Electrons and holes

At 0 K every bond in a silicon crystal is complete. Above 0 K some bonds break and free their electrons.

Figure to be added

Figures 11.1 and 11.2 — a silicon lattice at 0 K with every bond complete, and above 0 K with a broken bond: a free electron and the hole it left.

Hole

Where a bond has lost its electron there is a shortage of one electron: a hole. The positive charge of the nucleus is no longer balanced there, so a hole behaves like a positive charge.

An electron from a neighbouring atom can drop into a hole, so the hole moves. Moving from atom to atom through the lattice, holes carry current too. Free electrons are negative charge carriers; holes are positive ones.

With a potential difference across a semiconductor, holes move towards the negative side and electrons towards the positive side, and the (conventional) current flows from positive to negative.

In metals the charge carriers are free negative electrons.
In semiconductors both free electrons and holes carry charge.
Every broken bond makes one free electron and one hole, so a pure semiconductor has equal numbers of each.
So a semiconductor crystal is electrically neutral.