arxiv: 2605.14964 · v1 · submitted 2026-05-14 · ❄️ cond-mat.other

Recognition: 1 theorem link

· Lean Theorem

Image Force Effects on Tunneling Currents in an STM -- I `Point charge in the Barrier Region' - Model

Malati Dessai , Arun V. Kulkarni

Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:41 UTC · model grok-4.3

classification ❄️ cond-mat.other

keywords STMtunneling currentimage potentialpoint chargebarrier modificationscanning tunneling microscopetunneling density

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The pith

Treating the tunneling electron as a point charge in an STM induces image forces that lower and narrow the barrier, greatly increasing the calculated tunneling current.

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

This paper models the tunneling electron in a scanning tunneling microscope as a point charge that induces image charges on the conducting tip and sample surfaces. These image charges reshape the potential barrier by lowering its height and reducing its effective width. The modified barrier produces tunneling current densities that are orders of magnitude larger than those obtained from the standard rectangular-barrier model. The authors calculate the enhancement as a function of tip-sample separation and bias voltage, but note that the enormous increase appears physically unrealistic and therefore questions the point-particle treatment of the electron.

Core claim

In an STM, modeling the tunneling electron as a point charge in the barrier region induces image charges on the conducting surfaces of the tip and sample. This image potential modifies the barrier by reducing its height and effective width, resulting in a huge increase in the tunneling current densities and currents as a function of tip-sample distance d and bias voltage eV_b.

What carries the argument

The image potential generated by the point-charge electron on the conducting tip and sample surfaces, which alters the shape of the rectangular potential barrier.

Load-bearing premise

The assumption that the electron in the barrier region can be treated as a classical point particle.

What would settle it

Precise measurement of tunneling current versus tip-sample distance at fixed bias, compared against the point-charge image-potential prediction and the standard barrier model without image forces.

Figures

Figures reproduced from arXiv: 2605.14964 by Arun V. Kulkarni, Malati Dessai.

**Figure 2.** Figure 2: FIG. 2: Image-charge construction for a point [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Plot of Trapezoid + Simmons Image [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Plot of the WKB tunneling current den [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Plot of the WKB tunneling current den [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: Plot of current density [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: Plot of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9: Division of the Spatial Region between [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8: Plots of the Russell Potential and its lin [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10: Plot of [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11: Plot of [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13: Plot of [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14: Plot of [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗

**Figure 17.** Figure 17: FIG. 17: Plot of current [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15: Plot of current [PITH_FULL_IMAGE:figures/full_fig_p013_15.png] view at source ↗

**Figure 16.** Figure 16: FIG. 16: Plot of current [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗

read the original abstract

In a Scanning Tunneling Microscope (STM), when a tunneling electron treated as a point charge enters the barrier region between the tip and the sample, it induces image charges on the conducting surfaces, which modifies the shape of the potential barrier it sees. In this paper, the effect of the modification in the barrier potential due to these induced charges on the tunneling current density and currents in an STM,is studied as a function of the tip-sample distance $d$ and the Bias Potential $eV_b$. The image potential is found to reduce the height and the effective width of the potential barrier, leading to a huge increase in the tunneling current densities. This huge increase (by several order of magnitudes) is however unreasonable, prompting a revisit of the assumption that the electron in the barrier region is a point particle.

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.

Desk Editor's Note private letter to a colleague

read the letter

The paper shows that treating the tunneling electron as a point charge in the STM barrier produces an unphysically large current increase, which the authors use to question the point-particle assumption. They apply the standard image-charge formulas to the tip-sample geometry and track how the potential changes with distance d and bias Vb. The barrier gets lower and thinner, and the tunneling current jumps by orders of magnitude. The authors flag this outcome as unreasonable right away. What the paper does well is to make the dependence on d and Vb explicit and to state the problem without trying to salvage the model. It is a clean demonstration that the classical point-charge picture fails badly in this setting. The soft spot is that the work stops at identifying the problem. There is no attempt to replace the point-charge assumption with a better description, such as spreading the charge or using a quantum-mechanical wave function for the electron in the barrier. Without that next step or a direct comparison to experimental STM I-V curves, the result remains more of a warning than a finished analysis. This kind of note is mainly for people who build theoretical models of STM tunneling. It reminds them why they cannot simply add image forces on top of a point-charge electron. Experimental groups might skim it for the same reason but would not use the numbers directly. I would bring it to a reading group on tunneling or surface physics because the calculation is easy to follow and the conclusion is clear. I would not cite it myself unless I needed the specific scaling they derive. It deserves peer review as a short paper because the central observation is reproducible and the authors are honest about its limitations.

Referee Report

1 major / 2 minor

Summary. The manuscript models the classical image potential induced by treating the tunneling electron as a point charge in the barrier region of an STM. It modifies the potential barrier height and width accordingly, computes the resulting tunneling current densities as functions of tip-sample distance d and bias eVb, and reports a large enhancement (several orders of magnitude). The authors explicitly flag this enhancement as unphysical and conclude that the point-particle assumption for the electron must be abandoned in favor of a more appropriate treatment.

Significance. The calculation illustrates the breakdown of semiclassical point-charge electrostatics when applied to quantum tunneling in STM geometries. By presenting the unphysically large current increase as evidence against the model's validity rather than as a physical prediction, the work usefully motivates the development of wave-function-based or delocalized-electron models for image forces. This self-critical framing is a strength, though the absence of direct experimental comparisons limits immediate applicability.

major comments (1)

[Results and Discussion] The central quantitative claim of a 'huge increase (by several order of magnitudes)' in tunneling current density is presented without explicit comparison to the standard WKB result without image forces or to measured STM currents at comparable d and Vb. This makes the assessment of 'unreasonableness' difficult to evaluate independently and weakens the load-bearing argument for abandoning the point-charge model.

minor comments (2)

[Abstract] The abstract and introduction should include at least one reference to the specific image-charge formula employed (e.g., the standard series for two parallel plates) and the tunneling integral method (WKB or exact) to allow readers to reproduce the barrier modification.
[Model section] Notation for the bias (eVb) and distance (d) is introduced without defining the sign convention for Vb or the range of d values considered; a short table or plot caption clarifying these would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation and constructive feedback. We agree that including explicit comparisons to the standard WKB result will strengthen the presentation of our results and have made the suggested revisions.

read point-by-point responses

Referee: [Results and Discussion] The central quantitative claim of a 'huge increase (by several order of magnitudes)' in tunneling current density is presented without explicit comparison to the standard WKB result without image forces or to measured STM currents at comparable d and Vb. This makes the assessment of 'unreasonableness' difficult to evaluate independently and weakens the load-bearing argument for abandoning the point-charge model.

Authors: We appreciate this comment and agree that direct comparisons would make the enhancement clearer. In the revised version, we have added calculations of the tunneling current density using the standard WKB approximation without image forces for the same parameters. We now include figures showing the ratio of the current density with image forces to that without, explicitly demonstrating the orders-of-magnitude increase. For comparison to experimental currents, we have added a brief discussion noting that typical STM tunneling currents at tip-sample distances of a few angstroms are on the order of 0.1 to 10 nA, whereas our calculated values with image forces exceed these by several orders of magnitude even at larger distances, reinforcing the unphysical nature of the point-charge model. We believe this addresses the concern and supports our conclusion. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper applies standard classical image-charge electrostatics to a point charge placed inside the barrier, modifies the potential barrier accordingly, inserts the result into a standard tunneling integral, obtains a large current increase, and explicitly flags the outcome as unphysical to argue that the point-particle assumption must be dropped. No equation reduces to its own input by construction, no fitted parameters are renamed as predictions, and no self-citation chain supplies the central result. The derivation is self-contained against external electrostatic and tunneling formulas; the reported increase is a direct calculational consequence of the model the authors themselves reject.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The model rests on classical electrostatic image-charge construction for a point charge between two conductors; no free parameters beyond the geometric variables d and Vb are stated in the abstract.

axioms (1)

domain assumption Electron in the barrier region can be treated as a classical point charge that induces image charges on the tip and sample surfaces.
Explicitly stated in the abstract as the modeling choice whose consequences are then calculated.

pith-pipeline@v0.9.0 · 5446 in / 1164 out tokens · 42926 ms · 2026-05-15T02:41:08.592288+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

[1]

Simmons [4] also makes several approx- imations in addition to the WKB approxima- tion, and calculates and plots tunnel resistiv- ities

used the net (non-trapezoidal) potential in a WKB approximation, thus obviating the need to solve the Schr¨ odinger equation ex- actly. Simmons [4] also makes several approx- imations in addition to the WKB approxima- tion, and calculates and plots tunnel resistiv- ities. It is difficult to fully estimate the effect of the image potentials in these calcul...

work page
[2]

The essence of the Saenz- Garcia [13] method is to treat the realistic STM as being made up of infinitesimal Planar Model STM’s laid along the field lines

is used to calculate tunneling currents for actual tip and sample shapes, without re- quiring a full 3 dimensional calculation, us- ing only planar model current densities. The essence of the Saenz- Garcia [13] method is to treat the realistic STM as being made up of infinitesimal Planar Model STM’s laid along the field lines. The planar model current den...

work page
[3]

The increase factor for this Figure is 7 to 10 orders of magnitude which is the same as that for Fig. 12. Also the two Figures 12 and 14 are remarkable similar in shape, suggest- ing that the results for similar electrodes are the same as for dissimilar electrodes provided the Bias Potential for the latter is corrected for the nonzero Contact Potential. T...

work page
[5]

Dessai and A

M. Dessai and A. V. Kulkarni, Calculation of tunneling current across trapezoidal po- tential barrier in a scanning tunneling mi- croscope, Journal of Applied Physics132 (2022)

work page 2022
[6]

Dessai, Theoretical studies on the scanning tunneling microscope (2024), arXiv:2402.00026 [cond-mat.other]

M. Dessai, Theoretical studies on the scanning tunneling microscope (2024), arXiv:2402.00026 [cond-mat.other]

work page arXiv 2024
[7]

J. G. Simmons, Generalized formula for the electric tunnel effect between similar elec- trodes separated by a thin insulating film, Journal of applied physics34, 1793 (1963)

work page 1963
[8]

Morse and H

P. Morse and H. Feshbach,Methods of The- oretical Physics(McGraw-Hill Book Com- pany, 1953)

work page 1953
[9]

Tanget al., Research report on resonant tunneling effect in double-barrier struc- tures: A transfer-matrix method study, Proceedings / SciTePress etc

C. Tanget al., Research report on resonant tunneling effect in double-barrier struc- tures: A transfer-matrix method study, Proceedings / SciTePress etc. (2025), uses TMM to compute transmission/reflection coefficients in double-barrier quantum wells

work page 2025
[10]

Dehghani, S

V. Dehghani, S. A. Alavi, A. Soylu, and F. Koyuncu, Transfer matrix method as a unified method for determination of bound, antibound, resonance, decay half- life, fusion and elastic scattering cross- sections, The European Physical Jour- nal A61, 10.1140/epja/s10050-025-01573- x (2025), extends TMM into a unified for- malism including tunneling, scatterin...

work page doi:10.1140/epja/s10050-025-01573- 2025
[11]

P. Pereyra, The transfer matrix method and the theory of finite periodic systems, phys- ica status solidi (b) or similar (2022), re- views TMM, scattering amplitudes, sym- metry properties, and applications (includ- ing tunneling)

work page 2022
[12]

Umesakiet al., Tunneling effect in pro- ton transfer: Transfer matrix approach, The Journal of Physical Chemistry A (2023), applies TMM to proton-transfer barrier crossing problems

K. Umesakiet al., Tunneling effect in pro- ton transfer: Transfer matrix approach, The Journal of Physical Chemistry A (2023), applies TMM to proton-transfer barrier crossing problems

work page 2023
[13]

Figueroa, I

J. Figueroa, I. Gonzalez, and D. Salinas- Arizmendi, A novel transfer matrix frame- work for multiple dirac delta potentials, Elsevier Physics (assuming) (2025), ana- lytical TMM for N equally spaced delta- barriers in 1D tunneling systems

work page 2025
[14]

D. Sebbaret al., Modeling of the effects of non-uniform electric field on electronic transport in superlattices using the trans- fer matrix method, Sigma Journal of Engi- 15 neering & Natural Sciences41, 1292 (2023), uses TMM to compute transmission in su- perlattices under electric field variation

work page 2023
[15]

Y. Wanget al., Transfer-matrix theory of monolayer graphene/bilayer graphene het- erostructures and barrier tunneling, Jour- nal of Applied Physics116, 164317 (2014), applies TMM to barrier-transmission in graphene heterostructures (Klein tunneling context)

work page 2014
[16]

J. J. S´ aenz and R. Garc´ ıa, Near field emis- sion scanning tunneling microscopy, Ap- plied physics letters65, 3022 (1994)

work page 1994
[17]

A. M. Russell, Electron trajectories in a field emission microscope, Journal of Ap- plied Physics33, 970 (1962)

work page 1962
[18]

Moon and D

P. Moon and D. E. Spencer,Field Theory Handbook(Springer-Verlag Berlin Heildel- berg New York, 1971)

work page 1971
[19]

Cutler, J

P. Cutler, J. He, J. Miller, N. Miskovsky, B. Weiss, and T. Sullivan, Theory of elec- tron emission in high fields from atomi- cally sharp emitters: Validity of the fowler- nordheim equation, Progress in surface sci- ence42, 169 (1993)

work page 1993
[20]

R. P. Brent, Algorithms for minimization without derivatives (Prentice-Hall, Engle- wood Cliffs, NJ, 1973) Chap. 4

work page 1973