What is Fermi-Dirac Distribution Function?
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-EF)/KT
where F(E) = Probability in energy level, E,
E = energy level in which we are finding,
EF = 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> EF , F(E1) = 0 %, T = 0K (Here E1 is an energy level above fermi energy level)
E2< EF , F(E2) = 100%, T = 0K (Here E2 is the energy level below fermi energy level)
E = EF , F(EF) = 50% , T> 0K (at fermi energy)
Fermi-Dirac distribution function cannot provide the probability of fermi level at 0K. It is undefined.
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.
Table of Content
- Fermi Energy
- Fermi Level
- Fermi Energy Vs Fermi Level
- Fermi-Dirac Distribution Function
- Fermi Level in Both Semiconductors
- Intrinsic Semiconductor
- Extrinsic Semiconductor