We extend quantum models of nanowire surface scattering to incorporate bulk resistivity and extract an expression for the increased resistivity due to surface roughness. To learn how to improve conductivity, we calculate conductivity degradation from individual wavelengths of surface roughness, and show how these can be convolved to give resistivity for arbitrary surfaces. We review measurements from Cu films and conclude that roughness at short wavelengths (less than 100 nm) dominates scattering, and that primarily specular scattering should be achievable for RMS roughness below about 0.7 nm.As the minimum feature size in semiconductor technology continues to shrink, metal nanowires with thickness <45 nm are now needed to interconnect electronic nanodevices. However, measurements show nanowires have substantially higher resistivity than bulk metals [1,2], leading to interconnect delays, power loss, and other limits on performance. Scattering from surfaces, interfaces and grain boundaries are the causes of this conductivity degradation, but microscopic understanding of these effects and quantitative predictions of their magnitude have been limited. Here, we investigate the detailed dependence of conductivity on surface roughness profile and analyze the resulting technological impact.The first quantitative treatments of surface and size effects in thin films or wires were the semiclassical methods of Fuchs [3] and Sondheimer [4]. These approaches assume a ratio p of carrier collisions with the surface reflect specularly, while 1−p scatter diffusely. Such theories can be fit to experiment with p as a free parameter, but do not provide insight into how to improve conductivity.More recently, surface roughness scattering has raised the attention of researchers in industry [5,6,7], and quantum mechanical approaches to surface scattering calculations have been proposed. The two primary approaches include the Kubo linear response theory of Tesanović et al. [8] and Trivedi and Ashcroft [9], and the diagrammatic Keldysh formalism of Meyerovich and collaborators [10,11,12]. Here we follow the approach of Meyerovich et al., which is readily applied to arbitrary surface roughness profiles. We calculate the contribution of each spatial frequency of surface roughness and convolve with roughness data extracted from experiments to gain insight into the nature of surface roughness scattering.In our conductivity calculations, we consider a thin film because it reproduces the major qualitative results of a wire (and matches quantitatively when Eq. (9) below holds), while avoiding strong localization and other effects that make 1D systems problematic to deal with theoretically [12,13]. For the technologically important 10-100 nm scale, wire conductivity can be accurately estimated by combining effects of scattering from sidewalls to that from top and bottom surfaces.In a thin film of thickness L, boundary conditions at the surfaces lead to a density of states quantized in the transverse direction. As a result, the conduction band, d...
