A method of electrically linking the contacts of a semiconductor device to their corresponding digit lines. The method includes disposing a quantity of mask material into a trench through which the contact is exposed. The mask also abuts a connect region of a conductive element of a corresponding digit line and, therefore, protrudes somewhat over a surface of the semiconductor device. A layer of insulative material is disposed over the semiconductor device with the mask material being exposed therethrough. The mask material is then removed, leaving open cavities that include the trench and a strap region continuous with the trench and with a connect region of the corresponding digit line. Conductive material is disposed within the cavity and electrically isolated from conductive material disposed in adjacent cavities, which define conductive plugs or studs and conductive straps from the conductive material. These plugs or studs and straps provide an electrically conductive link between each contact of the semiconductor device and its corresponding digit line. Semiconductor devices that include features that have been fabricated in accordance with the method of the present invention are also within the scope of the present invention.