What is so special about semiconductors? In high school, I hear a lot about semiconductors. Semiconductors are used to make transistors and diodes. A semiconductor material has an electrical conductivity value falling between that of a conductor, such as metallic copper, and an insulator, such as glass. In my textbook, they say that its conducting properties may be altered in useful ways by introducing impurities ("dopants") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created.
Now, the different materials created from "doping" are called "p" and "n" materials. But, why semiconductors? Can't we dope insulators and conductors to make a diode instead of a semiconductor? If not, Why? (I know this question is vague, but I just wanted to know if there is a very special reason we like semiconductors so much. It is fine if it involves complected math and physics)
 A: The properties of semi-conductors arise from the structure of the energy levels that electrons can occupy in the material.
Put simply, electron energy levels can be divided into lower energy valence band levels, where electrons are attached to a particular atom, and higher energy conduction band levels, where electrons can move throughout the material. Electrons in conduction band levels can carry charge throughout the material and so allow a current to flow if an electric field is applied to the material.
In a conductor the valence band levels merge into the conduction band levels, and there are always many electrons in the conduction band acting as charge carriers. In an insulator there is a big gap (the band gap) between the top of the valence band and the bottom of the conduction band, and there are very few electrons in the conduction band. Nothing is a perfect insulator, but it takes a very strong electric field to free electrons from atoms in an insulator.
In a semi-conductor, there is a smaller gap between top of the valence band and the bottom of the conduction band. The Fermi level, which is the maximum energy level of electrons averaged over time, lies in this band gap. However, at any time there are always a few electrons with energies above the Fermi level, so these can enter the conduction band and act as charge carriers. Doping the semi-conductor moves the Fermi level up or down in the band gap.
Doping a conductor might increase its conductivity slightly, but the conductivity of conductors like metals is so high anyway that this would make little difference. Doping an insulator does not generally reduce the size of its wide band gap, so there are still few electrons in the conduction band, and a doped insulator is usually still an insulator (although there are some exceptions).
There is a more detailed explanation of how semi-conductors work in this Wikipedia article.
A: Materials are either conductors (metals) or insulators (most stuff: plastics, salt, sugar, etc).
Some insulators can be made conductive by doping, adding tiny amounts of other atoms. Some of such materials can be doped in two ways: with electrons ($n$-type) or with "holes" ($p$-type). These are charge carriers that are mobile at room temperature and give rise to electrical conductivity.
At the boundaries between such materials one gets a $pn$ junction. This acts as a diode, a one-way street for current. And one can also do a lot of other electronics (amplifiers, memory) with such materials.
Elements that are suitable are germanium and silicon. A common compound is gallium arsenide but there are many others (used in light-emitting diodes). And then there are the organic (carbon-based) materials.
Many insulators can be doped without the charges being mobile at room temperature. This is for example the case in salts or in diamond where these charges are bound in F-centers (color centers). Or there may be some hopping mobility as in lithium-doped nickel oxide etc. Or there may be conductivity but only of one type.
Doping a metal cannot create diodes etc. The conductivity is always large in both directions.
