29 - Many-body aspects of excitonic luminescence

Summary

In the previous chapter, we have already discussed that the microscopic origin of spontaneous light emission in semiconductors is significantly more complicated than for the atomistic situation where a single entity, i.e., an isolated electron–ion pair, emits a photon. In the artificial situation of a purely excitonic population without any Fermionic substructure, all the plasma contributions vanish and the semiconductor luminescence equations (SLE) predict that, e.g., the emission at the 1s energy stems only from the 1s-exciton population. The very same conclusion follows from the simplified atomic picture analyzed in Chapters 16–23 because the isolated atomic entities are uniquely defined by their eigenstates |φ_λ〉 and the eigenenergies E_λ. For example, the two-level luminescence Eq. (23.44) yields an emission that is proportional to the population of the excited state.

In reality, the semiconductor excitations are hardly ever dilute enough for the electron–hole pairs to be treated as isolated entities. Instead, the excited quasiparticles interact collectively with the emitted photons. Consequently, it is not justified to omit the Fermionic aspects from Eq. (28.47). In addition, semiconductors with a continuous band structure always have a much greater number of available plasma than exciton states and both of them usually contribute to the excitonic luminescence.