Mechanism for generating interstitial atoms by thermal stress during silicon crystal growth

It has been known that, in growing silicon from melts, vacancies (Vs) predominantly exist in crystals obtained by high-rate growth, while interstitial atoms (Is) predominantly exist in crystals obtained by low-rate growth. To reveal the cause, the temperature distributions in growing crystal surfaces were measured. From this result, it was presumed that the high-rate growth causes a small temperature gradient between the growth interface and the interior of the crystal; in contrast, the low-rate growth causes a large temperature gradient between the growth interface and the interior of the crystal. However, this presumption is opposite to the commonly-accepted notion in melt growth. In order to experimentally demonstrate that the low-rate growth increases the temperature gradient and consequently generates Is, crystals were filled with vacancies by the high-rate growth, and then the pulling was stopped as the extreme condition of the low-rate growth. Nevertheless, the crystals continued to grow spontaneously after the pulling was stopped. Hence, simultaneously with the pulling-stop, the temperature of the melts was increased to melt the spontaneously grown portions, so that the diameters were restored to sizes at the moment of pulling-stop. Then, the crystals were cooled as the cooling time elapsed, and the temperature gradient in the crystals was increased. By using X-ray topographs before and after oxygen precipitation in combination with a minority carrier lifetime distribution, a time-dependent change in the defect type distribution was successfully observed in a three-dimensional manner from the growth interface to the low-temperature portion where the cooling progressed. This result revealed that Vs are uniformly introduced in a grown crystal regardless of the pulling rate as long as the growth continues, and the Vs agglomerate as a void and remain in the crystal, unless recombined with Is. On the other hand, Is are generated only in a region where the temperature gradient is large by low-rate growth. In particular, the generation starts near the peripheral portion in the vicinity of the solid–liquid interface. First, the generated Is are recombined with Vs introduced into the growth interface, so that a recombination region is always formed which is regarded as substantially defect free. Excessively generated Is after the recombination agglomerate and form a dislocation loop region. Unlike conventional Voronkov's diffusion model, Is hardly diffuse over a long distance. Is are generated by re-heating after growth.[In a steady state, the crystal growth rate is synonymous with the pulling rate. Meanwhile, when an atypical operation is performed, the pulling rate is specifically used.]This review on point defects formation intends to contribute further silicon crystals development, because electronic devices are aimed to have finer structures, and there is a demand for more perfect crystals with controlled point defects.     

Segregation of Ga during growth of Si single crystal

Segregation phenomenon of Ga in Czochralski (CZ)–Si crystal growth has been investigated. The effective segregation coefficient, k_eff, of Ga was obtained for different growth rates by assuming the simple relationship between the concentration of Ga in Si crystal and the bulk Ga concentration in melt. Applying BPS theory to effective segregation coefficients which is valid for the melt-solidified fraction up to 0.38, an equilibrium segregation coefficient of Ga was obtained, k₀=0.0079.     

Numerical simulation of thermal and mass transport during Czochralski crystal growth of sapphire

The thermal and flow transport in an inductively heated Czochralski crystal growth furnace during a crystal growth process is investigated numerically. The temperature and flow fields inside the furnace, coupled with the heat generation in the iridium crucible induced by the electromagnetic field generated by the RF coil, are computed. The results indicate that for an RF coil fixed in position during the growth process, although the maximum value of the magnetic, temperature and velocity fields decrease, the convexity of the crystal‐melt interface increases for longer crystal growth lengths. The convexity of the crystal‐melt interface and the power consumption can be reduced by adjusting the relative position between the crucible and the induction coil during growth. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of magnetic field effect on pressure in cylindrical and hemispherical silicon CZ crystal growth

The effect of axial magnetic field of different intensities on pressure in silicon Czochralski crystal growth is investigated in cylindrical and hemispherical geometries with rotating crystal and crucible and thermocapillary convection. As one important thermodynamic variable, the pressure is found to be more sensitive than temperature to magnetic field with strong dependence upon the vorticity field. The pressure at the triple point is proposed as a convenient parameter to control the homogeneity of the grown crystal. With a gradual increase of the magnetic field intensity the convection effect can be reduced without thermal fluctuations in the silicon melt. An evaluation of the magnetic interaction parameter critical value corresponding to flow, pressure and temperature homogenization leads to the important result that a relatively low axial magnetic field is required for the spherical system comparatively to the cylindrical one.     

Influence of Coriolis force on thermal convection and impurity segregation during crystal growth under microgravity

In contrast with the generally accepted viewpoint, it is shown that the Coriolis force caused by rotation of an orbital station can appreciably affect natural convection and impurity distribution during the growth of crystals from a melt in orbital flight conditions. 2D and 3D steady and oscillatory convection in a rectangular enclosure is considered. The resonance phenomenon arising due to the interaction of the Coriolis force and harmonic oscillations of the gravity force is demonstrated. It is shown that for moderate values of the Ekman number the Coriolis force suppresses convection in one direction and amplifies it in the other, which in turn results in deformation of the impurity distribution over the cross-section of the crystal.     

Optimization of thermal conditions during crystal growth in a multi‐zone resistance furnace

The thermal condition is one the of most important control parameters for crystal growth. In this paper we present an effective numerical method in detail for optimizing thermal conditions in multi‐zone crystal growth facilities, especially for crystal growth by the float zone (FZ) technique. A furnace function Ω is introduced to integrate the character of a growth furnace into a linear equation system. The desired power distribution can be therefore approached by solving the linear equation system iteratively. An expert systemlike algorithm has been developed in order to obtain a more suitable solution for practical applications. This method was used to investigate thermal parameters for experiments of SiGe/GeSi single crystal growth by the FZ technique. It is an individual program which can be combined with any commercial finite element/finite volume (FE/FV) program such as FIDAP^TM.     

Kinetic studies on the influence of temperature and growth rate history on crystal growth

Crystallization experiments of sucrose were performed in a batch crystallizer to study the effect of temperature and growth rate history on the crystal growth kinetics. In one of the growth methods adopted, the isothermal volumetric growth rate (R_V) is determined as a function of supersaturation (S) at 35, 40 and 45 ºC. In the other, crystals are allowed to grow at constant supersaturation by automatically controlling the solution temperature as the solute concentration decreased. Using the latter method R_V is calculated as the solution is cooled. The obtained results are interpreted using empirical, engineering and fundamental perspectives of crystal growth. Firstly, the overall activation energy (E_A) is determined from the empirical growth constants obtained in the isothermal method. The concept of falsified kinetics, widely used in chemical reaction engineering, is then extended to the crystal growth of sucrose in order to estimate the true activation energy (E_T) from the diffusion‐affected constant, E_A. The differences found in the isothermal and constant supersaturation methods are explained from the viewpoint of the spiral nucleation mechanism, taking into account different crystal surface properties caused by the growth rate history in each method. Finally, the crystal growth curve obtained in the batch crystallizer at 40 ºC is compared with the one obtained in a fluidized bed crystallizer at the same temperature. Apparently divergent results are explained by the effects of crystal size, hydrodynamic conditions and growth rate history on the crystallization kinetics of sucrose. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relationship between defects and optical properties in Er-doped GaN

The density of the vacancy-type defect in Er doped GaN was measured by positron annihilation spectrometry (PAS) and the correlation between the intensity of the Er-related luminescence was studied. A luminescence peak at 558 nm originating from ⁴S_3/2 to ⁴I_15/2 transition of Er³⁺ was observed in Er-doped GaN. The intensity of the luminescence increased with increasing Er concentration and showed the maximum with the Er concentration of around 4.0 at%. The PAS measurements showed that the vacancy-type defect density increased with increasing Er concentration up to 4 at%, and around 4 at% of Er, the formation of defect complex such as V_Ga–V_N was suggested. The contribution of the defect to the radiative recombination of intra-4f transition of Er is discussed.     

Global heat loss and thermal stress analysis in Czochralski crystal growth

Based on our invention of an energy‐efficient Czochalski crystal growth furnace, a 2D‐axisymmetric numerical simulation model of LiNbO₃ crystal growth is developed. The heat transfer, melt and gas flow, radiation and the interface deflection have been examined. Heat losses in the furnace and the insulator, as well as the heating power and thermal stress distribution at three stages of crystal growth are calculated in detail. It is found that a large proportion of heat dissipates through the water‐cooling system, and at the steel shell of the furnace, gas convection heat transfer is the major cooling mechanism. Less heat dissipation by radiation and more heat flux by gas convection to the crystal sidewall results in a larger concentrated thermal stress, which may induce large crystal cracks in the growth process. The simulation results of heating power are in coincidence with the actual power of our furnace, which verifies the feasibility of our model. The detailed information with respect to the device obtained from simulation can help to optimize the energy‐saving design and growth process.     

Relationship between processing conditions, defects and thermal degradation of poly(vinylidene fluoride) in the β-phase

Poly(vinylidene fluoride), PVDF, in its β-phase is an electroactive polymer with many technological applications. There are two main ways to prepare this polymer in its electroactive β-phase: by high temperature stretching from the α-phase and directly from solution. In this paper, the influence of the processing methods in the thermal stability of the samples was studied by UV-VIS spectroscopy and thermogravimetric analysis. The number of chain defects was measured by ¹H NMR. The results obtained were compared to a commercial β-PVDF sample. The number of head to head defects in the different samples is found to be between 6% and 9%. The onset temperature for thermal degradation and the average activation energy (∼76.5 kJ mol⁻¹) of the process are approximately equal for the α-phase sample and the β-phase obtained from it. Larger values of the onset temperature and average activation energy (∼100 kJ mol⁻¹) are found for the β-phase sample directly obtained from the solution and for the commercial β-phase sample. The thermal degradation of the samples occurs in two steps, independently of the phase of the sample, the degree of crystallinity and the processing method.     

Studies on the crystal growth,crystal structure,optical and thermal properties of an organic crystal: Benzophenone hydrazone

Single crystals of benzophenone hydrazone (BH) were successfully grown by slow evaporation method at constant temperature, 30 °C. The crystal structure of BH has been determined, and it belongs to the noncentrosymmetric space group P2₁. The grown crystal has been characterized by FT-IR). The optical transition and the lower cutoff wavelength of the BH have been identified by UV–vis–NIR studies. Thermo gravimetric analysis and differential thermal analysis have been carried out; the BH was found to be thermally stable up to 104 °C. Powder second harmonic generation (SHG) was investigated to explore its nonlinear optical (NLO) properties. The high SHG is due to one dimensional charge transfer between amine and phenyl group. Both the real ε_r and imaginary ε_i components of the dielectric constant have been calculated as functions of photon energy.     

Thermochemical analysis of native point defects and substitutional carbon and boron in GaAs crystal growth

The phase extent of GaAs has been analyzed and compared with published phase diagrams as related to total and partial point defect equilibria including charged and uncharged Frenkel, Schottky, antisite defects and substitutional carbon and boron on both sublattices. The well-known transition between semiconducting and semi-insulating behaviour at 300 K as a function of melt stoichiometry in LEC crystals can be reproduced in our model in which complete equilibrium exists above, only electronic equilibrium below a freeze-in temperature of 1100 K. The corresponding model standard enthalpy of formation of neutral Schottky defects is 4.0 eV, of a pair of neutral uncorrelated antisite defects 3.8 eV, of neutral Ga Frenkel defects 4.1 eV and of neutral As Frenkel defects 3.6 eV. Defect reactions in cooling processes after crystal growth are discussed and shown to be quite different for crystals with high or low dislocation density. Semi-insulating behaviour requires the existence of carbon acceptors if dislocations provide internal sources and sinks for point defects. For ideal crystals carbon would not be necessary. The possible site distribution of C and B is analyzed in its dependence on temperature and chemical potential of As. Constitutional supercooling is negligible in LEC growth. Macrosegregation is severe if the As fraction in the melt deviates more than ±0.02 from the stoichiometric value 0.5.     

Optimization of thermal environment during crystal growth of large‐sized Nd:YAG by Temperature Gradient Technique

A finite‐element model is employed to analysis the thermal environments in Temperature Gradient Technique (TGT) furnace during the growth of large‐sized Nd:YAG crystal. The obtained results show that when the crucible is located at the lower position inside of the heater, a flatter solid‐liquid interface is established, which makes it easier to obtain the core‐free Nd:YAG crystal. Meanwhile, the lower crucible position can induce higher axial temperature gradient, which is beneficial to the release of latent heat. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis,crystal growth,spectral, thermal and optical properties of acenaphthene picrate

The crystalline material of acenaphthene picrate (ACP) was synthesized and the single crystals of the title compound grown by slow evaporation solution growth technique. The solubility of the complex compound was estimated using different solvents as chloroform, ethanol, (1:1) chloroform ‐ acetone mixture. The material was characterized through elemental analysis; powder XRD, NMR and FTIR techniques. The various planes of reflection have been identified from the XRD powder pattern. The formation of the charge transfer complex was confirmed by UV‐VIS spectroscopy. The thermal stability of the crystals was studied using TG/DTA analyses techniques. The second harmonic generation (SHG) of the material was confirmed by using Nd: YAG laser. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Investigation on growth,optical, thermal,mechanical and dielectric studies of Benzimidazolium L-aspartate NLO crystal

The organic salt of Benzimidazolium L-aspartate (BLA) has been synthesised and single crystals were grown by slow evaporation solution growth technique at room temperature using water as the solvent. The grown crystal was subjected to single crystal X-ray diffraction analysis and confirmed it belongs to monoclinic crystal system with space group P2₁/c. The crystalline perfection was studied using High resolution X-ray diffraction (HRXRD). The functional groups were analysed by FT-IR analysis. The optical transmittance and the lower cut-off wavelength of the BLA crystal have been identified by UV-Vis study. The thermal stability of the title crystal was investigated by TGA/DTA analyses. The Vickers microhardness analysis was carried out to study the mechanical strength of the crystal. The dielectric response of the crystal was studied in the frequency range 100 to 5 MHz at different temperatures. The surface morphology of the grown BLA crystal was studied by scanning electron microscopy (SEM). The second harmonic generation efficiency was measured in comparison with KDP by employing Kurtz Perry Powder method.