Electron-phonon scattering from Green's function transport combined with molecular dynamics: Applications to mobility predictions

Markussen, Troels; Palsgaard, Mattias Lau Nøhr; Stradi, Daniele; Gunst, Tue; Brandbyge, Mads; Stokbro, Kurt

doi:10.1103/physrevb.95.245210

Cited by 41 publications

(38 citation statements)

References 41 publications

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“…In Ref. 146 we showed that the average transmission from a thermal distribution of configurations accurately describes the inelastic electron transmission spectrum due to electron-phonon scattering at this temperature. In the special thermal displacement (STD) method, the average is replaced with a single representative configuration, which may drastically reduce the computational cost of inelastic transport simulations.…”

Section: Special Thermal Displacement Methodsmentioning

confidence: 95%

QuantumATK: an integrated platform of electronic and atomic-scale modelling tools

Smidstrup¹,

Markussen²,

Vancraeyveld³

et al. 2019

J. Phys.: Condens. Matter

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1,107

662

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QuantumATK is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers. While different aspects and individual modules of the platform have been previously presented, the purpose of this paper is to give a general overview of the platform. The QuantumATK simulation engines enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations. Density functional theory is implemented using either a plane-wave basis or expansion of electronic states in a linear combination of atomic orbitals. The platform includes a long list of advanced modules, including Green's-function methods for electron transport simulations and surface calculations, first-principles electron-phonon and electron-photon couplings, simulation of atomic-scale heat transport, ion dynamics, spintronics, optical properties of materials, static polarization, and more. Seamless integration of the different simulation engines into a common platform allows for easy combination of different simulation methods into complex workflows. Besides giving a general overview and presenting a number of implementation details not previously published, we also present four different application examples. These are calculations of the phonon-limited mobility of Cu, Ag and Au, electron transport in a gated 2D device, multi-model simulation of lithium ion drift through a battery cathode in an external electric field, and electronic-structure calculations of the composition-dependent band gap of SiGe alloys.

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Section: Special Thermal Displacement Methodsmentioning

confidence: 95%

QuantumATK: an integrated platform of electronic and atomic-scale modelling tools

Smidstrup¹,

Markussen²,

Vancraeyveld³

et al. 2019

J. Phys.: Condens. Matter

Self Cite

1,107

662

View full text Add to dashboard Cite

show abstract

“…Correspondingly, electron transport is calculated for configurations with fixed atomic positions which are, however, displaced from the equilibrium lattice sites to simulate the temperature induced atomic vibrations. One direct approach to create an appropriate set of atomic displacements is to superpose all allowed modes and generate one corresponding configuration [52,53], while another approach employs repeated calculations over an ensemble of systems in order to account for thermodynamic fluctuations [38], where each system exhibits different random displacements which are determined by molecular dynamics [38] or a chosen spatial distribution function [37,54]. In this work, we displace both bulk and surface atoms in the scattering region from their equilibrium position by a vector Δ, which is randomly determined for each atom by independently choosing its x, y, and z-coordinates from a uniform distribution…”

Section: Computational Proceduresmentioning

confidence: 99%

“…First-principles simulations that explicitly account for the atomic level structure and associated electronic structure of the thin film are expected to yield correct transport data for very thin films and nanowires [15,21,[36][37][38][39][40][41][42]. They do not directly provide a functional form for ρ as a function of, for example, layer thickness, surface roughness, bulk (phonon) scattering or metal element.…”

Section: Introductionmentioning

confidence: 99%

Resistivity scaling due to electron surface scattering in thin metal layers

Zhou

Gall

2018

Phys. Rev. B

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The effect of electron surface scattering on the thickness-dependent electrical resistivity ρ of thin metal layers is investigated using non-equilibrium Green's function density functional transport simulations. Cu(001) thin films with thickness d = 1-2 nm are used as a model system, employing a random one-monolayer-high surface roughness and frozen phonons to cause surface and bulk scattering, respectively. The zero-temperature resistivity increases from 9.7±1.0 μΩ•cm at d = 1.99 nm to 18.7±2.6 μΩ•cm at d = 0.90 nm, contradicting the asymptotic T = 0 prediction from the classical Fuchs-Sondheimer model. At T = 900 K, ρ = 5.8±0.1 μΩ•cm for bulk Cu and ρ = 13.4±1.1 and 22.5±2.4 μΩ•cm for layers with d = 0.90 and 1.99 nm, respectively, indicating an approximately additive phonon contribution which, however, is smaller than for bulk Cu or atomically smooth layers. The overall data indicates that the resistivity contribution from surface scattering is temperature-independent and proportional to 1/d, suggesting that it can be described using a surface scattering mean free path λ s for 2D transport which is channel-independent and proportional to d. Data fitting indicates λ s = 4×d for the particular simulated Cu(001) surfaces with a one-monolayer-high surface roughness. The 1/d dependence deviates considerably from previous 1/d 2 predictions from quantum models, indicating that the small-roughnessapproximation in these models is not applicable to very thin (< 2 nm) layers, where the surface roughness is a considerable fraction of d.

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“…33. Such DFT calculation of the resistivity of metals is computationally demanding as one needs to integrate the electron-phonon coupling over both electron and phonon wave vectors (k-and q-space, respectively), and only few studies of the electron-phonon coupling in metals exist that includes a full integration [8,25,36,37]. For the integration of the scattering rate we use a sampling of 30×30×30 q-points and tetrahedron integration.…”

Section: Bulk Characteristicsmentioning

confidence: 99%

First-Principles Evaluation of fcc Ruthenium for its use in Advanced Interconnects

Philip¹,

Lanzillo²,

Gunst

et al. 2020

Phys. Rev. Applied

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As the semiconductor industry turns to alternate conductors to replace Cu for future interconnect nodes, much attention has been focused on evaluating the electrical performance of Ru. The typical hexagonal close-packed (hcp) phase has been extensively studied, but relatively little attention has been paid to the face-centered cubic (fcc) phase, which has been shown to nucleate in confined structures and may be present in tight-pitch interconnects. Using ab initio techniques, we benchmark the performance of fcc Ru. We find that the phonon-limited bulk resistivity of the fcc Ru is less than half of that of hcp Ru, a feature we trace back to the stronger electron-phonon coupling elements in hcp Ru that are geometrically inherited from the modified Fermi surface shape of the fcc crystal. Despite this benefit of the fcc phase, high grain boundary scattering results in increased resistivity compared to Cu-based interconnects with similar average grain size. We find, however, that the line resistance of fcc Ru is lower than that of Cu below 21 nm line width due to the conductor volume lost to adhesion and wetting liners. In addition to studying bulk transport properties, we evaluate the performance of adhesion liners for fcc Ru. We find that it is energetically more favorable for fcc Ru to bind directly to silicon dioxide than through conventional adhesion liners such as TaN and TiN. In the case that a thin liner is necessary for the Ru deposition technique, we find that the vertical resistance penalty of a liner for fcc Ru can be up to eight times lower than that calculated for conventional liners used for Cu interconnects. Our calculations, therefore, suggest that the formation of the fcc phase of Ru may be a beneficial for advanced, low-resistance interconnects. arXiv:2001.02216v3 [cond-mat.mtrl-sci] a) fcc b) hcp

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Electron-phonon scattering from Green's function transport combined with molecular dynamics: Applications to mobility predictions

Cited by 41 publications

References 41 publications

QuantumATK: an integrated platform of electronic and atomic-scale modelling tools

QuantumATK: an integrated platform of electronic and atomic-scale modelling tools

Resistivity scaling due to electron surface scattering in thin metal layers

First-Principles Evaluation of fcc Ruthenium for its use in Advanced Interconnects

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