Band Theory of Conductors

Band theory is derived from the theory of molecular orbitals and is based on quantum mechanics. When several atoms are combined to form a molecule, their atomic orbitals combine to form a layer of molecular orbitals, each with a different energy. The energy levels in the giant molecule are so close that they can be considered a continuum. Even though the different atomic orbitals interact with one another, they do not mix. They instead form a layer. Because there is a difference in energy in the same orbital of another atom, the same atomic orbital “n” combines to form “n” molecular orbit, forming a layer. The continuous band refers to these continuous layers of energy levels. The difference in energy levels is referred to as the energy gap or bandgap. The energy bands are close together, and the two uppermost bands are the valence band and the conduction band.

Overview

Plotting the available energies for electrons in the materials is a useful way to visualise the difference between conductors, insulators, and semiconductors. The available energy states form bands rather than discrete energies as in the case of free atoms. The presence or absence of electrons in the conduction band is critical to the conduction process. In insulators, electrons in the valence band are separated from the conduction band by a large gap; in conductors such as metals, the valence band overlaps the conduction band; and in semiconductors, the gap between the valence and conduction bands is small enough that thermal or other excitations can bridge the gap. With that kind of a small gap, the presence of a small percentage of a doping material can dramatically increase conductivity.

The electrons in the valence band have lower energy levels and are referred to as valence electrons. The innermost electrons in an atom are much less attracted by neighbouring atoms and have discrete energy levels. We can say that the conduction band is empty in a semiconductor. If enough energy is applied, electrons in the valence band will jump to the conduction band because the energy gap between the valence and conduction bands in a semiconductor is smaller. Doping can enhance the phenomenon of electrons jumping to the conduction band. Doping is the addition of impurities such as intrinsic material at the junction or gap between the conduction and valence bands. It closes the gap by allowing holes and electrons to pass through.

Band theory of solids

The band theory of solids is a conceptual model that explains the states of electrons in solid materials that can only have energy values within certain ranges. The quantum state that an electron takes inside a metal solid is described by the band theory of solids. Every molecule contains a number of discrete energy levels. The behaviour of electrons within a molecule is well explained by band theory. Band Theory arose from scientific knowledge gained during the quantum revolution.

Following Pauli’s exclusion principle, electrons in atoms are filled in their respective energy orbits. A molecular orbit is formed when two atomic orbitals combine to form a molecular orbit with two distinct energy levels. 1023 stacked up lines confined in a tiny space would resemble a band in solids. As a result, an energy continuum known as energy bands is formed. By plotting available energies for an electron in a material, band theory helps to visualise the difference between a conductor, a semiconductor, and an insulator.

There are many energy bands in solid band theory, but the three most important energy bands in solids are as follows:

• Valence Band: The valence band is the energy band that consists of valence electron energy levels. The valence band exists beneath the conduction band, and the electrons in this band are loosely bound to the atom’s nucleus.
• Conduction Band: The conduction band is the energy band that consists of free electron energy levels. External energy must be applied in order for valence electrons to be pushed into the conduction band and become free.
• Forbidden Band: The forbidden band, also known as the forbidden gap, is the energy gap between the valence band and the conduction band. The electrical conductivity of a solid is determined by the forbidden gap as well as the materials’ classification as conductors, semiconductors, or insulators.

If you only have one atom or if you have gas. Atoms in gas are far apart/infinitely far apart; we can treat them as single atoms. Every atom in this system has a discrete energy level; if an electron wants to move from one level to another, it must jump because no continuous energy is available (It is similar to steps).

As atoms come closer together and eventually form a solid, they form an energy continuum, which we call a band. The available energy levels are constant within the bands. As a result, it comes as no surprise that the name of this theory is “The band theory of solids.”

Band theory of conductors

The difference in conductivity is also affected by temperature. When the temperature rises, the atoms in the metal move even faster, causing electrons to be forced or strained in their motions or movements. As a result, resistance grows. (Au) Gold and (Ag) Silver are the best conductors of electricity, but they are used infrequently due to their high cost (like gold). As a result, the alternative components used in microchips in semiconductors are (Al) Aluminium and (Cu) Copper.

Metals like copper (Cu) and aluminium (Al) have no forbidden gap resentment between their conduction and valence bands.

The valence band and conduction band overlap here. As a result, even at room temperature, a large number of electrons are available for conduction.

As a result of the use of any extra or additional energy, these metal types have a large number of free electrons and are thus known as good conductors.

In such a conductor, either the valence band is not completely filled with electrons or the “filled valence band” overlaps with the vacant conduction band.

In general, both states occur concurrently, so electrons can move within the partially filled (V.B) valence band or within the bands that overlap.

In a conductor, there is no band gap between the conduction and valence bands.

In the scenario of a conductor, the band occupied by the final energy levels is only partially filled. According to “Pauli’s exclusion principle,” the lowest levels are occupied one at a time by the possible electrons.

This leaves an unoccupied portion of the band known as the conduction band.

Electrons move freely in the conduction band, which is partially filled in the valence band.

At absolute zero temperature, electrons occupy the topmost energy level in the partially filled conduction band, which is referred to as the “Fermi level,” and the equivalent energy is referred to as the “Fermi energy.”

Band theory of conductors, semiconductors and insulators

There are no band gaps between the valence and conduction bands in a conductor. The conduction and valence bands partially overlap in some metals. This means that electrons can freely move between the valence and conduction bands.

Only a portion of the conduction band is filled. This means that there are places for electrons to move. Electrons from the valence band are free to move when they enter the conduction band. This enables conduction.

The gap between the valence band and the conduction band is smaller in a semiconductor. There is enough energy available at room temperature to move some electrons from the valence band into the conduction band. This allows for some conduction to occur.

A semiconductor’s conductivity increases as temperature rises because more electrons have enough energy to move into the conduction band.

The valence band and conduction band of an insulator are separated by a large gap. Because no electrons can move up to the conduction band, the valence band is full. As a result, the conduction band is completely empty.

Only electrons in a conduction band can move easily, so because an insulator’s conduction band lacks electrons, the material cannot conduct.

FAQ’s

What is the band theory of solids?

The band theory of solids is a conceptual model that describes the states of electrons in solid materials that can only have energy values within certain ranges.

How do you explain solid categorization on the basis of band theory?

Solids can be classified as conductors, insulators, or semiconductors based on the distribution of electron energies in each atom. In a semiconductor or insulator, however, there is a gap between the bottom of the conduction band and the top of the valence band.

What do you mean by a forbidden gap as used in the band theory?

The forbidden energy gap that exists between the valence and conduct bands. It is considered as the distance between the valence and conduction bands. If this gap is larger, it indicates that valence band electrons are tightly bound to the nucleus.