Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.

First, let's understand the difference between metals and semiconductors in terms of their energy band structures. Metals possess continuous energy bands, while semiconductors have a small energy gap between the valence band (filled with electrons) and the conduction band (available for electron conduction).

When temperature increases, the atoms in a metal vibrate more rapidly. This increased atomic vibration interferes with the motion of electrons, causing them to scatter and reducing their ability to conduct electricity. Consequently, the electrical conductivity of metals decreases with increasing temperature.

Semiconductors can be classified into two types: intrinsic and extrinsic. Intrinsic semiconductors are pure materials, like silicon or germanium, and exhibit a small energy gap between the valence band and the conduction band. At low temperatures, the intrinsic semiconductor behaves like an insulator due to the band gap; however, at higher temperatures, some electrons can gain enough energy to jump from the largely filled valence band to the conduction band. This process creates electron-hole pairs, which contribute to increased conductivity.

As the temperature of an intrinsic semiconductor increases, the increased thermal energy causes more electrons to overcome the band gap and transition to the conduction band. This results in more electron-hole pairs and increased conductivity. However, it's important to note that this increase in conductivity reaches a limit, after which the semiconductor will start behaving more like a metal and its conductivity will slowly decrease with a further increase in temperature.

Extrinsic semiconductors are created by introducing impurities (doping) to the intrinsic semiconductor material, modifying its band structure. Doping can create either n-type (electron-rich) or p-type (hole-rich) semiconductors, both of which have a higher conductivity than intrinsic semiconductors.

In extrinsic semiconductors, the process of electron excitation from the valence to the conduction band still occurs with increasing temperature. However, the conductivity is already higher due to the presence of impurity levels. As such, the increased conductivity of extrinsic semiconductors is more significant when compared to intrinsic ones as the temperature increases. In summary, the conductivity of semiconductors increases with temperature (up to a certain point) due to the increased excitation of electrons from the valence band to the conduction band, generating more electron-hole pairs and higher conductivity. This behavior is opposite to that of metals, whose conductivity decreases with increasing temperature due to the increased atomic vibrations interfering with electron movement.