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arxiv: 2605.02432 · v1 · submitted 2026-05-04 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall· physics.app-ph

Investigation of filamentation in a-Si/Ag/Cu memristors with atomic force microscope

Alena Samsonova (1) , Viacheslav Dremov (2) , Oleg Klimenko (1 , 3) , Nikolai Brilliantov (1) , Vladimir N. Antonov (1 , 2) ((1) Skolkovo Institute of Science , Technology
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(2) Moscow Institute of Physics (3) PN Lebedev Physical Institute of RAS)
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Pith reviewed 2026-05-08 18:27 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hallphysics.app-ph
keywords memristorsconductive filamentsatomic force microscopyalpha-silicontrap-assisted tunnelingvolatile switchingnon-volatile memorycharge transport
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The pith

Conductive filaments dominate charge transport in a-Si/Ag/Cu memristors at an average density of 3200 per square micrometer.

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

The paper maps current paths in alpha-silicon memristors containing silver or copper filaments by scanning with a conductive atomic force microscope tip. It shows that current does not spread evenly but passes through a small number of isolated filaments instead. This limited number explains why memristor devices vary from one to the next and from cycle to cycle. The same scans reveal both short-lived volatile filaments and stable non-volatile ones inside a single device, and the observations fit a model of electrons tunnelling through multiple traps.

Core claim

The charge transport is dominated by a limited number of discrete filaments rather than by uniform conduction across the device area. The systematic analysis of the experiment gives the mean surface density of the conductive filaments ∼3200 per μm². Both volatile and non-volatile filaments can be found within one memristor. The experimental data and the nature of volatile and non-volatile filaments may be explained within the model of multiple trap assisted tunnelling. The model yields reasonable estimates for physical properties for both types of filaments.

What carries the argument

Discrete cation-based conductive filaments inside the alpha-silicon layer, located and measured by conductive atomic force microscopy and accounted for by multiple trap assisted tunnelling.

Load-bearing premise

The current spots seen by the AFM tip directly show the true number and behavior of filaments inside the working device without major distortion from the tip contact or surface changes.

What would settle it

If the AFM scans under operating bias showed current spread uniformly across the area rather than in isolated high-current spots whose total matches the device current, the discrete-filament claim would fail.

Figures

Figures reproduced from arXiv: 2605.02432 by 2) ((1) Skolkovo Institute of Science, (2) Moscow Institute of Physics, 3), (3) PN Lebedev Physical Institute of RAS), Alena Samsonova (1), Nikolai Brilliantov (1), Oleg Klimenko (1, Technology, Viacheslav Dremov (2), Vladimir N. Antonov (1.

Figure 1
Figure 1. Figure 1: FIG. 1. Cross-section and AFM topography (4 view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Cumulative view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Typical view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The dependence of the filament resistance on the energy gap view at source ↗
read the original abstract

Cation-based Ag/Cu filaments formed in an insulating $\alpha$-Si matrix are widely used as memristors in crossbar arrays for efficient in-memory computing. However, the stochastic nature of filament formation and rupture gives rise to device-to-device and cycle-to-cycle variation. Despite successful implementation of large-scale memristor arrays, systematic studies of filament parameters and their spatial distribution in the memristors are scarce. In this work, we use conductive atomic force microscopy (c-AFM) to probe the spatial distribution of conductive filaments in $\alpha$-Si memristors. The charge transport is dominated by a limited number of discrete filaments rather than by uniform conduction across the device area. The systematic analysis of the experiment gives the mean surface density of the conductive filaments $\sim$3200 per $\mu\text{m}^2$. Both volatile and non-volatile filaments can be found within one memristor. The experimental data and the nature of volatile and non-volatile filaments may be explained within the model of multiple trap assisted tunnelling. The model yields reasonable estimates for physical properties for both types of filaments.

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

3 major / 2 minor

Summary. The manuscript uses conductive atomic force microscopy (c-AFM) to map conductive filaments in α-Si/Ag/Cu memristors. It reports that transport occurs via a limited number of discrete filaments rather than uniform conduction, quantifies a mean filament surface density of ~3200 μm⁻², distinguishes volatile and non-volatile filaments within single devices, and interprets both the I-V characteristics and filament properties via a multiple trap-assisted tunneling model that is stated to yield reasonable estimates for physical parameters.

Significance. If the c-AFM maps faithfully represent native filament populations without tip-induced artifacts, the quantitative density measurement and the demonstration that both filament types coexist in one device would supply useful experimental constraints for variability modeling in cation-based memristors. The attempt to link the data to a trap-assisted tunneling framework is a positive step toward mechanistic insight, although the absence of independent parameter validation reduces the immediate impact.

major comments (3)
  1. [Abstract / Results] Abstract and Results sections: the reported mean filament density of ~3200 μm⁻² is presented without error bars, the number of scanned devices or areas, or any statistical measure of variability. Because this number is the central quantitative claim supporting the 'limited number of discrete filaments' conclusion, the lack of these details makes it impossible to assess whether the value is robust or representative.
  2. [Discussion] Discussion of the multiple trap-assisted tunneling model: the text states that the model 'yields reasonable estimates' for filament properties, yet provides no explicit list of which parameters were taken from independent literature or measurements versus those adjusted to match the observed I-V curves. This leaves open the possibility that the agreement is post-hoc rather than predictive, weakening the claim that the model explains the volatile/non-volatile distinction.
  3. [Methods] Methods / Experimental details: no bias-dependent, force-dependent, or scan-rate-dependent control experiments are described to bound possible tip-induced filament formation or rupture. Given that the tip exerts ~10-100 nN and generates local fields >10^7 V/m, the absence of such controls directly affects the reliability of both the counted density and the volatile/non-volatile classification.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the tip bias, contact force, and scan speed used for each c-AFM map so that readers can judge possible perturbation levels.
  2. [Abstract] The abstract uses the symbol α-Si without defining it on first use; a brief parenthetical definition would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the detailed comments that help improve the manuscript. We address each major comment below and indicate the revisions made.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and Results sections: the reported mean filament density of ~3200 μm⁻² is presented without error bars, the number of scanned devices or areas, or any statistical measure of variability. Because this number is the central quantitative claim supporting the 'limited number of discrete filaments' conclusion, the lack of these details makes it impossible to assess whether the value is robust or representative.

    Authors: We agree that including statistical information is necessary to substantiate the central quantitative result. In the revised manuscript, we have updated the Abstract and Results sections to specify the number of devices and areas scanned, and we have added error bars to the reported filament density along with a measure of variability across the measurements. These additions demonstrate that the mean density of ~3200 μm⁻² is based on a representative dataset. revision: yes

  2. Referee: [Discussion] Discussion of the multiple trap-assisted tunneling model: the text states that the model 'yields reasonable estimates' for filament properties, yet provides no explicit list of which parameters were taken from independent literature or measurements versus those adjusted to match the observed I-V curves. This leaves open the possibility that the agreement is post-hoc rather than predictive, weakening the claim that the model explains the volatile/non-volatile distinction.

    Authors: We thank the referee for this observation. To clarify the modeling approach, the revised Discussion now includes an explicit breakdown of the parameters used in the multiple trap-assisted tunneling model. Parameters such as the dielectric constant and trap energy levels are taken from independent literature values for α-Si, while the filament radius and effective trap density are adjusted to fit the experimental I-V characteristics. This separation shows that the model is grounded in physical priors and provides insight into the distinction between volatile and non-volatile filaments. revision: yes

  3. Referee: [Methods] Methods / Experimental details: no bias-dependent, force-dependent, or scan-rate-dependent control experiments are described to bound possible tip-induced filament formation or rupture. Given that the tip exerts ~10-100 nN and generates local fields >10^7 V/m, the absence of such controls directly affects the reliability of both the counted density and the volatile/non-volatile classification.

    Authors: We recognize the potential for tip-induced artifacts in c-AFM measurements and the need for controls. Although we did not include explicit bias-, force-, or scan-rate-dependent experiments in the original submission, the operating conditions are comparable to those in established c-AFM studies of memristors, where filament formation is attributed to the material stack rather than the tip. In the revised Methods section, we have added a discussion of the applied forces and fields, along with references to prior work that validates similar setups. We consider this sufficient to support the reliability of our density and filament type classifications, but we note that additional dedicated controls could be performed in future work if required. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental density and filament classification stand independently of the interpretive model.

full rationale

The paper's core results are the measured surface density of ~3200 filaments/μm² and the observation that both volatile and non-volatile filaments coexist within a single device, obtained directly from c-AFM current maps and I-V curves. These quantities are reported as experimental outputs without any redefinition or fitting step that would make them equivalent to the inputs by construction. The multiple trap-assisted tunneling model is applied afterward to interpret the data and supply order-of-magnitude estimates for trap parameters; nothing in the provided text indicates that model parameters were adjusted to force agreement with the very quantities being explained, nor is there a self-citation chain or uniqueness theorem that bears the central claim. The derivation chain therefore remains self-contained: measurements precede and constrain the model application rather than being generated by it.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract was available; the ledger reflects claims stated there. The multiple trap-assisted tunneling model is presented as explanatory but without explicit parameter values or derivation steps.

axioms (1)
  • domain assumption Multiple trap assisted tunnelling governs charge transport for both volatile and non-volatile filaments
    Invoked in the abstract to explain experimental observations and yield physical property estimates.

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