Effects of Thermocapillary Convection on the Growth Process in Industrial 8-inch Silicon Czochralski Growth

Czochralski (CZ) crystal growth process is a widely used technique in manufacturing of silicon crystals and other semiconductor materials. The ultimate goal of the IC industry is to have the highest quality substrates, which are free of point defect, impurities and micro defect clusters. The scale up of silicon wafer size from 200 mm to 300 mm requires large crucible size and more heat power. Transport phenomena in crystal growth processes are quite complex due to melt and gas flows that may be oscillatory and/or turbulent, coupled convection and radiation, impurities and dopant distributions, unsteady kinetics of the growth process, melt crystal interface dynamics, free surface and meniscus, stoichiometry in the case of compound materials. A global model has been developed to simulate the temperature distribution and melt flow in an 8-inch system. The present program features the fluid convection, magnetohydrodynamics, and radiation models. A multi-zone method is used to divide the Cz system into different zones, e.g., the melt, the crystal and the hot zone. For calculation of temperature distribution, the whole system inside the stainless chamber is considered. For the convective flow, only the melt is considered. The widely used zonal method divides the surface of the radiation enclosure into a number of zones, which has a uniform distribution of temperature, radiative properties and composition. The integro-differential equations for the radiative heat transfer are solved using the matrix inversion technique. The zonal method for radiative heat transfer is used in the growth chamber, which is confined by crystal surface, melt surface, heat shield, and pull chamber. Free surface and crystal/melt interface are tracked using adaptive grid generation. The competition between the thermocapillary convection induced by non-uniform temperature distributions on the free surface and the forced convection by the rotation of the crystal determines the interface shape, dopant distribution, and striation pattern. The temperature gradients on the free surface are influenced by the effects of the thermocapillary force on the free surface and the rotation of the crystal and the crucible.

Growth of Silicon Carbide Bulk Crystals by Physical Vapor Transport Method and Modeling Efforts in the Process Optimization

Silicon carbide bulk crystals were grown in an induction-heating furnace using the physical vapor transport method. Crystal growth modeling was performed to obtain the required inert gas pressure and temperatures for sufficiently large growth rates. The SiC crystals were expanded by designing a growth chamber having a positive temperature gradient along the growth interface. The obtained 6H-SiC crystals were cut into wafers and characterized by Raman scattering spectroscopy and X-ray diffraction, and the results showed that most parts of the crystals had good crystallographic structures.

Floating zone convection

The microgravity research, as a branch of the advanced sciences and a spe- cialized field of high technology, has been made in China since the late 1980's. The research group investigating microgravity fluid physics consisted of our col- leagues and the authors in the Institute of Mechanics of the Chinese Academy of Sciences (CAS), and we pay special attention to the floating zone convection as our first research priority. Now, the research group has expanded and is a part of the National Microgravity Laboratory of the CAS, and the research fields have been extended to include more subjects related to microgravity science. Howev- er, the floating zone convection is still an important topic that greatly holds our research interests.

Small angle X-ray scattering of the colloidal crystal

The monodisperse polystyrene spheres are assembled into the colloidal crystal on the glass substrate by vertical deposition method, which is aimed at the so-called photonic crystal applications. The structural information of the bulk colloidal crystal is crucial for understanding the crystal growth mechanism and developing the various applications of colloidal crystal. Small-angle X-ray scattering (SAXS) technique was used to obtain the bulk structure of the colloidal crystal at Beamline 1W2A of BSRF. It is found that the SAXS pattern is sensitive to the relative orientation between the colloidal sample and the incident X-ray direction. The crystal lattice was well distinguished and determined by the SAXS data.

The Sustainability of `Sustainable´ Energy Use: Historical Evidence on the Relationship between Economic Growth and Renewable Energy

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Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

Growth, characterization and optical quality of CaF2 single crystals grown by the temperature gradient technique

The CaF2 single crystals with diameters up to 200 mm were successfully grown by modified temperature gradient technique (TGT), which are suitable for application as optical elements in the ultraviolet range. The optimizations of various growth parameters were systematically studied. Properties of as-grown CaF2 crystals were characterized by the nature of inclusions, dislocations, crystallinity, and impurities contents. The results showed that the dislocations and multinucleation were mostly constrained in the conical part of the crystals with the cylindrical parts having the best crystalline quality and lowest impurity contents. The high optical quality of TGT-grown CaF2 single crystals was also confirmed to have excellent optical transmission in 190-2500 nm and refractive index homogeneity. (c) 2005 Elsevier Ltd. All rights reserved.

Growth and characterization of new transparent conductive oxides single crystals beta-Ga2O(3): Sn

Tin oxide doped beta-Ga2O3 single crystals are recognized as transparent conductive oxides (TCOs) materials. They have a larger band gap (4.8 eV) than any other TCOs, thus can be transparent in UV region. This property shows that they have the potential to make the optoelectronic device used in even shorter wavelength than usual TCOs. beta-Ga2O3 single crystals doped with different Sn4+ concentrations were grown by the floating zone technique. Their optical properties and electrical conductivities were systematically studied. It has been found that their conductivities and optical properties were influenced by the Sn4+ concentrations and annealing. (c) 2006 Elsevier Ltd. All rights reserved.

Growth and spectral characterization of beta-Ga2O3 single crystals

Beta gallium oxide (beta-Ga2O3) single crystals were grown by the floating zone technique. The absorption spectra and the luminescence of the crystals were measured. The absorption spectra showed an intrinsic short cutoff edge around 260 nm with two shoulders at 270 and 300 nm. Not only the characteristic UV (395 nm), blue (471 nm) and green (559 nm) lights, but also the red (692 nm) light can be seen in the emission spectra. The deep UV light was attributed to the existing of quantum wells above the valence band and the red light was owed to the electron-hole recombination via the vicinity donors and acceptors. (c) 2006 Elsevier Ltd. All rights reserved.

Influence of vapor transport equilibration on the crystal quality and thermal-expansion coefficients of gamma-LiAlO2

gamma-LiAlO2 (LAO) single crystal has been grown by the Czochralski method. However, its quality was deteriorated due to lithium volatilization during the crystal growth. The full width at half maximum value drops from 116.9 to 44.2 arc sec after the LAO slice was treated by vapor transport equilibration at 1000, 1100, and 1200 degrees C/48 h in sequence. The treated slice shows higher optical transmission than the as-grown one in the measured wavelength range of 190-1900 nm, meanwhile, its absorption edge exhibits a blueshift. According to Raman spectra, the treated slice has homogeneous quality at different depths from surface to 0.01 mm. The expansion coefficient of the treated slice for a axis drops from 17.2398x10(-6)/degrees C to 16.5240x10(-6)/degrees C, and that for c axis drops from 10.7664x10(-6)/degrees C to 10.0786x10(-6)/degrees C.

导模法生长晶体研究进展

导模法是一种极具应用潜力的晶体生长方法,具有生长速度快,加工成本低的优点,广泛用于生长各种形状的晶体。对导模法的原理、特点和发展历史进行了简单介绍,着重论述了导模法在生长有形蓝宝石和硅晶体中的发展和应用,对目前导模法生长晶体过程中存在的问题做了简单的介绍。

铝酸钇晶体中的生长小面

采用提拉法生长了掺Ce、掺Yb和掺Mn的铝酸钇(YAlO3,YAP)晶体,晶体均完整透明,无肉眼可见的气泡、散射和包裹物等宏观缺陷。通过化学腐蚀和同步辐射白光形貌实验检测了YAP晶体中的生长小面缺陷。结果表明:晶体生长过程中,由于凸向熔体的固-液界面,造成了小面生长现象。沿[101]方向生长的YAP晶体中出现的小面为(102),(201),(121)和(121)奇异面。X射线摇摆曲线表征的结果表明:生长小面的存在严重破坏了晶体的微观结构完整性和均匀性,并导致了小角度晶界缺陷的产生。

Hydrothermal growth and characterization of ZnO crystals

ZnO crystals with dimensions of 30 x 38 x 8 turn 3 have been grown by the hydrothermal method using a mixed solution of KOH, LiOH and H2O2. The growing rates for +c(0001) and -c(000 (1) over bar) were 0.17 and 0.09 mm/day, respectively. The crystal color was very light green for +c sector and dark brown for -c sector. For the +c sector, the resistivity at room temperature was 80 0 cm, the carrier concentration was about 10(4)/cm(3), and the mobility was about 100 cm(2)/Vs. The full-width at half-maximum (FWHM) of double axis X-ray rocking curve for the polished Zn face cut from +c sector was 45 arcsec. The photoluminescence (PL) spectrum and the absorption spectrum of +c part of the crystals at room temperature were also reported and discussed in this paper. (c) 2008 Elsevier B.V. All rights reserved.