Emil Zolotoyabko - Introduction to Solid State Physics for Materials Engineers

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Emil Zolotoyabko

Author

Professor Emil ZolotoyabkoTechnion - Israel Institute of Technology Department of Materials Science and Engineering Technion City 32000 Haifa Israel

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Print ISBN:978-3-527-34884-8 ePDF ISBN:978-3-527-83158-6 ePub ISBN:978-3-527-83159-3

To My Wife Roza With the Deepest Feeling of Gratitude for Her Life-Long Love, Support, and Assistance

Powerful personal computers and smart phones, huge flat TV screens and bright shining lights in our streets and city squares, immense fields of solar cells providing clean electrical energy, infrared imaging and laser technologies, strong superconducting magnets used in particle accelerators and medical devices for magnetic resonance imaging (MRI) – all these and many other things surrounding us are the outcome of discoveries and inventions made during the development of solid state physics. It is a rather young branch of science which began to advance only at the beginning of twentieth century. Though, as we see, its impact on society is tremendous and continues to grow with time. For this reason, learning solid state physics is obligatory for materials scientists and engineers.

There exist many excellent solid-state physics textbooks. Some of these, however, especially general books written by theoreticians for physicists, are difficult for materials engineers to use because of the latter's insufficient knowledge in advanced quantum mechanics. Further, these books pay much less attention to key applications (new materials and devices). In contrast, more specialized manuscripts written by experts in specific fields do not provide a big picture since they mostly deal with practically important issues with less emphasis on basic ideas.

Very few books have tried to fill this gap. One of the best, in my opinion, is “Intermediate quantum theory of crystalline solids” by Alexander Animalu from MIT. It was published, however, in 1977, and since then many new branches of solid state physics have been developed, such as high-temperature superconductivity, giant magnetoresistance, photovoltaics, graphene, Mott metal-insulator transitions, quantum Hall effects, topological insulators, etc. All these, as well as traditional classical issues, are described in the present book together with the most important applications such as MOSFET transistors, permanent and superconducting magnets, thermoelectric materials, solar cells and light-emitting diodes, metamaterials, photonic materials, magnetic and ferroelectric memories, SQUID, infrared detectors, and CCD.

To be able to read this book, it is enough to have very basic knowledge of mechanics, thermodynamics, electricity and magnetism, quantum mechanics, plus a little familiarity with statistical physics. More complicated issues or those that could be omitted during a first reading will be found in the Appendices.

Mathematical tools are restricted by simple differential equations, vector algebra and a bit of tensors (matrices), which all are familiar to materials students.

The book comprises 13 chapters, which are used as the basis for 13 lectures of the one-semester solid-state physics course delivered in the Department of Materials Science and Engineering at the Technion-Israel Institute of Technology. Before each chapter, the list of sub-subjects touched upon in it is given, which is wider than the list of numerated subsections. Certainly, not all aspects of solid-state physics are covered. For example, amorphous and highly disordered systems are not within this book's scope. This book is intended for the wide community of undergraduate and graduate students in materials science and engineering, as well as for beginners who for some reasons are interested in particular aspects of solid state physics. In summary, this book can be considered as an extended introduction to the subject, which will enable its readers to be well prepared for understanding of more advanced textbooks, if needed.

Haifa

March 2021

If we consider a crystalline state, the quintessence of solid state physics is the propagation of electron waves and acoustic waves (phonons) in a medium with translational symmetry and further interaction of electrons with phonons and photons, as well as an interaction between electrons themselves. This statement determines the structure of the present book.

The book starts with a discussion of the general impact of translational symmetry in crystals on solid state physics ( Chapter 1) and includes a brief description of crystal symmetry in real space; the interrelation between symmetry and physical properties in crystals; wave propagation in periodic media and construction of reciprocal lattices; and qualitative considerations regarding the diffraction of valence electrons on periodic lattice potential and band gap formation.

In Chapter 2, the band gap formation at the Brillouin zone boundary is quantitatively treated by solving the Schrödinger equation in periodic medium. In addition, the structure of energy bands in metals, semiconductors, and insulators is considered, including some aspects of orbital hybridization and the band structure of graphene. At the end of this chapter we discuss the concept of a Fermi surface, its measurement by different methods and its connection to electron conduction.

Chapter 3is devoted to elastic wave propagation in crystals and includes definitions of acoustic and optical phonons, and a description of the thermal properties of crystals. Here we introduce Debye temperature and Bose–Einstein statistics. Additionally, we show how to calculate the velocities of bulk acoustic waves and surface (Rayleigh) acoustic waves.

In Chapter 4, we deal with electrical conductivity in metals in the framework of classical Drude theory and performing quantum–mechanical calculations. Contributions to metal resistivity from electron scattering by phonons and lattice defects are thoroughly analyzed. Here we introduce Fermi–Dirac statistics and establish the interrelation between Fermi energy and chemical potential.