3D Finite Volume Scheme for Czochralski Crystal Growth

A general three-dimensional model is developed for simulation of the growth process of silicon single crystals by Czochralski technique. The numerical scheme is based on the curvilinear non-orthogonal finite volume discretization. Numerical solutions show that the flow and temperature fields in the melt are asymmetric and unsteady for 8’’ silicon growth. The effects of rotation of crystal on the flow structure are studied. The rotation of crystal forms the Ekman layer in which the temperature gradient along solid/melt surface is small.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

A Finite Element Analysis of a Crack Penetrating or Deflecting into an Interface in a Thin Laminate

The crack tip driving force of a crack growing from a pre-crack that is perpendicular to and terminating at an interface between two materials is investigated using a linear fracture mechanics theory. The analysis is performed both for a crack penetrating the interface, growing straight ahead, and for a crack deflecting into the interface. The results from finite element calculations are compared with asymptotic solutions for infinitesimally small crack extensions. The solution is found to be accurate even for fairly large amounts of crack growth. Further, by comparing the crack tip driving force of the deflected crack with that of the penetrating crack, it is shown how to control the path of the crack by choosing the adhesion of the interface relative to the material toughness.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

Institutional designs to face the dark side of total allowable catches

Setting total allowable catches (TACs) is an endogenous process in which different agents and institutions, often with conflicting interests and opportunistic behaviour, try to influence policy-makers. Such policy-makers, far from being the benevolent social planners many would wish them to be, may also pursue self-interest when making final decisions. Although restricted knowledge of stock abundance and population dynamics, and weakness in enforcement, have effects, these other factors may explain the reason why TAC management has failed to guarantee sustainable exploitation of fish resources. Rejecting the exogeneity of the TAC and taking advantage of fruitful debate on economic policy (i.e. the rules vs. discretion debate, and that surrounding the independence of central banks), two institutional developments are analysed as potential mechanisms to face up to misconceptions about TACs: long-term harvest control rules, and a central bank of fish.

Apoyo de la Contabilidad de Dirección Estratégica a la fidelización de la clientela a través de la motivación de los recursos humanos y de la gestión de la calidad total

El tema que vamos a desarrollar se orienta a la satisfacción y fidelización de la clientela como objetivo esencial de la empresa, lo que pemitirá aumentar la competitividad y pilotar la organización por la senda de la máxima eficiencia posible, en un enfoque sistématico de mejora continua hacia la excelencia empresarial.

Systhema de medidas adaptaveis para a progressiva e total extincção do trafico, e da escravatura no Brasil / confeccionado e aprovado pela Sociedade Contra o Trafico de Africanos, e Promotora da Colonisação, e da Civilisação dos Indigenas

Proposta da Sociedade ao Governo Imperial para a gradual e total extinção da escravatura no Brasil.