The band theory of solids is a modification of classical electrostatics where every molecule was said to have discreet energy levels associated with it. Electrons occupied these energy levels. Electrons with high energy associated with them occupied lower levels and were considered non-conducting. Electrons with low energy associated with them occupied higher levels and were considered responsible for the conduction of electricity in solids.
The band theory modified this approach. In solids, the molecules are so closely packed together that the energy levels of molecules end up overlapping each other. Therefore, in place of discreet energy levels, a series of continuous bands are formed. These bands are the valence band and the conduction band.
The valence band is formed by overlapping all the energy levels in the valence shell of a molecule. The valence shell is the outermost shell, where the electrons farthest away from the nucleus are present. They are still attracted to the nucleus by the nuclear forces. They are completely filled in most of the cases. It is important to note that the valence band consists of electrons having the highest occupied energy.
Some electrons are so loosely attached to the nucleus that they break free from them. These electrons are more attracted to other molecules. These wandering electrons are responsible for the creation of the conduction band. The electron occupying conduction band are responsible for the flow of electricity in solids. They are generally partially filled. It is important to note that the conduction band consists of electrons having the lowest occupied energy.
The energy gap between the valence and the conduction band is called the forbidden energy gap. The magnitude of energy required to push an electron from the valence band to the conduction band is called the forbidden energy. For a material to start conducting, the conduction band should have plenty of electrons present in them.
If the forbidden energy gap is too high, it means that the nucleus tightly holds the valence electrons. Some amount of external energy is required to push the electrons from the valence bands to the conduction band.
Based on the forbidden energy gap, materials can be divided into conductors, insulators and semiconductors.
According to the band theory of solids, conductors are defined as the materials for which the valence and the conduction bands overlap with each other. It means that the forbidden energy gap is zero. Conductors have many electrons present in their conduction band. This makes it very easy for conductors to conduct electricity.
If the voltage across a conductor is increased even slightly, the corresponding change in the current flow is large. Also, holes are not formed by conductors, as the electrons are sufficient to conduct electricity.
Insulators are materials that have a very high forbidden energy gap. The energy gap in such materials is as high as 9 eV (electron volts). The high energy gap means that there are no electrons present in the conduction band to conduct electricity. This makes them bad conductors and is instead called insulators.
Even if the voltage across a conductor is increased by a large magnitude, the corresponding change in the current flow is insignificant. However, if some insulators are heated, they may become partially conducting. The energy gained from thermal energy is absorbed by the electrons to jump from the valence band to the conduction band.
Semiconductors are materials for which the forbidden energy gap lies around 1.1 eV. Semiconductors are neither good conductors nor good insulators. To make them conductors, a small amount of energy is needed. Semiconductors conduct electricity with the help of the formation of holes. This means that the electricity flows in the opposite direction as that of the conductor. A semiconductor's conductivity can be increased by mixing foreign materials with them, which help in the formation of even more holes. This process is called doping.
A semiconductor is an insulator at 0K. However, at room temperature, the conduction band of the semiconductor is slightly filled. This is because the forbidden energy gap is small, and the thermal energy at room temperature is enough to push the electrons from the valence band to the conduction band.
Semiconductors are the backbone of our hardware industry. Semiconductors are used to manufacture all the microprocessors that we use in our devices. The microprocessors of today are small enough to fit the tip of a pen.