Dear Bibek Chettri , the equation above is only valid for semiconductors and insulators. The physical reason for this behavior is that the band gap is a forbidden region in energy for the electrons (and holes). The occupation of the allowed states is given by the Fermi distribution function. Electrons are excited from the valence band to the conduction band in order to achieve electric conductivity, and this is expressed by the exponential function in the conductivity. The pre-exponential term is then related to the electron density, I.e. the number of electronto be excited from the valence to the conductance band. The you have, obtained for different materials with identical band gaps… hope this helps, Dirk