Fermi Level In Semiconductors

The Fermi Level is the maximum energy point that an electron could reach at absolute zero temperature. Because all electrons are in the lowest energy level at 0 K, the Fermi level falls between the valence and conduction bands. The Fermi level can be thought of as a sea of electrons above which no electrons exist due to a lack of energy at 0 Kelvin. As the solids are heated, and electrons are supplied to or removed from them, the Fermi level changes. Fermi level & Fermi energy are commonly used interchangeably and might be confusing, and they are not the same at other temperatures.

Fermi level

The Fermi-Dirac distribution describes the electrons that occupy the orbits, and the distribution takes the form of 1/{1+exp[(E−u)/KT]}. The energy of a system is E, the fermi level is u, the Boltzmann constant is K, and the temperature is T. At various energies, the Fermi-Dirac distribution compensates for the density level. E/u=1 and KT=u are the Fermi levels. The density n equals 1/2 whenever the system is at the Fermi level. If the Fermi level is raised high enough, a portion of the tail will migrate to a conduction band. As a result, the electron would have a simpler transition to the conduction band, increasing conductivity.

Valence band and conduction band both are types of band energy. We can differentiate the valence band and conduction band as follows; 

Valence Band

A Valence band is an energy band consisting of valence electrons in an atomic structure’s outermost shell. These free electrons travel between the valence band and conduction band when given enough energy, resulting in conductivity. In the energy level diagram, it is at a lower energy level than that of the conduction band and is represented as VB. The prohibited energy gap is the amount of energy that separates these two bands. This valence bandgap is determined by the type of material, which is either a conductor, an insulator, or a semiconductor.

Conduction Band

A conduction band is an energy band made up of free electrons and is responsible for conduction. As a result, this band’s name was chosen. To facilitate conduction, electrons transported out of the valence band by an external force are relocated to a higher energy band. A conduction band exists just above the Fermi energy level, indicating that it is in a higher energy state. As a result, electrons take a substantial amount of exciting state to reach the conduction band, resulting in electric current. Its abbreviation is CB, and it permits electrons to travel within it freely.

Energy Band or Band Energy

According to the energy band or band energy definition, several atoms inside a crystal stone can be nearer together, and many electrons can interact. Changes in the energy levels of electrons within their shell will cause them to shift their energy levels. The energy band’s most distinguishing feature is that electron energy levels in electronics remain stable throughout a large frequency range. As a result, an atom’s energy level in the valence and conduction bands will change.

According to Bohr’s hypothesis, each atom’s shell has a varying quantity of electricity at different levels. This theory is primarily concerned with electron interaction between the internally and externally shells. According to the notion of band energy, the band energy is divided into three groups, including the following.

• Valence Band
• Forbidden Gap
• Conduction Band

Theory of Energy Bands

When two isolated charges are placed near together, the electrons inside the outermost orbit sense a strong attraction from the nearest or adjacent atomic nucleus. As a result, electron energies would not be equal, so that electron energy levels would be changed to a value more or lower than the electron’s initial energy level. In contrast, the energy of interior orbit electrons is stable in the presence of adjacent atoms. Electrons in the same orbit have different energy levels. The phrase “energy band” refers to how these varied energy levels are grouped.

Conclusion

At absolute zero temperature, the topmost of a collection of electron energy levels is the “Fermi level.” Fermi-Dirac statistics inspired this concept. Because electrons are fermions, they cannot exist in equivalent energy states. So they pack into the lowest accessible energy states at absolute zero, forming a “Fermi sea” of electron energy levels. At absolute zero, the Fermi level is indeed the sea’s surface where no electrons have just enough energy to climb beyond the surface. The orbital occupancy of solid materials like metals can be determined using an estimation based on crystal structures.