Complex lightwave manipulation such as broadband absorption has been realized with metasurfaces based on laterally arranged metal-dielectric-metal cavities with different geometries. However, application of these metasurfaces for optoelectronic devices by incorporating functional dielectrics remains challenging. Here, we integrate a quantum well infrared photodetector (QWIP) with a metasurface made of a patchwork of square cavities with different dimensions arranged in a subwavelength unit cell. Our detector realizes wideband photoresponse approaching the entire responsivity spectrum of the QWIP-single-sized square cavities can utilize only 60% of the possible bandwidth-and external quantum efficiencies of up to 78% at 6.8 µm. Our highly flexible design scheme enables integration of photodetectors and metasurfaces with arbitrary arrangements of cavities selectively responding to incidence with a specific wavefront.