All depends on required thickness you want to achieve. Normally in nanometer range you can go for CVD and PVD methods

I think the most important to have a procedure which insures to create "a freshly formed copper surfaces in patches or in full scale over the some how oxidized copper surface during the CVD applications." This can be achieved by injecting hydrogen flashing pulses while keeping the carburizing gas flow in steady state regime during annealing treatment. Here Hydrogen molecules, which are impinging on the oxidized copper surface in patches act as scribers to remove the oxygen add atoms just creating freshly formed copper surface that has very high affinity to capture the carbon atoms simultaneously sweeping the surface.