In this paper, the design of a graphene/silicon photodetector working at both 2 μm and room temperature is reported. The device is a Schottky diode and the absorption mechanism is based on the internal photoemission effect. In order to quantify the performance of the photodetector, quantum efficiency, dark current density and efficiency-dark current density ratio, are numerically calculated. Performance comparison of our proposed device with typical Schottky photodetectors based on metals, is reported. Graphene/silicon devices show a promising efficiency of 23.66% at 2 micron, a dark current density of only 0.81 nA/μm² and a quantum efficiency-dark current density ratio of about 2.93 cm²/A. This photodetector can find applications in trace-gas detection, medical sensing, environmental monitoring industrial process control.