We perform a theoretical study of the optical transitions for different excitonic complexes in highly symmetric strain-free GaAs quantum dots (QDs) fabricated by epitaxially filling nanoholes (NHs) in an AlGaAs surface. NHs are formed by local droplet etching. As a first step, we propose a QD shape modeling consistent with atomic force microscopy (AFM) profiles and an experimental growth procedure. We investigate the QD height dependence of s- and p- shell exciton recombination energies in the framework of the effective mass approximation with an exact numerical diagonalization method. A comparison between theoretical results and available spectroscopic data is carried out. Systematic evolution of the binding energies of neutral (X), charged excitons (X, X+) and the biexciton (XX), with QD height, is interpreted in terms of a balance between the Coulomb interactions and charge carrier correlation effects. Our calculations demonstrate the important role of the correlation energies in elucidating the bound character of all few-particle states especially the biexciton.

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