We propose a hybrid device consisting of a graphene/silicon (Gr/Si) Schottky\ndiode in parallel with a Gr/SiO2/Si capacitor for high-performance\nphotodetection. The device, fabricated by transfer of commercial graphene on\nlow-doped n-type Si substrate, achieves a photoresponse as high as 3 AW^(-1)\nand a normalized detectivity higher than 3.5 10^12 cmHz^(1/2) W^(-1) in the\nvisible range. The device exhibits a photocurrent exceeding the forward\ncurrent, because photo-generated minority carriers, accumulated at Si/SiO2\ninterface of the Gr/SiO2/Si capacitor, diffuse to the Gr/Si junction. We show\nthat the same mechanism, when due to thermally generated carriers, although\nusually neglected or disregarded, causes the increased leakage often measured\nin Gr/Si heterojunctions. At room temperature, we measure a zero-bias Schottky\nbarrier height of 0.52 eV, as well as an effective Richardson constant A**=4\n10^(-5) Acm^(-2) K^(-2) and an ideality factor n=3.6, explained by a thin (<\n1nm) oxide layer at the Gr/Si interface.\n