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Although AlGaN-based deep ultraviolet (UV) light-emitting diodes (LEDs) have been studied extensively, their quantum efficiency and optical output power still remain extremely low compared to the InGaN-based visible color LEDs. Electron leakage has been identified as one of the most possible reasons for the low internal quantum efficiency (IQE) in AlGaN based UV LEDs. The integration of a p-doped AlGaN electron blocking layer (EBL) or/and increasing the conduction band barrier heights with prompt utilization of higher Al composition quantum barriers (QBs) in the LED could mitigate the electron leakage problem to an extent, but not completely. In this context, we introduce a promising approach to alleviate the electron overflow without using EBL by utilizing graded concave QBs instead of conventional QBs in AlGaN UV LEDs. Overall, the carrier transportation, confinement capability and radiative recombination are significantly improved. As a result, the IQE, and output power of the proposed concave QB LED were enhanced by ~25.4% and ~25.6% compared to the conventional LED for emission at ~254 nm, under 60 mA injection current.