We investigate the prospects of n-type (0001)n-ZnO/(0001)p-GaN heterostructures as ultraviolet photodetectors. The performance of these devices with different acceptor concentrations in the GaN side is elaborately studied as a function of incident photon energy and photon power. Our study reveals that these devices can serve as highly efficient visible-blind-ultraviolet photodetectors with response times as low as 0.7 ns even in the selfpowered mode. Peak responsivity as high as 11 mA/W and the detectability of a light signal as faint as 9 nW at zero bias condition have been achieved. Acceptor concentration in the GaN side is found to strongly influence the temporal performance of these devices. Moreover, the response times of these detectors can be electrically controlled. Our investigation attributes the fast response characteristics of these devices to the 2D electron gas channel formed at the ZnO side of the interface due to the difference in spontaneous polarization between the two materials. The channel significantly enhances the speed of these devices by providing a high mobility pathway for the photogenerated carriers.