A method for forming contacts for a graphene field-effect transistor, FET, comprising: providing a graphene layer having a graphene surface on a substrate; depositing a first metal layer having a work function, WF, < 4.3 eV on the graphene surface; oxidizing the first metal layer to form a first metal oxide layer; etching the first metal oxide layer to provide open surface contact regions including a first and a second region of the graphene layer for providing a graphene surface source contact and a graphene surface drain contact, respectively; depositing a second metal layer comprising a second metal layer portion providing a source with a source contact over the graphene surface source contact and a second metal layer portion providing a drain with a drain contact over the graphene surface drain contact; the method being characterised in that it comprises forming a graphene multilayer at an interface between the source contact and the graphene surface source contact and between the drain contact and the graphene surface drain contact; and in that either A) the step of depositing the second metal layer comprises pre-saturating the second metal layer with in-situ carbon to form a carbon pre-saturated second metal layer, and the step of forming said graphene multilayer comprises isothermal supersaturation of the second metal layer with carbon and carbon diffusion to said interface to form the graphene multilayer or cooling the carbon pre-saturated second metal layer to precipitate the carbon from the carbon pre-saturated second metal layer to form the graphene multilayer; or B) the step of forming said graphene multilayer comprises carbon ion implantation of the second metal layer or depositing an amorphous C layer on top of the second metal layer; and then performing annealing in a temperature range from 200°C to 1,000 °C. providing a graphene layer having a graphene surface on a substrate; depositing a first metal layer having a work function, WF, < 4.3 eV on the graphene surface; oxidizing the first metal layer to form a first metal oxide layer; etching the first metal oxide layer to provide open surface contact regions including a first and a second region of the graphene layer for providing a graphene surface source contact and a graphene surface drain contact, respectively; depositing a second metal layer comprising a second metal layer portion providing a source with a source contact over the graphene surface source contact and a second metal layer portion providing a drain with a drain contact over the graphene surface drain contact; the method being characterised in that it comprises forming a graphene multilayer at an interface between the source contact and the graphene surface source contact and between the drain contact and the graphene surface drain contact; and in that either A) the step of depositing the second metal layer comprises pre-saturating the second metal layer with in-situ carbon to form a carbon pre-saturated second metal layer, and the step of forming said graphene multilayer comprises isothermal supersaturation of the second metal layer with carbon and carbon diffusion to said interface to form the graphene multilayer or cooling the carbon pre-saturated second metal layer to precipitate the carbon from the carbon pre-saturated second metal layer to form the graphene multilayer; or B) the step of forming said graphene multilayer comprises carbon ion implantation of the second metal layer or depositing an amorphous C layer on top of the second metal layer; and then performing annealing in a temperature range from 200°C to 1,000 °C. A) the step of depositing the second metal layer comprises pre-saturating the second metal layer with in-situ carbon to form a carbon pre-saturated second metal layer, and the step of forming said graphene multilayer comprises isothermal supersaturation of the second metal layer with carbon and carbon diffusion to said interface to form the graphene multilayer or cooling the carbon pre-saturated second metal layer to precipitate the carbon from the carbon pre-saturated second metal layer to form the graphene multilayer; or B) the step of forming said graphene multilayer comprises carbon ion implantation of the second metal layer or depositing an amorphous C layer on top of the second metal layer; and then performing annealing in a temperature range from 200°C to 1,000 °C.