Few-layer graphene films were grown by chemical vapor deposition and transferred onto n-type crystalline silicon wafers to fabricate graphene/n-silicon Schottky barrier solar cells. In order to increase the power conversion efficiency of such cells the graphene films were doped with nitric acid vapor and an antireflection treatment was implemented to reduce the sunlight reflection on the top of the device. The doping process increased the work function of the graphene film and had a beneficial effect on its conductivity. The deposition of a double antireflection coating led to an external quantum efficiency up to 90% across the visible and near infrared region, the highest ever reported for this type of devices. The combined effect of graphene doping and antireflection treatment allowed to reach a power conversion efficiency of 8.5% exceeding the pristine (undoped and uncoated) device performance by a factor of 4. The optical properties of the antireflection coating were found to be not affected by the exposure to nitric acid vapor and to remain stable over time.