In this letter, we report an InAsSb p(+)-n junction photodetector grown on InAs substrate by liquid phase epitaxy. Electrical and optical characterizations of the device have been carried out at room temperature for operation of the device in the mid-infrared region. The study revealed that the dark current of the photodetector under reverse bias is dominated by a trap-assisted tunnelling current component, which degrades the detectivity of the device. Further, by operating the device at a suitable low reverse bias it is possible to improve the room-temperature detectivity significantly as compared to its value at zero bias.