Conductive contact structure of a circuit structures and methods of fabrication thereof are provided. The fabrication includes, for instance, providing at least one contact opening disposed over a semiconductor substrate; forming a carbon-rich contact liner material including a carbon-containing species and an elemental carbon disposed therein, the carbon-containing species and the elemental carbon together defining a set carbon content within the carbon-rich contact liner material; and depositing the carbon-rich contact liner material conformally within the at least one contact opening disposed over the semiconductor substrate.