Therefore, disclosed above are embodiments of a multi-fin field effect transistor structure (e.g., a multi-fin dual-gate FET or tri-gate FET) that provides low resistance strapping of the source/drain regions of the fins, while also maintaining low capacitance to the gate by raising the level of the straps above the level of the gate. Embodiments of the structure of the invention incorporate either conductive vias or taller source/drain regions in order to electrically connect the source/drain straps to the source/drain regions of each fin. Also, disclosed are embodiments of associated methods of forming these structures.