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We investigate the quantum confinement effects on excitons in several types of strain-free GaAs/Al<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mrow> <mn>0.3</mn> </mrow> </msub> </semantics> </math> </inline-formula>Ga<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mrow> <mn>0.7</mn> </mrow> </msub> </semantics> </math> </inline-formula>As droplet epitaxy (DE) quantum dots (QDs). By performing comparative analyses of energy-dispersive X-ray spectroscopy with the aid of a three-dimensional (3D) envelope-function model, we elucidate the individual quantum confinement characteristics of the QD band structures with respect to their composition profiles and the asymmetries of their geometrical shapes. By precisely controlling the exciton oscillator strength in strain-free QDs, we envisage the possibility of tailoring light-matter interactions to implement fully integrated quantum photonics based on QD single-photon sources (SPSs).