Question

On decreasing temperature $\rho$ decreases in insulator and semiconductor. Why?

Answer 1

In case of an insulator, there is a large energy gap between the two bands. So, if the temperature rises, the electrons will go to the upper band. But since it is not crowded due to less number of electrons, so the conductance will increase due to the availability of free electrons in the conduction band. So, the resistance decreases with increase in temperature in the insulator.

Semi-conductors act as non-metals at low temperatures - the electrons are trapped within the atom. As the temperature of the semiconductor is increased, the electrons in the valence band gain sufficient energy to escape the confines of their atoms. As a result, at higher temperatures, a semiconductor valence electrons become free, thus resistivity decreases.