Organic-inorganic hybrid ultraviolet photodetectors with tunable spectral response are desirable for many different applications. In this work, we blended poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine] (PTAA) with ZnO nanoparticles in weight ratios of 1 : 1 and 2 : 1 to create charge traps within the active layers for devices with the conventional structure ITO/PEDOT : PSS/PTAA : ZnO/BCP/Al. Thin (150-200 nm) and thick (1400-1900 nm) active layers were employed to utilize charge collection narrowing (CCN). Both thickness and composition of the active layer impacted the spectral tunability of the photoresponse. A single narrow response peak centered at 420 nm (the PTAA absorption edge) with a full width at half maximum of 12 nm was achieved from the device with a 1900 nm active layer and PTAA : ZnO weight ratio of 1 : 1. Decreasing the active layer thickness to 150 nm resulted in a broad spectral response between 320-420 nm with an external quantum efficiency (EQE) value of 295% under 350 nm illumination and a -1 V bias, exhibiting photomultiplication via charge trapping and injection even at small reverse biases. Increasing the weight ratio of PTAA : ZnO to 2 : 1 lowered both the dark current and photocurrent, eliminated photomultiplication in the thin device, and diminished the efficacy of CCN to narrow the spectral photoresponse in the thick device. Transfer matrix method (TMM) and 3-dimensional finite-difference time-domain (3D-FDTD) simulations were performed to understand the impact of thickness and composition of the active layer on the spectral response of UV photodetectors in terms of exciton generation rate and electric field distribution within the devices.