three-dimensional nucleation, while limiting the transport of nutrients to the growth surface. These conditions increase the tendency for stacking fault formation on 1 0 0 surfaces and small angle branching, which eventually results in spherulitic growth. The growth of high quality ETS-4 single crystals (from less viscous synthesis mixtures) occurred at lower surface nucleation rates. Data suggest that these high quality, large crystals grew due to one-dimensional nucleation at spiral hillocks, and indicate that under these conditions un-faulted growth is preferred.     

Evidence of free carrier concentration gradient along the c-axis for undoped GaN single crystals

Results of measurements of infrared reflectivity and micro-Raman scattering on the undoped GaN high pressure grown single crystals are reported. These crystals have usually a high electron concentration due to unintentional doping by oxygen. We show, by the shift of the plasma edge (infrared reflectivity measurements), that the free electron concentration is always higher on the (0 0 0  )N face of the GaN single crystal than on the (0 0 0 1)Ga face. In order to determine the profile of the free carrier concentration, we performed transverse micro-Raman scattering measurements along the (0 0 0 1) c-axis of the crystal with spatial resolution of 1 μm. Micro-Raman experiments give a quantitative information on the free carrier concentration via the longitudinal optical phonon–plasmon (LPP) coupling modes. Thus, by studying the behavior of the LPP mode along the c-axis, we found the presence of a gradient of free electrons. We suppose that this gradient of electrons is due to the gradient of the main electron donor, in undoped GaN single crystals, i.e. oxygen impurity. We propose a growth model which explains qualitatively the incorporation of oxygen during the growth of GaN crystal under high pressure of nitrogen.     

Single crystal growth of copper phthalocyanine using exaltation–evaporation growth method

A new method of growing single crystal for β-form copper phthalocyanine (CuPc) is presented in this paper. Melted anthracene was used as solvent of CuPc. The method, vaporizing the solvent using an automatic exaltation machine, was employed to grow CuPc single crystals. The needle-like single crystals of CuPc up to 11.6 mm in length were obtained by applying this method. The influences of different temperatures, exaltation speeds and concentrations on the single crystals growth were also discussed. The method was called exaltation–evaporation growth method.     

Flux growth and characterizations of NdPO4 single crystals

Neodymium phosphate single crystals, NdPO₄, have been grown by a flux growth method using Li₂CO₃-2MoO₃ as a flux. The as-grown crystals were characterized by X-ray powder diffraction(XRPD), differential thermal analysis (DTA) and thermogravimetric analysis (TG) techniques. The results show that the as-grown crystals were well crystallized. The crystal was stable over the temperature range from 26 to 1200 °C in N₂. The specific heat of NdPO₄ crystal at room temperature was 0.41 J/g °C. The absorption and the fluorescence spectra of NdPO₄ crystal were also measured at room temperature.     

Growth and characterization of a new nonlinear optical material: Potassium p-nitrophenolate dihydrate (NO2–C6H4–OK·2H2O) with new bonding properties

Single crystals of potassium p-nitrophenolate dihydrate (NPK·2H₂O) have been grown successfully using the isothermal solvent evaporation technique. It is a new semiorganic nonlinear optical crystal, possessing a d_eff of about 1.5 times that of lithium niobate and in which the K⁺ ions are bonded to the nitro group instead of bonding with the phenolic O⁻. Large single crystals of dimension upto 20×6×4 mm³ are harvested within a period of 60 days. The grown crystals are subjected to single crystal X-ray, FTIR and DRS-UV visible spectral, thermal and microhardness analyses. Single crystal X-ray analysis confirms the molecular formula and the structure of the crystal. FTIR spectral studies verify the functional groups present in the crystal. The DRS-UV visible spectrum proved the optical transparency of the crystal in the entire visible and near infrared region. Thermal studies reveal that the crystals are stable upto 180 °C. Microhardness measurements on the cleaved plane (1 1 0) explain the strength and slip direction in the crystal. The SHG efficiency of the crystal is examined by performing the Kurtz powder test using Nd:YAG laser.