Probablity Distribution Function

Electrons are fermions, which satisfy the exclusion principle. So, it maintains the Fermi-Dirac distribution.

Where, K is Boltzmann’s constant.

K=1.38×10^-23J/K

Or K=8.62×10^-5eV/K

T is absolute temperature.

E_F is Fermi level.

Let, E=E_F

So that, f(E)= ½

So E_F is the Fermi energy level at which the PDF is ½ .

If T=0K the distribution takes the simple rectangular, shown in figure.