Contacts for semiconductor devices are formed where a barrier layer comprising graphene is situated between a first layer comprising a conductor, and a second layer comprising a second conductor or a semiconductor. For example, a metal layer can be formed on a graphene layer residing on a semiconductor. The barrier layer can be directly formed on some second layers, for example, graphene can be transferred from an organic polymer/graphene bilayer structure and the organic polymer removed and replaced with a metal or other conductor that comprises the first layer of the contact. The bilayer can be formed by CVD deposition on a metallic second layer, or the graphene can be formed on a template layer, for example, a metal layer, and bound by a binding layer comprising an organic polymer to form an organic polymer/graphene/metal trilayer structure. The template layer can be removed to yield the bilayer structure. Contacts with the graphene barrier layer display enhanced reliability as the graphene layer inhibits diffusion and reaction between the layers contacting the barrier layer.