A broadband graphene-on-Si3N4-membrane photodetector for the visible-IR spectral range is realised by simple lithography and deposition techniques. Photo-current is produced upon illumination due to presence of the build-in potential between dissimilar metal electrodes on graphene as a result of charge transfer. The sensitivity of the photo-detector is ∼1.1∼1.1 μμ A/W when irradiated with 515 and 1030 nm wavelengths; a smaller separation between the metal contacts favors gradient formation of the built-in electric field and increases the efficiency of charge separation. This optically-thin graphene-on-membrane photodetector and its interdigitated counterpart has the potential to be used within 3D optical elements, such as photonic crystals, sensors, and wearable electronics applications where there is a need to minimise optical losses introduced by the detector.