Which correctly describes how electrical resistivity changes when the temperature is raised? Assume the semiconductor is in the intrinsic regime.

Answer: B. It increases for metals and decreases for intrinsic semiconductors

In metals the concentration of conduction electrons is nearly independent of temperature, and as temperature rises, scattering by lattice vibrations (phonons) increases and the mobility falls, so the resistivity increases roughly in proportion to temperature near room temperature. In intrinsic semiconductors, the number of electrons and holes excited across the band gap increases exponentially with temperature, far outweighing the drop in mobility, so the resistivity falls sharply. This difference is exploited in platinum resistance thermometers (positive temperature coefficient) and NTC thermistors made of oxide semiconductors (negative temperature coefficient). The choice in which the metal decreases and the semiconductor increases has the directions reversed, and the choice in which both increase treats the semiconductor as behaving like a metal.