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Fibre (rod) and sheet-shaped crystals with specified size for use as final products without additional machining are required in various applications of modern engineering. In order to avoid formation of internal mechanical stress in the crystal, lateral surface shaping without contact with container walls is preferred. As the crystal is not restricted by crucible walls, its cross-section is determined by the meniscus-shaping capillary forces and the heat and mass-exchange in the melt-crystal system. Any variation of the pulling rate, pressure, temperature gradient in the furnace, and melt temperature at the meniscus base leads to a change in the crystal cross-section and to pinch formation. Over the past two decades, many experimental and theoretical studies have been reported on a powerful approach to crystal lateral surface shaping without contact with container walls, namely the so-called edge-defined film-fed growth (EFG) technique. The shape and size of a single crystal grown by EFG is determined by the shape and size of the meniscus, (i.e: the liquid bridge retained between the die and the crystal) which depend on the radius or half-thickness of the die and other properties such as pulling rate, pressure, temperature gradient and melt temperature. In this book, theoretical and numerical results are obtained using a non-linear mathematical model of the EFG method. Theoretical results presented for fibres and sheets are rigorously obtained on the basis of the equations of the model. Numerical results are obtained on the basis of theoretical results using experimental data. Such results offer a complete package of the possibilities of the model for equipment designers and practical crystal growers.
Aims to present effective methods of estimation of the regions of attraction of asymptotically stable steady states in the case of autonomous analytical differential equations and also of discrete semi-dynamical systems. It also shows how these regions can be used.
This volume offers an overview of the growth of shaped crystals (oxides, fluorides, etc.) by the micro-pulling-down technique. Both melt and solution (flux) growth are considered. The advantages and disadvantages of the method are discussed in detail and compared with related crystal-growth processes. The authors attempt to give a practical introduction to this technique, thereby also explaining how its application can help to solve problems commonly encountered in other melt-growth methods.
Silicon, as a single-crystal semiconductor, has sparked a revolution in the field of electronics and touched nearly every field of science and technology. Though available abundantly as silica and in various other forms in nature, silicon is difficult to separate from its chemical compounds because of its reactivity. As a solid, silicon is chemically inert and stable, but growing it as a single crystal creates many technological challenges. Crystal Growth and Evaluation of Silicon for VLSI and ULSI is one of the first books to cover the systematic growth of silicon single crystals and the complete evaluation of silicon, from sand to useful wafers for device fabrication. Written for engineers and researchers working in semiconductor fabrication industries, this practical text: Describes different techniques used to grow silicon single crystals Explains how grown single-crystal ingots become a complete silicon wafer for integrated-circuit fabrication Reviews different methods to evaluate silicon wafers to determine suitability for device applications Analyzes silicon wafers in terms of resistivity and impurity concentration mapping Examines the effect of intentional and unintentional impurities Explores the defects found in regular silicon-crystal lattice Discusses silicon wafer preparation for VLSI and ULSI processing Crystal Growth and Evaluation of Silicon for VLSI and ULSI is an essential reference for different approaches to the selection of the basic silicon-containing compound, separation of silicon as metallurgical-grade pure silicon, subsequent purification, single-crystal growth, and defects and evaluation of the deviations within the grown crystals.