Fermi function or Fermi dirac didtribution funtion

 

Fermi function or Fermi Dirac distribution function

The probability that a particular quantum state of energy E of fermions is occupied at a particular temperature T is given by a function f (E) and is called Fermi function. 

Let a system of electrons is in thermal equilibrium at a temperature T kelvin. 

The probability f(E) of an electron occupying a particular energy level E is given by

 

 

Where f (E) is Fermi function

E_F is called Fermi energy

K is Boltzmann constant
K = 1.38 × 10 ⁻²³ J/K

Value of Boltzmann constant in eV  is K = 8.62 × 10 ⁻⁵ eV/K

T is absolute temperature

For a filled energy level f (E) = 1

For an unfilled energy level f (E) = 0

Fermi function is obeyed by Fermions

Fermions are half integer spin particles.  Example : electrons which obey Pauli’s Exclusion principle.

Application of Fermi function or Fermi Dirac distribution function

 

 

Important Formula

 

Questions

1. what is fermi funtion or fermi dirac distribution function ?
2. What is Fermi level?
3. What is Fermi energy?  
4. Define Fermi velocity.
   
5. Explain thermal equilibrium in in semiconductors.
6. write the equation for the Fermi level energy in n – type semiconductor.    
7. What is Fermi’s golden rule?
8. Discuss in detail the dependence of Fermi level on carrier concentration and temperature.
9. What do you mean by occupation probability?
10. Write the expression for the Fermi level energy in n – type semiconductor.

Numerical Problems

Important Notice : 

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