Exciton complexes in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum dots

Multiexciton complexes in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum dots in the weak-confinement regime have been investigated by photoluminescence spectroscopy at $T=2\mathrm{}\mathrm{K}.$ The lateral dot sizes varied down to about 50 nm so that the transition from the quantum well to the quantum dot case could be studied. The biexciton binding energy $\Delta {(X}_2)$ increases with decreasing dot size, depending on the height of the confinement potential. The splitting of the biexciton emission by a magnetic field $(B<~8\hspace{0.5em}\mathrm{T})$ arises from the spin splitting of the exciton in the final state of the optical transition, because the biexciton is a spin-singlet state. A magnetic field reduces $\Delta {(X}_2)$ by approximately the exciton spin splitting. This reduction is due to the decrease of the energy gap between the biexciton transition into the spin ground-state of the exciton and the transition of the spin ground- state exciton. The formation of complexes consisting of three and four excitons becomes possible due to the three-dimensional quantum dot confinement. Because of the Pauli principle the Coulomb correlations in the three-exciton complex result in a net repulsion energy that increases strongly with decreasing dot size. The multiexciton interaction energies are reduced by a magnetic field because the exciton repulsion decreases when the magnetic length becomes smaller than the quantum dot size. In the four-exciton-complex we find an exchange energy splitting of states corresponding to carrier configurations with parallel and antiparallel spins. The energy differences between exciton transitions from excited and ground states are about equal to the corresponding energy splittings of the single-particle electron and hole states. These findings indicate that the strong Pauli repulsion between electrons and holes determines the formation of exciton complexes. Based on these results a shell model for quantum dot multiexciton states is discussed.