When you have a material that allows electric charges to move through it, electric current would be the overall flow of those charges through that material. Now that "charge" is what is carried by electrons.

In a material like metal, some of the outer layer electrons are not held as tightly by the core of the atom. These are called the "valence" electrons. Instead of "belonging" to any one specific atom, they can just spread out and move around through the metal and be a part of a shared electronic system. On the other hand, the positive atomic cores (positive because the part left behind has more positive charge than negative charge, since electrons with "-" charge leave and more protons with "+" charge remain), stay in place and form a "regular lattice". See this Wikipedia page.

When you connect a battery, the battery creates an electric field in that material, and that electric field gives the electrons a slight push in one direction. Every electron moves slowly overall but because there is just so many of them moving together, their combined motion produces enough "electric current" that we can measure.

Now silicon is different because its outer electrons can be shared in covalent bonds. Each silicon atom has four valence electrons, (see the previous Wikipedia page if haven't already) and it shares those electrons with four neighboring silicon atoms. This then creates a crystal structure where the atoms are bonded together in an orderly pattern. 


Si — Si — Si — Si
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Si — Si — Si — Si
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Si — Si — Si — Si

In the above-shown ideal bonding structure, the electrons no longer have the tendancy to move through the material (maybe at some higher temperatures some of them break free). Now once an electron is released, it can move through the crystal, but you can easily see how it will leave behind an empty spot where an electron can be used, and that empty spot behaves like a positive carrier called a "hole". So, in intrinsic silicon, current can be carried by both free electrons and holes. The free electrons are the actual negative charges moving through the crystal, but the holes are different. A hole is not really a separate positive particle moving through the silicon, it's rather an empty bonding state that nearby electrons can move into and out of. When an electron moves into a hole, it fills that empty spot, but it also leaves a new empty spot behind. This cycle repeats and electrons move from bond to bond, but the empty spot itself appears to move through the crystal. That moving empty spot becomes like a positive charge carrier, so in semiconductor physics they say that the hole carries current.

But the problem is pure silicon barely has any such carriers at room temperature. Most of its electrons are tied up in bonds and there aren't many free electrons or holes to carry current. Because of that, practical semiconductor devices use something called "doping" where they add a small number of impurity atoms into the silicon crystal on purpose. These impurity atoms then fit into the silicon lattice, but they change the number of mobile carriers available. In other words, it gives us a way to control the conductivity of the material and how easily the current can flow through.

Now, phosphorus is a common n-type dopant for silicon. It has five valence electrons, while silicon only has four. When a phosphorus atom replaces a silicon atom in the crystal, four of its electrons are used to form the bonds with the neighboring silicon atoms, and that leaves one extra electron. Now given that this fifth electron is not needed for bonding, it's only weakly held by the phosphorus atom, and with a tiny amount of energy, it can break away and move through the crystal. Once that happens, it becomes a mobile negative charge carrier, which means it can contribute to the electric current. 


Si — Si — Si — Si — Si
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Si — P  — Si — P  — Si
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Si — Si — Si — Si — Si

You can see how the P atom fits in the strucutre, and since electrons are the majority carriers, the material is called an "n-type silicon", and when a voltage is applied, these mobile electrons move and form current, as previously mentioned.

Doping and its discovery/usage in general is super cool to me.
Props to Russell Ohl and Jack Scaff at Bell labs, in the 40s.
The OG paper: https://www.worldradiohistory.com/Archive-Bell-System-Technical-Journal/40s/Bell-1947a.o.pdf
Page 24 describes this beautifully controllable property in their own words: "The body resistance of the silicon is controlled by the kind and quantity of the impurities present."