In this work, we study multiple epitaxial layer structures incorporating a resonant tunneling diode photodetector utilizing the In0.53Ga0.47As/InP material system for operation at the near-infrared region of 1.55 and 1.31 micrometers. We study the photodetection speed of response for these devices and the physical limitations affecting their bandwidth. We show that resonant tunneling diode-based photodetectors have bandwidth limitations due to the charge accumulation near the barriers and report on an operating bandwidth reaching up to 1.75 GHz in particular structures, which is the highest number reported for such detectors to the authors' best knowledge.