Formation of Bands in Semiconductors: Understanding Silicon and Gallium Arsenide

This lecture discusses the formation of bands in semiconductors, focusing on silicon and gallium arsenide. It begins by explaining how atoms with varying numbers of available electrons can form one-dimensional, two-dimensional, and three-dimensional structures. The instructor describes the electronic structure of silicon, highlighting its four valence electrons and the tetrahedral bonding configuration that allows for covalent bonds with adjacent atoms. The lecture also covers the characteristics of III-V semiconductors, such as gallium arsenide, and their electronic properties. The crystalline structure is examined, including the concept of unit cells and Miller indices, which are essential for understanding crystal planes. The instructor explains how the arrangement of atoms leads to the formation of valence and conduction bands, as well as the forbidden band gap. The lecture concludes with a discussion on the implications of these concepts for the behavior of electrons and phonons in crystalline materials, emphasizing the importance of band theory in semiconductor physics.