Progress In Modeling Of Fluid Flows In Crystal Growth Processes

Modeling of fluid flows in crystal growth processes has become an important research area in theoretical and applied mechanics. Most crystal growth processes involve fluid flows, such as flows in the melt, solution or vapor. Theoretical modeling has played an important role in developing technologies used for growing semiconductor crystals for high performance electronic and optoelectronic devices. The application of devices requires large diameter crystals with a high degree of crystallographic perfection, low defect density and uniform dopant distribution. In this article, the flow models developed in modeling of the crystal growth processes such as Czochralski, ammonothermal and physical vapor transport methods are reviewed. In the Czochralski growth modeling, the flow models for thermocapillary flow, turbulent flow and MHD flow have been developed. In the ammonothermal growth modeling, the buoyancy and porous media flow models have been developed based on a single-domain and continuum approach for the composite fluid-porous layer systems. In the physical vapor transport growth modeling, the Stefan flow model has been proposed based on the flow-kinetics theory for the vapor growth. In addition, perspectives for future studies on crystal growth modeling are proposed. (c) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

Growth Mechanism And Joint Structure Of Zno Tetrapods

Regular zinc oxide (ZnO) tetrapods with a flat plane have been obtained on Si(1 0 0) substrate via the chemical vapour deposition approach. The x-ray diffraction result suggests that these tetrapods are all single crystals with a wurtzite structure that grow along the (0 0 0 1) direction and corresponding electron backscatter diffraction analysis reveals the crystal orientation of growth and exposed surface. Furthermore, we find some ZnO tetrapods with some legs off and the angles between every two legs are measured with the aid of scanning electron microscopy and image analysis, which benefit to reveal the structure of ZnO tetrapods joint. The structure model and growth mechanism of ZnO tetrapods are proposed. Besides, the stable model of the interface was obtained through the density-functional theory calculation and the energy needed to break the twin plane junction was calculated as 5.651 J m(-2).

Diffusion dominated process for the crystal growth of a binary alloy

The pure diffusion process has been often used to study the crystal growth of a binary alloy in the microgravity environment. In the present paper, a geometric parameter, the ratio of the maximum deviation distance of curved solidification and melting interfaces from the plane to the radius of the crystal rod, was adopted as a small parameter, and the analytical solution was obtained based on the perturbation theory. The radial segregation of a diffusion dominated process was obtained for cases of arbitrary Peclet number in a region of finite extension with both a curved solidification interface and a curved melting interface. Two types of boundary conditions at the melting interface were analyzed. Some special cases such as infinite extension in the longitudinal direction and special range of Peclet number were reduced from the general solution and discussed in detail.

Crystal-growth in floating zone with phase-change and thermosolutal convections

Floating zone crystal growth in microgravity environment is investigated numerically by a finite element method for semiconductor growth processing, which involves thermocapillary convection, phase change convection, thermal diffusion and solutal diffusion. The configurations of phase change interfaces and distributions of velocity, temperature and concentration fields are analyzed for typical conditions of pulling rates and segregation coefficients. The influence of phase change convection on the distribution of concentration is studied in detail. The results show that the thermocapillary convection plays an important role in mixing up the melt with dopant. The deformations of phase change interfaces by thermal convection-diffusion and pulling rods make larger variation of concentration field in comparison with the case of plane interfaces.

Long-Term Growth and Persistence with Endogenous Depreciation: Theory and Evidence

Previous research has shown a strong positive correlation between short-term persistence and long-term output growth as well as between depreciation rates and long-term output growth. This evidence, therefore, contradicts the standard predictions from traditional neoclassical or AK-type growth models with exogenous depreciation. In this paper, we first confirm these findings for a larger sample of 101 countries. We then study the dynamics of growth and persistence in a model where both the depreciation rate and growth are endogenous and procyclical. We find that the model s predictions become consistent with the empirical evidence on persistence, long-term growth and depreciation rates.

Crystal growth and spectroscopic characterization of Yb-doped and Yb, Na-codoped CaF2 laser crystals by TGT

High-quality 2at%-doped Yb:CaF2 and Yb,Na:CaF2 single crystals with diameter of 76mm were grown by the temperature gradient technique. For the first time, distribution coefficients (KO) of Yb in the two crystals were determined to be 1.07 and 0.91, respectively, by measuring the Yb concentrations at the growth starting position in the as-grown boules. Absorption and emission spectra of the two different crystals were measured at room temperature. Experimental results show that Na+ ions codoping with Yb3+ as charge compensators make Yb3+ ions in CaF2 lattice to be a quasi-single-center system, and greatly suppress the deoxidization of Yb3+ to Yb2+ (c) 2005 Elsevier B.V. All rights reserved.

Crystal growth and optical properties of Gd1.99-xYxCe.0.01SiO5 single crystals

Gd1.99-xYxCe0.01SiO5 (Ce:GYSO) crystals (x = 0, 0.0995, 0.199) have been grown by the Czochralski (Cz) method. Crystal structure and the distribution coefficients of Ce have been determined for all three crystals. Spectroscopic measurements indicate that optical transmittance and luminescence intensity of Gd1.99-xYxCe0.01SiO5 (x = 0.0995, 0.199) crystals are Substantially higher than those of Ce:Gd2SiO5 (Ce:GSO), especially at x = 0.0995, which makes them good candidate materials for scintillation applications. The particularly important result is that the alloyed Ce:GYSO crystals can be grown easily by the Cz method and, unlike Ce:GSO, they do not undergo cleavage during the growth process or subsequent mechanical treatment. (c) 2005 Elsevier B.V. All rights reserved.

Crystal growth and properties of Yb : FAP laser crystal

A large and transparent Yb:FAP crystal with dimensions up to circle divide 30 mm x 85 mm has been grown by the Czochralski method. The preparation of the raw material has been investigated. X-ray power diffraction studies of Yb:FAP crystal confirm that the as-grown crystal is isostructural with the FAP crystal. The crystalline quality has been studied using X-ray rocking curve analysis. The segregation coefficient of Yb3+ in the Yb:FAP crystal has been also determined. Linear thermal expansion coefficients in [001] and [100] directions have been measured in the 30-800 degrees C temperature range. (c) 2005 Elsevier B.V. All rights reserved.

Bulk crystal growth and efficient diode-pumped laser performance of Yb 3+:Sc2SiO5

A bulk crystal of Yb:Sc2SiO5 (Yb:SSO) with favorable thermal properties was successfully obtained by the Czochralski method. The energy level diagrams for Yb:SSO crystal were determined by optical spectroscopic analysis and semi-empirical crystal-field calculations using the simple overlap model. The full width at half maximum of the absorption band centering at 976 nm was calculated to be 24 nm with a peak absorption cross-section of 9.2x10(-21) cm(2). The largest ground-state splitting of Yb3+ ions is up to 1027 cm(-1) in a SSO crystal host. Efficient diode-pumped laser performance of Yb:SSO was primarily demonstrated with a slope efficiency of 45% and output power of 3.55 W.

Crystal growth, spectroscopic characterization, and laser performance of Tm:LiLuF4 crystal

The National Science Foundation of China(Grant No. 60578044).