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Thermal boundary resistance predictions with non-equilibrium Green's function and molecular dynamics simulations

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read With Büttiker probes, non-equilibrium Green's function transport reproduces molecular-dynamics thermal boundary resistance for mass ratios 1 to 10.

desk verdict A clean, honest benchmark showing NEGF with Böttiker probes reproduces MD thermal boundary resistance across mass ratios 1–10, with the main caveat being the untested transferability of the fitted scattering parameters from bulk Si to heavy-Si. read the letter →

arxiv 1908.11578 v3 pith:V6NDGBZT submitted 2019-08-30 physics.app-ph

Yuanchen Chu , Jingjing Shi , Kai Miao , Yang Zhong , Prasad Sarangapani , Timothy S. Fisher , Gerhard Klimeck , Xiulin Ruan
show 1 more author
Tillmann Kubis
This is my paper · ORCID
classification physics.app-ph
keywords thermalboundaryresistancenon-equilibriumGreen'sfunctionBüttikerprobephonontransportanharmonicscatteringmoleculardynamicsSi/heavy-Siinterfacespectralcurrent
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that non-equilibrium Green's function (NEGF) phonon transport can include anharmonicity by attaching a Büttiker probe to each atom, and that the resulting method predicts thermal boundary resistance reliably. It tests this on a Si/heavy-Si interface, where the two materials differ only in atomic mass. After tuning two scattering parameters against a molecular dynamics (MD) bulk thermal conductivity calculation, the NEGF thermal boundary resistance agrees quantitatively with MD across mass ratios from 1 to 10. The method also removes the artificial interface resistance that a ballistic, scattering-free Landauer approach produces at a virtual interface in a homogeneous material. The practical payoff is a spectral, mode-resolved way to compute boundary resistance at finite temperature without the cost of full self-consistent Born scattering.

What carries the argument

The load-bearing object is the Büttiker probe self-energy, a complex, frequency-dependent insertion placed on every atom and vibrational direction: $\Sigma^R_{BP(i,m)}(\omega)=-i\,2\omega\hbar^2/\tau_{i,m}(\omega)$, with the Umklapp lifetime $\tau_i^{-1}(\omega)=BT_i\omega^2 e^{-C/T_i}$. The probe temperatures $T_i$ are unknowns solved iteratively so that each probe conserves energy, which turns the coherent, elastic NEGF calculation into a dissipative one within a recursive Green's function scheme. This object is what removes the spurious interface resistance in homogeneous systems and what lets the energy-resolved current be read directly from the steady-state Green's functions.

What would settle it

Run the same NEGF setup with the same fitted scattering parameters for a mass ratio inside 1 to 10 that is not shown in the paper, such as MR=6, and compare with molecular dynamics; if the boundary resistance deviates substantially from the MD value, the claimed quantitative agreement across the mass-ratio range fails.

Watch

Extended reading notes

Core claim

The central claim is that NEGF with Büttiker probe self-energies, calibrated once on homogeneous bulk Si, gives correct thermal boundary resistance for the Si/heavy-Si interface across mass ratios 1 to 10, and yields zero interface resistance in a perfectly homogeneous system. The probes add a phenomenological scattering rate to each atom that enforces energy conservation through self-consistently solved probe temperatures; the calibration parameters are chosen so the NEGF bulk Si thermal conductivity matches MD. With this calibration, the boundary resistance rises exponentially with mass ratio and agrees with MD, while the artificial resistance of the ballistic Landauer approach disappears. The natural spectral output shows that inelastic scattering allows phonons above the heavy-Si cutoff to propagate, and that mode-resolved currents are controlled by how evenly a phonon mode is distributed across both sides of the interface.

Load-bearing premise

The whole calculation rests on the assumption that the scattering strength fitted in ordinary silicon also applies to the heavier silicon and to the atoms right at the interface, even though heavier atoms vibrate more slowly and the interface may not be as anharmonic as the bulk.

Editorial extensions

If this is right

  • NEGF can now predict thermal boundary resistance at finite temperature with anharmonicity included at a fraction of the cost of self-consistent Born scattering.
  • Homogeneous systems produce exactly zero interface resistance, so spurious boundary terms that plague Landauer-type calculations are eliminated.
  • Energy-resolved, mode-resolved spectral currents come out directly, enabling interface resistance to be traced to specific phonon modes without transformation.
  • The approach is almost free of finite-size effects in the transport direction because it uses open boundary conditions with semi-infinite leads.
  • The fitted scattering parameters transfer from bulk calibration to the interface over mass ratios 1 to 10, supporting the use of Büttiker probes as a practical anharmonicity model.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • This suggests the same fit-to-bulk calibration strategy could work for other homogeneous host materials, though the explicit neglect of mass-dependent scattering means recalibration is likely needed for very large mass contrasts.
  • Because NEGF is spectral and shares a common framework with electronic transport, coupling these phonon Büttiker probes to electron NEGF is a natural route to self-heating and thermoelectric simulations, a direction the paper motivates but does not demonstrate.
  • A testable extension is to vary the bath temperatures; the paper only benchmarks at 320 K and 280 K, so temperature transferability of the fitted parameters remains open.
  • The disappearance of artificial resistance also suggests Büttiker-probe NEGF could serve as a calibration reference for other approximate phonon transport methods that suffer from spurious contact resistances.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This manuscript presents a methodology for including anharmonic phonon scattering in non-equilibrium Green's function (NEGF) calculations of thermal transport, using Büttiker probe self-energies with a phenomenological scattering rate of the form B T ω² exp(−C/T). The two parameters B and C are fitted to reproduce the MD-computed bulk Si thermal conductivity. The method is then applied to Si/heavy-Si interfaces with mass ratios from 1 to 10. The predicted thermal boundary resistance (TBR) agrees quantitatively with MD simulations, and unlike the coherent Landauer approach, the NEGF with Büttiker probes yields zero TBR in homogeneous systems. Spectral analysis of energy-resolved currents and local phonon densities of states illustrates how inelastic scattering enables heat flow by high-frequency phonons above the heavy-Si cutoff and how modal overlap between regions controls the spectral current distribution.

Significance. The paper addresses a real bottleneck in phonon NEGF—the treatment of anharmonicity—and offers a computationally light, spectral alternative to MD. The benchmark against MD over a mass-ratio range of 1–10 is a strong and appropriate test, and the explicit demonstration that the Büttiker-probe NEGF removes the artificial interface resistance plaguing the Landauer approach is a useful contribution. The manuscript is honest about its key approximation (transferability of B and C), and the spectral results are informative. However, the central claim of predictive transferability rests on an assumption that is not directly validated, which limits the strength of the conclusions as currently stated.

major comments (2)
  1. [Methods, Eq. (3) and following paragraph; Results, Fig. 2(b)] The central claim that the Büttiker probe parameters fitted to bulk Si thermal conductivity transfer to Si/heavy-Si interfaces is not directly tested for the mass and interface dependence of the scattering rate. Eq. (3) uses a single functional form for the scattering lifetime, and the same constants B and C are applied in Si and heavy-Si, as stated in the paragraph following Eq. (3). The only calibration is the bulk Si conductivity (Fig. 2(a)), and no homogeneous heavy-Si conductivity is computed or compared. The thermal boundary resistance at high mass ratio is largely controlled by high-frequency Si phonons that must down-convert in heavy-Si through the inelastic Büttiker self-energy; therefore, the agreement in Fig. 2(b) could in principle be coincidental if the true mass dependence of the anharmonic scattering rate differs from the assumed ω² exp(−C/T) form. I request a direct validation: compute NEGF and MD thermal conductivities of homogeneous heavy-Si (for at least MR = 2, 4, 8) with the same B and C, and compare them. If these agree, the transferability claim is substantiated; if they do not, the agreement in Fig. 2(b) should be discussed in that light and the conclusion (which states the parameters 'proved to be transferable') should be softened.
  2. [Results, Fig. 2(b) and surrounding text] The claim of 'quantitative agreement' is not fully supported by the presented data. The MD standard deviations (1.6–4.6%) are reported in the text but are deliberately not plotted, and no numerical values for the relative difference (dotted line) are given. Without error bars or a table of the computed TBR values with uncertainties, the reader cannot assess whether the deviations between NEGF and MD are within statistical uncertainty. Please include the MD error bars in Fig. 2(b) (or provide a table of values with uncertainties for both methods and the relative differences) and state the maximum relative difference observed across MR = 1–10.
minor comments (4)
  1. [Methods, paragraph on Büttiker probes and RGF] The text states that 'each discretized atom in the system has a Büttiker probe applied to it' but later says the RGF method 'requires the Büttiker probe self-energies to be equal throughout each slab.' Please clarify whether the probes are per atom or per slab, and if per atom, how the slab-wise constant approximation is justified.
  2. [Conclusion and Abstract] The claim that the present NEGF approach is 'numerically more efficient than MD' is not supported by any timing, scaling, or resource comparison in the manuscript. Please either include a quantitative efficiency comparison or qualify the claim.
  3. [Fig. 5 caption] The notation '∑4i=1 Ri = 1' should be typeset properly as '∑_{i=1}^{4} R_i = 1' for clarity.
  4. [Methods, local temperature extraction] The paper does not specify how the local temperature profile is extracted in the NEGF calculations (as opposed to the MD simulations). Since Eq. (1) is phrased in terms of a local phonon number density, it would be helpful to state explicitly how the NEGF Green's functions are used to obtain the temperature profile for the TBR extraction.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: B and C are fitted to bulk Si thermal conductivity, while the interface resistance is an independent transferability benchmark against MD.

full rationale

The paper calibrates two Büttiker probe parameters, B and C, to reproduce the MD-calculated bulk Si thermal conductivity (Fig. 2a). The target claim is the thermal boundary resistance of Si/heavy-Si interfaces for mass ratios MR=1–10, which is a different observable not used in the fitting procedure. The agreement in Fig. 2(b) is therefore a genuine transferability test rather than a fit renamed as a prediction. The statement around Eq. (3) that the same B and C are used in Si and heavy-Si, explicitly ignoring mass dependence of the scattering rate and interface anharmonicity, is a clearly acknowledged approximation; it weakens the predictive claim but does not make the derivation circular. The absence of artificial interface resistance in homogeneous systems is a structural consequence of the self-consistent Büttiker probe treatment, not an input fitted to the benchmark. The scattering model form is taken from prior work by the same group (Refs. 21 and 28), but the present paper validates the resulting method against independent MD simulations, so the self-citation is not load-bearing. No equation in the paper reduces the target interface resistance to the fitted bulk conductivity by construction, and no uniqueness claim from author-derived results is used to force the choice. Thus no circular step can be exhibited, and the appropriate score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on two fitted parameters (B and C) and on the assumption that a simple isotropic Böttiker probe model calibrated on bulk Si transfers to heavy-Si and to the interfacial region. No new physical entities are introduced; the Böttiker probes are a known phenomenological tool.

free parameters (2)
  • Böttiker probe scattering amplitude B = 5e-20 s/K
    Fitted so that NEGF with Böttiker probes reproduces the MD bulk Si thermal conductivity (Fig. 2a). Used in Eq. (3) and applied identically to Si and heavy-Si.
  • Böttiker probe temperature exponent C = 430 K
    Fitted together with B against MD bulk Si thermal conductivity (Fig. 2a). Appears in the exponential factor of Eq. (3).
assumptions (4)
  • domain assumption Anharmonic phonon-phonon scattering can be represented by an isotropic, Umklapp-only Böttiker probe lifetime of the form τ^(-1) = B T ω^2 e^(-C/T).
    Invoked in Eq. (3) and the accompanying text. This is a phenomenological model, not derived from the Tersoff potential or from the anharmonic Hamiltonian.
  • ad hoc to paper The same B and C values are applicable to heavy-Si and to atoms near the interface, ignoring mass dependence of anharmonicity and interface-specific anharmonicity.
    Stated explicitly in the Methods: 'The same values of B and C are used in Si and heavy-Si... the dependence of the scattering rate on the atomic mass and deviations of the anharmonicity near the interface... are ignored.' This is a load-bearing modeling choice.
  • domain assumption Local temperature can be defined by fitting the phonon energy density to a Bose-Einstein distribution (Eq. 1).
    Standard local-equilibrium assumption. If phonon modes are strongly out of equilibrium, the local temperature extracted this way is not uniquely defined; used for both MD and NEGF.
  • domain assumption Linear extrapolation of R versus 1/L to the limit 1/L=0 removes finite-size effects.
    Used for both MD and NEGF following Ref. [22]. The different boundary treatments produce different slopes (Fig. 3), so the extrapolated values may carry systematic offsets.

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Cite this review

Pith. "Pith review of Thermal boundary resistance predictions with non-equilibrium Green's function and molecular dynamics simulations." pith.science (2026). https://pith.science/paper/V6NDGBZT

@misc{pith2026190811578,
  author       = {Pith},
  title        = {Pith review of: Thermal boundary resistance predictions with non-equilibrium Green's function and molecular dynamics simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6NDGBZT}},
  note         = {Machine review of arXiv:1908.11578}
}
read the original abstract

The non-equilibrium Green's function (NEGF) method with B\"uttiker probe scattering self-energies is assessed by comparing its predictions for the thermal boundary resistance with molecular dynamics (MD) simulations. For simplicity, the interface of Si/heavy-Si is considered, where heavy-Si differs from Si only in the mass value. With B\"uttiker probe scattering parameters tuned against MD in homogeneous Si, the NEGF-predicted thermal boundary resistance quantitatively agrees with MD for wide mass ratios. Artificial resistances that the unaltered Landauer approach yield at virtual interfaces in homogeneous systems are absent in the present NEGF approach. Spectral information result from NEGF in its natural representation without further transformations. The spectral results show that the scattering between different phonon modes plays a crucial role in thermal transport across interfaces. B\"uttiker probes provide an efficient and reliable way to include anharmonicity in phonon related NEGF. NEGF including the B\"uttiker probes can reliably predict phonon transport across interfaces and at finite temperatures.

Figures

Figures reproduced from arXiv: 1908.11578 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Simulation domain considered in this work. Regio [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Thermal conductivity of bulk Si calculated with M [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a) Energy resolved (transverse momentum integrate [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. The ratio of the phonon mode in regions 1 [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

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Reference graph

Works this paper leans on

35 extracted references · 16 canonical work pages

  1. [1]

    merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translat...

    2010

  2. [2]

    merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translat...

    2010

  3. [3]

    merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translati...

    2010

  4. [4]

    merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translati...

    2010

  5. [5]

    merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translati...

    2010

  6. [7]

    Faist , author F

    author author J. Faist , author F. Capasso , author D. L. \ Sivco , author C. Sirtori , author L. Albert , author T. Hall , author J. Faist , author F. Capasso , author D. L. \ Sivco , author C. Sirtori , author A. L. \ Hutchinson , \ and\ author A. Y. \ Cho ,\ title title Quantum Cascade Laser Hutchinson and Alfred Y . Cho Published by : American Associa...

    work page arXiv 1994

  7. [8]

    Nakamura , author T

    author author S. Nakamura , author T. Mukai , \ and\ author M. Senoh ,\ title title Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes , \ 10.1063/1.111832 journal journal Applied Physics Letters \ volume 64 ,\ pages 1687--1689 ( year 1994 ) ,\ http://arxiv.org/abs/arXiv:1011.1669v3 arXiv:arXiv:1011.1669v3 NoStop

    arXiv

  8. [9]

    author author M. L. \ Tsai , author S. H. \ Su , author J. K. \ Chang , author D. S. \ Tsai , author C. H. \ Chen , author C. I. \ Wu , author L. J. \ Li , author L. J. \ Chen , \ and\ author J. H. \ He ,\ title title Monolayer MoS2heterojunction solar cells , \ 10.1021/nn502776h journal journal ACS Nano \ volume 8 ,\ pages 8317--8322 ( year 2014 ) ,\ htt...

    arXiv

Show all 35 references
  1. [10]

    author author E. T. \ Swartz \ and\ author R. O. \ Pohl ,\ title title Thermal boundary resistance , \ 10.1103/RevModPhys.61.605 journal journal Reviews of Modern Physics \ volume 61 ,\ pages 605--668 ( year 1989 ) NoStop

    1989 doi

  2. [11]

    author author E. S. \ Landry \ and\ author A. J. H. \ McGaughey ,\ title title Thermal boundary resistance predictions from molecular dynamics simulations and theoretical calculations , \ 10.1103/PhysRevB.80.165304 journal journal Physical Review B \ volume 80 ,\ pages 165304 ...

    doi

  3. [12]

    author author P. K. \ Schelling , author S. R. \ Phillpot , \ and\ author P. Keblinski ,\ title title Comparison of atomic-level simulation methods for computing thermal conductivity , \ 10.1103/PhysRevB.65.144306 journal journal Physical Review B \ volume 65 ,\ pages 1--12 ( ...

    doi

  4. [13]

    author author P. E. \ Hopkins ,\ title title Multiple phonon processes contributing to inelastic scattering during thermal boundary conductance at solid interfaces , \ 10.1063/1.3169515 journal journal Journal of Applied Physics \ volume 106 ( year 2009 ),\ 10.1063/1.3169515 NoStop

    doi

  5. [14]

    author author S. Datta ,\ title title Nanoscale device modeling: the Green's function method , \ 10.1006/spmi.2000.0920 journal journal Superlattices and Microstructures \ volume 28 ,\ pages 253--278 ( year 2000 ) NoStop

    2000

  6. [15]

    Knoch , author S

    author author J. Knoch , author S. Mantl , \ and\ author J. Appenzeller ,\ title title Impact of the dimensionality on the performance of tunneling fets: Bulk versus one-dimensional devices , \ https://doi.org/10.1016/j.sse.2007.02.001 journal journal Solid-State Electronics \...

    doi

  7. [16]

    M \' a ty \' a s , author T

    author author A. M \' a ty \' a s , author T. Kubis , author P. Lugli , \ and\ author C. Jirauschek ,\ title title Comparison between semiclassical and full quantum transport analysis of THz quantum cascade lasers , \ 10.1016/j.physe.2009.12.028 journal journal Physica E: Low-...

    doi

  8. [17]

    S\"a\"askilahti , author J

    author author K. S\"a\"askilahti , author J. Oksanen , author J. Tulkki , \ and\ author S. Volz ,\ title title Role of anharmonic phonon scattering in the spectrally decomposed thermal conductance at planar interfaces , \ 10.1103/PhysRevB.90.134312 journal journal Phys. Rev. B...

    doi

  9. [18]

    Feng , author W

    author author T. Feng , author W. Yao , author Z. Wang , author J. Shi , author C. Li , author B. Cao , \ and\ author X. Ruan ,\ title title Spectral analysis of nonequilibrium molecular dynamics: Spectral phonon temperature and local nonequilibrium in thin films and across in...

    doi

  10. [19]

    Stieger , author A

    author author C. Stieger , author A. Szabo , \ and\ author M. Luisier ,\ title title Ab-initio quantum transport simulation of self-heating in single-layer 2-D materials Ab-initio quantum transport simulation of self-heating in single-layer 2-D materials , \ 10.1063/1.4990384 ...

    doi

  11. [20]

    Luisier ,\ title title Atomistic modeling of anharmonic phonon-phonon scattering in nanowires , \ 10.1103/PhysRevB.86.245407 journal journal Phys

    author author M. Luisier ,\ title title Atomistic modeling of anharmonic phonon-phonon scattering in nanowires , \ 10.1103/PhysRevB.86.245407 journal journal Phys. Rev. B \ volume 86 ,\ pages 245407 ( year 2012 ) NoStop

    2012 doi

  12. [21]

    author author J. T. \ Gaskins , author G. Kotsonis , author A. Giri , author S. Ju , author A. Rohskopf , author Y. Wang , author T. Bai , author E. Sachet , author C. T. \ Shelton , author Z. Liu , author Z. Cheng , author B. M. \ Foley , author S. Graham , author T. Luo , au...

  13. [22]

    author author C. A. \ Polanco , author R. Rastgarkafshgarkolaei , author J. Zhang , author N. Q. \ Le , author P. M. \ Norris , \ and\ author A. W. \ Ghosh ,\ title title Design rules for interfacial thermal conductance: Building better bridges , \ 10.1103/PhysRevB.95.195303 j...

    doi

  14. [23]

    author author N. Q. \ Le , author C. A. \ Polanco , author R. Rastgarkafshgarkolaei , author J. Zhang , author A. W. \ Ghosh , \ and\ author P. M. \ Norris ,\ title title Effects of bulk and interfacial anharmonicity on thermal conductance at solid/solid interfaces , \ 10.1103...

    doi

  15. [24]

    Shi , author X

    author author J. Shi , author X. Yang , author T. S. \ Fisher , \ and\ author X. Ruan ,\ @noop title Dramatic increase in the thermal boundary conductance and radiation limit from a nonequilibrium landauer approach , \ ( year 2018 ),\ http://arxiv.org/abs/1812.07910 arXiv:1812...

    2018 arXiv

  16. [25]

    Tersoff ,\ title title Modeling solid-state chemistry: Interatomic potentials for multicomponent systems , \ 10.1103/PhysRevB.39.5566 journal journal Phys

    author author J. Tersoff ,\ title title Modeling solid-state chemistry: Interatomic potentials for multicomponent systems , \ 10.1103/PhysRevB.39.5566 journal journal Phys. Rev. B \ volume 39 ,\ pages 5566--5568 ( year 1989 ) NoStop

    1989 doi

  17. [26]

    Sadasivam , author N

    author author S. Sadasivam , author N. Ye , author J. P. \ Feser , author J. Charles , author K. Miao , author T. Kubis , \ and\ author T. S. \ Fisher ,\ title title Thermal transport across metal silicide-silicon interfaces: First-principles calculations and Green's function ...

    doi

  18. [27]

    Sellan , author E

    author author D. Sellan , author E. Landry , author J. Turney , author a. McGaughey , \ and\ author C. Amon ,\ title title Size effects in molecular dynamics thermal conductivity predictions , \ 10.1103/PhysRevB.81.214305 journal journal Physical Review B \ volume 81 ,\ pages ...

    doi

  19. [28]

    author author S. Plimpton ,\ 10.1006/jcph.1995.1039 title Fast parallel algorithms for short-range molecular dynamics , \ ( year 1995 ),\ http://arxiv.org/abs/nag.2347 arXiv:nag.2347 [10.1002] NoStop

    1995

  20. [29]

    author author B. J. \ Alder \ and\ author T. E. \ Wainwright ,\ title title Studies in molecular dynamics. i. general method , \ 10.1063/1.1730376 journal journal The Journal of Chemical Physics \ volume 31 ,\ pages 459--466 ( year 1959 ) ,\ http://arxiv.org/abs/https://doi.or...

    doi

  21. [30]

    Steiger , author M

    author author S. Steiger , author M. Povolotskyi , author H. H. \ Park , author T. Kubis , \ and\ author G. Klimeck ,\ title title Nemo5: A parallel multiscale nanoelectronics modeling tool , \ 10.1109/TNANO.2011.2166164 journal journal IEEE Transactions on Nanotechnology \ vo...

    2011

  22. [31]

    Paul , author M

    author author A. Paul , author M. Luisier , \ and\ author G. Klimeck ,\ 10.1007/s10825-010-0332-9 title Journal of Computational Electronics ,\ Vol. volume 9 \ ( year 2010 )\ pp.\ pages 160--172 ,\ http://arxiv.org/abs/1009.6188 arXiv:1009.6188 NoStop

    2010 arXiv

  23. [32]

    B\"uttiker ,\ title title Four-terminal phase-coherent conductance , \ 10.1103/PhysRevLett.57.1761 journal journal Phys

    author author M. B\"uttiker ,\ title title Four-terminal phase-coherent conductance , \ 10.1103/PhysRevLett.57.1761 journal journal Phys. Rev. Lett. \ volume 57 ,\ pages 1761--1764 ( year 1986 ) NoStop

    1986 doi

  24. [33]

    Miao , author S

    author author K. Miao , author S. Sadasivam , author J. Charles , author G. Klimeck , author T. S. \ Fisher , \ and\ author T. Kubis ,\ title title B \" u ttiker probes for dissipative phonon quantum transport in semiconductor nanostructures , \ 10.1063/1.4944329 journal journ...

    doi

  25. [34]

    author author Y. S. \ Ju \ and\ author K. E. \ Goodson ,\ title title Phonon scattering in silicon films with thickness of order 100 nm , \ 10.1063/1.123994 journal journal Applied Physics Letters \ volume 74 ,\ pages 3005--3007 ( year 1999 ) NoStop

    doi

  26. [35]

    Datta ,\ 10.1017/CBO9781139164313 title Quantum Transport: Atom to Transistor \ ( publisher Cambridge University Press ,\ year 2005 ) NoStop

    author author S. Datta ,\ 10.1017/CBO9781139164313 title Quantum Transport: Atom to Transistor \ ( publisher Cambridge University Press ,\ year 2005 ) NoStop

    2005 doi

  27. [36]

    author author S. Datta ,\ 10.1017/CBO9780511805776 title Electronic Transport in Mesoscopic Systems ,\ Cambridge Studies in Semiconductor Physics and Microelectronic Engineering\ ( publisher Cambridge University Press ,\ year 1995 ) NoStop

    doi

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