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arxiv: 2604.22155 · v1 · submitted 2026-04-24 · ❄️ cond-mat.mes-hall

Microscopic Modeling of Surface Roughness Scattering in Inversion Layers of MOSFETs Based on Ando's Linear Model

Nobuyuki Sano This is my paper

Pith reviewed 2026-05-08 10:27 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords surface roughness scatteringMOSFETinversion layersmicroscopic modelingAndo's modelGreen's functionnonlocal scattering
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The pith

A microscopic model based on Ando's linear approach resolves the discrepancy between theory and experiment in surface roughness scattering for MOSFET inversion layers by introducing a probability density for roughness positions at atomic 0.

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

The paper develops a microscopic model for surface roughness scattering in bulk-MOSFET inversion layers, extending Ando's linear model. It accounts for the stochastic nature of roughness by defining a probability density of roughness position at each atomic site, derived from discontinuities in the spatial derivatives of the electrostatic potential and wave function at the interface. This leads to roughness parameters that match experimental values without additional fitting. The resulting scattering rate, calculated via Green's functions, is nonlocal across subband indices and positions, and self-consistent calculations show significant deviations from Fermi's golden rule, particularly at strong fields and low energies, implying that conventional models underestimate mobility.

Core claim

The roughness parameters in the proposed model are consistent with those from experiments, eliminating the discrepancy between theory and experiment. The SR scattering rate is intrinsically nonlocal with respect to subband indices and position, and the self-consistent scattering rate greatly deviates from those obtained by Fermi's golden rule in regimes of strong effective fields and low electron energies, causing the conventional model to predict smaller SR-limited mobility.

What carries the argument

The probability density of roughness position at each atomic site, derived from the discontinuity of the spatial derivatives of the electrostatic potential and wave-function at the semiconductor/dielectric interface.

If this is right

  • The SR scattering rate is intrinsically nonlocal (nondiagonal) with respect to subband indices and position.
  • The self-consistent scattering rate deviates from Fermi's golden rule results in strong effective fields and low electron energies.
  • Conventional models based on Fermi's golden rule tend to predict smaller SR-limited mobility.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This nonlocal character implies that transport calculations must account for inter-subband mixing effects induced by the interface.
  • Device simulations using this model could predict higher mobilities in inversion layers under typical operating conditions.
  • The approach suggests that atomic-scale interface modeling is key to accurate scattering predictions without empirical parameters.

Load-bearing premise

A probability density of roughness position can be meaningfully introduced at each atomic site based solely on the discontinuity of the spatial derivatives of electrostatic potential and wave-function at the semiconductor/dielectric interface.

What would settle it

Measurements of electron mobility in MOSFET inversion layers at high effective fields and low energies that align with the self-consistent Green's function rates rather than those from Fermi's golden rule.

Figures

Figures reproduced from arXiv: 2604.22155 by Nobuyuki Sano.

Figure 2
Figure 2. Figure 2: FIG. 2. (a) SR scattering rates in Si obtained by the self view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. SR-limited electron mobility in Si as a function of ef view at source ↗
read the original abstract

A microscopic model of surface roughness (SR) scattering in inversion layers of bulk-MOSFETs based on Ando's linear model is proposed. Taking into account the stochastic nature of roughness position induced by discontinuity of the spatial derivatives of electrostatic potential and wave-function at the semiconductor/dielectric interface, a probability density of roughness position is introduced at each atomic site. The roughness parameters in the proposed model are consistent with those from experiments, and thus, there is no discrepancy between theory and experiment. The SR scattering rate is then derived by using the Green's function scheme, and we find that the scattering rate is intrinsically nonlocal (nondiagonal) with respect to subband indices and position. In addition, the self-consistent scattering rate greatly deviates from those obtained by Fermi's golden rule in the regimes of strong effective fields and low electron energies. As a result, the conventional model tends to predict smaller SR-limited mobility.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a microscopic model of surface roughness (SR) scattering in bulk-MOSFET inversion layers, extending Ando's linear model. It introduces a probability density of roughness position at each atomic site, derived from discontinuities in the spatial derivatives of the electrostatic potential and wave-function at the semiconductor/dielectric interface. The authors claim that this yields roughness parameters consistent with experiments without additional fitting, resolving the theory-experiment discrepancy. The SR scattering rate is computed via Green's functions and shown to be intrinsically nonlocal (nondiagonal) in subband indices and position; the self-consistent rate deviates substantially from Fermi's golden rule at strong effective fields and low electron energies, implying conventional models underestimate SR-limited mobility.

Significance. If the mapping from interface discontinuities to a unique probability density can be rigorously established, the model would supply a microscopically grounded, parameter-consistent description of SR scattering that accounts for nonlocal effects and improves upon local perturbative approximations. The Green's function treatment of nondiagonal scattering rates constitutes a methodological step beyond standard Fermi-golden-rule implementations.

major comments (2)
  1. [Model construction] The introduction of the probability density of roughness position at each atomic site (model construction following Ando's linear model): the mapping from the discontinuity of spatial derivatives of potential and wave-function to a specific density is asserted but not derived explicitly, nor is uniqueness or normalization demonstrated. This assumption is load-bearing for the central claim that roughness parameters match experimental values without further fitting.
  2. [Scattering rate derivation] Abstract and scattering-rate section: the assertion that the self-consistent scattering rate 'greatly deviates' from Fermi's golden rule in strong effective fields and low electron energies is stated without quantitative benchmarks (specific field strengths, energy ranges, or comparison metrics with uncertainties). This prevents assessment of whether the deviation is sufficient to alter mobility predictions materially.
minor comments (1)
  1. [Abstract] The abstract refers to 'strong effective fields' without numerical ranges or units, which would aid immediate readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We address each major comment point by point below, indicating the revisions we will implement to improve clarity and support for our claims.

read point-by-point responses

  1. Referee: [Model construction] The introduction of the probability density of roughness position at each atomic site (model construction following Ando's linear model): the mapping from the discontinuity of spatial derivatives of potential and wave-function to a specific density is asserted but not derived explicitly, nor is uniqueness or normalization demonstrated. This assumption is load-bearing for the central claim that roughness parameters match experimental values without further fitting.

    Authors: We agree that the mapping requires a more explicit derivation to fully substantiate the model. In the revised manuscript, we will add a dedicated subsection that derives the probability density step by step from the discontinuities in the spatial derivatives of the electrostatic potential and wave function, as induced by the stochastic roughness position in Ando's linear model. We will explicitly demonstrate normalization over atomic sites and discuss uniqueness under the model's physical assumptions (e.g., local interface discontinuities and linear response). This will reinforce how the resulting roughness parameters align with experimental values without additional fitting. revision: yes

  2. Referee: [Scattering rate derivation] Abstract and scattering-rate section: the assertion that the self-consistent scattering rate 'greatly deviates' from Fermi's golden rule in strong effective fields and low electron energies is stated without quantitative benchmarks (specific field strengths, energy ranges, or comparison metrics with uncertainties). This prevents assessment of whether the deviation is sufficient to alter mobility predictions materially.

    Authors: We acknowledge that quantitative benchmarks are essential for evaluating the deviation's significance. In the revised manuscript, we will expand the scattering-rate section with specific benchmarks, including effective field strengths (e.g., 0.3–1.5 MV/cm) and electron energies (e.g., 0–0.1 eV), along with tables or figures showing relative deviations (with estimated uncertainties from the Green's function calculations). These will directly compare the self-consistent nonlocal rates to Fermi's golden rule results and quantify the resulting impact on SR-limited mobility predictions. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation adds independent elements

full rationale

The paper extends Ando's linear model by introducing a probability density for roughness position at atomic sites based on derivative discontinuities at the Si/SiO2 interface, then derives the scattering rate via Green's functions to show it is nonlocal (nondiagonal in subband indices and position) and deviates from Fermi's golden rule at strong fields and low energies. The claim that roughness parameters match experiments without additional fitting follows from these additions rather than reducing to a fit or self-citation by construction. No equations or steps in the provided text exhibit a direct equivalence where a prediction equals its input; the central results on nonlocality and deviation provide independent content beyond the cited Ando framework.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The claim rests on extending Ando's linear model with a new stochastic probability density; no explicit new fitted constants are introduced beyond the consistency statement with experiment.

free parameters (1)
  • roughness parameters
    Stated to be taken directly from experiment for consistency, but the model must still select or adjust their values to achieve the claimed agreement.
axioms (1)
  • domain assumption Ando's linear model applies to the interface potential and wave-function discontinuities
    The entire construction is built on this established framework for surface roughness scattering.
invented entities (1)
  • probability density of roughness position at each atomic site no independent evidence
    purpose: To capture the stochastic nature induced by derivative discontinuities at the semiconductor/dielectric interface
    New postulated distribution introduced to enable the microscopic treatment; no independent falsifiable prediction outside the model is provided.

pith-pipeline@v0.9.0 · 5456 in / 1400 out tokens · 84662 ms · 2026-05-08T10:27:25.174725+00:00 · methodology

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Reference graph

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