Various methods and structures for fabricating a contact for a semiconductor FET or FinFET device. A semiconductor FET structure includes a substrate, a source/drain region layer and source/drain contact. First and second gate spacers are adjacent respective first and second opposing sides of the source/drain contact. The source/drain contact is disposed directly on and contacting the entire source/drain region layer, and at a vertical level thereabove, the source/drain contact being recessed to a limited horizontal area continuing vertically upwards from the vertical level. The limited horizontal area horizontally extending along less than a full horizontal length of a vertical sidewall of the first and second gate spacers, and less than fully covering the source/drain region layer. A method uses a reverse contact mask to form a shape of the source/drain contact into an inverted “T” shape.