Bound-state symmetries and optical transitions in GaAs/AlAs quantum wells and superlattices with impurities and defects

We consider $\left(\mathrm{GaAs}{)}_m\right(\mathrm{AlAs}{)}_n$ superlattices as single crystals whose structure depends on the growth direction and numbers of monolayers within the slabs of constituent materials. We study point defects such as impurities (substitutional and interstitial) or single vacancies and molecular defects such as paired impurities, double vacancies, or vacancy-impurity complexes in $\left(\mathrm{GaAs}{)}_m\right(\mathrm{AlAs}{)}_n$ superlattices grown along the [001], [110], and [111] directions. The possible site symmetries of the defects as well as the state symmetries for carriers bound to them have been determined. In contrast to bulk GaAs or AlAs, no defect can present $T_d$ symmetry. The atoms located in the center of the slabs occupy, in most of the [001]- and [110]-grown superlattices, sites with higher symmetries ${(D}_{2d}$ and $C_{2v},$ respectively). This results in different selection rules for optical transitions involving the same impurity atom which substitutes the same host atom (Ga, Al, or As) at sites with different symmetries. The effect can be important in optical spectra of superlattices with very thin slabs. The modifications of the selection rules when including the spin-orbit interaction have been derived. Quantum wells can be treated as a particular case of superlattices when barriers become very thick. We present their three-dimensional diperiodic space groups. Quantum wells do not differ from superlattices from the points of view of possible site symmetries and selection rules for optical transitions involving defects. All the above results are also valid for any pseudomorphic superlattice or quantum well made of two binary compounds with zinc-blende structures and identical cations or anions, such as in the GaN/AlN system.