Pith. sign in

REVIEW 4 major objections 5 minor 47 references

Multiscale ensemble Monte Carlo of transport and gas sensing in monolayer MoS$_2$

T0 review · 4 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A single ensemble Monte Carlo transport kernel, calibrated once, reproduces measured transport, transistor, and gas-sensing behaviour in monolayer MoS2.

desk verdict Honest, useful EMC framework for MoS2, but the 'physically grounded' claim rests on one calibrated acoustic deformation potential and a compact-model device stand-in. read the letter →

arxiv 2607.18895 v1 pith:SZPYSHA2 submitted 2026-07-21 cond-mat.mes-hall cond-mat.mtrl-sci

Lado Filipovic This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords ensembleMonteCarlotransition-metaldichalcogenideMoS2electrontransportgassensingmultiscalemodellingdensity-functionalperturbationtheory
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 aims to establish that one semiclassical ensemble Monte Carlo transport framework can span the full range from electron-phonon coupling to terminal current and chemical sensing in monolayer MoS2. The claim matters because it would give device designers a physically grounded, reusable simulation basis for 2D-material transistors and gas sensors, replacing purely empirical mobility models and lumped compact models. The author shows that with a single global calibration—the acoustic deformation potential—the same Boltzmann-transport kernel reproduces substrate-specific mobility power laws, the velocity-field characteristic, the measured transfer curves of a CVD device in air and vacuum, and the concentration-dependent response to O2, NO2, and NH3 across several independent devices. If true, this would unify transport and sensing physics under one computational umbrella.

What carries the argument

The central object is the ensemble Monte Carlo Boltzmann-transport kernel, which stochastically propagates carrier ensembles through field-driven flights and self-scattering events, coupled self-consistently to Poisson's equation with a degenerate 2D closure. Its output velocity-field characteristic v(E), fitted to the Caughey-Thomas form, feeds a one-dimensional gradual-channel model for the transistor drain current, while an adsorbate model couples coverage-dependent charge transfer and Coulomb scattering into the same conductivity. The key identity is the transduction S(θ)=σ0/σ(θ)−1, computed directly by the EMC, with only the per-device adsorption constant K fitted.

What would settle it

A first-principles electron-phonon (EPW) calculation of the acoustic deformation potential in monolayer MoS2 that differs materially from the calibrated value, or a measured suspended-device mobility that deviates from the predicted T^(-1.49) power law, would falsify the transport backbone. A simpler check: if the model's v(E) fails to reproduce the transfer characteristic of a device with a different channel length or contact design, the bulk-to-channel coupling would be invalid.

Watch

Extended reading notes

Core claim

The central discovery is that a self-consistent ensemble Monte Carlo kernel with a full scattering stack—acoustic deformation potential, intervalley phonons, polar-optical Fröhlich and piezoelectric coupling, remote substrate phonons, screened charged impurities, and surface roughness—verified against density-functional perturbation theory for seven parameters, reproduces a broad set of measurements without per-result fitting. The temperature-dependent mobility follows a substrate-specific power law whose exponent rises from γ=1.49 for suspended films to γ=1.79 on HfO2; the multiscale coupling to a one-dimensional velocity-saturation channel model reproduces the measured transfer characteris

Load-bearing premise

The load-bearing premise is that the effective acoustic deformation potential, fixed by a single global calibration rather than computed from first principles, remains valid across all carrier densities, temperatures, and devices—a premise the paper itself flags as unverified for the acoustic scattering coupling.

Editorial extensions

If this is right

  • Substrate choice is predictive: each dielectric yields a distinct mobility power-law exponent, and stiff-mode insulators like CaF2 retain high mobility despite a large dielectric discontinuity.
  • The intrinsic phonon-limited mobility provides an upper bound that quantifies the extrinsic (contact, defect, substrate) limitation of any measured device.
  • The same velocity-field characteristic explains the linear-to-saturation transition in a real gated channel and the air→vacuum mobility recovery ratio.
  • The sensor response shape is an output of the transport kernel, so transistor and sensor behaviour share a common microscopic basis.
  • The transport backbone requires only one global calibration; remaining fits are confined to device parameters (Vth, SS, Rc) and per-gas adsorption constants.

Reading between the lines

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

  • Because the single calibrated acoustic deformation potential is not first-principles-verified, a future EPW calculation that disagrees would require re-testing the model's transferability across densities and temperatures.
  • The coverage-dependent transduction curve could be probed with time-resolved or noise measurements to separate the charge-transfer and scattering contributions directly.
  • The same framework should extend to other monolayer TMDs (WS2, WSe2) with only material parameters changed, offering a strong test of the mechanism.
  • The bulk v(E) replacing a full gated-channel EMC may break down for very short channels or significantly different contact resistances; a full device simulation with proper terminal extraction would be needed to confirm the multiscale coupling.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper presents a self-consistent ensemble Monte Carlo (EMC) framework for monolayer MoS2, implemented in ViennaEMC, with a full scattering stack (acoustic and intervalley deformation-potential phonons, polar-optical Fröhlich and piezoelectric coupling, remote substrate phonons, screened charged impurities, surface roughness, and adsorbates), degenerate statistics, and self-consistent Poisson coupling. The intrinsic electronic-structure and polar-phonon inputs are compared to DFPT calculations, and seven quantities are claimed to match the reference parametrization. The EMC velocity-field characteristic feeds a one-dimensional velocity-saturation channel model, used to reproduce the transfer characteristic of a CVD monolayer device in air and vacuum. An ambient/adsorbate extension is then used to reproduce oxygen partial-pressure conductivity, NO2, and NH3 gas-sensing data from several devices. The manuscript explicitly separates predicted from fitted quantities and concludes that the framework is a physically grounded, reusable basis for 2D-material FET and gas-sensor modelling.

Significance. The paper makes a useful open-source contribution: it ships an EMC transport kernel plus DFPT input decks and simulation data, and it provides a genuine DFPT check of seven electronic-structure and polar-phonon parameters. Several outputs are genuine EMC predictions rather than fits: the temperature exponents and substrate ordering in Figs. 2 and 4, the non-monotonic density dependence with a peak near 10^13 cm^-2, the shape of the velocity-field characteristic v(E), and the shape S(theta) of the adsorbate transduction curve. These are real strengths. However, the load-bearing acoustic deformation potential D_ac in Eq. (5) is a single calibrated constant that the paper itself concedes is not DFPT-verified, and the device and sensor validations depend on additional fitted parameters (V_th, SS, R_c, DeltaN, K). The claim that the framework is 'physically grounded rather than empirical' is therefore only partially supported: the relative trends are plausible, but the absolute mobility and the quantitative sensor response are not first-principles predictions in the strong sense stated in the abstract.

major comments (4)
  1. [Sec. 5.6, Eq. (5), Table 3] The calibrated D_ac is load-bearing and undermines the 'essentially parameter-free' claim. Eq. (5) makes the acoustic scattering rate proportional to D_ac^2, and this rate enters every transport result: mu(T) in Figs. 2-3, the velocity-field characteristic feeding Fig. 5, and the mobility baseline in Eq. (13). Section 5.6 explicitly concedes that the DFPT comparison 'confirms the electronic-structure and polar-phonon inputs but not the acoustic scattering coupling,' and that the frozen-strain ~13 eV value is a different quantity. Yet Table 3 lists mu(T) as resting on a 'single global calibration' while the text describes the backbone as 'essentially parameter-free.' Calibrating D_ac at room temperature can absorb errors in other scattering rates and still give the correct low-field mobility while producing incorrect temperature dependence or substrate ordering. The authors should report
  2. [Sec. 4.1, Eqs. (10)-(12)] The device-level validation is substantially weaker than the abstract implies. The manuscript states that direct EMC terminal-current extraction 'does not yield a clean Id-Vg' and was abandoned; the transfer characteristic is instead computed from a 1D gradual-channel compact model with fitted V_th, SS, and R_c, using the bulk EMC v(E) as input. The agreement in Fig. 5(b) therefore tests the compact model plus fitted device parameters more than the scattering stack. To support the multiscale claim, the authors should quantify the sensitivity of the reproduced Id-Vg to V_th/SS/R_c, and ideally show that the EMC v(E) differs from a generic Caughey-Thomas form in a way that measurably affects the transferred characteristic. Without that, the device panel does not independently corroborate the transport kernel.
  3. [Sec. 4.2, Eq. (13), Table 3] The gas-sensing 'validation' is partly a curve-fitting exercise. The EMC output is the transduction shape S(theta), but the mapping theta(C)=KC/(1+KC) uses K fitted per device (and per dataset), DeltaN is fitted per gas/device, and N_max_c is introduced without being listed in Table 3. Consequently, the NO2 and NH3 concentration curves in Figs. 7-8 are not predictions from the framework; they are fits to each dataset. A meaningful predictive test would be to fix DeltaN and N_max_c from one device and K from an independent adsorption measurement or from one pressure point, and then predict another device's concentration response. As written, the sensor section demonstrates interpolation within a flexible model, not predictive power.
  4. [Abstract, Conclusion, Sec. 5.6] The language of the abstract and conclusion overstates the evidential basis. The conclusion says the framework 'establishes a physically grounded and reusable basis,' while Sec. 5.6 correctly acknowledges the main limitations: the acoustic scattering coupling is unverified and the gate-tunable few-layer sensing mechanism is outside scope. Since the only parameter controlling the absolute mobility is calibrated, and direct device simulation failed, the strong claim that the model is 'physically grounded rather than empirical' should be softened to something like 'microscopic scattering-based with transparent parameter accounting.' The paper would be more credible if the calibrated and fitted elements were described as such throughout, rather than only in Sec. 5.6.
minor comments (5)
  1. [Throughout] The manuscript has several encoding/typesetting problems: 'I d-Vg', 'Fr¨ ohlich', and other LaTeX artifacts appear in the extracted text. Please ensure the final PDF uses consistent math typesetting.
  2. [Fig. 3] The annotation 'EMC intrinsic (this work) 194' beside the experimental bars is unclear. State explicitly that this is the room-temperature intrinsic mobility at the same density used for the Kaasbjerg limit, and how it relates to the 135-195 cm2/Vs range quoted in Sec. 5.1.
  3. [Table 2] The 'in-plane epsilon_inf (slab)' entry says it 'needs 2D unfold.' Since this quantity enters screening in Eq. (7), spell out how the slab value was used, or whether a literature value was substituted.
  4. [Eq. (13)] Define n0, DeltaN, and N_max_c in physical units and clarify the donor/acceptor sign convention in the text before Eq. (13). The upper/lower sign description is terse.
  5. [Sec. 5.5] The multilayer and few-layer results (Late et al., Mamun et al.) are described in Sec. 5.6 as corroboration only. Consider labeling them as such in the main text and figure captions as well, or moving them to supplementary material.

Circularity Check

2 steps flagged · score 5.0 of 10

Transport absolute mobility and sensor concentration curves rest on fitted inputs (D_ac; ΔN and K), while temperature exponents, substrate ordering, density peak, and coverage-shape retain genuine EMC content.

  1. fitted input called prediction [Sec. 5.6 (Scope and limitations); Eq. (5); Table 3]
    "The transport backbone is essentially parameter-free, resting on a single global deformation-potential calibration, after which the temperature exponent, the density peak and the substrate ordering are predictions. ... the frozen-strain deformation potential ... is a different quantity from the effective scattering deformation potential that enters the mobility ... so the DFPT comparison confirms the electronic-structure and polar-phonon inputs but not the acoustic scattering coupling."

    Eq. (5) makes the acoustic scattering rate proportional to D_ac^2, so D_ac controls the absolute mobility through every downstream result: μ(T) in Figs. 2–3, the v(E) curve in Fig. 5, and the μ baseline in Eq. (13). If D_ac is obtained by a global calibration, the 'absolute μ' listed as EMC-predicted in Table 3 is not an independent prediction; comparisons of absolute mobility to measured devices are consistency checks with the fitted parameter. The temperature exponent and substrate ordering remain genuine outputs, so the circularity is partial.

  2. fitted input called prediction [Sec. 5.6; Eq. (13); Figs. 7–8; Table 3]
    "The fitting burden is concentrated in the sensor transduction, where the per-gas charge-transfer amplitude and one adsorption constant per dataset are fitted while the shape S(θ) is an EMC output."

    In Eq. (13), S(θ) is controlled by n_s(θ)=n0∓ΔN·θ, μ(n_s,N_c), and the Langmuir map θ(C)=KC/(1+KC). With ΔN and K fitted per dataset, the NO2/NH3 concentration-response curves in Figs. 7–8 are two-parameter fits to each measured dataset, so the claimed reproduction of the measured concentration dependence is not a parameter-free prediction. The residual EMC content is the functional shape of μ(n_s,N_c), but the amplitude and coverage-to-concentration mapping are supplied by the fit, making the sensor validation partially circular.

full rationale

The paper is unusually transparent, and much of its derivation chain is genuinely self-contained: the DFPT verification of seven electronic-structure and phonon parameters is an independent check, and the EMC predictions of the temperature exponent, substrate ordering, density-dependent mobility peak, and the coverage-shape S(θ) are not forced by the fitted parameters. However, two load-bearing quantities reduce to fitted inputs rather than independent predictions. First, the single global deformation-potential calibration determines the absolute mobility and therefore the magnitude of every transport and device/sensor result that uses μ; the paper itself concedes that DFPT does not validate the acoustic scattering coupling. Second, the sensor response curves are reproduced using per-dataset values of ΔN and K, so the concentration dependence is effectively fitted. These are disclosed as fitted in Table 3 and Sec. 5.6, which prevents a verdict of full circularity, but they do weaken the strongest claim that the framework is a parameter-free, physically grounded prediction tool. There is no load-bearing self-citation chain, no imported uniqueness theorem, and no renaming of a known result. Score 5 reflects the partial reduction of central quantitative claims to fitted inputs, balanced by genuine independent content in the shape and trend predictions.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim depends on a small number of calibrated parameters (D_ac, per-gas DeltaN, per-device K) and on standard domain assumptions about the 2D scattering stack and Langmuir adsorption. No new physical entities are introduced.

free parameters (7)
  • D_ac (effective acoustic deformation potential) = not stated in text (global calibration)
    Eq. (5) acoustic rate; calibrated globally (Sec 5.6, Table 3); not DFPT-verified.
  • DeltaN (charge transfer per adsorbate at saturation) = per gas; not stated in text
    Eq. (13) n_s(theta)=n0∓DeltaN*theta; fitted per gas/dataset (Sec 5.6, Table 3).
  • K (Langmuir adsorption constant) = NH3: 6.3e-4 ppm^-1; NO2: 1.9e-2 and 1.6e-3 ppm^-1; NO2 Vth: 8.6e-3 ppm^-1
    theta(C)=KC/(1+KC); fitted per dataset (Fig. 7, 8 captions).
  • N_max_c (areal density of adsorbate Coulomb centres) = not stated
    Eq. (13) enters mobility via Eq. (7); no value given; presumably fitted or from literature.
  • V_th (threshold voltage) = not stated
    Device I-V fit (Sec 4.1, Table 3).
  • SS (subthreshold swing) = not stated
    Device I-V fit (Eq. 11, Table 3).
  • R_c (contact resistance) = not stated
    Series contact resistance applied self-consistently (Sec 4.1, Table 3).
assumptions (6)
  • domain assumption Semiclassical Boltzmann transport equation with Monte Carlo self-scattering is valid for carrier transport in monolayer MoS2.
    Sec 2.1 uses the BTE and self-scattering technique; standard for semiconductor transport.
  • domain assumption Scattering rates from Kaasbjerg et al. (2012) and Ma & Jena (2014) parametrizations are applicable to this system.
    Sec 2.2 builds the intrinsic and extrinsic scattering stack on these references.
  • domain assumption Non-parabolic k·p dispersion (Eq. 2) captures the conduction band.
    Used to compute group velocity and density of states; not independently validated here.
  • domain assumption Langmuir isotherm maps gas concentration to adsorbate coverage.
    Sec 4.2 defines theta(C)=KC/(1+KC).
  • domain assumption Gradual-channel approximation with Caughey-Thomas velocity saturation describes the device current (Eqs. 10-12).
    Sec 4.1 replaces a full device simulation after direct EMC terminal extraction failed.
  • domain assumption PBE/DFPT with norm-conserving pseudopotentials is an adequate level for the material inputs.
    Sec 3 uses PBE; the reference parametrization is also PBE, so this is internally consistent but not a higher-level check.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Multiscale ensemble Monte Carlo of transport and gas sensing in monolayer MoS$_2$." pith.science (2026). https://pith.science/paper/SZPYSHA2

@misc{pith2026260718895,
  author       = {Pith},
  title        = {Pith review of: Multiscale ensemble Monte Carlo of transport and gas sensing in monolayer MoS$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SZPYSHA2}},
  note         = {Machine review of arXiv:2607.18895}
}
abstract

Two-dimensional semiconductors, such as monolayer MoS$_2$, combine a technologically useful band gap with an all-surface geometry, making them attractive both as field-effect-transistor channels and as chemically sensitive devices. Predictive device design requires a transport model that is (i) physically grounded rather than empirical, (ii) validated against experiments, and (iii) able to span the scales from electron-phonon coupling to terminal current and sensor response. We present a self-consistent ensemble Monte Carlo (EMC) framework for monolayer MoS$_2$ built on the ViennaEMC solver, comprising a Boltzmann-transport kernel with a full intrinsic and extrinsic scattering stack (deformation-potential acoustic and intervalley phonons, polar-optical Fr\"ohlich and piezoelectric coupling, remote substrate phonons, screened charged-impurity and surface-roughness scattering), degenerate free-carrier statistics, and a self-consistent Poisson coupling. The intrinsic transport parameters are verified against first-principles density-functional perturbation theory (DFPT), and seven quantities (lattice constant, conduction-band effective mass, band gap, Born effective charges, the longitudinal-optical phonon energy, and both in-plane sound velocities) agree with the reference parametrization. In a multiscale coupling, the EMC velocity-field characteristic feeds a one-dimensional velocity-saturation channel model, which captures the velocity-saturated field dependence and reproduces the measured transfer characteristics of a CVD monolayer device in air and vacuum. Finally, an ambient/adsorbate extension reproduces the measured conductivity response to oxygen partial pressure and the concentration dependence of NO$_2$ and NH$_3$ sensing measured in several independent devices.

Figures

Figures reproduced from arXiv: 2607.18895 by the authors.

Figure 1
Figure 1. Self-consistent ensemble Monte Carlo cycle of the ViennaEMC framework [37]. DFPT-verified material and scattering parameters enter at the top. The dashed block is repeated each time step, alternating a Poisson solve with a free-flight/self-scattering update of the carrier ensemble. solved by successive over-relaxation on the device grid in the established device-simulation manner [10]. Because accumulation-mode 2D c… view at source ↗
Figure 2
Figure 2. Temperature-dependent mobility µ(T) for different substrates. Each insulator has its own power-law exponent γ (µ ∝ T −γ). The suspended (intrinsic) film has the shallowest slope (γ = 1.49). Every supporting dielectric adds a thermally activated remote surface-optical phonon channel whose scattering grows with temperature and steepens the falloff, most strongly for the soft, polar high-κ HfO2 (γ = 1.79). The exponent… view at source ↗
Figure 3
Figure 3. The EMC intrinsic phonon-limited mobility sets an upper bound below the Kaasbjerg phonon limit, against which the measured monolayer and multilayer device mobilities are benchmarked, each falling below the bound by an amount that quantifies its extrinsic (contact, defect and substrate) limitation [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The mobility is limited both by the supporting dielectric, resolved in (a) as the remote-surface-optical-phonon-limited mobility for the different substrates, and by the carrier density, shown in (b) as a non-monotonic dependence µ(ns) that is low at small sheet densit…
Figure 5
Figure 5. Figure 5: One-dimensional velocity-saturation channel model fed by the EMC v(E). (a) EMC velocity-field characteristic and Caughey-Thomas fit (µ0, vsat). (b) Transfer Id-Vg versus the measured monolayer FET of Ahn et al. [21] in air and vacuum. al., multilayer [44]) as direction…
Figure 6
Figure 6. Figure 6: The ambient conductivity response of the channel is shown in (a) as the EMC σ(θ) versus adsorbate coverage, overlaid with measured device data from Ahn et al. (2017) and Li et al. (2023), and is decomposed in (b) into the charge-transfer carrier-depletion and adsorbate…
Figure 7
Figure 7. Figure 7: The same EMC transduction σ(θ) reproduces the measured gas response of two devices, shown in (a) as the NH3 donor response of a 2-layer device and in (b) as the NO2 acceptor response referenced to a single-layer device [43] with a 2-layer device [2] as a secondary refe…
Figure 8
Figure 8. Figure 8: Device-level charge transfer across two recent (2025) FETs of opposite polarity. (a) Melamine donor Id-Vg (multilayer) [44], reproduced by the multiscale model as a donor left shift of ∆Vth ≈ −21 V. (b) NO2 acceptor Vth versus concentration (single-layer) [43] [PITH_F…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references · 28 canonical work pages

  1. [1]

    Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011Nature Nanotechnology 6147–150https://doi.org/10.1038/nnano.2010.279

    doi:10.1038/nnano.2010.279 2010

  2. [2]

    Late D J, Huang Y K, Liu B, Acharya J, Shirodkar S N, Luo J, Yan A, Charles D, Waghmare U V, Dravid V P and Rao C N R 2013ACS Nano74879–4891 https://doi.org/10.1021/nn400026u 10

    work page doi:10.1021/nn400026u

  3. [3]

    Kurosawa T 1966 Monte Carlo calculation of hot electron problemsProceedings of the International Conference on the Physics of Semiconductors(Journal of the Physical Society of Japan, Supplementvol 21) (Kyoto, Japan) pp 424–426 URL https://www.jps.or.jp/books/jpsjs/21/jpsj.21s.424.pdf

    1966

  4. [4]

    Fawcett W, Boardman A D and Swain S 1970Journal of Physics and Chemistry of Solids31 1963–1990https://doi.org/10.1016/0022-3697(70)90001-6

    work page doi:10.1016/0022-3697(70)90001-6 1963

  5. [5]

    Kurosawa T and Maeda H 1971Journal of the Physical Society of Japan31668–678 ISSN 1347-4073https://doi.org/10.1143/jpsj.31.668

    work page doi:10.1143/jpsj.31.668

  6. [6]

    Rees H D 1969Journal of Physics and Chemistry of Solids30643–655 https://doi.org/10.1016/0022-3697(69)90018-3

    work page doi:10.1016/0022-3697(69)90018-3

  7. [7]

    Jacoboni C and Reggiani L 1983Reviews of Modern Physics55645–705 https://doi.org/10.1103/RevModPhys.55.645

    work page doi:10.1103/revmodphys.55.645

  8. [8]

    Price P J 1979 Monte Carlo calculation of electron transport in solidsLasers, Junctions, Transported Willardson R K and Beer A C (New York: Elsevier) chap 4, pp 249–308 https://doi.org/10.1016/s0080-8784(08)60267-7

    work page doi:10.1016/s0080-8784(08)60267-7 1979

Show all 47 references
  1. [9]

    Jacoboni C and Lugli P 1989The Monte Carlo Method for Semiconductor Device Simulation (Wien: Springer-Verlag)https://doi.org/10.1007/978-3-7091-6963-6

    doi

  2. [10]

    Selberherr S 1984Analysis and Simulation of Semiconductor Devices(Wien: Springer-Verlag) https://doi.org/10.1007/978-3-7091-8752-4

    doi

  3. [11]

    Hess K (ed) 1991Monte Carlo Device Simulation: Full Band and Beyond(Boston: Kluwer Academic)https://doi.org/10.1007/978-1-4615-4026-7

    doi

  4. [12]

    Moglestue C 1993Monte Carlo Simulation of Semiconductor Devices(London: Chapman & Hall)https://doi.org/10.1007/978-94-015-8133-2

    doi

  5. [13]

    Tomizawa K 1993Numerical Simulation of Submicron Semiconductor Devices(Boston: Artech House) ISBN 978-0890066201 URL https://api.semanticscholar.org/CorpusID:116364667

  6. [14]

    Jungemann C and Meinerzhagen B 2003Hierarchical Device Simulation: The Monte-Carlo Perspective(Wien: Springer-Verlag)https://doi.org/10.1007/978-3-7091-6086-2

    doi

  7. [15]

    Fischetti M V and Laux S E 1988Physical Review B389721–9745 https://doi.org/10.1103/PhysRevB.38.9721

    doi

  8. [16]

    Fischetti M V 1991IEEE Transactions on Electron Devices38634–649 https://doi.org/10.1109/16.75176

    doi

  9. [17]

    Kaasbjerg K, Thygesen K S and Jacobsen K W 2012Physical Review B85115317 https://doi.org/10.1103/PhysRevB.85.115317

    doi

  10. [18]

    Ma N and Jena D 2014Physical Review X4011043 https://doi.org/10.1103/PhysRevX.4.011043

    doi

  11. [19]

    Baugher B W H, Churchill H O H, Yang Y and Jarillo-Herrero P 2013Nano Letters13 4212–4216https://doi.org/10.1021/nl401916s

    doi

  12. [20]

    Radisavljevic B and Kis A 2013Nature Materials12815–820 https://doi.org/10.1038/nmat3687

    doi

  13. [21]

    Ahn J H, Parkin W M, Naylor C H, Johnson A T C and Drndi´ c M 2017Scientific Reports7 4075https://doi.org/10.1038/s41598-017-04350-z

    doi

  14. [22]

    Li J, Peng S, Jin Z, Tian H, Wang T and Peng X 2023Crystals131501 https://doi.org/10.3390/cryst13101501

    doi

  15. [23]

    Li X, Mullen J T, Jin Z, Borysenko K M, Buongiorno Nardelli M and Kim K W 2013Physical Review B87115418https://doi.org/10.1103/PhysRevB.87.115418 11

    doi

  16. [24]

    Restrepo O D, Krymowski K E, Goldberger J and Windl W 2014New Journal of Physics16 105009https://doi.org/10.1088/1367-2630/16/10/105009

    doi

  17. [25]

    Gunst T, Markussen T, Palsgaard M L N, Stokbro K and Brandbyge M 2017Physical Review B96161404https://doi.org/10.1103/PhysRevB.96.161404

    doi

  18. [26]

    Ponc´ e S, Li W, Reichardt S and Giustino F 2020Reports on Progress in Physics83036501 https://doi.org/10.1088/1361-6633/ab6a43

    doi

  19. [27]

    Fischetti M V and Vandenberghe W G 2016Physical Review B93155413 https://doi.org/10.1103/PhysRevB.93.155413

    doi

  20. [28]

    Schedin F, Geim A K, Morozov S V, Hill E W, Blake P, Katsnelson M I and Novoselov K S 2007Nature Materials6652–655https://doi.org/10.1038/nmat1967

    doi

  21. [29]

    Perkins F K, Friedman A L, Cobas E, Campbell P M, Jernigan G G and Jonker B T 2013 Nano Letters13668–673https://doi.org/10.1021/nl3043079

    2013 doi

  22. [30]

    Donarelli M and Ottaviano L 2018Sensors183638https://doi.org/10.3390/s18113638

    doi

  23. [31]

    Cho B, Hahm M G, Choi M, Yoon J, Kim A R, Lee Y J, Park S G, Kwon J D, Kim C S, Song M, Jeong Y, Nam K S, Lee S, Yoo T J, Kang C G, Lee B H, Ko H C, Ajayan P M and Kim D H 2015Scientific Reports58052https://doi.org/10.1038/srep08052

    doi

  24. [32]

    Sarkar D, Liu W, Xie X, Anselmo A C, Mitragotri S and Banerjee K 2014ACS Nano8 3992–4003https://doi.org/10.1021/nn5009148

    doi

  25. [33]

    Lundstrom M 2000Fundamentals of Carrier Transport2nd ed (Cambridge, UK: Cambridge University Press) ISBN 978-0511618611https://doi.org/10.1017/CBO9780511618611

    doi

  26. [34]

    Ridley B K 1982Journal of Physics C: Solid State Physics155899–5917 https://doi.org/10.1088/0022-3719/15/28/021

    doi

  27. [35]

    Sohier T, Calandra M and Mauri F 2016Physical Review B94085415 https://doi.org/10.1103/PhysRevB.94.085415

    doi

  28. [36]

    Hockney R W and Eastwood J W 1988Computer Simulation Using Particles1st ed (Boca Raton: CRC Press) ISBN 9780367806934https://doi.org/10.1201/9780367806934

    doi

  29. [37]

    URL https://github.com/ViennaTools/ViennaEMC

    Filipovic Let al.2026 ViennaEMC: Ensemble Monte Carlo framework for semiconductors and metals institute for Microelectronics, TU Wien. URL https://github.com/ViennaTools/ViennaEMC

    2026

  30. [38]

    Giannozzi P, Andreussi O, Brumme T, Bunau O, Buongiorno Nardelli M, Calandra M, Car R, Cavazzoni C, Ceresoli D, Cococcioni M, Colonna N, Carnimeo I, Dal Corso A, de Gironcoli S, Delugas P, DiStasio Jr R A, Ferretti A, Floris A, Fratesi G, Fugallo G, Gebauer R, Gerstmann U, Giu...

  31. [39]

    Perdew J P, Burke K and Ernzerhof M 1996Physical Review Letters773865–3868 https://doi.org/10.1103/PhysRevLett.77.3865

    doi

  32. [40]

    Hamann D R 2013Physical Review B88085117 https://doi.org/10.1103/PhysRevB.88.085117

    doi

  33. [41]

    van Setten M J, Giantomassi M, Bousquet E, Verstraete M J, Hamann D R, Gonze X and Rignanese G M 2018Computer Physics Communications22639–54 https://doi.org/10.1016/j.cpc.2018.01.012

    2018 doi

  34. [42]

    Illarionov Y Y, Banshchikov A G, Polyushkin D K, Wachter S, Knobloch T, Thesberg M, Mennel L, Paur M, St¨ oger-Pollach M, Steiger-Thirsfeld A, Vexler M I, Waltl M, Sokolov N S, Mueller T and Grasser T 2019Nature Electronics2230–235 https://doi.org/10.1038/s41928-019-0256-8 12

    doi

  35. [43]

    Kumar S, Sharma A, Sao A K, Singh J P, Chowdhuri A and Tomar M 2025Chemical Physics Impact10100847https://doi.org/10.1016/j.chphi.2025.100847

    2025

  36. [44]

    Al Mamun M S, Takaoka T, Wang Z and Komeda T 2025ChemistrySelect10e202403982 https://doi.org/10.1002/slct.202403982

    doi

  37. [45]

    Giustino F 2017Reviews of Modern Physics89015003 https://doi.org/10.1103/RevModPhys.89.015003

    doi

  38. [46]

    Ponc´ e S, Margine E R, Verdi C and Giustino F 2016Computer Physics Communications209 116–133https://doi.org/10.1016/j.cpc.2016.07.028

    2016 doi

  39. [47]

    Filipovic L 2026 Ensemble Monte Carlo and DFPT simulation data for charge transport and gas sensing in monolayer MoS 2 dataset URLhttps://doi.org/10.48436/87zq1-28246 https://doi.org/10.48436/87zq1-28246 13

    2026 doi

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.