Introduction to Fermi energy

Fermi Band diagram In MOS Devices

Always wondered how an Nmos device functions on electron level?

 This blog will answer all your questions. Fermi energy is a quantum mechanic concept which refers to the energy difference between the highest and lowest energy state occupied by a single particle in a quantum system of non-interacting fermions at absolute zero temperature.Fermi level is the concept used to describe the top of  collection of electron energy levels at absolute zero temperature.Fermi level is “surface of sea” at absolute zero where no electrons will have enough energy to rise above  that surface. Fermi energy is the value of the Fermi level at absolute zero temperature (−273.15 °C). It can also be referred as the maximum kinetic energy an electron can attain at 0K.

So the Fermi Function gives the probability that a given available electron energy state will be occupied  at a given temperature.

                            
                                                      

Here Ef=Fermi energy

        kb=Boltzmann constant

T=Temperature

KbT=Thermal Energy

 Basic nature of this fermi function at ordinary temperatures is that  it most of the

levels upto the fermi level Ef are filled.Very few electrons have energies above

this fermi level.Thermal energy KT is approximately 0.026ev at 300K temperature

whereas fermi level is around 7ev (electron volts) for copper.By putting these

nominal values,we observe that fermi function’s value is 1 upto fermi level at

ordinary temperatures and approaches to zero above fermi level Ef.

How are the electrons distributed in the energy levels at a given temperature?

As the electrons follow pauli's exclusion principle and are indistinguishable particles. The Pauli’s exclusion principle postulates that only one fermion can occupy a single quantum state, so as the fermions are added to an energy band they fill the energy band just like water fills the bucket. In other words states with the lowest energy are filled first followed by the next higher ones.

Authors: Ruturaj Deshmukh,Dhanesh Manwani,Sukhanshu Dukare