It is an impressive feat of material science that our knowledge and applications for graphene in electronics has progressed faster than our ability to connect wires to it. To be able to apply graphene in industrial conditions metal-graphene contacts need to be able to be produced reliably with a low resistance (it should also be noted that many other 2D materials also rely on metal-graphene interface to operate). The problem is, we just can’t do it. The technology and processes employed to make the contact points results in a large range of resistances being found experimentally even for supposedly uniform interfaces.
It has been show in chromium, titanium, copper, gold, nickel, palladium and platinum (Cr, Ti, Cu, Au, Ni, Pd and Pt) that the resistance at the connecting point to the graphene is dependent on the deposition temperature and the layering pattern as well as more intrinsic qualities of the metal such as the work function. There have been some reports about the possibility of attaching the metal to the graphene at a defect sight which has been explained by stronger covalent bonding between carbon and metal or perhaps a greater proximity resulting in a greater electron orbital overlap.
In order to gain a greater insight into this effect theoretical models are produced which have proven to be quite successful. One of the first such models described the electrons tunnelling through the metal-graphene contact and then transferring into the conducting band for the graphene. But this study used assumptions which becom invalid when large numbers of electrons move as well as ignoring the vertical transport through the interface choosing to only describe it in one plane. Recently, in order to bolster the data we have on the electrodynamics of the contact point, a theory was created from basics to understand the most funadametal components of the effect. This as used to produce an analytical model which could be used to predict the result of experiments which could be performed. It was ultimately found that by adjusting the energy bands of the graphene near the contact (the effect the defects were having) reduced the contact resistance massively.
Paper links: Electrical properties of graphene-metal contacts