# Fermi Level

## What is Fermi Level?

We know that atoms consist of n number of energy levels, the fermi level is the highest filled energy level in the energy band at zero kelvin. The Fermi level is that energy level in the energy band diagram for which the probability of occupancy (in other words we can say the presence of majority charge carriers) becomes half. The Fermi level and Fermi energy will be changing depending on the type of material. i.e., different materials will have different Fermi levels and corresponding Fermi energy.

The concept of Fermi level and the Fermi energy are the most important topics to be studied in semiconductor physics to attain a detailed understanding regarding band structure and intrinsic properties of the semiconductor. Let us have a look at a detailed explanation and information about the Fermi level and the Fermi energy.

### Fermi Energy:

Now, what is fermi energy? The Fermi energy is defined at zero kelvin, in every semiconducting material defined at zero kelvin such that the energy obtained by the electrons at this level will be maximum. Therefore, the Fermi level is defined as the energy level at which the electrons will have maximum energy or in other words, at zero kelvin there exists an energy level such that no electron will have energy more than this.

### What is Fermi Level?

So according to the Fermi energy definition, it is the highest occupied energy level of any material at absolute zero. To be more specific, all the electrons in the material will occupy the energy level at or below that material Fermi level at 0k.  The concept of the Fermi level comes from Fermi-Dirac statistics. Electrons are the fermions (the particles with odd half-integral spin) and by the Pauli exclusion principle cannot exist in identical energy states. The energy level corresponding to the Fermi energy known as the Fermi level. We have to keep in mind that the Fermi level is defined for all the temperatures, whereas the Fermi energy is defined only at the zero kelvin.

So, now the Fermi level is just the surface of that conductor defined at absolute zero, where no electrons will have enough energy to rise above the surface. The concept of Fermi energy is a crucially important concept for the understanding of the electrical and thermal properties of solids.

Now, the question arose: why do we need fermi level or fermi energy? Suppose we increase the temperature of the system by 0K to say 100K then, then some of the electrons lying below the fermi level may get excited to certain energy levels, and in order to determine the density of electrons at that temperature, we introduce the fermi Dirac distribution.

As the temperature of material increases above absolute zero, the probability of electrons existing in an energy level greater than the fermi energy increases and hence there will not be a constant highest occupied energy level.

Let us have a look at the major differences between the Fermi level and Fermi energy:

## Difference Between the Fermi Energy and the Fermi Level:

 Sl. no. Fermi Energy Fermi level 1. What is fermi energy?Fermi energy is the energy difference between the lowest and highest occupied single-particle states in the quantum system of non-interacting fermions at absolute zero temperature. What is Fermi level?According to the Fermi level definition, the Fermi level is the energy level for the collection of particles at absolute zero temperature. 2. The Fermi energy is defined particularly at absolute zero temperature. The Fermi level is defined at every temperature not only at absolute zero temperature. 3. The Fermi energy is the kinetic energy difference between the lowest and highest occupied single-electron states. The Fermi level corresponds to the total kinetic energy and potential energy of the thermodynamic system. 4. The Fermi energy of a metal is the energy difference between the Fermi level and the lowest occupied single electron state or level. The Fermi level of any metal is the energy of the highest occupied single-particle state at absolute zero temperature. 5. The Fermi energy is defined only for non-interacting fermions. The Fermi level can also be defined for the fermions in the complex interacting systems.

These are few important and key differences between the Fermi energy and the Fermi level. One should not confuse the concept of the Fermi level and Fermi energy.

### Did You Know:

In metals, the Fermi energy lets us understand information about the velocities of the electrons which participate in ordinary electrical conduction. The total amount of energy that can be given to an electron in such conduction processes is on the order of micro-electron volts, thus only those electrons very close to the Fermi energy can participate. The Fermi velocity of these conduction electrons can be estimated from the Fermi energy.

The Fermi energy is crucial in understanding why electrons do not contribute substantially to the specific heat of solids at ordinary temperatures, despite being major contributors to thermal and electrical conductivity. Since only a small percentage of electrons in a metal are within the Fermi energy's thermal energy kT, they are frozen out of the heat capacity.