The experimentally measured resistivity of Co(0001) and Ru(0001) single crystal thin films, grown on c-plane sapphire substrates, as a function of thickness is modeled using the semiclassical model of Fuchs-Sondheimer. The model fits show that the resistivity of Ru would cross below that for Co at a thickness of approximately 20 nm. For Ru films with thicknesses above 20 nm, transmission electron microscopy evidences threading and misfit dislocations, stacking faults and deformation twins. Exposure of Co films to ambient air, and the deposition of oxide layers of SiO2, MgO, Al2O3 and Cr2O3 on Ru degrade the surface specularity of the metallic layer. However, for the Ru films, annealing in a reducing ambient restores the surface specularity. Epitaxial electrochemical deposition of Co on epitaxially-deposited Ru layers is used as an example to demonstrate the feasibility of generating epitaxial interconnects for back-end of line structures. An electron transport model based on a tight-binding (TB) approach is described, with Ru interconnects used an example. The model allows conductivity to be computed for structures comprising large ensembles of atoms (10 5 -10 6 ), scales linearly with system size and can also incorporate defects.

We investigate experimentally and theoretically the dynamics of a crack front during the microinstabilities taking place in heterogeneous materials between two successive equilibrium positions. We focus specifically on the spatio-temporal evolution of the front, as it relaxes to a straight configuration, after depinning from a single obstacle of controlled strength and size. We show that this depinning dynamics is not controlled by inertia, but instead, by the rate dependency of the dissipative mechanisms taking place within the fracture process zone. This implies that the crack speed fluctuations around its average value vm can be predicted from an overdamped equation of motion (v −vm)/v0 = (G−Gc(vm))/Gc(vm) involving the characteristic material speed v0 = Gc(vm)/G c (vm) that emerges from the variation of fracture energy with crack speed. Our findings pave the way to a quantitative description of the critical depinning dynamics of cracks in disordered solids and open up new perspectives for the prediction of the effective failure properties of heterogeneous materials.Woods, nacre, bones or rationally designed artificial materials, are all heterogeneous solids, with mechanical properties far exceeding those of their constitutive components. Understanding the role of microscale heterogeneities on the macroscale fracture behavior of solids still remains a query. This becomes especially relevant now, as rapid developments in microfabrication techniques allow the tailoring of microstructures at ever smaller scales, yielding new types of composites, known as meta-materials, with unprecedented mechanical properties [1][2][3][4][5][6]. Recently, significant progresses were made for weakly heterogeneous brittle solids where models describing a crack front as a deformed interface pinned by tough obstacles have been successfully applied [7][8][9][10][11]. The homogenized fracture properties can be computed exactly within the so-called weak pinning limit [12], where the elastic energy release rate G balances the fracture energy G c at any time and any position along the front. This approach holds for weak variations of toughness along the propagation direction. The crack evolution is then smooth and can be properly approximated by a continuous succession of equilibrium front configurations [13,14]. This approach was successfully used to design weakly heterogeneous systems with improved and new macroscopic failure properties [15][16][17][18].However, most natural and engineered materials have a microstructure composed of discontinuous heterogeneities which cannot be described within the weak pinning regime. The strong pinning regime that predominates for large toughness gradients challenges standard homogenization approaches. Crack propagation is not quasi-static but proceeds by intermittent and local micro-instabilities. Further, for a disordered distribution of obstacles, crack growth takes place close to the socalled depinning critical transition [19][20][21], so that the h s d = 141 �m, C = 1.2, v m = 24 �m/s FIG. 1. (a...

The resistivity size effect in Ir is quantified with in situ and ex situ transport measurements at 295 and 77 K using epitaxial layers with thickness d = 5–140 nm deposited on MgO(001) and Al2O3(0001) substrates. Data fitting with the Fuchs–Sondheimer model of the measured resistivity ρ vs d for single-crystal Ir(001)/MgO(001) layers deposited at Ts = 1000 °C yield an effective electron mean free path λeff = 7.4 ± 1.2 nm at 295 K, a room-temperature bulk resistivity ρo = 5.2 μΩ cm, and a temperature-independent product ρoλeff = (3.8 ± 0.6)×10−16 Ω m2, which is in good agreement with first-principles predictions. Layers deposited at Ts = 700 °C and stepwise annealed to 1000 °C exhibit a unique polycrystalline multi-domain microstructure with smooth renucleated 111-oriented grains that are >10 μm wide for d = 10 nm, resulting in a 26% lower ρoλeff. Ir(111)/Al2O3(0001) layers exhibit two 60°-rotated epitaxial domains with an average lateral grain size of 88 nm. The grain boundaries cause a thickness-independent resistivity contribution Δρgb = 0.86 ± 0.19 and 0.84 ± 0.12 μΩ cm at 295 and 77 K, indicating an electron reflection coefficient R = 0.52 ± 0.02 for this boundary characterized by a 60° rotation about the ⟨111⟩ axis. The overall results indicate that microstructural features including strain fields from misfit dislocations and/or atomic-level roughness strongly affect the resistivity size effect in Ir. The measured ρoλeff for Ir is smaller than for any other elemental metal and 69%, 43%, and 25% below reported ρoλ products for Co, Cu, and Ru, respectively, indicating that Ir is a promising alternate metal for narrow high-conductivity interconnects.

In situ transport measurements on 10-nm-thick epitaxial Cu(001), Co(001), and Rh(001) layers exhibit a characteristic increase in the sheet resistance ΔRs/Ro = 43%, 10%, and 4% when adding 4.0, 13.0, and 13.0 monolayers of Ti, respectively. Similarly, exposing these layers to 0.6 Torr O2 results in a 26%, 22%, and <5% increase in Rs. This suggests that adatoms on Cu and Co surfaces considerably disturb the surface potential, leading to diffuse electron scattering and a resulting resistance increase while these effects are negligible for Rh. A similarly small resistivity increase Δρ/ρ < 7% is measured during air exposure of 10-nm-thick epitaxial layers of electronegative metals including Ru, Rh, Ir, W, and Mo, while Δρ/ρ increases to 11%–36% for more electropositive metals including Cu, Ag, Co, Ni, and Nb. The Δρ for Ni, Co, and Nb is larger than what is expected for a complete transition from specular to diffuse surface scattering, indicating a breakdown of the semiclassical Fuchs–Sondheimer model, which needs to be replaced by a two-dimensional conductor description. The measured inverse correlation between electronegativity and Δρ/ρ suggests that the magnitude of the surface potential perturbation is the primary parameter affecting electron surface scattering in thin metal layers. More specifically, the charge transfer from electropositive metal surfaces to adatoms perturbs the surface potential and causes electron surface scattering and a resistance increase. Conversely, electronegative metals facilitate smooth surface potentials with specular electron reflection and a minimized resistance increase. They are, therefore, promising as conductors for highly scaled interconnect lines.