A graphene base transistor, comprising, on a semiconductor substrate surface: - at least one emitter pillar and at least one emitter-contact pillar (112.1, 112.2), which extend from a pillar foundation, through which they are electrically connected, in a vertical direction pointing perpendicularly away from the substrate surface; - a dielectric filling layer laterally embedding the emitter pillar and the emitter-contact pillar (112.1, 122.2), and separating them from each other in regions above the pillar foundation, - an electrically conductive base-contact structure, which is either arranged on or embedded in the dielectric filling layer and which includes a) a base-contact face (116.1), which is arranged at a lateral distance from the emitter pillar, and, b) at least one base-contact arm (116.2, 116.3), which extends from the base-contact face (116.1) in a direction parallel to the substrate surface and passes between the top surfaces of the emitter pillar and of the emitter contact-pillar without directly contacting them; - wherein 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 - a base layer of graphene forming a contiguous layer that extends between and covers an immediately adjacent top surface of the emitter pillar and at least a part of an immediately adjacent top surface of the at least one base-contact arm (116.2, 116.3); - a collector stack that comprises at least a collector-barrier layer, which is arranged immediately on the graphene layer, and an electrically conductive collector layer, which is arranged on the collector-barrier layer, wherein the collector stack and the base layer have the same lateral extension in a direction that is parallel to the substrate surface and perpendicular to those edges of the top surface of the emitter pillar and the base-contact arm (116.2, 116.3) that face each other. - at least one emitter pillar and at least one emitter-contact pillar (112.1, 112.2), which extend from a pillar foundation, through which they are electrically connected, in a vertical direction pointing perpendicularly away from the substrate surface; - a dielectric filling layer laterally embedding the emitter pillar and the emitter-contact pillar (112.1, 122.2), and separating them from each other in regions above the pillar foundation, - an electrically conductive base-contact structure, which is either arranged on or embedded in the dielectric filling layer and which includes a) a base-contact face (116.1), which is arranged at a lateral distance from the emitter pillar, and, b) at least one base-contact arm (116.2, 116.3), which extends from the base-contact face (116.1) in a direction parallel to the substrate surface and passes between the top surfaces of the emitter pillar and of the emitter contact-pillar without directly contacting them; a) a base-contact face (116.1), which is arranged at a lateral distance from the emitter pillar, and, b) at least one base-contact arm (116.2, 116.3), which extends from the base-contact face (116.1) in a direction parallel to the substrate surface and passes between the top surfaces of the emitter pillar and of the emitter contact-pillar without directly contacting them; - wherein 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 - a base layer of graphene forming a contiguous layer that extends between and covers an immediately adjacent top surface of the emitter pillar and at least a part of an immediately adjacent top surface of the at least one base-contact arm (116.2, 116.3); - a collector stack that comprises at least a collector-barrier layer, which is arranged immediately on the graphene layer, and an electrically conductive collector layer, which is arranged on the collector-barrier layer,