Fermi Level

As we all know, everything in this world around here is made up of atoms. Whether it may be a chalk or a big animal. Even our bodies are made up of millions of tiny particles called atoms. But have you ever thought about the question of what are atoms? What is it comprised of? Today you will get the answers to all such questions. An atom is comprised of those minute particles called protons, neutrons, and electrons. These altogether form the nucleus of an atom. I hope you are familiar with the term “nucleus”. A nucleus is located at the center of an atom in which protons and neutrons are present. There are a lot of energy levels present around the nucleus in which a large number of electrons keep revolving there. These energy levels are different and may vary for conductors, insulators, and semiconductors as a number of revolving electrons is also different in these cases. So in this article, we will dive deep into the world of science and understand the concepts of the energy levels of an atom, how electrons transit from one level to another and the energy possessed by each electron, and a lot more.

In this article, we will be going Through the Fermi level in the semiconductor, We will start our Article with what is fermi energy, and Then we will go to what is fermi level in semiconductors? After going through both the topics we will compare Fermi Energy and Fermi Level, Then we will go to Fermi-Dirac Distribution Function, Then we will go through fermi level of n-type and P-type semiconductor. At last, we will conclude our Article with Some FAQs.

Now as we discussed earlier about the atoms and electrons, we will now understand the concept of Fermi Energy. So, the free electrons in an atom is called as fermions. Fermi energy refers to the maximum Kinetic energy hold by a free electron at almost 0K temperature. In other words, we can say that the fermi energy of a system is only defined when the temperature is 0 K. No electron can achieve energy greater than fermi energy. But when the temperature is more than 0 K, the scenario changes. In this case, electrons exceed the range of fermi energy and acquire different energy states. Then there exists a level where the maximum number of electrons exist i.e fermi level (next topic). And we can also find the probability of finding electrons in other energy states with the concept of Fermi-Dirac distribution function which we will discuss in later sections.

Applications of Fermi Energy

• Substances: It is widely used in crystalline substances such as semiconductors & insulators.
• Defining properties: It is basically a characteristic to define properties of a substance.
• Electrical & Thermal conductivity: Fermi energy is used to distinguish the electrical & thermal conductivity of the solid.
• Conduction property: The concept of fermi energy can give a wide knowledge about conduction properties of substances.

Fermi level is that energy level in where there is a maximum probability of finding electron at absolute zero temperature. Now you must have been thinking that why 0 temperature! It is because at 0 K, no electron transition from one energy level to another. Whenever an electron moves from valence band, it reaches a highest energy level that is fermi level. It is the maximum level where an electron can reach which means above this level, there are no electrons present at absolute zero temperature. Fermi level exists between the valence band and the conduction band.

Fermi Level Formula can be Written as

F(E)=[Tex]\frac{1}{1+e^\frac{E-E_{F}}{KT}} [/Tex]

Their differences are shown in tabulated form:

Now, if at any energy level we want to find the probability of finding an electron, we can use the Fermi Dirac distribution function. Let us talk in brief. Now, there are two types of Quantum Particles- Fermions and boson. Boson obeys Bose Einstein distribution function but here we need to talk about fermions in detail. Fermions obey Fermi Dirac distribution function. Fermi-Dirac are the two scientists who found this useful method. If the temperature increases from 0 K then energy level also changes and then electrons move to different energy level above the fermi energy. So there we cannot find the exact position of electrons so we find the probability of finding electrons at a particular energy level E i.e P(E) through this fermi function.

Fermi-Dirac Statistics

F(E) = 1/ 1+ e^(E-E_F^)/KT

where F(E) = Probability in energy level, E,

E = energy level in which we are finding,

E_F = Fermi energy level,

K = Boltzmann’s constant = 1.38 ✖ 10^-23 J/k = 8.625 ✖ 10^-5 ev/k ,

T = absolute zero temperature.

By applying Fermi-Dirac statistics,

E1> E_F , F(E1) = 0 %, T = 0K (Here E₁ is an energy level above fermi energy level)

E2< E_F , F(E2) = 100%, T = 0K (Here E₂ is the energy level below fermi energy level)

E = E_F , F(E_F) = 50% , T> 0K (at fermi energy)

Fermi-Dirac distribution function cannot provide the probability of fermi level at 0K. It is undefined.

Semiconductors are broadly classified in two types

• Intrinsic Semiconductor
• Extrinsic Semiconductor

Pure semiconductors in which no doping is done. In these kind of semiconductors, number of electrons is equal to the number of holes. Thus, probability of finding electron in the conduction band is equal to the probability of finding holes in the valence band.

Fermi level is equidistance from valence band and conduction band.

Impure semiconductors and heavily doped. Some impurities are added to these semiconductors to change its properties or to increase the conductivity. These are further classified into two types:

• N-Type
• P-Type

In the above picture, fermi levels for both n type and p type semiconductors have been shown. In the n type semiconductors , the fermi level exists near the conduction band because maximum number of electrons moved from valence band to conduction band (fermi level is where maximum number of electrons exist ) . Whereas, in the p type semiconductors, fermi level is near the valence band because maximum number of electrons are present in the energy level of acceptor atoms.

Overall, we have discussed much about fermi energy and fermi level as it is a never ending topic. You can still get to know a lot of facts as Science has no end. But particularly from this article we came to know that there is immense use of fermi level in the world of atoms. In this article, we learnt about fermi level, fermi energy, how energy of electrons change with temperature. We also studied about finding the probability of electrons through Fermi-Dirac distribution function. We read about fermi level in both types of semiconductors i.e intrinsic as well as extrinsic semiconductors. We came across a lot of diagrams making your process of learning easier. So that’s all guys!! Keep studying Beginner.

What is doping?

Doping is the introduction of impurities into intrinsic semiconductors to modify their properties.

Which are the majority charge carriers in n-type semiconductors?

Electrons are the majority charge carriers in n-type semiconductors.

What are fermions?

Half spin substances such as electrons are called as fermions.

State Pauli’s Exclusion Principle

It states that no two electrons can occupy same quantum state.

What is the weight of an electron in vacuum?

Weight of an electron in vacuum is 9.1 * 10^-31 Kg.