  Neutrinoless double-$\beta$ decay of $^{76}$Ge is searched for with germanium
detectors where source and detector of the decay are identical. For the success
of future experiments it is important to increase the mass of the detectors. We
report here on the characterization and testing of five prototype detectors
manufactured in inverted coaxial (IC) geometry from material enriched to 88% in
$^{76}$Ge. IC detectors combine the large mass of the traditional semi-coaxial
Ge detectors with the superior resolution and pulse shape discrimination power
of point contact detectors which exhibited so far much lower mass. Their
performance has been found to be satisfactory both when operated in vacuum
cryostat and bare in liquid argon within the GERDA setup. The measured
resolutions at the Q-value for double-$\beta$ decay of $^{76}$Ge
(Q$_{\beta\beta}$ = 2039 keV) are about 2.1 keV full width at half maximum in
vacuum cryostat. After 18 months of operation within the ultra-low background
environment of the GERmanium Detector Array (GERDA) experiment and an
accumulated exposure of 8.5 kg$\cdot$yr, the background index after analysis
cuts is measured to be $4.9^{+7.3}_{-3.4}\times 10^{-4}$ counts
/(keV$\cdot$kg$\cdot$yr) around Q$_{\beta\beta}$. This work confirms the
feasibility of IC detectors for the next-generation experiment LEGEND.
