Band Theory

Metals conduct electricity with the help of valence electrons, which are present in the metal. The atomic orbitals or electron cloud of metals have the same energy, which combines to generate molecular orbitals whose energies are closer to one another, resulting in the formation of the ‘band’ of metals. Electrons can flow under the influence of an applied or exerted electric field with little effort if the band is partially filled or overlaps with another high energy-free (unoccupied C.B. i.e. conduction band). In this condition, the electrons can flow with little effort under the influence of an applied or exerted electric field, resulting in high conductivity. So, for example, sodium is used as an example in this section (Na).

Sodium’s atomic or electronic configuration is “1s2, 2s2, 2p6, 3s1.” Its chemical symbol is Na. One unpaired electron can be found in the 3s orbital of the atom Na. Because of this, the three-electron-valence orbitals of Na are overlapping with this type of orbital, which has the same energy as that of molecular orbitals in the creation of molecules.

Atomic orbitals continue to unite in a similar manner throughout the process, resulting in the formation of a band. The “energy spread” of this band is determined by the energy difference that exists between the highest energy “antibonding orbital” and the strongest restrained “bonding orbital” in the band.

When the energy band gap between the conduction and valence bands is sufficiently enough, the electrons are unable to make the transition from the valence band to the conduction band in a variety of circumstances. They are similar to these compounds in that they have significantly reduced or no conductivity. For example, in glass, when the energy band gap between the conduction and valence bands is small in size, a few electrons may be able to make the transition from the valence band to the conduction band, resulting in a little amount of conductivity being displayed. Semiconductors are a class of compounds that fall under this category. For example: Si, Ge (Silicon and Germanium respectively).

Band theory of semiconductors : 

Semiconductors are defined as having conductivity that is intermediate between that of an insulator and that of a conductor. Because of this feature, semiconductors are extremely widespread in everyday electronic devices because they are less likely to short circuit than conductors are. The fact that they have a tiny band gap contributes to their distinctive conductivity. Short circuits are prevented by the presence of a band gap because electrons are not continually in the conduction band. In order for the solid to have some conductivity, it must have a strong enough flow of electrons from the valence to conduction bands. A small band gap allows for this to happen.

Electrons in the conduction band are no longer bound by the nuclear charge of the atom and are free to move freely around the band as a result of this. In this case, the electron is referred to be a negative charge carrier since its presence in this band results in electrical conductivity of the material when it is free to move. As soon as the electron exits the valence band, the state changes to that of a positive charge carrier, also known as a hole.

Intrinsic Semiconductors are pure semiconductors whose properties are wholly determined by the nature of the substance in which they are made. The number of electrons in the conduction band is the same as the number of holes in the valence band in this case. These semiconductors are also referred to as i-type semiconductors.

Extrinsic Semiconductors are impure semiconductors that have been “doped” in order to increase their conductivity and conductivity of electricity. Extrinsic semiconductors are classified into two categories: p-type and n-type. In order to extract electrons from the valence band, a “dopant” atom is introduced into the lattice structure. This atom is referred to as an acceptor in the scientific community. Eventually, as the number of acceptors in the lattice increases, the number of holes begins to outnumber the number of negative charge carriers, resulting in a p-type (positive-charge-carrier) semiconductor being formed. In N-type semiconductors, there are a huge number of donors, also known as “dopant” atoms, which are responsible for donating electrons to the conduction band.

Band theory of a metal : 

According to band theory in solid-state physics, electron states in solids with energy values that are restricted to a narrow range are described. Everything around an electron in a solid affects how it behaves (and hence how much energy it has). A free electron, on the other hand, can have any amount of energy at any time. In a solid, the range of electron energies permissible in a material is referred to as the “allowable bands.”. Electrons in a solid are not allowed to have the energies in certain ranges between two such permissible bands, which are referred to as “forbidden bands.” Solid-state electronics technology is based on the band theory, which explains many of the electrical and thermal properties of solids. An atom’s authorized energy levels (or energy levels) are directly related to the band of allowable energies that can exist in a solid.

There is a valence band in solids formed by the accumulation of numerous electrons from individual atoms, which is caused by quantum mechanical effects on the discrete energy levels. Additionally, the conduction band, a band of typically empty levels, extends from the empty states of every individual atom in existence. Electrons in a solid can move from one energy level in a band to another in the same band or another band, often crossing a prohibited energy gap, just like electrons in an individual atom can move from one empty energy level to another.

Energy gap in band theory : 

The prohibited gap is the space between the valence band and the conduction band. The prohibited gap, as its name implies, is devoid of energy, and therefore no electrons can remain there. The valence band electrons are firmly bonded to the nucleus if the forbidden energy gap is larger. In order to close the forbidden energy gap, we need some external energy.

Conduction, valence, and prohibited energy gaps are shown in the diagram below.

Conclusion : 

Metals conduct electricity with the help of valence electrons, which are present in the metal. The atomic orbitals or electron cloud of metals have the same energy, which combines to generate molecular orbitals whose energies are closer to one another, resulting in the formation of the ‘band’ of metals.Semiconductors are defined as having conductivity that is intermediate between that of an insulator and that of a conductor. Because of this feature, semiconductors are extremely widespread in everyday electronic devices because they are less likely to short circuit than conductors are.