Solid State Physics

Siegfried Hunklinger, Christian Enss

• Publisher: De Gruyter
• Year: 2022
• ISBN:
  9783110667080
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Condensed Matter

This highly regarded textbook provides a general introduction to solid state physics. It covers a wide range of physical phenomena occurring in solids and discusses fundamental concepts for describing them. Traditional themes are complimented by modern topics, like low dimensional systems, strongly correlated materials, nanoscale systems and non-crystalline solids, which are gaining increasing technical and scientific importance. Helpful for exam preparation are numerous exercises in all chapters.

1 Introductory Remarks

Solid state physics deals with the structure and properties of solid materials. In the simplest approximation, solids are a collection of nuclei and electrons that interact with each other via electrostatic forces. In contrast to cosmology, astrophysics or high-energy physics, where the physical laws are not completely known, in solid state physics the relevant fundamental laws are very well known. In principle, almost all the properties of solids can be derived from the Schrödinger equation. Nonetheless, since solid state physics is in no way complete, there will always be unexpected discoveries and surprises in this area of physics due to the complexity arising from the many interacting constituents.

Solid materials, as they surround us in daily life, typically have volumes of a few cubic centimeters and thus consist of or more atoms. This very large number might suggest that a quantitative description of the properties of solids is hardly possible. This is all the more true if one considers the diverse range of solid state phenomena. We thus need to explain that certain materials are conducting, others insulating that there are transparent and opaque, hard and soft, ductile and brittle solids, and that while some solids respond strongly to magnetic fields, others hardly do. However, it turns out that in many cases it is precisely the large number of atoms that enables the development of models for a quantitative description. Of course, not all properties can be treated with a single approach, since the various classes of solids, such as insulators, semiconductors, metals or superconductors, are subject to different macroscopic laws and react differently to external fields.

Once the underlying principles are known, a further, technically-important step follows, the development of new materials or components with properties tailored to specific applications. In many cases, optimized materials and their targeted modification form the basis for new technologies, impressive examples being in information and communication technology, whose development is based on a comprehensive knowledge of solid state physics. One example of the practical application of superconductivity is that of the coils used to generate high magnetic fields for magnetic resonance imaging or in future fusion reactors. Extremely small magnetic fields can be detected with magnetometers that are based on the Josephson effect with a range of uses from medical diagnostics and ground exploration in geology. Further well-known applications are semiconductor lasers, used in every living room, and semiconductor detectors, which are used in the large high-energy physics experiments.

Which fundamental concepts come into play in solid state physics? As in many areas of physics, the Schrödinger equation certainly plays a central role. We will also encounter again and again the Pauli principle which has a significant influence on many properties of solids. Furthermore, we will find that Maxwell’s equations and the concepts of thermodynamics and statistical mechanics are very important. As already mentioned, the Coulomb interaction between nuclei and electrons dominates, whereas the magnetic interaction between the building blocks in non-magnetic materials is practically insignificant. As far as the application of thermodynamics is concerned, it is very important that the solids under consideration are either in equilibrium or near enough to thermodynamic equilibrium.

While in liquids or gases the position of atoms changes over time, their spatial arrangement in solids remains largely the same. In terms of their atomic order, solids can be roughly divided into two groups: A strictly periodic sequence of the atomic building blocks is typical of ideal crystals, whereas a completely disordered arrangement of the atoms characterizes ideal amorphous solids. The structures of real solids lie somewhere between these two limits, crystals having defects in their structure, and amorphous solids exhibiting a certain amount of local order. Most of the basic treatments of solid state physics assume the periodic structure of crystals and are therefore strictly speaking only applicable to this class of materials. They will be the focus of our considerations below. However, since interest in the properties and peculiarities of complex structures and irregularly-built solids has grown strongly in recent years and theoretical concepts for the description of such systems have increasingly been developed, we also include amorphous solids in our discussion, albeit to a lesser extent.

In the solid state, atoms are to be found in local minima of the potential energy and therefore occupy well-defined positions. Further, when a single atom is deflected, all other neighboring atoms begin to vibrate since they are all coupled to each other in the solid. On the other hand, we can start by considering the collective motion of all the atoms, which can be broken down into harmonic oscillations of the entire solid. An interesting aspect is that we find that the oscillation energies and thus also the amplitudes of these normal vibrations are quantized. In analogy with the energy quantum of electromagnetic radiation being named the photon, the energy quantum of these elastic vibrations is named the phonon. These atomic vibrations have a considerable influence on the elastic, thermal, electrical and optical properties of solids and are therefore an essential component of solid state theory.

Electrons are subject to the Pauli principle which states that two or more identical fermions cannot simultaneously occupy the same quantum state within a quantum system. For multi-electron systems, this means that as the number of electrons increases, they are forced to occupy states of higher and higher energy. In solids we can roughly distinguish between core electrons in states with low energy and valence electrons in states with higher energy. The electrons in the core are relatively firmly bound and are only slightly influenced by neighboring atoms or external fields. Apart from the magnetic behavior, the characteristic properties of solids are primarily determined by the valence electrons. They originate from the - and - states of the atoms involved, participate in the interatomic bond and react sensitively to external fields.

Of course, in practice there are no perfect crystals nor perfect amorphous solids. Each crystal has defects that manifest themselves as local deviations from the rest of the structure. Defects have a strong influence on the properties of real solids. They alter the mechanical and thermal properties, increase the electrical resistance and impair the optical transparency of the materials. Examples of such defects are missing atoms in crystals or impurity atoms which are incorporated during production, or extended defects which usually also occur during sample production. With amorphous solids, the characterization of defects is much more difficult owing to their irregular structure. Unsaturated chemical bonds provide typical defects in amorphous materials held together by covalent atomic bonds and do not occur in crystals in this form. Another important consideration is that in disordered structures local rearrangements of atoms are possible which, of course, cannot take place in the ordered crystals. Unsaturated bonds and structural rearrangements crucially influence many properties of amorphous solids.

2 Bonding in Solids

In the following sections we will see that the diversity of solid state properties is based on the interplay of various factors. Clearly, the atomic properties play a crucial role, but the arrangement of the atoms and the bonds between them are at least as important. In order to gain a deeper understanding of the properties of solids, it is essential to study their structures and bonding mechanisms. Therefore, we will first take a closer look at the bonds between the atomic building blocks and then deal with the ensuing structures of solids and the methods for their determination.

2.1 Types of Bonds

In both crystalline and amorphous solids, five basic types of bonds occur differing primarily in the spatial distribution of the electrons involved in the bond. In general, however, these basic bonding types are not found in pure form, but several act in combination. The hydrogen bond, which is found in hydrogen-containing substances, is a special case. This type of bond is discussed at the end of this chapter.

An important consideration for the properties of solids is whether the valence electrons of the constituent atoms are in closed shells or not. The closed-shell case is relevant to solids consisting of molecules or noble gas atoms. Here, only the relatively weak Van der Waals force provides the binding force between the atoms or molecules. In the case of molecular crystals, we can distinguish between intramolecular and intermolecular interactions, depending on whether we are interested in the forces within or between the molecules. In ionic crystals, an electron transfer takes place between the binding partners, to create closed shells. In this case oppositely-charged ions are held together by the relatively strong Coulomb forces. Tis type of bond is known as an ionic bond .

A covalent bond is a type of bond that results from atoms sharing electron pairs in order to complete a closed common outer shell. In such bonds, two valence electrons are shared and located between the atoms involved. In many insulators or semiconductors, the atoms are held together by this mechanism. Such covalent bonds play a central role in molecular chemistry, but the treatment of this aspect would be far beyond the scope of this book.

Completely different is the metallic bond, in whic...