  Copper nanolines fabricated by the damascene process are commonly used as
interconnects in advanced electronic devices. The copper resistivity increases
above the bulk value because of confinement, in detriment of performance.
Recent electronic transport measurements clearly exhibit this effect for
nanolines whose widths range between 80 and 500 nm at low and room
temperatures. An interpretation in terms of finite size effects that consider
semiclassical models for electron-surface and grain-boundary scattering was
presented, but the fits do not capture the strong linewidth dependence in the
data below 100 nm. The present letter explains how the excess resistivity
arises from a quantum mechanical surface roughness effect that begins to
contribute strongly in lines narrower than the mean free path. This type of
roughness scattering would contribute a 40% increase in resistivity for future
20 nm-interconnects.
