Conductivity

The reciprocal of $\rho$ (resistivity) is the conductivity $\sigma$, measured in $(\Omega m{)}^{-1}=S\cdot m^{-1}$. Analogously we also have the conductance as the reciprocal of the resistance.

$$\vec{J}=\sigma \vec{E}$$

For a semiconductor, the conductivity is given by:

$$\sigma =N_{p}e{\mu }_p+N_{n}e{\mu }_n$$

For a good conductor, $N_p{\mu }_p\ll N_n{\mu }_n$, and the above reduces down to:

$$\sigma =-{\rho }_{vn}{\mu }_n=N_n{\mu }_{n}e$$