Рубрика: Physical and mathematical

Today, it is difficult to imagine all spheres of human activity without personal computers, solid-state electronic devices, micro- and nanoelectronics, photoconverters, and mobile communication devices. The basic material of modern electronics and for all of these industries is semiconductor silicon. Its properties and applications are determined by defects in its crystal structure. However, until now, there has been no complete and reliable description of the creation and transformation of such a defective structure. This book solves this mystery through two different approaches to semiconductor silicon: the classical and the probabilistic. This book brings together, for the first time, all existing experimental and theoretical information on the internal structure of semiconductor silicon. It will appeal to a wide range of readers, from materials scientists and practical engineers to students and can be used as a textbook.

Link to the publisher: www.cambridgescholars.com

The knowledge of fundamental silicon questions and all aspects of silicon technology give the possibility of improvement both initial silicon material and devices on silicon basis. The articles for this book have been contributed by the very respected researchers in this area and cover the most recent developments and applications of silicon technology and some fundamental questions. This book provides the latest research developments in important aspects of silicon including: nanoclusters, solar silicon, porous silicon, some technological processes and silicon devices and also fundamental question about silicon structural perfection. This book is of interest to both fundamental research and also to practicing scientists and also will useful to all engineers and students in industry and academia.

Link to the publisher (you can download all articles): www.intechopen.com

The diffusion model of the formation of grown-in microdefects has been considered as applied to the description of defect formation in heat-treated silicon single crystals. It has been shown that, in the framework of the proposed kinetic model of defect formation, the formation and development of the defect structure during the growth of a crystal and its heat treatment can be considered within a unified context. The mathematical apparatus of the diffusion model can provide a basis for the development of a program package for the analysis and calculation of the formation of growth and postgrowth microdefects in dislocation-free silicon single crystals. It has been demonstrated that the diffusion model of the formation of growth and postgrowth microdefects allows one to determine necessary conditions for the growth of a crystal and the regimes of its heat treatment for the preparation of a precisely defined defect structure.

The physical model of the formation of grown-in microdefects in dislocation-free Si single crystals has been analyzed. The mathematical models used to describe the processes of defect formation in crystals during their growth are proven to be adequate to the physical model. A technique is proposed to determine and calculate the defect structure in dependence of the crystal growth conditions (growth technique, growth rate, temperature gradients, cooling rate). It is shown that the theoretical study of the real crystal structure in the dependence of the thermal growth conditions using an original virtual technique for analyzing and calculating the formation of grown-in microdefects is a new experimental technique.

The main aspects of the diffusion model for the formation of grown-in microdefects in dislocation-free silicon single crystals are presented.

A kinetic model of the formation and growth of dislocation loops in course of consequent as-grown crystal’s cooling has been proposed. It demonstrates that dislocation loops are formed following the processes of high-temperature precipitation of background oxygen and carbon impurities during crystal growth. Elastic deformation caused by growing precipitate is released due to the formation and growth of dislocation loops. Interstitial dislocation loops are formed, when the crystal growth ratio is Vg/G < Ccrit. We have compared the kinetic model calculation data with the experimental research findings related to the formation of dislocation loops.

A brief review of the current state of theoretical description of the formation of the defect structure of dislocation-free silicon single crystals was carried out. Emphasis was placed on a new diffusion model of formation grown-in microdefects. It is shown that the diffusion model can describe the high-temperature precipitation of impurities during the cooling of the crystal after growth. Shown that the model of the dynamics of point defects can be considered as component part of the diffusion model for formation grown-in microdefects.

A kinetic model of growth and coalescence of oxygen and carbon precipitates has been proposed. This model in combination with the kinetic model of the formation of oxygen and carbon precipitates represents a unified model of precipitation in as-grown dislocation-free silicon single crystals during their cooling in the temperature range from 1683 to 300 K. It has been demonstrated that the results of the calculations are in good agreement with the experimental data obtained from investigations of grown-in microdefects.

A software as a virtual experimental instrument for analyzing and calculating the formation of grown-in microdefects in undoped dislocation-free silicon single crystals has been proposed. Using the software and also using growth parameters (crystal growth rate, crystal diameter, temperature gradients, cooling rate), one can calculate the characteristics of the oxygen and carbon precipitation process during crystal cooling after growing from the crystallization temperature to room temperature. The software allows analyzing and calculating the formation of vacancy microvoids and interstitial dislocation loops.

The defect structure of dislocation-free silicon single crystals has been calculated using the approximate solution of the Fokker–Planck partial differential equations. It has been demonstrated that the precipitation starts to occur near the crystallization front due to the disappearance of excess intrinsic point defects on sinks whose role is played by oxygen and carbon impurities.