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$_{betabeta}$ = 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$_{betabeta}$. This work confirms the feasibility of IC detectors for the next-generation experiment LEGEND.
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