Size-dependent resistivity of nanometric copper wires

Higher electrical resistivity is observed in metals when dimensions approach the mean free path of the electrons. The effects of electron scattering at surfaces and at grain boundaries are then becoming substantial. This issue has been extensively studied on thin films but rarely on wires, where both small dimensions (width and height) influence the resistivity increase. In this study, copper wires having variable width and height down to 100 nm are investigated. An alternative approach is suggested in which the resistivity of such wires at different temperatures is compared to that of films having thickness that is equal to the height of the wires. The main outcome is a reliable model that overcomes the well-known difficulty of separating the contribution of surfaces to the resistivity from that of grain boundaries. It is shown that when both width and height of the wire are larger than one third of the mean free path, its resistivity exhibits a filmlike behavior with a separate contribution to the resistivity of each small dimension. The scattering of electrons at the surfaces of the investigated wires was best described by a zero specularity parameter, indicating the importance of this effect for the resistivity increase in small wires.