Resistivity Scaling Transition in Ultrathin Metal Film at Critical Thickness and Its Implication for the Transparent Conductor Applications

Understanding of ultrathin metal film's electrical and optical properties at sub-10 nm thickness may provide important engineering insight on its application as a transparent conductor. Here, a rapid change is observed in the ultrathin metal film's electrical and optical scaling properties as the thickness shrinks to below a certain critical thickness dc. Below this thickness, the metal film's electrical properties are shown to be strongly influenced by the inhomogeneity of the film which can be modeled via general effective media theory by incorporating size-effect contribution. As a result, below dc, carrier's scattering time rapidly decreases with a reduced mean free path leading to a rapid rise in resistivity. Also, the film's optical loss increases while the optical transmission plateaus below dc. As one promising application of thin metal film is transparent conductor where the film's electrical and optical properties are equally important, its maximum theoretical figure-of-merit is shown, which is determined at this dc serving as an important engineering metric.