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In this work the design of a graphene/silicon Schottky photodetector operating at 1550 nm, is reported. The device is a Schottky diode incorporated into an optical microcavity able to greatly enhance the graphene absorption. In order to quantify the performance of the photodetector, graphene absorbance, quantum efficiency and responsivity are numerically calculated. In a properly designed device, a maximum graphene absorbance, efficiency and responsivity of 44%, 15.1% and 0.19 A/W, are respectively obtained. Our work paves the way to the realization of high-performance silicon compatible photodetectors to be employed in Si photonics.