Residual Resistivity

The resistivity σ of the conductor is due to the scattering of free electrons within the conductor. This scattering of electrons from positive ions is termed thermal scattering. In an ideal lattice, the free electrons suffer only thermal scattering. A free electron in such a lattice would observe a periodic change in the electric potential as it travels through the lattice. In general some impurity ions and/or defects are always present. The potential function undergoes sudden change in the neighborhood of the impurity and causes an electron to scatter. It gives rise to additional resistivity called a residual resistivity ρR. It is independent of temperature of depends only on the impurities and defects present in the metal. ρR is constant for a particular specimen.

Total resistivity ρ = Resistivity due to thermal scattering ρT + ρR.
Hence at absolute zero or very low temperature, ρ = ρR.