Theory of Excitons

Abstract

In crystals of insulators and semiconductors, when an incident photon is absorbed exciting an electron from the valence to the conduction band, a positive charged vacancy, called a hole, is created in the valence band. The attractive Coulomb interaction between the excited electron and the hole thus created binds them together to form a bound neutral compound system of the two charge carriers such as a hydrogen atom. Such a bound system of a pair of charge carriers is called an exciton. An exciton carries a crystal pseudomomentum equivalent to the vector sum of the individual momenta of the electron and the hole and their relative momentum. While the pseudomomentum enables an exciton to move throughout a crystal, the relative momentum determines its internal structure. Because of the attractive Coulomb interaction between the electron and the hole in an exciton, the internal exciton states are analogous to those of a hydrogen atom, and some of the lower energy states lie below the conduction band by an energy equivalent to the exciton binding energy in that state.