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 -23 J/K Or K=8.62×10 -5 eV/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.
Solid State Electronic Devices Theory