A method of manufacturing a thin-film transistor or like structure provides conductive “tails” below an overhang region formed by a top gate structure. The tails increase in thickness as they extend outward from a point under the overhang to the source and drain contacts. The tails provide a low resistance conduction path between the source and drain regions and the channel, with low parasitic capacitance. The thickness profile of the tails is controlled by the deposition of material over and on the lateral side surfaces of the gate structure.