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.

Numerical Simulation of the Flow Field and Concentration Distribution in the Bulk Growth of Silicon Carbide Crystals

The physical vapor transport (PVT) method is being widely used to grow large-size single SiC crystals. The growth process is associated with heat and mass transport in the growth chamber, chemical reactions among multiple species as well as phase change at the crystal/gas interface. The current paper aims at studying and verifying the transport mechanism and growth kinetics model by demonstrating the flow field and species concentration distribution in the growth system. We have developed a coupled model, which takes into account the mass transport and growth kinetics. Numerical simulation is carried out by employing an in-house developed software based on finite volume method. The results calculated are in good agreement with the experimental observation.

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.

Formation of dendritic nanostructures in Pyrex glass anodically bonded to silicon coated with an aluminum thin film

Anodic bonding with thin films of metal or alloy as an intermediate layer, finds increasing applications in micro/nanoelectromechanical systems. At the bonding temperature of 350 degrees C, voltage of 400 V, and 30 min duration, the anodic bonding is completed between Pyrex glass and crystalline silicon coated with an aluminum thin film with a thickness comprised between 50 and 230 nm. Sodium-depleted layers and dendritic nanostructures were observed in Pyrex 7740 glass adjacent to the bonding interface. The sodium depletion width does not increase remarkably with the thickness of aluminum film. The dendritic nanostructures result from aluminum diffusion into the Pyrex glass. This experimental research is expected to enhance the understanding of how the depletion layer and dendritic nanostructures affect the quality of anodic bonding. (C) 2007 Elsevier B.V. All rights reserved.

Shape effects on the yield stress and deformation of silicon nanowires: A molecular dynamics simulation

The tension and compression of single-crystalline silicon nanowires (SiNWs) with different cross-sectional shapes are studied systematically using molecular dynamics simulation. The shape effects on the yield stresses are characterized. For the same surface to volume ratio, the circular cross-sectional SiNWs are stronger than the square cross-sectional ones under tensile loading, but reverse happens in compressive loading. With the atoms colored by least-squares atomic local shear strain, the deformation processes reveal that the failure modes of incipient yielding are dependent on the loading directions. The SiNWs under tensile loading slip in {111} surfaces, while the compressive loading leads the SiNWs to slip in the {110} surfaces. The present results are expected to contribute to the design of the silicon devices in nanosystems.

Nutrient-phytoplankton interrelationships in the Eastern Tropical Pacific Ocean

ENGLISH: Near surface nutrient distributions in the eastern tropical Pacific Ocean, using data from the EASTROPAC Expedition of 1967-68 and pre~EASTROPAC data, are described. Nutrient concentrations were maximal along the equator, in the Peru Current and its offshore extension, and in the Costa Rica Dome and westward tensions of this feature. Nutrient-poor water was found north of the equator well offshore. In this water nitrate was often undetectable (<0.1 µg-at/liter) at the surface, but phosphate and silicic acid concentrations were moderate. Enrichment experiments showed that nitrogen was the primary limiting nutrient in poor water even though large amounts of organic N were found. Half saturation constants (K s ) were determined for ammonium-supported phytoplankton growth. These data were used to calculate near-surface primary productivity values which compared favorably with 14C values. Assimilation ratio measurements indicated that algae were not extremely nitrogen-deficient. Laboratory-determined K, values for phosphate and silicic acid indicated that these nutrients were rarely limiting. In rich water, chlorophyll levels were less than expected from nutrient levels, and this anomaly may be related to limitation by nutrients other than nitrogen (N), phosphorus (P), or silicon (Si), or to grazing. SPANISH: Se describe la distribución subsuperficial de los nutrientes en el Océano Pacífico oriental tropical, empleando los datos de la Expedición EASTROPAC de 1967~68 y datos anteriores a éstos. La concentración de nutrientes fue máxima a lo largo del ecuador, en la Corriente del Perú, en su prolongación mar afuera, en el Domo de Costa Rica y en las prolongaciones occidentales de esta característica. Se encontraron aguas pobres en nutrientes al norte del ecuador y bastante mar adentro. En estas aguas el nitrato era casi imperceptible (<0.1 µg-at/litro) en la superficie, pero las concentraciones de fosfato y ácido silícico fueron moderadas. Los experimentos de enriquecimiento indicaron que el nitrógeno era el principal nutriente limitante en aguas pobres, aun cuando se encontraron grandes cantidades de nitrógeno orgánico. Se determinaron las constantes de saturación media (K s ) para el desarrollo del fitoplancton sostenido por el amonio. Estos datos se emplearon para calcular los valores de la productividad primaria cerca a la superficie que pueden compararse favorablemente con los valores del 14C. Las medidas de la proporción de asimilación indican que las algas no tenían una deficiencia extremada de nitrógeno. Los valores determinados en el laboratorio de K, para el fosfato y ácido silícico indicaron que estos nutrientes limitaron rara vez la producción. En aguas ricas, los niveles de clorofila fueron inferiores a lo esperado según los niveles nutritivos y esta anomalía puede relacionarse a la alimentación o a la escasez de otros nutrientes distintos al nitrógeno (N), fósforo (P) o silicio (Si).