Temperature Dependence Of Conductivity

Unlike metals, semiconductors have a negative temperature coefficient of resistance, meaning their resistance decreases as temperature rises. The dominant reason is that thermal energy breaks additional covalent bonds, exponentially increasing the number of free electrons and holes available to carry current. Although increased lattice vibrations at higher temperature do scatter carriers more and slightly reduce mobility, this effect is far weaker than the rapid exponential growth in carrier concentration. The net result is that conductivity rises and resistance falls. Mathematically the carrier concentration depends on temperature through an exponential factor of the form (e^{-E_g/2kT}), so even a modest rise in temperature can multiply the carrier population substantially, whereas mobility only declines as a gentle power of temperature. The option claiming fewer carriers is wrong, as that describes metals where added scattering raises resistance. The option that the band gap widens is incorrect; the gap actually narrows slightly with temperature, further aiding conduction. The option crediting mobility is wrong because mobility in fact decreases with heating. As a sanity check, this strong carrier-generation effect is precisely why semiconductor devices like thermistors are used as temperature sensors and why semiconductor resistance behaviour is opposite to that of ordinary metallic conductors.