Size-Dependent Resistivity in Nanoscale Interconnects

As the dimensions of conductors shrink into the nanoscale, their electrical conductivity becomes dependent on their size even at room temperature. Although the behavior varies dramatically as temperatures increase from nanokelvins to hundreds of kelvins, the effect is generally to increase the resistivity above that of bulk material. As such, the underlying size-dependent phenomena have become increasingly important as advanced technologies have shifted their focus first from macro- to microscale and more recently from micro- to nanoscale dimensions. Indeed, the size-dependent increase of electrical resistivity that results from electron scattering on external and internal surfaces of copper conductors has already become technology limiting in modern microelectronics. This article summarizes the phenomena that underlie size effects, focusing on conduction in copper lines in particular. Attention is given to describing key innovations in both theoretical and experimental assessments that have significantly modified, facilitated, or advanced understanding.