Introduction to Solid State Physics for Materials Engineers. Emil Zolotoyabko

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СКАЧАТЬ is devoted to electrical conductivity via electrons and holes in intrinsic (undoped) and doped semiconductors. In this chapter the p–n junction concept is introduced and the key phenomenon of band bending in the depletion region is analytically derived. Further, the working principles of semiconductor diodes and transistors are described, including the metal-oxide-semiconductor field-effect transistor (MOSFET).

      Chapter 7 is dedicated to contact phenomena arising at the boundary between a metal and a vacuum, as well as at the metal–semiconductor junctions (Schottky contacts). We introduce the important concept of work function and describe methods to measure it by a Kelvin probe, the photoelectric effect or angle-resolved photoemission spectroscopy (APRES). After that, thermionic emission at elevated temperatures and under electric field application is comprehensively treated, bearing in mind the upmost importance of the latter for an invention of field-emission gun.

      In Chapters 8 and 9, we discuss light (photon) interaction with materials. In Chapter 8, we describe some key issues regarding this in metals and insulators. Among them are skin effect, light reflection from metal surfaces, plasma frequency, metamaterials, and structural colors. In Chapter 9, we discuss light interaction with semiconductors. Particular topics include photovoltaics, solar cells, solid state radiation detectors, charge-coupled device (CCD), light-emitting diodes, semiconductor lasers, and photonic materials.

      The last four chapters are dedicated to cooperative (correlated) phenomena in electron and ion systems. For example, in Chapter 10, we consider superconductivity. The discussed issues include: Cooper pair formation, isotope effect, Giaever tunneling and the Josephson effect, the Meissner effect, superconductors of type I and type II, superconducting magnets, the superconducting quantum interference device (SQUID), and high temperature superconductivity.

      Chapter 11 is devoted to ferromagnetism. Sub-subjects comprise determination of atomic magnetic moments, paramagnetism and diamagnetism, the Weiss molecular field, spontaneous magnetization, exchange interaction, the Ising model, magnetic structures, the subdivision of magnetic materials into ferromagnetics, antiferromagnetics and ferrimagnetics, magnetic domains and domain walls, and giant magnetoresistance.

      Chapter 12 is called “Ferroelectricity as cooperative phenomenon.” Here we discuss the following issues: ferroelectric crystals, ferroelectric phase transitions in the framework of Landau–Ginzburg theory, dielectric permittivity near the Curie temperature, ferroelectric domains and domain walls, piezoelectric effect in ferroelectrics, and ferroelectrics-based devices.

      Other examples of cooperative phenomena in electron systems are given in Chapter 13. They include metal–insulator (Mott) transition and quantum Hall effects: integer and fractional, and topological insulators.

1 General Impact of Translational Symmetry in Crystals on Solid State Physics

      Atomic order in crystals.

      Local and translational symmetries.

      Symmetry impact on physical properties in crystals.

      Wave propagation in periodic media.

      Quasi-momentum conservation law.

      Reciprocal space.

      Wave diffraction conditions.

      Degeneracy of electron energy states at the Brillouin zone boundary.

      Diffraction of valence electrons and bandgap formation.

      In contrast to liquids or gases, atoms in a solid state, in average (over time), are located at fixed atomic positions. The thermally assisted movements around them or between them are strongly limited in space (as for thermal vibrations in potential wells) or have rather low probabilities (as for long-range atomic diffusion). According to the types of the averaged long-range atomic arrangements, all solid materials can be sub-divided into the three following classes, i.e. regular crystals, amorphous materials, and quasicrystals.

Most solid materials are regular (conventional) crystals with fully ordered and periodic atomic arrangements, which can be described by the set of translated elementary blocks (unit cells) densely covering the space with no voids. Nowadays, using the advanced characterization methods, such as high-resolution electron microscopy or scanning tunneling microscopy, it is possible to directly visualize this atomic periodicity (Figure 1.1). Due to the translational symmetry, the key phenomenon – namely, diffraction of short-wavelength quantum beams (electrons, X-rays, neutrons) – takes place. As we show in the following text, sharp diffraction peaks (or spots), which are the “visiting card” of crystalline state, are originated from the quasi-momentum (quasi-wavevector) conservation law in 3D.

In contrary, amorphous materials, being characterized by some kind of short-range ordering, do not reveal atomic order on a long range (Figure 1.2). In other words, certain correlations between atomic positions exist within a few first coordination spheres only and rapidly attenuate and disappear at longer distances. Correspondingly, diffraction patterns taken from amorphs show diffuse features only (called amorphous halo), rather than sharp diffraction peaks.

Figure 1.1 High-resolution scanning transmission electron microscopy image of atomic columns in crystalline GaSb. Cations and anions within dumbbells are separated by 0.15 nm.

Figure 1.2 Structural motifs in silicon dioxide (SiO₂): (a) – ordered atomic arrangement in crystalline quartz; (b) – disordered arrangement in amorphous silica. Large open circles and black filled circles indicate oxygen and silicon atoms, respectively.

Quasicrystals in some sense occupy a niche between crystals and amorphs. They have been discovered in the beginning of 1980s by Dan Shechtman during his studies (by electron diffraction) of the structure of rapidly solidified Al–Mn alloys. Quasicrystals can be described as fully ordered, but non-periodic arrangements of elementary blocks densely covering the space with no voids. An example of filling the 2D space in this fashion, by the so-called Penrose tiles (rhombs having smaller angles equal 18° and 72°), is shown in Figure 1.3. Amazingly that despite the lack of the long-range translational symmetry, quasicrystals, like regular crystals, also produce sharp diffraction СКАЧАТЬ