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A graphene/AlGaN deep-ultraviolet(UV)photodetector is presented with ultrahigh responsivity of 3.4× 105 A/W at 261 nm incident wavelength and 149 pW light power.A gain mechanism based on electron trapping at the potential well is proposed to be responsible for the high responsivity.To optimize the trade-off between responsivity and response speed,a back-gate electrode is designed at the AlGaN/GaN two-dimensional electron gas(2DEG)area which eliminates the persistent photocurrent effect and shortens the recovery time from several hours to milliseconds.The 2DEG gate is proposed as an alternative way to apply the back gate electrode on AlGaN based devices on insulating substrates.This work sheds light on a possible way for weak deep-UV light detection.