We know that in a semiconductor in every instant of time some electrons get excited from valence band to conduction band and some electrons are deexcited from conduction band to valence band. In this process, a dynamic equilibrium is reached and the total number of electrons in the conduction band in this equilibrium condition is decided by the Fermi-Dirac distribution. Can we calculated the life time of an electron in conduction band if we know the Fermi energy and the absolute temperature?
Yes, we can calculate the electron lifetime. The main difficulty comes from accounting for the appropriate relaxation mechanisms, relevant to specific material and conditions (additional to the obvuious radiative recombination). To mention the principal ones:
- Radiative recombination: electron recombines with a whole, emitting a photon.
- Auger recombination: electron recombines with a hole while being scattered off another electron (or hole), giving the latter the excess energy.
- Trap-assisted recombination, where the recombination happens via the impurity levels. The particularity here is that the gap energy s split into smaller pieces, which can be carried away, e.g., by phonons.
Wikipedia article on carrier recombination seems to give a rather decent overview of the variety of radiative and non-radiative processes.