Due to their band-structure and optical properties, InAs/InP quantum dots (QDs) constitute a promising system for single-photon generation at third telecom window of silica fibers and for applications in quantum communication networks. However, obtaining the necessary low in-plane density of emitters remains a challenge. Such structures are also still less explored than their InAs/GaAs counterparts regarding optical properties of confined carriers. Here, we report on the growth via metal-organic vapor phase epitaxy and investigation of low-density InAs/InP QD-like structures, emitting in the range of 1.2-1.7 ${mu}$m, which includes the S, C, and L bands of the third optical window. We observe multiple photoluminescence (PL) peaks originating from flat QDs with height of small integer numbers of material monolayers. Temperature-dependent PL reveals redistribution of carriers between families of QDs. Via time-resolved PL, we obtain radiative lifetimes nearly independent of emission energy in contrast to previous reports on InAs/InP QDs, which we attribute to strongly height-dependent electron-hole correlations. Additionally, we observe neutral and charged exciton emission from spatially isolated emitters. Using the 8-band k${cdot}$p model and configuration-interaction method, we successfully reproduce energies of emission lines, the dispersion of exciton lifetimes, carrier activation energies, as well as the biexciton binding energy, which allows for a detailed and comprehensive analysis of the underlying physics.
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