Crystalline Solid State Physics

This book has been developed based on a course in basic condensed matter physics taught by the author for 5 years. Designed for a first course in condensed matter physics where the basic concepts of condensed matter physics are covered. This book is divided into 3 parts for clarity. In Part 1, the terminologies, and notions of perfect crystalline structures in 2-dimensions and in 3-dimensions are defined and elaborated. Then x-ray diffraction is discussed and how it is used to determine the structures of crystals. Next, the book discusses how crystals bind themselves together in a stable manner.

In Part 2, the book considers thermal effects on the crystal lattice which cause vibrations of the atoms about their equilibrium positions. The properties of the resulting lattice waves are derived and discussed. Then the quantum nature of these lattice waves is considered. This results in the perspective of "packets of lattice vibrational energy" called "phonons" which are treated as quasi-particles. Interactions between phonons are briefly discussed. As a vibrating lattice can store thermal energy, this leads to the heat capacity property of the lattice (under the topic of lattice thermodynamics). The experimental low temperature behaviour of the lattice heat capacity can't be explained using classical physics. Thus quantum mechanics is used with Debye's model to explain the low temperature lattice heat capacity behaviour satisfactorily.

In Part 3, the book considers the electronic properties of crystalline solids. As a crudest approximation, the electrons in a metal are treated as a free Fermi gas in an infinite 3-dimensional box. This model turns out to be able to explain the experimental behaviour of low temperature electronic heat capacity of metals. Next, to be more realistic, the periodic background crystal potential is included. This gave rise to Bloch's theorem which constrains the form of quantum mechanical wavefunction in the presence of a periodic potential. Then, under the approximation of a weak periodic crystal potential, we derive the consequence of energy gaps. These gaps break the electronic energies into bands and so this framework is also called "electronic band theory". Finally, we go into intrinsic semiconductors and derive the intrinsic carrier concentration in their conduction bands. Then the process of doping semiconductors with impurities is discussed which is for the purpose of controlling the carrier concentration and allows them to be used for technological applications.

The contents of this book are similar to many basic textbooks on condensed matter physics but this book is unique in that it has interactive features to enable students to visualise the concepts better. Many concepts in condensed matter physics can be made clearer by animation and using interactive elements but no condensed matter textbook has made use of that yet. This book hopes to be the first condensed matter course text to explore this possibility. Also, the detailed calculations given in this book allow students to learn the calculations easily and appreciate the physical implications of them. Students will not be hindered by trying to fill in missing steps in the calculations and hence lack time to understand the physical implications.