Fine structure of bright and dark excitons in asymmetric droplet epitaxy GaAs/AlGaAs quantum dots

Abstract

We have calculated the exciton fine structure splittings (FSS) of asymmetric GaAs/AlGaAs quantum dots (QDs) obtained after Al droplet epitaxy and subsequent nanoholes formation followed by annealing and GaAs filling of nanoholes. We used a $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model and considered the heavy-hole and light-hole mixing to calculate the electron-hole exchange interaction (EI). The two components, long-range (LR) and short-range (SR) of the EI, were deduced. The exciton fine structure is organized, as usual in zinc-blende compounds, into two groups of states: bright (optically active) and dark states. The bright-dark and bright-bright splittings contain LR and SR contributions, the LR part representing 5 to 68% of the total bright-dark splitting and 69 to 76% of the total bright-bright splitting for sizes experimentally explored. In QDs having ${\mathrm{C}}_{2v}$ symmetry, LR and SR contributions to dark-dark splitting have to be calculated at the second order of perturbation theory. A good agreement between the theory and experiment is obtained for QDs with different degrees of asymmetry, from QD having an isotropic shape to QD with a very anisotropic shape.