What is the Fermi Level?

In Physics, there are some topics and concepts that can cause headaches to many students. The concept of the Fermi Level can be one such topic. If you want to understand the concept of the Fermi Level, you can refer to this article. This article contains a detailed explanation of the 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 the 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 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? 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 the 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's Fermi Level at 0k.  The concept of the Fermi Level comes from Fermi-Dirac statistics. Electrons are Fermions (the particles with odd half-integral spin) and by the Pauli exclusion principle cannot exist in identical energy states. The energy level corresponds 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.


The Fermi Level can also be described as the maximum energy level of an electron at 0 Kelvin at which it can reach. Because all electrons are in the lowest energy state at absolute zero temperature, the Fermi Level falls between the valence and conduction bands. The Fermi Level can be thought of as a sea of Fermions (or electrons) above which no electrons exist due to a lack of energy at 0 Kelvin. As the solids are heated and electrons are added to or removed from them, the Fermi Level changes. 


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 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:

There is not much distinction between these two ideas. According to Wikipedia, Fermi Energy and Fermi Level are two notions that are closely connected. Fermi Energy, according to my knowledge, is the greatest occupied energy level of a system at absolute zero? Is that accurate? What is the distinction between Fermi Energy and Fermi Level, then? The highest energy band (i.e. the conduction band) is half filled in a common metal. Due to the continuity of the conduction band, electrons can be excited by the heat energy which in turn leaves the holes in the lower band. There is no thermal energy at absolute zero, thus electrons fill the band from the bottom up, with a severe cut-off at the highest occupied energy level. Fermi Energy is defined by this energy. Because thermal energy continuously excites electrons within the band at finite temperatures, there is no sharply defined highest energetic electron. The Fermi Level is the best you can accomplish when it comes to defining the energy level with a 50% chance of occupation.


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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 the 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.

Fermi Energy is defined particularly at absolute zero temperature.

The Fermi Level is defined at every temperature, not only at absolute zero temperature.

3.

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.

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 a 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, 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.


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 Fermi Energy's thermal energy kT, they are frozen out of the heat capacity.

The Fermi Conundrum

We all know that a paradox is a notion or a seemingly contradictory statement that, when analyzed, may turn out to be well-founded or true. In science, many paradoxes are difficult to resolve. The Fermi paradox, twin paradox, black hole information paradox, and Faraday paradox are all well-known paradoxes. Let us learn more about the Fermi-paradox in this article.

What Exactly is the Fermi Paradox?

The Fermi paradox is a debate about the scale and chance of intelligent life existing elsewhere in the universe other than Earth. There is no evidence that it ever existed elsewhere. Enrico Fermi, a Physicist who researched the existence of extraterrestrial civilization, was the first to investigate the Fermi paradox. He had mostly raised the following concerns: There are billions of stars that are billions of years older than the solar system, much like the Sun; There are worlds that are comparable to ours and may have evolved intelligent life; These sophisticated beings may have developed the ability to travel between galaxies.

Energy Level of Fermi

Because of Pauli's exclusion principle, which stipulates that two Fermions cannot occupy the same quantum state, this energy level exists. Due to this, each Fermion in a system with more than one has its own set of magnetic quantum numbers. The Fermi temperature can be calculated by dividing the energy of the Fermi Level by Boltzmann's constant. The temperature at which the electron's energy equals the Fermi Energy is also known as the Fermi temperature. In metal's lower energy states, it is the number of electrons present in them. 

FAQs on Fermi Level

1. What is Fermi Energy Level? Define Fermi Level.

The Fermi level is just an energy level for the collection of particles at absolute zero temperature. The Fermi level is the surface of that conductor defined at absolute zero where no electrons will have enough energy to rise above the surface.  

2. Why is the Fermi Level Important in Semiconductors?

Suppose we increase the temperature of the system from 0K to say 100K, 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 introduced the fermi Dirac distribution.

3. What is Fermi?

In physics, Fermi is a unit of measurement and is mostly used in nuclear physics. One should not confuse the Fermi energy and Fermi level with just fermi. One fermi is equal to 10-15m.

4. What is the difference between the Fermi Level and Fermi Energy?

There are a lot of differences in Fermi Level and Fermi Energy. You can define Fermi Level for any particular temperature but if you want to define Fermi Energy, you can do that only at absolute zero or when the temperature is equal to zero Kelvin. Fermi Level, on one hand, is the total energy that includes both kinetic and potential energies but Fermi Energy, on the other hand, is given by the energy difference which is usually corresponding to the kinetic energy. 

5. What are the different factors on which Fermi Level depends?

There can be various factors on which Fermi Level depends but the key factor on which Fermi Level depends very much is temperature. If you want to know the exact position of the Fermi Level concerning valence and or conduction bands, you have to consider various parameters which mainly include temperature. Some other factors on which the Fermi Level depends are the number of free electrons & holes and the effective masses of both electrons and holes.

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