  Ando's model provides a rigorous quantum-mechanical framework for
electron-surface roughness scattering, based on the detailed roughness
structure. We apply this method to metallic nanowires and improve the model
introducing surface roughness distribution functions on a finite domain with
analytical expressions for the average surface roughness matrix elements. This
approach is valid for any roughness size and extends beyond the commonly used
Prange-Nee approximation. The resistivity scaling is obtained from the
self-consistent relaxation time solution of the Boltzmann transport equation
and is compared to Prange-Nee's approach and other known methods. The results
show that a substantial drop in resistivity can be obtained for certain
diameters by achieving a large momentum gap between Fermi level states with
positive and negative momentum in the transport direction.
