Paper EM-TuM12
Metal Resistivity Below 10 nm

Tuesday, November 11, 2014, 11:40 am, Room 314

Electron scattering at surfaces and grain boundaries causes the resistivity of metals to increase with decreasing wire width or film thickness. This effect is quantified using (i) in situ transport measurements on single-crystal, atomically smooth Cu(001) layers, (ii) textured Cu(111) layers and patterned Cu wires with independently varying grain size, thickness and line width, (iii) in situ grown interfaces including Cu-Ni, Cu-Ta, Cu-MgO, Cu-Ti, Cu-SiO₂ and Cu-oxygen, and (iv) epitaxial layers of various other metals including Ag(001), W(001), Ta(001), Ni(001), and TiN(001). The layers are grown by ultra-high vacuum magnetron sputter deposition on MgO(001) substrates and are found to be atomically smooth single crystals by a combination of x-ray diffraction θ-2θ scans, ω-rocking curves, pole figures, reciprocal space mapping, Rutherford backscattering, x-ray reflection, transmission electron microscopy, and in-situ scanning tunneling microscopy.

The measured resistivity is interpreted within the classical models by Fuchs and Sondheimer for surface scattering and Mayadas-Shatzkes for grain boundary scattering. The data is well described by these models. However, fitting of the resistivity vs thickness for metal layers with non-spherical Fermi surfaces provides values for the bulk electron mean free paths that deviates from the expected free-electron values by factors of 5-10, indicating the breakdown of these semiclassical models. In addition, the F-S model also does not correctly predict the temperature dependence, as the measured scattering specularity as well as the product of bulk resistivity times mean free path are temperature dependent.

First-principles density functional (DFT) calculations are employed to develop an understanding of electron transport in metals at reduced length scales: (i) The Fermi surface of the bulk metal is determined and the electronic-structure contribution to the conductivity calculated by integration over the Brillouin zone. This provides, in combination with the known bulk resistivity, values for the bulk electron mean free path of 40, 3.3, and 16 nm for Cu, Ta, and W, respectively. (ii) Application of the Boltzmann transport equation and simultaneous integration over real and reciprocal space of the thin film and Brillouin zone, shows considerable anisotropy effects. For example, electron scattering at a W(100) surface has a two times larger effect on the resistivity than scattering on W(110). (iii) Simulation of transport using the 2D Fermi surfaces of thin films, and (iv) non-equilibrium DFT simulations are used quantitatively determine electron scattering which will be directly mapped on a phenomenological model.