1. FERMI DIRAC DISTRIBUTION NAME – NIKHIL KUMAR MAHESHWARI GUIDED BY : VENIKA GANJIR

2. Contents  History  Some basic concepts  Fermi statistics and Bose statistics  Postulates of Fermi particles  Fermi Dirac Distribution Function  Conclution  References

3. HISTORY :  F–D statistics was first published in 1926 by Enrico Fermi and Paul Dirac. According to Max Born, Pascual Jordan developed in 1925 the same statistics, which he called Pauli statistics, but it was not published in a timely manner. According to Dirac, it was first studied by Fermi, and Dirac called it "Fermi statistics" and the corresponding particles "fermions".Enrico FermiPaul DiracMax BornPascual JordanPauli

4. * FERMI LEVEL : Fermi level is the highest energy state occupied by electrons in a material at absolute zero temperature. * FERMI ENERGY : This is the maximum energy that an electron can have at 0K. i.e. the energy of fastest moving electron at 0K. It is given by : Ef = ½ mvf^2 * FERMI VELOCITY : It is the velocity of electron at Fermi level. * The band theory of solids gives the picture that there is a sizeable gap between the Fermi level and the conduction band of the semiconductor. At higher temperatures, a larger fraction of the electrons can bridge this gap and participate in electrical conduction

5. FERMI STATISTICS AND BOSE STATISTICS :  The wave function of a system of identical particle must be either symmetrical (Bose) or antisymmetrical (Fermi) in permutation of a particle of the particle coordinates (including spin). It means that there can be only the following two cases :  1. Fermi-Dirac Distribution  2. Bose-Einstien Distribution  The differences between the two cases are determined by the nature of particle. Particle which follow Fermi-statistics are called Fermi particles (fermions) and those which follow Bose-statistics are called Bose-particles (bosons).  Electrons, Positrons, protons, and neutrons are Fermi-particles, where as photons are bosons, Fermion has a spin ½ and boson has integral spin.

6. POSTULATES OF FERMI PARTICLE : N1N2 …………… Nn

7. FERMI DIRAC DISTRIBUTION FUNCTION(DERIVATION) :

10.  Density of states tells us how many states exist at a given energy E.  The Fermi function f(E) specifies how many of the existing states at the energy E will be filled with electrons. Whereas (1-f(E)) gives the probability that energy state E will be occupied by a hole.  The function f(E) specifies, under equilibrium conditions, the probability that an available state at an energy E will be occupied by an electron. It is a probability distribution function.

12. FERMI-DIRAC DISTRIBUTION : Consider T → 0 K

13. CLASSICAL LIMIT  For sufficiently large ε we will have (ε-μ)/kT>>1, and this limit.  This is just the Boltzmann distribution. The high-energy tail of the fermi Dirac distribution is similar to the Boltzmann distribution. The condition for the approximate validity of the Boltzmann distribution for all energies ε>=0 is that

14. FERMI DIRAC DISTRIBUTION FUNCTION :

15. REFERENCES :  Statistical Physics, F. Mandl.  Basics of Statistical Physics, H.J.W.  Wikipedia

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