Some of the most important applications of quantum mechanics are in semiconductor physics and technology based on the properties of electrons in a periodic lattice of ions. This problem is discussed on the basis of the nearly-free-electron model of the crystalline solids in this chapter. In this model, the entire solid is represented by a quantum well of macroscopic dimensions. The spatially-varying electron potential due to the periodic lattice of ions inside the well is considered a perturbation on the free-electron states leading to the Bloch states and the band structure of the semiconductor. The concepts of effective mass and group velocity of the electrons and holes in the conduction and valence bands separated by an energy-gap are introduced. The electrons and holes are distributed over the available Bloch states in these bands depending on the location of the Fermi level according to Fermi statistics. The transport properties of these charge-carriers and their influence on the electrical conductivity of the semiconductor are discussed. When impurities are present, the electrical properties can be drastically altered, resulting in n-type and p-type semiconductors. The p–n junction is a key element in modern semiconductor electronic and photonic devices.

Molecular orbital picture of the valence and conduction bands of semiconductors

Atoms can be brought together to form crystalline solids through a variety of mechanisms. Most of the commonly used semiconductors are partially covalently and partially ionically bonded crystals of diamond or zincblende structure.