Exciton in semi-conductor I don't understand why an exciton describes only the interaction between an electron hole and an electron in the conduction band? How is this interaction different from the interaction between an electron in the valence band and an electron hole there? Or do electrons in the valence band not interaction with the holes?
 A: The exciton is a quasi-particle. It can be thought of just the interaction energy between the hole and electron. This pair of particles obeys the Coulomb field and is a bound state. Much like the hydrogenic bound states, the exciton's energy is quantized through discrete levels. I suppose in the context of a many-body system, a hole will have local electrostatic effects to other electrons but the exciton is a bound pair of electron and hole, which is different than a possibly free electron interacting with a positive charge. There can be many excitons in a semiconductor.
A: One of the most important attribute of an exciton is its binding energy. This energy is calculated by subtracting the exciton energy from the difference in energy levels of the conduction and valence bands. The binding energy is NOT the same as the exciton energy. So the exciton is stable when its binding energy exceed zero. When Pauli blocking mechanism sets in due to high exciton density or other external factors (temperature),
the binding energy decreases and the exciton is destabilized. Hence the exciton is linked to the hole (in the valence band) and the electron (in the conduction band).
Of course there are interactions that occur between the electrons and holes within the same valence band, and consequently influence the overall binding energy of the exciton.
The mathematical formulism for the many-body exciton is therefore complex in a realistic modelling of solid state systems.
