skip to main content

Title: First-principles prediction of electron grain boundary scattering in fcc metals
The electron reflection probability r at symmetric twin boundaries Σ3, Σ5, Σ9, and Σ11 is predicted from first principles for the eight most conductive face-centered cubic (fcc) metals. r increases with decreasing interplanar distance of atomic planes parallel to the boundary. This provides the basis for an extrapolation scheme to estimate the reflection probability r r at random grain boundaries, which is relatively small, r r = 0.28–0.39, for Cu, Ag, and Au due to their nearly spherical Fermi surfaces, but approximately two times higher for Al, Ca, Ni, Rh, and Ir with a predicted r r = 0.61–0.72. The metal resistivity in the limit of small randomly oriented grains with fixed average size is expected to be proportional to the materials benchmark quantity ρ o λ × r r /(1 − r r ), where ρ o and λ are the bulk resistivity and bulk electron mean free path, respectively. Cu has the lowest value for this quantity, indicating that all other fcc metals have a higher resistivity in the limit of small randomly oriented grains. Thus, the conductivity benefit of replacement metals for narrow Cu interconnect lines can only be realized if the grains are larger than the linewidth or exhibit symmetric orientation relationships where r < r r .  more » « less
Award ID(s):
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Applied Physics Letters
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Ru(0001) and Co(0001) films with thickness d ranging from 5 to 300 nm are sputter deposited onto Al2O3(0001) substrates in order to quantify and compare the resistivity size effect. Both metals form epitaxial single crystal layers with their basal planes parallel to the substrate surface and exhibit a root-mean-square roughness < 0.4 nm for Ru and < 0.9 nm for Co. Transport measurements on these layers have negligible resistance contributions from roughness and grain boundary scattering which allows direct quantification of electron surface scattering. The measured resistivity ρ vs d is well described by the classical Fuchs-Sondheimer model, indicating a mean free path for transport within the basal plane of λ = 6.7 ± 0.3 nm for Ru and λ = 19.5 ± 1.0 nm for Co. Bulk Ru is 36% more resistive than Co; in contrast, Ru(0001) layers with d ≤ 25 nm are more conductive than Co(0001) layers, which is attributed to the shorter λ for Ru. The determined λ-values are utilized in combination with the Fuchs-Sondheimer and Mayadas-Shatzkes models to predict and compare the resistance of polycrystalline interconnect lines, assuming a grain boundary reflection coefficient R = 0.4 and accounting for the thinner barrier/adhesion layers available to Ru and Co metallizations. This results in predicted 10 nm half-pitch line resistances for Ru, Co, and Cu of 1.0, 2.2, and 2.1 kΩ/µm, respectively. 
    more » « less
  2. Abstract Owing to its superlative carrier mobility and atomic thinness, graphene exhibits great promise for interconnects in future nanoelectronic integrated circuits. Chemical vapor deposition (CVD), the most popular method for wafer-scale growth of graphene, produces monolayers that are polycrystalline, where misoriented grains are separated by extended grain boundaries (GBs). Theoretical models of GB resistivity focused on small sections of an extended GB, assuming it to be a straight line, and predicted a strong dependence of resistivity on misorientation angle. In contrast, measurements produced values in a much narrower range and without a pronounced angle dependence. Here we study electron transport across rough GBs, which are composed of short straight segments connected together into an extended GB. We found that, due to the zig-zag nature of rough GBs, there always exist a few segments that divide the crystallographic angle between two grains symmetrically and provide a highly conductive path for the current to flow across the GBs. The presence of highly conductive segments produces resistivity between 10 2 to 10 4 Ω μ m regardless of misorientation angle. An extended GB with large roughness and small correlation length has small resistivity on the order of 10 3 Ω μ m, even for highly mismatched asymmetric GBs. The effective slope of the GB, given by the ratio of roughness and lateral correlation length, is an effective universal quantifier for GB resistivity. Our results demonstrate that the probability of finding conductive segments diminishes in short GBs, which could cause a large variation in the resistivity of narrow ribbons etched from polycrystalline graphene. We also uncover spreading resistance due to the current bending in the grains to flow through the conductive segments of the GB and show that it scales linearly with the grain resistance. Our results will be crucial for designing graphene-based interconnects for future integrated circuits. 
    more » « less
  3. Abstract Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on weak recovery of the community based on the graph G , with o ( K ) misclassified vertices on average, in the sublinear regime n 1- o (1) ≤ K ≤ o ( n ). A critical parameter is the effective signal-to-noise ratio λ = K 2 ( p - q ) 2 / (( n - K ) q ), with λ = 1 corresponding to the Kesten–Stigum threshold. We show that a belief propagation (BP) algorithm achieves weak recovery if λ > 1 / e, beyond the Kesten–Stigum threshold by a factor of 1 / e. The BP algorithm only needs to run for log * n + O (1) iterations, with the total time complexity O (| E |log * n ), where log * n is the iterated logarithm of n . Conversely, if λ ≤ 1 / e, no local algorithm can asymptotically outperform trivial random guessing. Furthermore, a linear message-passing algorithm that corresponds to applying a power iteration to the nonbacktracking matrix of the graph is shown to attain weak recovery if and only if λ > 1. In addition, the BP algorithm can be combined with a linear-time voting procedure to achieve the information limit of exact recovery (correctly classify all vertices with high probability) for all K ≥ ( n / log n ) (ρ BP + o (1)), where ρ BP is a function of p / q . 
    more » « less
  4. Beta-phase gallium oxide ([Formula: see text]-Ga 2 O 3 ) is a promising semiconductor for high frequency, high temperature, and high voltage applications. In addition to the [Formula: see text]-phase, numerous other polymorphs exist and understanding the competition between phases is critical to control practical devices. The phase formation sequence of Ga 2 O 3 , starting from amorphous thin films, was determined using lateral-gradient laser spike annealing at peak temperatures of 500–1400 °C on 400 μs to 10 ms timescales, with transformations characterized by optical microscopy, x-ray diffraction, and transmission electron microscopy (TEM). The resulting phase processing map showed the [Formula: see text]-phase, a defect-spinel structure, first nucleating under all annealing times for temperatures from 650 to 800 °C. The cross-sectional TEM at the onset of the [Formula: see text]-phase formation showed nucleation near the film center with no evidence of heterogeneous nucleation at the interfaces. For temperatures above 850 °C, the thermodynamically stable [Formula: see text]-phase was observed. For anneals of 1–4 ms and temperatures below 1200 °C, small randomly oriented grains were observed. Large grains were observed for anneals below 1 ms and above 1200 °C, with anneals above 4 ms and 1200 °C resulting in textured films. The formation of the [Formula: see text]-phase prior to [Formula: see text]-phase, coupled with the observed grain structure, suggests that the [Formula: see text]-phase is kinetically preferred during thermal annealing of amorphous films, with [Formula: see text]-phase subsequently forming by nucleation at higher temperatures. The low surface energy of the [Formula: see text]-phase implied by these results suggests an explanation for the widely observed [Formula: see text]-phase inclusions in [Formula: see text]-phase Ga 2 O 3 films grown by a variety of synthesis methods. 
    more » « less
  5. Extreme ultraviolet (XUV) light sources based on high harmonic generation are enabling the development of novel spectroscopic methods to help advance the frontiers of ultrafast science and technology. In this account we discuss the development of XUV-RA spectroscopy at near grazing incident reflection geometry and highlight recent applications of this method to study ultrafast electron dynamics at surfaces. Measuring core-to-valence transitions with broadband, femtosecond pulses of XUV light extends the benefits of x-ray absorption spectroscopy to a laboratory tabletop by providing a chemical fingerprint of materials, including the ability to resolve individual elements with sensitivity to oxidation state, spin state, carrier polarity, and coordination geometry. Combining this chemical state sensitivity with femtosecond time resolution provides new insight into the material properties that govern charge carrier dynamics in complex materials. It is well known that surface dynamics differ significantly from equivalent processes in bulk materials, and that charge separation, trapping, transport, and recombination occurring uniquely at surfaces governs the efficiency of numerous technologically relevant processes spanning photocatalysis, photovoltaics, and information storage and processing. Importantly, XUV-RA spectroscopy at near grazing angle is also surface sensitive with a probe depth of 3 nm, providing a new window into electronic and structural dynamics at surfaces and interfaces. Here we highlight the unique capabilities and recent applications of XUVRA spectroscopy to study photo-induced surface dynamics in metal oxide semiconductors, including photocatalytic oxides (Fe2O3, Co3O4 NiO, and CuFeO2) as well as photoswitchable magnetic oxide (CoFe2O4). We first compare the ultrafast electron self-trapping rates via small polaron formation at the surface and bulk of Fe2O3 where we note that the energetics and kinetics of this process differ significantly at the surface. Additionally, we demonstrate the ability to systematically tune this kinetics by molecular functionalization, thereby, providing a route to control carrier transport at surfaces. We also measure the spectral signatures of charge transfer excitons with site specific localization of both electrons and holes in a series of transition metal oxide semiconductors (Fe2O3, NiO, Co3O4). The presence of valence band holes probed at the oxygen L1-edge confirms a direct relationship between the metal-oxygen bond covalency and water oxidation efficiency. For a mixed metal oxide CuFeO2 in the layered delafossite structure, XUV-RA reveals that the sub-picosecond hole thermalization from O 2p to Cu 3d states of CuFeO2 leads to the spatial separation of electrons and holes, resulting in exceptional photocatalytic performance for H2 evolution and CO2 reduction of this material. Finally, we provide an example to show the ability of XUV-RA to probe spin state specific dynamics in a the photo-switchable ferrimagnet, cobalt ferrite (CoFe2O4). This study provides a detailed understating of ultrafast spin switching in a complex magnetic material with site-specific resolution. In summary, the applications of XUV-RA spectroscopy demonstrated here illustrate the current abilities and future promise of this method to extend molecule-level understanding from well-defined photochemical complexes to complex materials so that charge and spin dynamics at surfaces can be tuned with the precision of molecular photochemistry. 
    more » « less