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Heterostructures of magnetic topological insulators (MTIs) and superconductors (SCs) in two-dimensional (2D) slab and one-dimensional (1D) nanoribbon geometries have been predicted to host, respectively, chiral Majorana edge states (CMESs) and Majorana bound states (MBSs). We study the topological properties of such MTI/SC heterostructures upon variation of the geometry from wide slabs to quasi-1D nanoribbon systems and as a function of the chemical potential, the magnetic doping, and the induced superconducting pairing potential. To do so, we construct effective symmetry-constrained low-energy Hamiltonians accounting for the real-space confinement. For a nanoribbon geometry with finite width and length, we observe different phases characterized by CMESs, MBSs, as well as coexisting CMESs and MBSs, as the chemical potential, the magnetic doping and/or the width are varied.

We develop an accurate nanoelectronic modeling approach for realistic three-dimensional topological insulator nanostructures and investigate their low-energy surface-state spectrum. Starting from the commonly considered four-band $\boldsymbol{\mathrm{k\cdot p}}$ bulk model Hamiltonian for the Bi$_2$Se$_3$ family of topological insulators, we derive new parameter sets for Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$. We consider a fitting strategy applied to \emph{ab initio} band structures around the $\Gamma$ point that ensures a quantitatively accurate description of the low-energy bulk and surface states, while avoiding the appearance of unphysical low-energy states at higher momenta, something that is not guaranteed by the commonly considered perturbative approach. We analyze the effects that arise in the low-energy spectrum of topological surface states due to band anisotropy and electron-hole asymmetry, yielding Dirac surface states that naturally localize on different side facets. In the thin-film limit, when surface states hybridize through the bulk, we resort to a thin-film model and derive thickness-dependent model parameters from \emph{ab initio} calculations that show good agreement with experimentally resolved band structures, unlike the bulk model that neglects relevant many-body effects in this regime. Our versatile modeling approach offers a reliable starting point for accurate simulations of realistic topological material-based nanoelectronic devices.

We study transport through interfaces in topological nodal-line semimetals, focusing on two geometries: a single interface between two large samples, one nodal-line semimetal and one metal, and an infinite nodal-line semimetal slab in between two metallic regions. We investigate the dependence of the spectra on the boundary conditions, showing how they affect the surface states and the band dispersion. We find a set of drum states, arising from the hybridization of the drumhead states on opposite surfaces at finite slab width, and describe their signatures in the transport properties of a clean sample. Finally, we compute the electronic trajectories in the ballistic regime and show that there is a series of resonant angles that ensure perfect transmission. We also show how the current density profile acquires an inhomogeneous distribution in the radial direction., Comment: 18 pages, 14 figures. v2: Discussion of the results expanded, figure and references added. Accepted version

We present low-temperature magnetoconductance measurements on Bi$_{1.5}$Sb$_{0.5}$Te$_{1.8}$Se$_{1.2}$ kinks with ribbon-shaped legs. The conductance displays a clear dependence on the in-plane magnetic field orientation. The conductance modulation is consistent with orbital effect-driven trapping of the topological surface states on different side facets of the legs of the kink, which affects their transmission across the kink. This magnetic field-driven trapping and conductance pattern can be explained with a semiclassical picture and is supported by quantum transport simulations. The interpretation is corroborated by varying the angle of the kink and analyzing the temperature dependence of the observed magnetoconductance pattern, indicating the importance of phase coherence along the cross section perimeter of the kink legs., Comment: Main Text (7 pages, 4 figures) and Supplemental Material (3 pages, 3 figures)

Inducing Cooper pairing in a thin ferromagnetic topological insulator in the quantum anomalous Hall state (called quantum anomalous Hall insulator, QAHI) is a promising way to realize topological superconductivity with associated chiral Majorana edge states. However, finding evidence of superconducting proximity effect in a QAHI has proven to be a considerable challenge due to inherent experimental difficulties. Here we report the observation of crossed Andreev reflection (CAR) across a narrow superconducting Nb electrode contacting the chiral edge state of a QAHI, evinced by a negative nonlocal voltage measured downstream from the grounded Nb electrode. This is an unambiguous signature of induced superconducting pair correlation in the chiral edge state. Our theoretical analysis demonstrates that CAR processes of the chiral edge are not strongly dependent on the nature of the superconductivity that mediates them. Nevertheless, the characteristic length of the CAR process is found to be much longer than the superconducting correlation length in Nb, which suggests that the CAR is in fact mediated by superconductivity induced on the QAHI surface. The approach and results presented here provide a foundation for future studies of topological superconductivity and Majorana physics, as well as for the search for non-Abelian zero modes., Comment: 45 pages total; 27 pages of main text with 4 figures, 18 pages of supplement with 9 figures

We theoretically discuss electronic transport via Majorana states in magnetic topological insulator-superconductor junctions with an asymmetric split of the applied bias voltage. We study normal-superconductor-normal (NSN) junctions made of narrow (wire-like) or wide (film-like) magnetic topological insulator slabs with a central proximitized superconducting sector. The occurrence of charge non-conserving Andreev processes entails a nonzero conductance related to an electric current flowing to ground from the proximitized sector of the NSN junction. We show that topologically-protected Majorana modes require an antisymmetry of this conductance with respect to the point of equally split bias voltage across the junction.

We present low-temperature magnetotransport measurements on selectively-grown Sb$_2$Te$_3$-based topological insulator ring structures. These topological insulator ring geometries display clear Aharonov-Bohm oscillations in the conductance originating from phase-coherent transport around the ring. The temperature dependence of the oscillation amplitude indicates that the Aharonov-Bohm oscillations originate from ballistic transport along the ring arms. The oscillations can therefore be attributed to topological surface states, which can maintain a quasi-ballistic transport regime in the presence of disorder. Further insight on the phase coherence is gained by comparing with similar Aharonov-Bohm-type oscillations in topological insulator nanoribbons exposed to an axial magnetic field. Here, quasi-ballistic phase-coherent transport is confirmed for closed-loop topological surface states in transverse direction enclosing the cross-section of the nanoribbon. In contrast, the appearance of universal conductance fluctuations indicates phase-coherent transport in the diffuse regime, which is attributed to bulk carrier transport. Thus, it appears that even in the presence of diffusive $p$-type charge carriers in Aharonov-Bohm ring structures, phase-coherent quasi-ballistic transport of topologically protected surface states is maintained over long distances., Comment: 11 pages (including Supplementary Material), 5 figures, 4 supplementary figures

Magnetic topological insulators in the quantum anomalous Hall regime host ballistic chiral edge channels. When proximitized by an $s$-wave superconductor, these edge states offer the potential for realizing topological superconductivity and Majorana bound states without the detrimental effect of large externally-applied magnetic fields on superconductivity. Realizing well-separated unpaired Majorana bound states requires magnetic topological insulator ribbons with a width of the order of the transverse extent of the edge state, however, which is expected to bring the required ribbon width down to around 100 nm. In this regime, it is known to be extremely difficult to retain the ballistic nature of chiral edge channels and realize a quantized Hall conductance. In this paper, we study the impact of disorder in such magnetic topological insulator nanoribbons and compare the fragility of ballistic chiral edge channels with the stability of Majorana bound states when the ribbon is covered by a superconducting film. We find that the Majorana bound states exhibit greater robustness against disorder than the underlying chiral edge channels., Comment: 6 pages, 5 figures

Topological insulator (TI) nanoribbons with proximity-induced superconductivity are a promising platform for Majorana bound states (MBSs). In this work, we consider a detailed modeling approach for a TI nanoribbon in contact with a superconductor via its top surface, which induces a superconducting gap in its surface-state spectrum. The system displays a rich phase diagram with different numbers of end-localized MBSs as a function of chemical potential and magnetic flux piercing the cross section of the ribbon. These MBSs can be robust or fragile upon consideration of electrostatic disorder. We simulate a tunneling spectroscopy setup to probe the different topological phases of top-proximitized TI nanoribbons. Our simulation results indicate that a top-proximitized TI nanoribbon is ideally suited for realizing fully gapped topological superconductivity, in particular when the Fermi level is pinned near the Dirac point. In this regime, the setup yields a single pair of MBSs, well separated at opposite ends of the proximitized ribbon, which gives rise to a robust quantized zero-bias conductance peak., Comment: 12 pages, 5 figures

Quantum spin Hall (QSH) insulators have unique electronic properties, comprising a band gap in their two-dimensional interior and one-dimensional spin-polarized edge states in which current flows ballistically. In scanning tunneling microscopy (STM), the edge states manifest themselves as a localized density of states. However, there is a significant research gap between the observation of edge states in nanoscale spectroscopy, and the detection of ballistic transport in edge channels which typically relies on transport experiments with microscale lithographic contacts. Here, we study few-layer films of the three-dimensional topological insulator (Bi$_{x}$Sb$_{1-x})_2$Te$_3$, for which a topological transition to a two-dimensional topological QSH insulator phase has been proposed. Indeed, an edge state in the local density of states is observed within the band gap. Yet, in nanoscale transport experiments with a four-tip STM, 2 and 3 quintuple layer films do not exhibit a ballistic conductance in the edge channels. This demonstrates that the detection of edge states in spectroscopy can be misleading with regard to the identification of a QSH phase. In contrast, nanoscale multi-tip transport experiments are a robust method for effectively pinpointing ballistic edge channels, as opposed to trivial edge states, in quantum materials.

The resistivity scaling of metals is a crucial limiting factor for further downscaling of interconnects in nanoelectronic devices that affects signal delay, heat production, and energy consumption. Here, we generalize a commonly considered figure of merit for selecting promising candidate metals with highly anisotropic Fermi surfaces in terms of their electronic transport properties at the nanoscale. For this, we introduce a finite-temperature transport tensor, based on band structures obtained from first principles. This transport tensor allows for a straightforward comparison between highly anisotropic metals in nanostructures with different lattice orientations and arbitrary transport directions. By evaluating the temperature dependence of the tensor components, we also assess the validity of a Fermi surface-based evaluation of the transport properties at zero temperature, rather than considering standard operating temperature conditions., Comment: 15 pages, 9 figures, updated numerical integration scheme and analysis of temperature dependence

Three-dimensional topological insulator (3D TI) nanowires display various interesting magnetotransport properties that can be attributed to their spin-momentum-locked surface states such as quasiballistic transport and Aharonov-Bohm oscillations. Here, we focus on the transport properties of a 3D TI nanowire with a gated section that forms an electronic Fabry-P\'erot (FP) interferometer that can be tuned to act as a surface-state filter or energy barrier. By tuning the carrier density and length of the gated section of the wire, the interference pattern can be controlled and the nanowire can become fully transparent for certain topological surface-state input modes while completely filtering out others. We also consider the interplay of FP interference with an external magnetic field, with which Klein tunneling can be induced, and transverse asymmetry of the gated section, e.g., due to a top-gated structure, which displays an interesting analogy with Rashba nanowires. Due to its rich conductance phenomenology, we propose a 3D TI nanowire with gated section as an ideal setup for a detailed transport-based characterization of 3D TI nanowire surface states near the Dirac point, which could be useful towards realizing 3D TI nanowire-based topological superconductivity and Majorana bound states., Comment: 22 pages, 11 figures

Three-dimensional topological insulators (TIs) host helical Dirac surface states at the interface with a trivial insulator. In quasi-one-dimensional TI nanoribbon structures the wave function of surface charges extends phase-coherently along the perimeter of the nanoribbon, resulting in a quantization of transverse surface modes. Furthermore, as the inherent spin-momentum locking results in a Berry phase offset of $\pi$ of self-interfering charge carriers an energy gap within the surface state dispersion appears and all states become spin-degenerate. We investigate and compare the magnetic field dependent surface state dispersion in selectively deposited Bi$_2$Te$_3$ TI micro- and nanoribbon structures by analysing the gate voltage dependent magnetoconductance at cryogenic temperatures. While in wide microribbon devices the field effect mainly changes the amount of bulk charges close to the top surface we identify coherent transverse surface states along the perimeter of the nanoribbon devices responding to a change in top gate potential. We quantify the energetic spacing in between these quantized transverse subbands by using an electrostatic model that treats an initial difference in charge carrier densities on the top and bottom surface as well as remaining bulk charges. In the gate voltage dependent transconductance we find oscillations that change their relative phase by $\pi$ at half-integer values of the magnetic flux quantum applied coaxial to the nanoribbon, which is a signature for a magnetic flux dependent topological phase transition in narrow, selectively deposited TI nanoribbon devices., Comment: 20 pages, 5 figures

We use a superconducting microresonator as a cavity to sense absorption of microwaves by a superconducting quantum point contact defined by surface gates over a proximitized two-dimensional electron gas. Renormalization of the cavity frequency with phase difference across the point contact is consistent with adiabatic coupling to Andreev bound states. Near $\pi$ phase difference, we observe random fluctuations in absorption with gate voltage, related to quantum interference-induced modulations in the electron transmission. We identify features consistent with the presence of single Andreev bound states and describe the Andreev-cavity interaction using a dispersive Jaynes-Cummings model. By fitting the weak Andreev-cavity coupling, we extract ~GHz decoherence consistent with charge noise and the transmission dispersion associated with a localized state.

Topological surface states of three-dimensional topological insulator nanoribbons and their distinct magnetoconductance properties are promising for topoelectronic applications and topological quantum computation. A crucial building block for nanoribbon-based circuits are three-terminal junctions. While the transport of topological surface states on a planar boundary is not directly affected by an in-plane magnetic field, the orbital effect cannot be neglected when the surface states are confined to the boundary of a nanoribbon geometry. Here, we report on the magnetotransport properties of such three-terminal junctions. We observe a dependence of the current on the in-plane magnetic field, with a distinct steering pattern of the surface state current towards a preferred output terminal for different magnetic field orientations. We demonstrate that this steering effect originates from the orbital effect, trapping the phase-coherent surface states in the different legs of the junction on opposite sides of the nanoribbon and breaking the left-right symmetry of the transmission across the junction. The reported magnetotransport properties demonstrate that an in-plane magnetic field is not only relevant but also very useful for the characterization and manipulation of transport in three-dimensional topological insulator nanoribbon-based junctions and circuits, acting as a topoelectric current switch., Comment: Main Text (8 pages, 5 figures) + Supplemental Material (13 pages, 10 figures)

The potential of a wide range of layered ternary carbide and nitride MAX phases as conductors in interconnect metal lines in advanced CMOS technology nodes has been evaluated using automated first principles simulations based on density functional theory. The resistivity scaling potential of these compounds, i.e. the sensitivity of their resistivity to reduced line dimensions, has been benchmarked against Cu and Ru by evaluating their transport properties within a semiclassical transport formalism. In addition, their cohesive energy has been assessed as a proxy for the resistance against electromigration and the need for diffusion barriers. The results indicate that numerous MAX phases show promise as conductors in interconnects of advanced CMOS technology nodes., Comment: 26 pages, 4 figures, 4 tables

The temperature coefficients of the resistivity (TCR) of Cu, Ru, Co, Ir, and W thin films have been investigated as a function of film thickness below 10 nm. Ru, Co, and Ir show bulk-like TCR values that are rather independent of the thickness whereas the TCR of Cu increases strongly with decreasing thickness. Thin W films show negative TCR values, which can be linked to high disorder. The results are qualitatively consistent with a temperature-dependent semiclassical thin film resistivity model that takes into account phonon, surface, and grain boundary scattering., Comment: 11 pages, 4 figures

In clean Dirac electron systems such as graphene, electron-electron interactions can dominate over other relaxation mechanisms such as phonon or impurity scattering. It has been predicted that in this limit, collective electron dynamics can be described by hydrodynamic equations. The prerequisites for electron liquids are already fulfilled in current experiments and hints of electron hydrodynamics have been identified in transport measurements. Here, we show that a nozzle geometry, implemented for example in a graphene sample, can cause a transition from subsonic to supersonic flow and provides an interesting probe for the hydrodynamic regime of Dirac electrons. In particular, we predict two distinct transport features that can be seen in the experimentally measurable voltage characteristics on the exit side of the nozzle: a pronounced negative local resistance, and an abrupt change of the electrostatic potential induced by an electron shock wave. Our results pave the way for an experimental identification of supersonic hydrodynamic electron flow and for the experimental study of electron shock waves., Comment: Main Text (9 pages, 3 figures) + Supplemental Material (16 pages, 9 figures), major update including corrected shock front position and treatment of viscous nozzle flow

We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorder-induced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to realize a twisted bulk Fermi ribbon with nontrivial winding number. Our results put forward a paradigm for the exploration of non-Hermitian topological phases of matter., Comment: Main Text (6 pages, 2 figures) + Supplemental Material (7 pages, 1 figure)

We investigate the diffusive electron-transport properties of charge-doped graphene ribbons and nanoribbons with imperfect edges. We consider different regimes of edge scattering, ranging from wide graphene ribbons with (partially) diffusive edge scattering to ribbons with large width variations and nanoribbons with atomistic edge roughness. For the latter, we introduce an approach based on pseudopotentials, allowing for an atomistic treatment of the band structure and the scattering potential, on the self-consistent solution of the Boltzmann transport equation within the relaxation-time approximation and taking into account the edge-roughness properties and statistics. The resulting resistivity depends strongly on the ribbon orientation, with zigzag (armchair) ribbons showing the smallest (largest) resistivity and intermediate ribbon orientations exhibiting intermediate resistivity values. The results also show clear resistivity peaks, corresponding to peaks in the density of states due to the confinement-induced subband quantization, except for armchair-edge ribbons that show a very strong width dependence because of their claromatic behavior. Furthermore, we identify a strong interplay between the relative position of the two valleys of graphene along the transport direction, the correlation profile of the atomistic edge roughness, and the chiral valley modes, leading to a peculiar strongly suppressed resistivity regime, most pronounced for the zigzag orientation., Comment: 13 pages, 7 figures

We study the magnetotransport properties of patterned 3D topological insulator nanostructures with several leads, such as kinks or Y-junctions, near the Dirac point with analytical as well as numerical techniques. The interplay of the nanostructure geometry, the external magnetic field and the spin-momentum locking of the topological surface states lead to a richer magnetoconductance phenomenology as compared to straight nanowires. Similar to straight wires, a quantized conductance with perfect transmission across the nanostructure can be realized across a kink when the input and output channels are pierced by a half-integer magnetic flux quantum. Unlike for straight wires, there is an additional requirement depending on the orientation of the external magnetic field. A right-angle kink shows a unique $\pi$-periodic magnetoconductance signature as a function of the in-plane angle of the magnetic field. For a Y-junction, the transmission can be perfectly steered to either of the two possible output legs by a proper alignment of the external magnetic field. These magnetotransport signatures offer new ways to explore topological surface states and could be relevant for quantum transport experiments on nanostructures which can be realized with existing fabrication methods., Comment: 12 pages, 8 figures, including corrections in accordance with Erratum Phys. Rev. B 103, 079902 (2021)

Ru has been considered a candidate to replace Cu-based interconnects in VLSI circuits. Here, a methodology is proposed to predict the resistivity of (Ru) interconnects. First, the dependence of the Ru thin film resistivity on the film thickness is modeled by the semiclassical Mayadas-Shatzkes (MS) approach. The fitting parameters thus obtained are then used as input in a modified MS model for nanowires to calculate wire resistivities. Predicted experimental resistivities agreed within about 10%. The results further indicate that grain boundary scattering was the dominant scattering mechanism in scaled Ru interconnects., Comment: 4 pages. 2 figures

It is generally understood that the resistivity of metal thin films scales with film thickness mainly due to grain boundary and boundary surface scattering. Recently, several experiments and ab initio simulations have demonstrated the impact of crystal orientation on resistivity scaling. The crystal orientation cannot be captured by the commonly used resistivity scaling models and a qualitative understanding of its impact is currently lacking. In this work, we derive a resistivity scaling model that captures grain boundary and boundary surface scattering as well as the anisotropy of the band structure. The model is applied to Cu and Ru thin films, whose conduction bands are (quasi-)isotropic and anisotropic respectively. After calibrating the anisotropy with ab initio simulations, the resistivity scaling models are compared to experimental resistivity data and a renormalization of the fitted grain boundary reflection coefficient can be identified for textured Ru., Comment: 12 pages, 7 figures

We report on the thin film resistivity of several platinum-group metals (Ru, Pd, Ir, Pt). Platinum-group thin films show comparable or lower resistivities than Cu for film thicknesses below about 5\,nm due to a weaker thickness dependence of the resistivity. Based on experimentally determined mean linear distances between grain boundaries as well as ab initio calculations of the electron mean free path, the data for Ru, Ir, and Cu were modeled within the semiclassical Mayadas--Shatzkes model [Phys. Rev. B 1, 1382 (1970)] to assess the combined contributions of surface and grain boundary scattering to the resistivity. For Ru, the modeling results indicated that surface scattering was strongly dependent on the surrounding material with nearly specular scattering at interfaces with SiO2 or air but with diffuse scattering at interfaces with TaN. The dependence of the thin film resistivity on the mean free path is also discussed within the Mayadas--Shatzkes model in consideration of the experimental findings., Comment: 28 pages, 9 figures

A modeling approach, based on an analytical solution of the semiclassical multi-subband Boltzmann transport equation, is presented to study resistivity scaling in metallic thin films and nanowires due to grain boundary and surface roughness scattering. While taking into account the detailed statistical properties of grains, roughness and barrier material as well as the metallic band structure and quantum mechanical aspects of scattering and confinement, the model does not rely on phenomenological fitting parameters., Comment: 11 pages, 7 figures, accepted for publication in Microelectronic Engineering edition on Materials for Advanced Metallization

Fermi's golden rule underpins the investigation of mobile carriers propagating through various solids, being a standard tool to calculate their scattering rates. As such, it provides a perturbative estimate under the implicit assumption that the effect of the interaction Hamiltonian which causes the scattering events is sufficiently small. To check the validity of this assumption, we present a general framework to derive simple validity criteria in order to assess whether the scattering rates can be trusted for the system under consideration, given its statistical properties such as average size, electron density, impurity density et cetera. We derive concrete validity criteria for metallic nanowires with conduction electrons populating a single parabolic band subjected to different elastic scattering mechanisms: impurities, grain boundaries and surface roughness., Comment: 23 pages, 8 figures, revised article version accepted for publication in Journal of Physics: Condensed Matter

Ando's surface roughness model is applied to metallic nanowires and extended beyond small roughness size and infinite barrier limit approximations for the wavefunction overlaps, such as the Prange-Nee approximation. Accurate and fast simulations can still be performed without invoking these overlap approximations by averaging over roughness profiles using finite domain distribution functions to obtain an analytic solution for the scattering rates. The simulations indicate that overlap approximations, while predicting a resistivity that agrees more or less with our novel approach, poorly estimate the underlying scattering rates. All methods show that a momentum gap between left- and right-moving electrons at the Fermi level, surpassing a critical momentum gap, gives rise to a substantial decrease in resistivity., Comment: 5 pages, 5 figures

A self-consistent analytical solution of the multi-subband Boltzmann transport equation with collision term describing grain boundary and surface roughness scattering is presented to study the resistivity scaling in metal nanowires. The different scattering mechanisms and the influence of their statistical parameters are analyzed. Instead of a simple power law relating the height or width of a nanowire to its resistivity, the picture appears to be more complicated due to quantum-mechanical scattering and quantization effects, especially for surface roughness scattering., Comment: 6 pages, 5 figures

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., Comment: 25 pages, 11 figures

We calculate the resistivity contribution of tilted grain boundaries with varying parameters in sub-10nm diameter metallic nanowires. The results have been obtained with the Boltzmann transport equation and Fermi's golden rule, retrieving correct state-dependent relaxation times. The standard approximation schemes for the relaxation times are shown to fail when grain boundary tilt is considered. Grain boundaries tilted under the same angle or randomly tilted induce a resistivity decrease., Comment: 5 pages, 3 figures in 2015 Joint International EUROSOI Workshop and International Conference on Ultimate Integration on Silicon (EUROSOI-ULIS)

We study the resistivity scaling in nanometer-sized metallic wires due to surface roughness and grain-boundaries, currently the main cause of electron scattering in nanoscaled interconnects. The resistivity has been obtained with the Boltzmann transport equation, adopting the relaxation time approximation (RTA) of the distribution function and the effective mass approximation for the conducting electrons. The relaxation times are calculated exactly, using Fermi's golden rule, resulting in a correct relaxation time for every sub-band state contributing to the transport. In general, the relaxation time strongly depends on the sub-band state, something that remained unclear with the methods of previous work. The resistivity scaling is obtained for different roughness and grain-boundary properties, showing large differences in scaling behavior and relaxation times. Our model clearly indicates that the resistivity is dominated by grain-boundary scattering, easily surpassing the surface roughness contribution by a factor of 10., Comment: 19 pages, 5 figures