Electric current is the motion of electric charge through a material. That "charge" is typically carried by electrons.

In a metal, outer electrons of atoms (valence electrons) are not tightly bound. They sit in a shared pool that extends through the entire crystal. The metal still has a rigid lattice of positive atomic cores, but the outer electrons can move from atom to atom with little extra energy. See this Wikipedia page.

When you connect a battery, an electric field appears inside the metal. This field pushes the mobile electrons slightly in one direction. Each electron drifts slowly, but because there are so many of them, the net flow of charge is large enough to count as current. The field itself spreads through the conductor very quickly, so the response of the whole wire feels immediate.

In a semiconductor like silicon, the story is more constrained. A silicon atom has fourteen protons in its nucleus, and so fourteen electrons around it. Four of those electrons sit in the outer shell and can form covalent bonds with neighbors. The result is a regular crystal in which each atom links to four others.

A simple sketch of a small silicon region looks like this: 


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

Each line represents a shared pair of electrons between atoms. At very low temperature all these bonding electrons are locked into place. No electrons are free to move through the crystal, so there is almost no current.

As temperature rises, some bonding electrons gain enough thermal energy to break out of the bonds. When an electron leaves a bond it frees itself to move through the lattice. At the same time it leaves behind an empty place in the bond. That empty place is called a hole.

The hole behaves like a positive charge. Neighboring electrons can move to fill it, and that move creates a new hole where the electron came from. In this way the hole appears to hop from bond to bond in the direction opposite to the electron motion. In pure silicon, known as intrinsic silicon, current is carried by both these conduction electrons and the holes they leave behind.

The important point is that in intrinsic silicon the number of free carriers is set by temperature and by the size of the band gap of the material. At room temperature there are some electrons and holes, but not very many. The crystal is only a moderate conductor. To use silicon in practical circuits we want much more control over how many carriers are present.

That control comes from doping. Doping means introducing a small number of impurity atoms into the silicon lattice. These atoms bring a slightly different number of outer electrons. By choosing the right impurity we can create extra electrons or extra holes in a stable and predictable way.

Phosphorus is a common dopant for silicon. A phosphorus atom has five electrons in its outer shell instead of four. When phosphorus takes the place of a silicon atom in the lattice, four of its electrons form normal bonds with neighboring silicon atoms. The fifth electron does not fit into the bond pattern and is only weakly bound.

A region of silicon with phosphorus atoms mixed in can be depicted as follows. 


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

The P symbols mark phosphorus atoms. Each of those atoms contributes one extra electron that is not part of a bond. These extra electrons are available as mobile charge carriers even at relatively low temperatures. They can move under a small electric field without waiting to be thermally released from a bond.

Because electrons are the majority carriers in this doped material, it is called n type silicon. The added electrons raise the conductivity by many orders of magnitude compared to intrinsic silicon. Now when a voltage is applied across the material, a large number of electrons drift through the lattice and produce a noticeable current.

In a more detailed picture, you have two main mechanisms in play. In intrinsic silicon, you get a trap and release pattern. Thermal energy occasionally lifts an electron from a bond into the conduction band. The electron can then move, while its original bond site behaves like a hole. The system constantly creates and recombines such pairs, and that balance sets the intrinsic carrier density.

In doped n type silicon with phosphorus, many electrons never need that thermal activation step. They start out weakly bound and are easily promoted into states where they move through the lattice. The network of covalent bonds remains, but the dopant supplied electrons glide through the spaces between atoms, guided by the electric field.

From the external point of view, current in a doped semiconductor still looks like a flow of charge from one terminal to another. Inside the material it is the combination of the crystal structure, the presence of dopant atoms, and the ambient thermal energy that decides how many electrons are free and how easily they move. By tuning the doping and geometry of silicon pieces, device designers shape where current can flow and where it cannot.

The same basic idea of electron motion under an electric field applies in metals and in semiconductors. What changes is how electrons are held in place, how they are released, and how many mobile carriers are available. In silicon the role of chemical bonding, thermal energy, and doping creates a controlled path for electrons, which is what allows current to flow from one side of a device to the other in a precise and useful way.