AlGaN is the material of choice for high-efficiency deep UV light sources, which is the only alternative technology to replace mercury lamps for water purification and disinfection. At present, however, AlGaN-based mid- and deep UV LEDs exhibit very low efficiency. Here, we report a detailed investigation of the epitaxy and characterization of LEDs utilizing an AlGaN/GaN/AlGaN tunnel junction structure, operating at $～265\mathrm{nm}$, which have the potential to break the efficiency bottleneck of deep UV photonics. A thin GaN layer was incorporated between ${\mathrm{p}}^{}$ and ${\mathrm{n}}^{}$-AlGaN to reduce the tunneling barrier. By optimizing the thickness of the GaN layer and thickness of the top $\mathrm{n}$-AlGaN contact layer, we demonstrate AlGaN deep UV LEDs with a maximum external quantum efficiency of 11% and wall-plug efficiency of 7.6% for direct on-wafer measurement. It is also observed that the devices exhibit severe efficiency droop under low current densities, which is explained by the low hole mobility, due to the hole hopping conduction in the Mg impurity band and the resulting electron overflow.