Conductivity size effect of polycrystalline metal nanowires

It is well known that the conductivity of metal nanowires decreases with the wire diameter. This size effect was first studied for metal thin films when the film thickness approaches the electron mean free path. Fuchs & Sondheimer (FS) pointed out that the external surface scattering of the electrons contributes to the conductivity decrease. Mayadas and Shatzkes (MS) pointed out that the grain boundary scattering plays a major role for polycrystalline thin films. As is clear that nanowires are 2-d constrained instead of 1-d for thin film, so the size effect would be more eminent. However, today the mostly used physical model for the conductivity of metal nanowires is still the MS theory. This paper proposes a more complete model suitable for circular cross-section polycrystalline metal nanowires, which takes into account of background scattering, external surface scattering, as well as grain boundary scattering. Comparison with experiment data showed that our model can well explain the conductivity size effect of polycrystalline metal nanowires.