Fermi Energy

Bookmark added to your notes.
View Notes

What is Fermi Energy?

Energy might have various forms like light energy, electrical energy, heat energy, thermal energy, etc. when it comes to explaining terms like atoms and molecules. This fundamental concept of energy gets more complicated in quantum physics. In this branch of Physics, we observe that scientists explain the concept of what is fermi energy. It refers to the energy at the highest occupied quantum state at an absolute zero temperature in a system of fermions. To understand what is meant by Fermi energy is crucially important as it helps to explain the electrical and thermal properties of the solid. 

What is Meant by Fermi Energy?

Physicist Enrico Fermi is the one who explained what is the Fermi energy, and the term was coined after his name. The measure of the energy of the least tightly confined electrons within a solid defines what is fermi level. The thermal and the electrical properties of the solid are determined through this concept. The concept of what is fermi energy is described below in simple words.

What do we mean by the Fermi energy? In quantum mechanics, it usually brings the energy difference between the highest and lowest occupied single-particle states of non-interacting fermions in a quantum system at absolute zero temperature. At an absolute zero temperature, the value of the Fermi level calculation (−273.15 °C) is called the Fermi energy. This is the highest kinetic energy an electron can achieve at 0K, and this also states what is Fermi level energy. The Fermi energy remains constant for every solid. 

(Image to be added soon)

Calculating Fermi Energy

For calculating the Fermi energy of a system, we need to categorize the states having equal energy into sets and organize them in increasing order of energy. The particles have to be added one at a time, slowly filling up the empty quantum states with the lowest energy. After all the particles are arranged accordingly, the highest occupied state’s energy is called the Fermi energy. Despite the extraction of all potential energy from the metal through cooling near absolute zero temperature (0 Kelvin), the electrons still move freely in the metal. The quickest ones travel at a velocity corresponding to a kinetic energy equal to a Fermi energy. 

What is Fermi level and Fermi Energy? 

The idea of what is fermi level is the same as the fermi energy at absolute zero temperature. Both these terms are often used interchangeably, and this seems to create confusion. Though they are the same at absolute zero temperature, they differ at other temperatures. 

What Do You Mean by Fermi Level?

Fermi level is the highest energy level that an electron obtains at absolute zero temperature. The Fermi level is the state between the conduction band and valence band because at absolute zero temperature the electrons remain in the lowest energy state. At 0 Kelvin there is a lack of sufficient energy, and so the Fermi level can be regarded as a sea of fermions or electrons above which no electrons subsist. When the solid begins to warm up, there is an alteration in the fermi level as electrons are eliminated or added from the solid. 

Did You Know?

The Band of Solid Theory helps to explain the quantum state that an electron attains inside a solid metal. Each molecule is made up of different discrete energy levels and how an electron functions within a molecule is described appropriately in this theory. Fermi level is an important part of this theory which states about the top of the available electron energy levels at low temperatures. The position of the Fermi level for the conduction band is a vital parameter in determining the electrical properties. 

FAQ (Frequently Asked Questions)

1. What is the Fermi Energy Level?

To understand what is fermi energy level and its existence, we have to know Pauli’s exclusion principle. It states that two fermions cannot have a similar quantum state, and this is the reason for the existence of this energy. In case, a system has more than one fermion; every fermion will have an individual set of magnetic quantum numbers connected with it. The Fermi temperature is represented as a Fermi energy level divided by Boltzmann's constant. In other words, the Fermi energy level is fermi temperature multiplied by Boltzmann’s constant. At this temperature, the energy of the electron is equal to the Fermi energy. It measures the electrons in its lowest state of energy in metal. 

2. What are the Applications of Fermi Energy?

We know what is meant by fermi energy, and its concept is important in the study of condensed matter physics and quantum mechanics. Some of the applications of Fermi energy are listed below.

  • It is used in insulators and semiconductors. 

  • Its theory is used in the description of metals, insulators, and semiconductors. 

  • Fermi energy is used to explain and determine the thermal and electrical characteristics of a solid. 

  • Fermi energy is crucial in nuclear physics to describe the stability of white dwarfs. These are the stars that have a comparable mass like the Sun, but the radius is about a hundredth of it.