What factors decrease the conductivity of a conductor as temperature increases? Are these factors also present in a Semiconductor, and if so, how can its conductivity vary with temperature in the opposite sense?

Resistance is inversely proportional to temperature. In other words, as you increase the temperature of the materials, their resistance will decrease. But this is not true for every material, that is, not all materials have the same temperature dependence.

As the temperature increase, the vibration of positive ions produces more disturbances to the electron wave, and thus the resistivity increases, and thus the conductivity decreases.

At zero temperature, there are still electrons in the conduction band, so the conductor is still a conductor at zero temperature. On the other hand, at zero temperature, there is no electron in the conduction band for the semiconductor, so it is an insulator at zero temperature.

As the temperature increases, the conduction band of the semiconductor will be partially filled with electrons, and thus the conductivity increases as the temperature increases for semiconductors. The vibration of positive ions will still produce disturbance to the electron wave, but this factor is less important compared to the additionally available electrons from the higher temperature…