  We report the realization of a spatial and spectrally tunable air-gap
Fabry-Perot type microcavity of high finesse and cubic-wavelength-scale mode
volume. These properties are attractive in the fields of opto-mechanics,
quantum sensing and foremost cavity quantum electrodymanics. The major design
feature is a miniaturized concave mirror with atomically smooth surface and
radius of curvature as low as 10 micrometer produced by CO2 laser ablation of
fused silica. We demonstrate excellent mode-matching of a focussed laser beam
to the microcavity mode and confirm from the frequencies of the resonator modes
that the effective optical radius matches the physical radius. With these small
radii, we demonstrate sub-wavelength beam waists. We also show that the
microcavity is sufficiently rigid for practical applications: in a cryostat at
4K, the root-mean-square microcavity length fluctuations are below 5 pm.
