In the realm of optoelectronics, photodetectors play a pivotal role, with applications spanning from high-speed data communication to precise environmental sensing. Despite the advancements, conventional photodetectors grapple with challenges with response speed and dark current. In this study, we present a photodetector based on a lateral MoTe₂ p-n junction, defined by a semi-floating ferroelectric gate. The strong ferroelectric field and the depletion region of the p-n junction in the device are notably compact, which serves to diminish the carrier transit time, thereby enhancing the speed of the photoelectric response. The non-volatile MoTe₂ homojunction, under the influence of external gate voltage pulses, can alter the orientation of the intrinsic electric field within the junction. As a photovoltaic detector, it achieves an ultra-low dark current of 20 pA, and a fast photo response of 2 μs. The spectral response is extended to the shortwave infrared range at 1550 nm. Furthermore, a logic computing system with light/no light as binary input is designed to convert the current signal to the voltage output. This research not only underscores the versatility of 2D materials in the realm of sophisticated photodetector design but also heralds new avenues for their application in energy-efficient, high-performance optoelectronic devices.