The electrical conductivity of a semiconductor increases with increase in temperature because

The relation between temperature, conductivity & resistivity is explained below

In Metals:

• As the temperature increases, the carrier concentration remains almost the same, but there is a decrease in mobility due to lattice scattering or the frequency of collision increases and hence resistance also increases.
• So that conductivity decreases & resistivity increases, which implies the temperature coefficient of resistivity for metals is positive.

In Semiconductors:

• As the temperature increases, the carrier concentration increases significantly, this is because of extra electrons are excited from the valence band to the conduction band, due to which a number of free electrons increases.
• So that conductivity increases & resistivity decreases, which implies the temperature coefficient of resistivity is negative intrinsic semiconductors
• The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the variation of the number of charge carriers with temperature.
• When copper & pure silicon are heated, then resistivity of copper increases due to the positive temperature coefficient & the resistivity of pure silicon is decreased due to the negative temperature coefficient i.e. Copper is a metal & pure silicon is a semiconductor.

​