Realizing an optimal Schottky interface of graphene on Si is challenging, as the electrical transport strongly depends on the graphene quality and the fabrication processes. Such interfaces are of increasing research interest for integration in diverse electronic devices as they are thermally and chemically stable in all environments, unlike standard metal/semiconductor interfaces. We fabricate such interfaces with n-type Si at ambient conditions and find their electrical characteristics to be highly rectifying, with minimal reverse leakage current ($