The bandstructure and optical properties of semiconductors we have discussed so far are based on the assumption that the valence band is filled with electrons and the conduciton band is empty. The effect of electrons in the conduction band and holes in the valence band is only manifested through the occupation probabilities without altering the bandstructure. In reality, of course, there is a Coulombic interaction between an electron and another electron or hole. Some very important properties are modified by such interactions. The full theory of the electron-electron interaction depends upon many body theory, which is beyond the scope of this text. However, there is one important problem, that of excitonic effects in semiconductors, that can be addressed by simpler theoretical techniques.
In Fig. 10.1 we show how exciton effects arise. On the left-hand side, we show the bandstructure of a semiconductor with a full valence band and an empty conduction band. There are no allowed states in the bandgap. Now consider the case where there is one electron in the conduction band and one hole in the valence band. In this new configuration, the Hamiltonian describing the electronic system has changed. We now have an additional Coulombic interaction between the electron and the hole. The electronic bandstructure should thus be modified to reflect this change. The electron-hole system, coupled through the Coulombic interaction, is called the exciton and will be the subject of this chapter.