Forbidden Band in a Crystal

Introduction
In a crystal, such as a semiconductor or an insulator, the energy levels of electrons are organized into bands. These bands are formed by the overlapping of atomic orbitals of neighboring atoms. The energy levels within these bands determine the behavior of electrons in the crystal. One of the bands that exist in a crystal is called the forbidden band or band gap.

Explanation
The forbidden band, also known as the band gap, is an energy range in a crystal where no electron energy levels exist. It is the region between the valence band and the conduction band. In other words, it is the energy range that separates the highest occupied energy levels from the lowest unoccupied energy levels.

Valence Band
The valence band is the band that contains the highest energy levels occupied by electrons at absolute zero temperature. These electrons are tightly bound to their respective atoms and are not able to participate in the flow of electric current. The valence band is responsible for the electrical and thermal conductivity of a material.

Conduction Band
The conduction band is the band that contains energy levels that are higher in energy than those in the valence band. Electrons in the conduction band are not bound to any particular atom and are free to move throughout the crystal. These electrons are responsible for the flow of electric current in a material.

Forbidden Band
The forbidden band, as the name suggests, does not contain any energy levels. Electrons within the crystal are not allowed to have energy levels within this band. The width of the forbidden band determines the electrical behavior of the crystal.

- In an insulator, the forbidden band is relatively large, and it requires a significant amount of energy for electrons to move from the valence band to the conduction band. This makes insulators poor conductors of electricity.
- In a semiconductor, the forbidden band is smaller compared to an insulator. At room temperature, some electrons can acquire enough thermal energy to jump from the valence band to the conduction band, allowing for some conductivity.
- In a conductor, the valence and conduction bands overlap, and electrons can easily move between the two bands. This results in excellent electrical conductivity.

Conclusion
In summary, the forbidden band, also known as the band gap, is a region in a crystal where no energy levels exist for electrons. It separates the valence band, which contains occupied energy levels, from the conduction band, which contains unoccupied energy levels. The width of the forbidden band determines the electrical properties of the crystal, with insulators having a large band gap, semiconductors having a smaller band gap, and conductors having overlapping bands.