  Electron beam lithography is a standard method for fabricating photonic
nanostructures around semiconductor quantum dots (QDs), which are crucial for
efficient single and indistinguishable photon sources in quantum information
processing. However, this technique lacks direct 3D control over the
nanostructure shape, complicating the design and enlarging the 2D footprint to
suppress in-plane photon leakage while directing photons into the collecting
lens aperture. Here, we present an alternative approach to employ Xenon
plasma-focused ion beam (Xe-PFIB) technology as a reliable method for the 3D
shaping of photonic nanostructures containing low-density self-assembled
InAs/InP quantum dots emitting in the C-band range of the 3rd telecommunication
window. We explore both deterministic and non-deterministic fabrication
approaches, resulting in mesas naturally shaped as truncated cones. As a
demonstration, we fabricate mesas using a heterogeneously integrated structure
with a QDs membrane atop an aluminum mirror and silicon substrate.
Finite-difference time-domain (FDTD) simulations show that the angled sidewalls
significantly increase photon extraction efficiency, achieving {\eta} = 0.89
for NA = 0.65. We demonstrate experimentally a high purity of pulsed
single-photon emission (~99%) and a high extraction efficiency of {\eta} =
0.24, with the latter surpassing the highest reported values obtained using
electron beam lithography in the C-band.
