Band Theory of Solids

In solid-state physics, band theory is a theoretical model that describes the states of electrons in solid materials that can only have energy values within certain ranges. The behaviour of an electron (and thus its energy) in a solid is influenced by the behaviour of all other particles in the vicinity. This is in stark contrast to how an electron behaves in free space, where it can have any energy. The ranges of allowable electron energies in a solid are referred to as allowed bands. Permitted bands are energy ranges between two allowed bands in which electrons within the solid are not allowed to have these energies.

Band Theory of Solids

The band theory of solids differs from other theories in that the atoms are arranged in close proximity to one another. The energy levels of the outermost orbital electrons are changed as a result. The energy level of the innermost electrons, on the other hand, is unaffected by the nearby atoms. It’s a hypothesis that describes how an electron takes on a quantum state inside a metal solid. Every molecule has a number of distinct energy levels. This theory explains how electrons act inside a molecule in great detail. Electrons in atoms complete their respective energy orbits according to Pauli’s exclusion principle. Two atomic orbitals unite to generate a molecular orbit with two distinct energy levels in molecules.

Moreover, 1023 stacked lines contained in a small space will appear as a band in solids. As a result, it forms an energy continuum known as energy bands. With this theory, we can visualise all of the accessible energies for electrons in materials, which is a highly useful way of showing the difference between conductors, insulators, and semiconductors.

As a result, instead of discrete energies like those found in unbound atoms, the possible energy levels are organised into bands. There are multiple energy bands in solids’ in-band theory. The following are the most important energy bands in solids i.e:

Valence Band

The valence band is the energy band that contains the energy levels of valence electrons. This band can be found beneath the conduction band. In addition, the electrons in this band are tightly bound to the nucleus of the atom and are not free to move.

Conduction Band

This energy band contains the energy level of unbound electrons. External energy must be applied in such a way that the valence electrons push to the conduction band and become free in order for electrons to be free.

Forbidden Band

This is the energy difference between the valence band and the conduction band. This is also known as the forbidden gap. The prohibited gap is used to calculate a solid’s electrical conductivity. Furthermore, we can classify the materials as conductors, semiconductors, or insulators.

Energy band

Atoms that are close to each other due to changes in the energy levels of electrons within their shell are referred to as energy bands. Molecules in solids are structured in such a way that atoms tend to travel into the orbits of the atoms closest to them. As a result, when atoms collide, electron orbits overlap. Several bands of energy levels are produced by combining atoms in the solid state. Energy Bands are the names given to these energy levels.

Formation of energy band

Molecules in gaseous substances are grouped in such a way that they are not in close proximity to one another. They are closer to one another when they are in liquid substances. In a single atom, the electrons in each orbit have a precise amount of energy. All of the atoms in solids are densely packed together. Because of the surrounding atoms, this has an impact on the energy level of electrons in outer orbit. When two solitary atoms are brought together, the electrons in one of the atoms’ outer orbits are pushed by the atom closer to it. The electron energies alter as a result of this action. This implies that the energy levels will be different. The electrons’ value is modified to a higher or lower energy level than the electron’s original energy level.

Every time, the energy levels of electrons in the same orbit are different. The energy band is generated when these various energy levels are grouped together. Atoms that are closer to electrons in inner orbits have no effect on their energy levels.

Conclusion

In solid-state physics, band theory is a theoretical model that describes the states of electrons in solid materials that can only have energy values within certain ranges. The band theory of solids differs from other theories in that the atoms are arranged in close proximity to one another. This theory explains how electrons act inside a molecule in great detail. Two atomic orbitals unite to generate a molecular orbit with two distinct energy levels in molecules. The valence band is the energy band that contains the energy levels of valence electrons.