Excitons and biexcitons in spheroidal quantum dots А$_{2}$B$_{6}$

In the limit of strong quantum confinement the lower energy states of excitons and biexcitons in spheroidal quantum dots of semiconductors with a fourfold degenerate vertex of the valence band, which are active in the dipole approximation at one- and two-photon excitation, have been considered. The comparative analysis of the order of energy levels of the hole in the potentials of the infinitely deep quantum well and a three-dimensional harmonic oscillator taking into account the axial anisotropy of the quantum dot (QD) shape is carried out. It is shown that the anisotropy of the QD shape can lead to the opposite sign of splitting with respect to angular momentum projection $\pm$ 3/2, $\pm$ 1/2 for spatially odd $(1 P _3/2)$ and even $(1 S _3/2)$ levels of the hole. At the same time, in the case of the potential of an infinitely deep quantum well, an inversion of the order of $1 S _3/2$ and $1 P _3/2$ levels can be observed at values of the ratio of the effective masses of the light and heavy holes $\beta=m _lh/ m _hh\approx$ 0.14. The type of the trial wave functions of the hole for the state $1 P _3/2$ in the potential of an isotropic three-dimensional harmonic oscillator depending on $\beta$ is proposed. The dependence of the binding energy of excitons in the considered potentials on $\beta$ is presented and the possibility of formation of various biexcitonic states is considered.