Energy Bands

Introduction

In solid state physics, energy bands are ranges of energy that an electron within a solid may have and are based on the energies of atomic orbitals. The concept of energy bands and band gaps is a central concept that helps explain the electronic properties of solids, such as conductors, insulators, and semiconductors.

Atomic Orbitals and Energy Levels

In isolated atoms, electrons occupy distinct atomic orbitals, each with a different energy level. When atoms come together to form a solid, the energy levels of the atomic orbitals overlap, resulting in the formation of energy bands.

Band Theory

Band theory describes the behavior of electrons in solids by postulating the existence of energy bands. It extends the concept of the molecular orbital theory from individual molecules to solids, resulting in the formation of bands of allowed energy levels.

Band Structure

The band structure of a solid describes the ranges of energy that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it may not have (called band gaps or forbidden bands).

gives the energy of an electron with wave vector .

Band Gap

The band gap is the energy difference between the top of the valence band (highest range of electron energies in which electrons are normally present at absolute zero temperature) and the bottom of the conduction band (lowest range of vacant electronic states). Materials with a small band gap are semiconductors, while those with a larger band gap are insulators.

Conductors, Insulators, and Semiconductors

The behavior of a solid as a conductor, insulator, or semiconductor is largely determined by its band structure. In conductors, the valence band and conduction band overlap, so electrons can flow freely. In insulators, there is a large band gap, so very little electrical current can flow. In semiconductors, the band gap is small enough that some electrons can jump from the valence band to the conduction band and carry current.

Conclusion

The concept of energy bands is fundamental in understanding the electrical and optical properties of solids. It is a central topic in solid state physics and materials science, and is critical to the design and operation of many electronic and optical devices, including diodes, transistors, and lasers.

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