  We utilize a droplet epitaxy scheme to fabricate low surface density
(2.8$\times$10$^8$ cm$^{-2}$) InAs quantum dots on an (001)InP substrate with
nearly symmetric quantum confinement potential, emitting at the third telecom
window. We show that the local etching of the In droplet results in the
formation of nearly-symmetric QDs with an arch-shaped base and we explain the
QD growth kinetics by the atom diffusion model. Electronic band structure
calculations reveal properties of neutral and charged excitons confined in the
dots, including respective emission and binding energies. These values are
confirmed in the high-spatially-resolved photoluminescence experiment. We show
that the quantum dots can be considered as non-classical photon emitters with a
high single-photon emission purity at $\sim$1500 nm.
