How do free charge carriers appear in pure semiconductors?

In semiconductors, there are two types of charge carriers – electrons and holes. If there are no free charge carriers – all electrons are bound to atoms and cannot move around the crystal, then the substance does not conduct electric current, i.e. is a dielectric. But this situation exists only at absolute zero temperature. With increasing temperature, the energy of vibrational motions of atoms increases, and some part of the electrons acquires energy sufficient to detach from the atom. The detached electron can freely move along the crystal lattice. In the place where the electron is knocked out, an uncompensated positive charge is formed, equal to the charge of the electron. This is the hole. It can also freely move through the crystal due to the jump of a valence electron from neighboring atoms, as a result of which the hole is at the neighboring atom, and then this process is repeated. As a result, an electron-hole pair is formed. This process is usually described as a result of the collision of an electron with a phonon. Phonon is a quantum of energy of vibrational motions of atoms of the crystal lattice. In a collision, the phonon disappears, its energy is transferred to the electron.
The process of formation of electron-hole pairs under the influence of thermal motion is called thermogeneration. Along with thermal generation, the reverse process also takes place – recombination – when a free electron combines with a hole and the valence bond is restored, the pair of carriers disappears.
An intrinsic (pure) semiconductor is a pure and defect-free semiconductor with an ideal crystal lattice. In its own semiconductor, electrons and holes are always formed in pairs and their concentrations are equal: n = p

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