In a gaz, the ionisation creates pairs of electron and ion. Why in the semiconductor, during an ionisation, there is no creation of an electron and an ion ? Thank you
First, because in the crystal, electron states (either in the conduction band or the valence band) aren't associated with individual nuclei. So when an electron is promoted to the conduction band, we can't say that any specific atom within the crystal is the one that "lost" that electron.
Second, we can't say an atom is ionized, because the electron didn't escape from the crystal, it only moved to a higher energy band within the crystal. The material as a whole remains neutrally charged, so there are no ions. It's analogous to the scenario where a hydrogen atom has its electron excited to the p orbital instead of the s orbital. The atom is still neutral, so it's not considered an ion, just an atom with an electron in an excited state.
A hole is just a model for an ion surrounded by non-ionised atoms. That means that an electron from a neighbouring atom can jump in and turn the ion back into a neutral atom, but the neighbouring atom then becomes an ion. So it looks like a "hole" has moved from the original atom to the neighbouring atom.