  Colour centres in silicon carbide emerge as a promising semiconductor quantum
technology platform with excellent spin-optical coherences.However, recent
efforts towards maximising the photonic efficiency via integration into
nanophotonic structures proved to be challenging due to reduced spectral
stabilities. Here, we provide a large-scale systematic investigation on silicon
vacancy centres in thin silicon carbide membranes with thicknesses down to
$0.25\,\rm\mu m$. Our membrane fabrication process involves a combination of
chemical mechanical polishing, reactive ion etching, and subsequent annealing.
This leads to highly reproducible membranes with roughness values of
$3-4\,\rm\r{A}$, as well as negligible surface fluorescence. We find that
silicon vacancy centres show close-to lifetime limited optical linewidths with
almost no signs of spectral wandering down to membrane thicknesses of $0.7
\,\rm\mu m$. For silicon vacancy centres in thinner membranes down to
$0.25\,\rm\mu m$, we observe spectral wandering, however, optical linewidths
remain below $200\,\rm MHz$, which is compatible with spin-selective excitation
schemes. Our work clearly shows that silicon vacancy centres can be integrated
into sub-micron silicon carbide membranes, which opens the avenue towards
obtaining the necessary improvements in photon extraction efficiency based on
nanophotonic structuring.
