Once the 5th valence electron of a donor atom left, it will be to the conduction band, so the donor atom becomes positively charged. My question is if it is possible, that a free electron from the conduction band recombines with the positively charged donor ion. So is regeneration possible because of the donor ion?
\$\begingroup\$ Yes, it's called recombination. In a semiconductor at room temperature we assume that all or nearly all of the dopant atoms are contributing charge carriers but there's nothing preventing them from accepting an electron or hole. They will probably lose it quickly thereafter though. \$\endgroup\$– virJul 1, 2022 at 16:56
\$\begingroup\$ Sure: electron-hole recombination is common, and can be helpful in an LED, or detrimental in a transistor. See eng.libretexts.org/Bookshelves/Materials_Science/… \$\endgroup\$– DrMoishe PippikJul 1, 2022 at 17:05
Recombination takes place when electron falls from conduction band to valence band, thus one free electron and one free hole disappear.
Jumping of electron from donor dopant atom onto conduction band is called donor ionization, and reverse process is called electron capture. In these cases holes concentration does not change.