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We have seen in Chapter 7 that metals are characterized by partially filled valence bands and that the electrons in these bands give rise to electrical conduction. On the other hand, the valence bands of insulators are completely filled with electrons. Semiconductors, finally, represent in some respect a position between metals and insulators. We mentioned in Chapter 6 that semiconductors have,...
A brief reivew on the failure modes in thin film metallizations is given emphasizing electromigration, thermomigration, and thermal grooving of the grain boundaries. The most important parameters which influence the failures, such as grain boundaries, grain boundary gradients, temperature gradients, activation energy for ion migration, etc., are discussed. Alternate methods which improve the electromigration...
Materials which are electrical (and thermal) insulators are of great technical importance and are, therefore, used in large quantities in the electronics industry, e.g., as handles for a variety of tools, as coatings for wires, or as casings for electrical equipment. Most polymeric materials have the required insulating properties and have been used for decades for this purpose. It came, therefore,...
At first we solve the Schrödinger equation for a simple but, nevertheless, very important case. We consider electrons which propagate freely, i.e., in a potential-free space in the positive x-direction. In other words, it is assumed that no “wall,” i.e., no potential barrier (V), restricts the propagation of the electron wave.
Heat was considered to be an invisible fluid, called caloric, until late into the eighteenth century. It was believed that a hot piece of material contained more caloric than a cold one and that an object would become warmer by transferring caloric into it. In the mid-1800s, Mayer, Helmholtz, and Joule discovered independently that heat is simply a form of energy. They realized that when two bodies...
The length, L, of a rod increases with increasing temperature. Experiments have shown that in a relatively wide temperature range the linear expansion, ΔL, is proportional to the increase in temperature, ΔT. The proportionality constant is called the coefficient of linear expansion, αL. The observations can be summarized in 22.1 $$ \frac{{\Delta L}}{L} = {\alpha_L}\Delta...
We assumed in the preceding chapter that the electrons behave like particles. This working hypothesis provided us (at least for small frequencies) with equations which reproduce the optical spectra of solids reasonably well. Unfortunately, the treatment had one flaw: For calculation and interpretation of the infrared (IR) absorption we used the concept that electrons in metals are free; whereas the...
This section attempts to interpret the thermal properties of materials using atomistic concepts. In particular, an interpretation of the experimentally observed molar heat capacity at high temperatures, Cv = 25 (J/mol · K) that is, 6 (cal/mol · K), is of interest.
The most apparent properties of metals, their luster and their color, have been known to mankind since metals were known. Because of these properties, metals were already used in ancient times for mirrors and jewelry. The color was utilized 4000 years ago by the ancient Chinese as a guide to determine the composition of the melt of copper alloys: the hue of a preliminary cast indicated whether the...
We shall now make use of the conceptual ideas which we introduced in the previous chapter, i.e., we shall cast, in mathematical form, the description of an electron as a wave, as suggested by Schrödinger in 1926. All “derivations” of the Schrödinger equation start in one way or another from certain assumptions, which cause the uninitiated reader to ask the legitimate question, “Why just in this way?”...
We stated in the last chapter that different types of magnetism exist, and that they are characterized by the magnitude and the sign of the susceptibility (see Table 14.1).
The production of ferro- and ferrimagnetic materials is a large-scale operation, measured in quantity as well as in currency. (This is in contrast to the products of the computer industry, where the price of the material that goes into a chip is a minute fraction of the device fabrication cost.) As an example, the annual sales of so-called electrical steel, used for electromotors and similar devices,...
In the preceding chapter, the optical constants and their relationship to electrical constants were introduced by employing the “continuum theory.” The continuum theory considers only macroscopic quantities and interrelates experimental data. No assumptions are made about the structure of matter when formulating equations. Thus, the conclusions which have been drawn from the empirical laws in Chapter...
The first observations involving electrical phenomena probably began with the study of static electricity. Thales of Miletus, a Greek philosopher, discovered around 600 BC that a piece of amber, having been rubbed with a piece of cloth, attracted feathers and other light particles. Very appropriately, the word electricity was later coined by incorporating the Greek word elektron, which means amber...
We have seen in the previous chapter that the classical electromagnetic theory is quite capable of explaining the essentials of the magnetic properties of materials. Some discrepancies between theory and experiment have come to light, however, which need to be explained. Therefore, we now refine and deepen our understanding by considering the contributions which quantum mechanics provides to magnetism...
This book is mainly concerned with the interactions of electrons with matter. Thus, the question “What is an electron?” is quite in order. Now, to our knowledge, nobody has so far seen an electron, even by using the most sophisticated equipment. We experience merely the actions of electrons, e.g., on a cathode-ray television screen or in an electron microscope. In each of these instances, the electrons...
The measurement of the optical properties of solids is simple in principle, but can be involved in practice. This is so because many bulk solids (particularly metals) are opaque, so that the measurements have to be taken in reflection. Light penetrates about 10 nm into a metal (see Table 10.1). As a consequence, the optical properties are basically measured near the surface, which is susceptible to...
Before we discuss the atomistic and quantum mechanical theories of the thermal properties of materials, we need to remind the reader on some relevant fundamental concepts and definitions which you might have been exposed to before in courses of physics and thermodynamics.
In the preceding chapters we considered essentially only one electron, which was confined to the field of the atoms of a solid. This electron was in most cases an outer, i.e., a valence, electron. However, in a solid of one cubic centimeter at least 1022 valence electrons can be found. In this section we shall describe how these electrons are distributed among the available energy levels. It is impossible...
The phenomenon of magnetism, i.e., the mutual attraction of two pieces of iron or iron ore, was surely known to the antique world. The ancient Greeks have been reported to experiment with this “mysterious” force. The designation magnetism is said to be derived from a region in Turkey which was known by the name of Magnesia and which had plenty of iron ore.
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