What is band theory?

Band theory is used to explain how metal atoms bond together and why they are such good conductors of electricity while other materials are insulators. In other words, it is a theory that explains how the metallic bond works.

In any piece of metal, like a nail or a piece of copper wire, for example, the atoms are very close together and very close to each other.

According to band theory, because of this closeness, their atomic orbitals (the place where their electrons meet) mix to form a single giant orbital that looks more like a “band” than an orbital.

When this happens, basically two bands are formed which are the Valencia Band and the Conduction Band (hence the plural in band theory).

This band is formed by the combination of the valence orbitals of each atom. These are the last orbitals that are occupied by electrons in each individual atom.

The valence band is where the electrons in a metal meet when the atoms are relaxed. That is, when they have not been excited by the application of an electric potential, for example.

Driving band

The conduction band is formed by the combination of the first unoccupied or empty orbitals of each atom. The conduction band is generally made up of pod orbitals that overlap each other laterally. This gives rise to a band that resembles a highway that passes through the space above and below the layers of atoms.

When an electron enters the conduction shell, it is said to be “delocalized” since it can move freely from one side to the other, and it is not located around any particular atom.

A useful analogy

To better understand the structure of the bands that are formed in metals, it is convenient to use some analogies.

A solid can be imagined as an apartment building in which each apartment is an atom, and the electrons found in them can be moved from one apartment to another.

In a non-conducting material , all the electrons are located around their respective atom. This is the same as saying that each apartment is closed and electrons are not free to move from one “apartment” to another (that is, from one atom to another), simply because it takes a lot of energy to open all the doors and leave.

On the other hand, in a conductive material like a metal, things are very different. The atoms are so close to each other that their orbitals (the rooms) combine with each other to form a single giant orbital. This would be like knocking down all the walls on one floor and making a single common room full of beds.

This giant room would be the equivalent of the ” valence band “, in which the electrons are found in their respective beds, but they are all in the same room. In addition to forming this room, right next to it you can get a wide corridor that the electrons can use to move from one place to another.

This large hallway represents what we call the ” conduction band .” When electrons are in the hallway, they are not located in any particular atom (they are delocalized) and they can move freely from one place to another without any problem.

Electrical conduction and band theory

Once the formation of valence and conduction bands is understood, it is easy to understand why some materials are good conductors and why others are not.

The key to electrical conduction is how difficult it is to move or excite electrons from the valence band to the conduction band.

This just depends on how close the energy levels of both bands are. Based on this energy difference, three types of materials can be distinguished:

Conductive materials

Conductive materials, such as metals, are characterized by having valence and conduction bands practically together and with almost no difference in energy between one and the other.

This means that the minimum excitation is capable of promoting the electrons of the valence layer and passing them to the conduction layer, from where they can move freely, thus conducting electricity.

Using the analogy mentioned above, this would be like saying that there is almost nothing separating the common room (the valence band) from the hallway (the conduction band). For this reason, an electron can easily reach the corridor, without any door blocking its way.

A room without walls and with many beds, is an image similar to the valence band that is formed in a metal. Electrons can easily pass from one place to another through corridors, which are equivalent to the conduction band

Non-conductive or insulating materials

What about materials like plastics or wood that don’t conduct electricity? In the cases of insulating materials, the valence band and the conduction band have very large energy differences.

This means that, to be able to take an electron from the valence shell to the conduction shell, it is necessary to invest too much energy, so these materials do not conduct electricity under normal conditions.

In the building analogy, this can be seen as electrons having to pass through many closed doors in order to get out of their rooms and into the hallway. They are literally trapped in their respective atoms.

Semiconductor materials

Between conductive and non-conductive materials we can find a third group of materials called semiconductors.

In these materials, the valence and conduction bands are not next to each other as in conductive materials, so there is an energy gap that the electrons must overcome in order to pass into the conduction band. However, this gap or difference in energy is not as high as in the case of non-conductive materials.

The energy gap between the two bands does not allow these materials to conduct electricity at low temperatures. However, when the temperature is increased, the energy of the vibrations of the atoms becomes sufficient to excite some electrons to the conduction band, so that the material can conduct electricity.

Since these materials are sometimes insulating and sometimes conductive, then they are called semiconductor materials. Some examples of these types of materials are Silicon, Gallium and Selenium.

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