By increasing the temperature, the specific resistance of a conductor and a semiconductor respectively

The resistivity $ρ$ of a material is given by $ρ = \frac{m}{ne^2\tau}$, where $m$ represents electron mass, $n$ the charge carrier density, $e$ the electron charge, and $\tau$ the relaxation time.

For conductors, $n$ remains nearly constant with temperature. Increased thermal agitation reduces $\tau$ due to more frequent electron-lattice collisions. Since $\tau$ decreases while $n$ is stable, resistivity increases.

For semiconductors, $n$ grows exponentially with temperature as more electrons enter the conduction band. Although $\tau$ may decrease slightly due to scattering, the dominant increase in $n$ causes resistivity to decrease significantly.

The resistivity of a conductor increases with temperature while that of a semiconductor decreases.