A copper interconnect structure has an intrinsic graphene cap for improving back end of line (BEOL) reliability of the interconnect by reducing time-dependent dielectric breakdown (TDDB) failure and providing resistance to electromigration. Carbon atoms are selectively deposited onto a copper layer of the interconnect structure by a deposition process to form a graphene cap. The graphene cap increases the activation energy of the copper, thus allowing for higher current density and improved resistance to electromigration of the copper. By depositing the graphene cap on the copper, the dielectric regions remain free of conductors and, thus, current leakage within the interlayer dielectric regions is reduced, thereby reducing TDDB failure and increasing the lifespan of the interconnect structure. The reduction of TDDB failure and improved resistance to electromigration improves BEOL reliability of the copper interconnect structure.