A graphene base transistor comprises on a semiconductor substrate surface an emitter pillar and an emitter-contact pillar, which extend from a pillar foundation in a vertical direction. A dielectric filling layer laterally embeds the emitter pillar and the emitter-contact pillar above the pillar foundation. The dielectric filling layer has an upper surface that is flush with a top surface of the emitter pillar and with the at least one base-contact arm of a base-contact structure. A graphene base forms a contiguous layer between a top surface of the emitter pillar and a top surface of the base-contact arm. A collector stack and the base have the same lateral extension parallel to the substrate surface and perpendicular to those edges of the top surface of the emitter pillar and the base-contact arm that face each other.