General Features and Fundamental Concepts

Recent interest in ion beam processing has focused on studies of ion implantation, ion beam mixing, ion-induced phase transformations, and ion beam deposition. These interests have been stimulated by the possibilities of synthesizing novel materials with potential applications in the semiconductor, tribological, corrosion, and optical fields. 

Schematic drawing of an ion implantation system. A mass-separating magnet is used to select the ion species (elements and isotopes) of interest. Beam-sweeping facilities are required for large-area uniform implantations 

Ion beam processing provides an alternative and non-equilibrium method of introducing dopant atoms into the lattice. In typical applications, a beam of dopant ions is accelerated through a potential of 10-100 kV. The implantation system shown in Fig. 1.1 illustrates the basic elements required in this technique ion source, acceleration column, mass-separator, and target chamber. With different types of ion sources available, a wide variety of beams may be produced with sufficient intensity for implantation purposes for integrated circuit technology 10 -10 ions cm (less than a monolayer see Sect. 1.4) is a representative ion dose. Ion dose is defined as the number of ions cm implanted into the sample. Alternatively, the term fluence is used instead of dose. The ion beam current density is expressed in units of A cm . The dose rate or flux is given in units of ions s cm .  

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In this chapter, an overview of the fundamentals, specific features, and selected systems of PTC is presented. An attempt is made to describe the basic concepts of PTC as clearly as possible and to confine its attention to those features of PTC that seem to be important for those who are interested in gaining a general knowledge of this attractive methodology. It is hoped that those embarking on research in PTC may find this chapter a useful initial guide. Undoubtedly, they are required to read more comprehensive reviews, series chapters, and books [8-19] for advanced study in the field of PTC. 

Models that seek to value options or describe a yield curve also describe the dynamics of asset price changes. The same process is said to apply to changes in share prices, bond prices, interest rates and exchange rates. The process by which prices and interest rates evolve over time is known as a stochastic process, and this is a fundamental concept in finance theory. Essentially, a stochastic process is a time series of random variables. Generally, the random variables in a stochastic process are related in a non-random manner, and so therefore we can capture them in a probability density function. A good introduction is given in Neftci (1996), and following his approach we very briefly summarise the main features here. 

As promised we will present a simple model that displays both the fundamental nature of the concept of resonances as well as the quality of relativistic principles. A Klein-Gordon-like equation will be derived with specific restrictions and interpretations. Although the representation turns up somewhat naive and ad hoc, we will appreciate some general and surprising features that reveal the underlying fundamental principles. 

In chemical kinetics the concept of the order of a reaction forms the basis of a kinematics which constitutes a frame for most of the molecular theories of chemical reactions. The fundamental magnitudes of this kinematics are the concentrations and the specific rate constants. In simple cases only the time enters as an independent variable, whereas in a diffusion process both time and space are involved. Diffusion processes are generally described in terms of diffusion coefficients, volume concentrations and thermodynamic potential or activity factors. Partial volume factors and friction coefficients associated with the components of the diffusing mixture are also essential in the description. A feature of the macro-dynamical theory is that it covers any region of concentration. Especially simple equations are connected with the differential diffusion process (diffusion with small concentration differences), for which the different coefficients or factors mentioned above are practically constant. 

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