Bloch States and Band Theory

Abstract

The topic of central interest in this book, i.e., electron transport in semiconductors, deals with the response to external forces of electrons that are able to move inside a semiconductor. Therefore, the determination of the states available to the electrons in the crystal and their energies is of fundamental importance. The knowledge of electron states in solids is essential also for the analysis of their optical properties. It is not surprising, therefore, that a great effort has been devoted in the past to develop both experimental and theoretical techniques able to yield information on this subject. The problem is not an easy one, however, owing to its many-body nature. Here, we shall review very briefly the main ideas and techniques, starting from the fundamental theorem, known in solid-state physics as Bloch theorem and in mathematical analysis as Floquet theorem. Demonstrated by mathematicians at the end of the nineteenth century, it leads to the definition of Bloch states, the basic bricks of any theoretical study of electronic properties of solids.