# How to understand effect of increase in band gap generated away from Fermi energy on conductivity?

An example would be that when we dope Nitrogen in graphene its conductivity decreases. This can be explained through other means. But can this be explained through the change in its band structure?

• What does "generated away from Fermi energy" mean here? – Kevin J. May Nov 29 '20 at 2:12

You are right to assume that the part of the band structure relevant for electronic conductivity is the one of electrons (and holes) with energies close to the Fermi energy.

However, electronic conductivity is not determined by the electronic band structure alone. If you take the simple Drude model for the conductivity

$$\sigma = \frac{ne^2\tau}{m^*}$$

you can think of the band structure providing the effective mass $$m^*$$, but not the relaxation time $$\tau$$ in between scattering events. This scattering time can be strongly affected by doping or other imperfections in the crystal.

P.S. Strong Nitrogen doping of graphene (of the order of a few %) will also affect the band structure near the Fermi energy - see e.g. section 3.2 in this randomly chosen preprint.