Abstract

We report the resistivity measured at temperatures between 5 K and 300 K of a Cu film 63 nm thick with grains that have a diameter d = 10.5 nm on the average. The resistivity of this film is described by the first quantum theory of resistivity of nano-scale metallic connectors [R C Munoz et al, App. Phys. Rev. 4 (2017) 011102]. We also report an improved version of this theory that includes a new analytical description of the effect of grain boundary disorder on electron transport. We employ the surface roughness and grain size distribution measured on this Cu film as input data to compute, using our heory, the room temperature resistivity of Cu wires of rectangular cross section, and compare with the resistivity of these wires reported in the literature [M H Van der Veen et al, 2018 IEEE International Interconnect Technology Conference (IITC) (2018)], that are used for designing Integrated Circuits (IC) for the 14 nm, 10 nm, 7 nm, 5 nm, 3 nm and 2 nm nodes, respectively. The quantum theory predicts an increase in resistivity with diminishing wire dimensions that accurately agrees with the room temperature resistivity measured on these Cu wires. The resistivity induced by electron-rough surface scattering accounts for about half of the increase over the bulk observed in the 3 nm and 2 nm tech node; scattering by non-uniform grain boundaries contributes the remaining increase in resistivity-the latter is responsible for the weak Anderson localization. According to the description of electron motion furnished by this improved quantum theory, the break down of Moore's law with shrinking wire dimensions is to be expected, since it originates from size effects triggered by electron scattering with rough surfaces and scattering by non-equally spaced grain boundaries, which become dominant as the dimensions of the metallic wire shrinks.