Write Fermi Dirac distribution function and explain the terms involved in it

The Fermi–Dirac distribution function gives the probability that an available energy state \(E\) is occupied by an electron at absolute temperature \(T\):

\[ f(E)=\frac{1}{1+e^{(E-E_F)/kT}} \]

Terms: \(f(E)\) = occupation probability (between 0 and 1); \(E\) = energy of the state; \(E_F\) = Fermi energy (Fermi level); \(k\) = Boltzmann constant \(=1.38\times10^{-23}\) J/K; \(T\) = absolute temperature in kelvin.

Behaviour: at \(T=0\) K, \(f(E)=1\) for \(E<E_F\) and \(f(E)=0\) for \(E>E_F\), so every state below \(E_F\) is filled and every state above it is empty. At \(T>0\) K, \(f(E_F)=\tfrac12\). So the Fermi level is the energy level whose probability of occupation is 50% at any temperature above 0 K.