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Period-dependent suppression of Fourier peaks for topography images: Analysis of periodicity of triple-step arrays on vicinal Si(h h m) surfaces

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read The period of triple-step arrays on silicon vicinal surfaces can be read directly from raw scanning tunneling microscopy images: when the ninth Fourier peak vanishes, the array period is 18 atomic rows, identifying the local Si(8 8 11) plan

desk verdict The zero-prediction in Eq. (6) is real and useful; the Si(8811) claim rests on an unproven link between DoG contrast and the adatom-density model. read the letter →

arxiv 2607.16699 v1 pith:DSIKYZ7D submitted 2026-07-18 cond-mat.mtrl-sci cond-mat.mes-hall

A. Yu. Aladyshkin , A. N. Chaika , V. N. Semenov , A. S. Aladyshkina , A. M. Ionov , S. I. Bozhko This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall
keywords difference-of-GaussiansFourieranalysisscanningtunnelingmicroscopyvicinalsiliconsurfacestriplestepsSi(557)Si(8811)perioddetermination
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 the periodicity of multiatomic step arrays on high-index silicon surfaces can be determined from raw STM images, without tilt or drift corrections, with precision close to one atomic row. The key is to Fourier-analyze difference-of-Gaussians maps of the topography; the relative intensities of the Fourier peaks at k_y=0 are controlled by the array period, and specific peaks are completely suppressed for particular periods. For the triple-step staircase on nominally Si(557) wafers, the suppression of the ninth peak implies a period of 18b = 5.99 nm in projection onto the Si(111) terrace plane, meaning the local surface is actually Si(8 8 11). The same method is shown to work for wider terraces on Si(556), and should generalize to other vicinal surfaces with terraces containing an integer number of reconstruction unit cells.

What carries the argument

The machinery is the difference-of-Gaussians (DoG) filter — subtracting two Gaussian-blurred copies of the topography image — applied to raw STM data, followed by a 2D FFT. DoG highlights local curvature where adatoms sit, flattening tilt and background so that atomic lattices appear across all terraces simultaneously. The Fourier amplitudes along k_y=0 are then interpreted with the closed-form envelope A_m(L) of Eq. (6), derived from a 1D model of the averaged adatom concentration with a 3:1:2:2:1:3 row-weight pattern. Commensurability between the 7×7 reconstruction wave number k0/7 and the array period wave number k0/L causes the zeros of this envelope to fall exactly on certain integer or

What would settle it

Acquire an atomically resolved STM image of an individual terrace on a Si(557) triple-step staircase and measure the actual lateral offsets of the 7×7 adatom rows relative to the 1×1 lattice. If those offsets are not ±b/2, ±3b/2, ±5b/2, then Eq. (6) predicts a nonzero ninth peak, and the claimed 18b period inference fails. Alternatively, if a similar wafer prepared by the same recipe shows no suppression of the ninth peak in the DoG-FFT analysis, the identification of Si(8 8 11) is contradicted.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is an interference effect in the Fourier transform of a periodic array of atomically flat terraces: for a stripe of width 5b with the Si(111)7×7 reconstruction repeating with period L, the amplitude of the m-th Fourier peak at k_y=0 is A_m = 3cos(5πm b/L) + cos(3πm b/L) + 2cos(πm b/L). This expression vanishes for specific (m, L) pairs — m=±8 for L=16b, m=±5 and ±12 for L=17b, m=±9 for L=18b — because the adatom rows at offsets ±b/2, ±3b/2, ±5b/2 with weights 3:1:2:2:1:3 produce exact cancellation at the corresponding wave vectors. In the experimental DoG map of a nominally Si(557) wafer, the ninth Fourier peak is strongly suppressed while the

Load-bearing premise

The whole period assignment rests on the model that each 7×7 terrace's adatom rows sit exactly at ±b/2, ±3b/2, ±5b/2 within a 5b-wide cell with fixed weights; if the real atomic offsets differ, the predicted vanishing of the ninth peak shifts or disappears.

Editorial extensions

If this is right

  • The period of triple-step arrays on Si(557) can be measured to within one atomic row directly from raw STM images, without prior plane subtraction or drift correction.
  • The nominal Si(557) wafers studied are locally Si(8 8 11) with a 5.99-nm period, not Si(557) or Si(7 7 10) as earlier works claimed.
  • Applying the same reasoning to Si(556) yields a 32b-period array with a fully suppressed 16th Fourier peak, confirming the rule for wider terraces.
  • Because scaling and affine distortions do not change which orders vanish, the pattern serves as an in-image calibration reference for rescaling raw data.
  • The method extends to any vicinal surface whose terraces contain an integer number of reconstruction unit cells (e.g., 5×5, 7×7, 9×9).

Reading between the lines

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

  • If the same envelope logic is applied to other reconstruction widths, one can predict the full set of suppressed orders for any L/b ratio; this could be turned into a general lookup rule for step-period metrology.
  • The zeros of A_m are sensitive to the assumed row offsets; comparing predicted and observed suppressions for different step geometries could discriminate between competing atomic models of triple steps.
  • The paper leaves open whether LEED patterns show analogous suppressed spots; modeling the electron-beam tilt could test the idea in reciprocal space, where no STM drift artifacts exist.
  • Using the crystal's own Fourier zeros as a ruler, one could calibrate piezo scanners in situ by measuring which peaks disappear, without any external length standard.
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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

3 major / 4 minor

Summary. The paper proposes that the periodicity of multiatomic step arrays on vicinal Si(hhm) surfaces can be determined from raw STM topography images by computing difference-of-Gaussians (DoG) maps and examining the FFT of these maps. A one-dimensional model represent the averaged adatom density of Si(111)7x7 stripes, with the adatom rows at positions ±b/2, ±3b/2, ±5b/2 relative to the stripe center and weights 3:1:2:2:1:3, leads to an analytical expression (Eq. 6) for the relative amplitudes A_m of Fourier orders. The zeros of A_m depend on L/b: for L=16b, m=±8 vanish; for L=17b, m=±5 and ±12 vanish; for L=18b, m=±9 vanish. The authors then apply this to a nominally Si(557) wafer, observe strong suppression of the ninth Fourier peak in the FFT of the DoG map, and conclude that the local period is 18b = 5.99 nm and that the surface corresponds to Si(8811). A second example on Si(556) gives L=32b and suppression of m=±16.

Significance. The analytic result in Eq. (6) is clean, parameter-free, and gives a striking and verifiable interference effect: the period-dependent suppression of selected Fourier peaks is a direct consequence of the specific arrangement of adatom rows. If the experimental connection can be made rigorous, the method could indeed provide a distortion-robust way to calibrate STM images and identify step periodicities on vicinal surfaces. The paper also correctly emphasizes that the zeros of A_m are unaffected by scaling or affine distortions, which is a genuine practical advantage. However, the central experimental claim relies on an identification between the DoG signal and the adatom-density model that is not theoretically justified. The manuscript does not yet establish that the suppression of the ninth peak in the experimental DoG spectrum is caused by the model's density profile rather than by the step-edge contrast that is necessarily present in DoG images of a triple-step staircase.

major comments (3)
  1. [§ Experiment: nominal Si(5 5 7)...; Eq. (1); Eq. (4); Fig. 4 vs Fig. 7] The model of Eq. (4) and the theoretical images in Fig. 4 describe the averaged adatom density on flat 7x7 stripes. The experimental observable D(x,y) is a band-pass filtered version of the raw topography z(x,y) via Eq. (1), and the surface contains triple steps of height ~0.94 nm repeating with the same period L. The Fourier transform of D is the sum of the adatom contribution and the step-edge contribution. The zero in A_m for m=9 does not imply a zero in the total DoG spectrum unless the step-edge contribution also vanishes at that k_x and k_y=0, or is proven negligible. The paper neither derives the step-edge contribution nor performs a simulation of a realistic stepped surface. The Conclusion explicitly states that the approach 'cannot be directly applied to topography images' because of tilt and quantized height changes, yet the experimental D is computed from raw topography via Eq
  2. [§ Experiment: nominal Si(5 5 7)...; Fig. 7] The central experimental evidence is taken from a single, hand-selected region ('the right part of panel b') where the 7x7 stripes 'display enhanced uniformity.' No quantitative selection criterion is given, and no independent repeated experiments or statistical analysis over multiple areas are presented. The later direct measurement of inter-terrace distances in Fig. 8 uses the FFT-determined L=18b as the reference to correct the image, so it is not an independent confirmation. The suppression of the ninth peak should be shown to be robust across multiple images and across different choices of the DoG parameters to rule out selection bias.
  3. [§ Model: periodic array of 7×7 stripes; Eq. (4)] The exact zero of A_m at m=9 depends on the assumed atomic row positions (at ±b/2, ±3b/2, ±5b/2) and the 3:1:2:2:1:3 weighting. The real atomic structure of triple steps on vicinal Si surfaces is explicitly disputed in the literature (refs [12–23]) and the authors defer the structural model to an unpublished manuscript (ref [25], 'in preparation'). If the actual structure places the adatom rows at different offsets, or if the step edges introduce additional rows with different weights, the zeros shift or disappear. The paper notes that adding/removing rows alters the effect, but it does not provide a sensitivity analysis. A small displacement of the rows could destroy the exact zero, so the inference from a single observed suppression to L=18b is less robust than the abstract implies.
minor comments (4)
  1. [Eq. (1)] There is a typographical error in the second integral: the Gaussian exponent is written with σ1² instead of σ2² in the denominator. As written, the second term is not a normalized Gaussian blur with width σ2. Please correct to exp(−((x−x')²+(y−y')²)/(2σ2²)).
  2. [Fig. 4 caption] The caption states 'image size 50×60 nm^{−2}' for the Fourier transforms. This should presumably be 'nm^{−1}' (or the axes labeled correctly) since k-space dimensions are inverse nanometers.
  3. [Abstract and § Experiment: nominal Si(5 5 7)...] The abstract says the surface 'may correspond locally to Si(8 8 11)', while the experimental section states the observations 'readily deduce' that the local orientation is (8 8 11). Given the model-experiment gap noted above, the more cautious wording is appropriate.
  4. [Conclusion] The Conclusion's statement that the approach 'cannot be directly applied to topography images' is confusing because the experimental method is applied to topography images after the DoG transformation. Clarify that the FFT analysis is applied to D(x,y), not to the raw z(x,y), and explain why the step-height information in z does not dominate the relevant part of the spectrum.

Circularity Check

1 steps flagged · score 4.0 of 10

Secondary confirmation loop is circular (FFT-derived L used to calibrate image then re-measured); central m=9 fingerprint is an independent prediction.

  1. fitted input called prediction [Results and Discussion, 'Experiment: nominal Si(5 5 7) surface becomes a Si(8 8 11) surface in reality' (Fig. 7d and Fig. 8)]
    "Using this L=5.99 nm value as a reference, we can rescale the raw image and effectively minimize all geometrical distortions in the lateral plane. ... By measuring the interval between the maxima of ¯D(x) within the flat terrace and associating this value with five inter-row spacings b, we can determine the periodicity of the terraces with the 7×7 reconstruction: 18b=5.99 nm, 19b=6.32 nm, and 20b=6.65 nm."

    The FFT of the uncorrected DoG map (Fig. 7d) is first used to infer L=18b from the m=9 zero. That same L=5.99 nm is then taken as the reference length to rescale and correct the raw image. Re-measuring the terrace spacing in the corrected image and finding 18b is therefore a restatement of the calibration input, not an independent confirmation. The paper presents it as 'consistent with' the FFT result, but the correction was built from that FFT result. The core inference (m=9 zero => L=18b) remains an independent trigonometric prediction from Eq. (6); this circularity is confined to the confirmatory re-measurement.

full rationale

The central claim is not circular: Eq. (6) gives A_m=0 at m=9 for L=18b purely trigonometrically, the zero position is independent of the Gaussian width sigma, and the harmonic order can be counted in an uncorrected FFT without knowing the absolute lateral scale. The experimental observation of a suppressed ninth peak in the DoG FFT is therefore a genuine test of the model rather than a fitted prediction. The DoG premise (D reflects atomic lattices) is an asserted modeling assumption from the authors' prior work [26,27] and could fail if step-edge curvature fills the predicted zero; that is a correctness risk, not a pith-circularity reduction. However, the paper's confirmatory step in Fig. 8 is circular: the L=5.99 nm obtained from the FFT fingerprint is used as the reference to rescale/correct the raw image, and the corrected image is then presented as independently confirming 18b; by construction it will reproduce the assumed calibration. Ref. [25] (same authors, in preparation) is cited for the Si(8811) identification, but the L-to-(8 8 11) correspondence is also given geometrically in Fig. 1, so that self-citation is corroborative rather than load-bearing. Overall, the central fingerprint is independent, while the secondary validation loop reduces by construction, giving a moderate circularity score.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The derivation is refreshingly parameter-free — no constant is fitted to produce the predicted zeros. The load-bearing content is two domain assumptions: the exact row geometry of a 5b-wide 7×7 stripe (Eq. 4), and the identification of DoG intensity with adatom density. Hand-chosen DoG widths (σ1, σ2 per image) set the k-space envelope but not the zero positions.

free parameters (2)
  • DoG filter widths σ1, σ2 per image = σ1 = 0.06–0.12 nm, σ2 = (1.5–2)·σ1
    Chosen by hand for each STM image (Figs 2, 7, 10) to balance contrast; they set the k-space envelope exp(−k²σ²/2) and therefore which peaks are 'notably intense', but do not shift the zeros of A_m (Eq. 6), so they are not load-bearing for the period assignment.
  • model Gaussian width σ (Eq. 4) = not specified numerically
    Width of the adatom concentration maxima in the model; appears only as a common prefactor exp(−k²σ²/2) in Eq. (5) and does not affect the predicted zero positions.
assumptions (5)
  • domain assumption The averaged adatom concentration of a 5b-wide 7×7 stripe follows the six-row profile 3:1:2:2:1:3 at positions ±b/2, ±3b/2, ±5b/2 (Eq. (4)).
    Assumed from the geometry of one complete rhombic 7×7 unit cell; not derived from an atomic model of the triple-step structure, which is disputed (refs 12–23). The m=±9 zero for L=18b is robust to the weights but still requires these row positions and the 5b cell width.
  • domain assumption The DoG differential signal D(x,y) is proportional to the local adatom density, so its FFT can be modeled by the FFT of the averaged concentration z̄(x).
    Asserted in the text around Fig. 3 and Eq. (4); step-edge contrast is omitted from the model entirely, yet real step risers (0.94 nm high) also produce DoG response.
  • domain assumption Periods are restricted to commensurate arrays L = n·b with integer n.
    Stated in the model section ('We limit our analysis to commensurable arrays'); real terraces show 18b, 19b, and 20b spacings (Fig. 8), i.e. the real surface is not perfectly commensurate.
  • standard math Comb identity Σ_m exp(−ikx mL) = (2π/L) Σ_m δ(kx − 2πm/L) and the Fourier transform of a Gaussian.
    Standard Fourier analysis used to derive Eq. (5).
  • standard math b = 0.333 nm = (√3/2)a with a = c√2, c = 0.543 nm; Si(111) interplanar distance d = 0.314 nm.
    Bulk Si crystallography, used throughout for b, k0, 3d ≈ 0.941 nm.

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Cite this review

Pith. "Pith review of Period-dependent suppression of Fourier peaks for topography images: Analysis of periodicity of triple-step arrays on vicinal Si(h h m) surfaces." pith.science (2026). https://pith.science/paper/DSIKYZ7D

@misc{pith2026260716699,
  author       = {Pith},
  title        = {Pith review of: Period-dependent suppression of Fourier peaks for topography images: Analysis of periodicity of triple-step arrays on vicinal Si(h h m) surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DSIKYZ7D}},
  note         = {Machine review of arXiv:2607.16699}
}
abstract

Reliable determination of the periodicity of multiatomic steps on high-Miller-index vicinal surfaces is often complicated by (i) the presence of relatively narrow terraces tilted at large angles relative to the scanning plane, and (ii) unavoidable distortions in the lateral direction resulting from creep and improper calibration of a piezo scanner. We argue that the period of the triple-step arrays on vicinal Si(5\,5\,6) and Si(5 5 7) single-crystal wafers can be determined from raw scanning tunneling microscopy data, without preliminary corrections, with precision approaching the interatomic distance. We demonstrate that the intensity of the Fourier peaks of the differential maps, derived from raw topography images by the difference-of-Gaussians approach, strongly depends on the period of the ordered triple-step arrays. This suppression of the ninth Fourier peak indicates that the regular array of triple steps has a period of $18b=5.99$ nm in projection onto the Si(1 1 1) terrace plane, where $b=0.333$ nm is the distance between atomic rows of the $1\times 1$ lattice in the $[\bar{1}\,\bar{1}\,2]$ direction. This means that the nominally (5\,5\,7)-oriented Si wafers may correspond locally to the Si(8 8 11) orientation. The method can be applied to the precise analysis of other vicinal surfaces with narrow and wide terraces containing an integer number of Si(1 1 1)$7\times 7$ unit cells.

Figures

Figures reproduced from arXiv: 2607.16699 by the authors.

Figure 1
Figure 1. Period 𝐿 of an array consisting of monatomic steps (∙) and triple steps (∘), aligned along the [¯1 1 0] direction, as a function of the miscut angle 𝜃 between the (ℎ ℎ 𝑚) and (1 1 1) crystallographic planes for various vicinal Si surfaces [24]. Insets illustrate the relationships between the interlayer distance 𝑑 = 𝑐/√ 3 = 0.314 nm and the step spacings: 𝐿 = 𝑑/ tan 𝜃 for monatomic steps and 𝐿 = 3𝑑/ tan 𝜃 for triple … view at source ↗
Figure 2
Figure 2. A typical map of the differential signal 𝐷(𝑥, 𝑦) corresponding to the topography image of a vicinal Si(5 5 6) surface with rather wide (1 1 1) terraces after applying geometrical corrections (corrected image size 42×20 nm2 , bias voltage 𝑈 = −0.6 V, tunneling current 𝐼 = 80 pA). This map was prepared using the difference-of-Gaussians procedure (1) as described in the text (smoothing parameters: 𝜎1 = 0.06 nm and 𝜎2 =… view at source ↗
Figure 3
Figure 3. a – Periodic model structure which consists of the Si(1 1 1)7 × 7 stripes, repeating with a period 𝐿 (here 𝐿 = 18𝑏). Yellow solid lines outline a unit cell for the 7 × 7 lattice, consisting of two equilateral triangles and containing twelve adatoms. White dots represent the positions of the Si(1 1 1)1×1 atoms. b – The local concentration of the adatoms, averaged along the vertical direction, is plotted as a function… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Top row – Model images 𝑧(𝑥, 𝑦) for the perfect Si(1 1 1)7 × 7 lattice (panel a) and for one-dimensional periodic arrays of stripes with the Si(1 1 1)7 × 7 reconstruction and periods 𝐿 = 16𝑏 (panel b), 17𝑏 (panel c), and 18𝑏 (panel d). These parameters correspond to the…
Figure 5
Figure 5. Figure 5: a, b – Model images 𝑧(𝑥, 𝑦) displaying one-dimensional periodic arrays of the 7 × 7 stripes with periods 𝐿 = 17𝑏 (panel a) and 18𝑏 (panel b) after applying the scaling and affine transformations. c, d – Fourier transforms |𝑧^(𝑘𝑥, 𝑘𝑦 )| computed for the images in panels…
Figure 7
Figure 7. Figure 7: a – Topography image 𝑧(𝑥, 𝑦) of the triple step staircase fabricated on vicinal Si(5 5 7) wafer after global plane subtraction (nominal image size 61.4 × 61.4 nm2 , bias voltage 𝑈 = 1.5 V, tunneling current 𝐼 = 60 pA). b, c – Maps of the differential signal 𝐷(𝑥, 𝑦), vi…
Figure 8
Figure 8. Figure 8: a – The map of the differential signal 𝐷(𝑥, 𝑦) prepared using the DoG procedure (1), corresponds to the central region of the image shown in figure 7e after applying geometrical corrections (corrected image size 50×25 nm2 , bias voltage 𝑈 = 1.5 V, tunneling current 𝐼 =…
Figure 9
Figure 9. Figure 9: One of potential configurations corresponding the stepped Si(8 8 11) surface with the period 𝐿 = 18𝑏. after normalization to the Si(1 1 1)7 × 7 unit cell for a variety of triple step structures observed on this periodic triple step staircase [25]. A possible model of t…
Figure 10
Figure 10. Figure 10: a, b – Aligned topography image 𝑧(𝑥, 𝑦) (panel a) and the map of the differential signal 𝐷(𝑥, 𝑦) (panel b) for the Si(5 5 6) surface (corrected image size 35 × 35 nm2 , bias voltage 𝑈 = +1.2 V, tunneling current 𝐼 = 50 pA). Filter parameters for preparing the DoG map …

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Reference graph

Works this paper leans on

43 extracted references · 28 canonical work pages

  1. [25]

    N., Aladyshkin A

    Chaika A. N., Aladyshkin A. Yu., Semenov V. N., A. S. Aladyshkina, Bozhko S. I., Ionov A. M.Atomically accurate triple step staircase on a vicinal silicon surface: Is it Si(557), Si(7710) or Si(8811)?(in preparation)

  2. [1]

    G., Zotov A

    Oura K., Lifshits V. G., Zotov A. V., Saranin A. A., KatayamaM.SurfaceScience:AnIntroduction,Springer- Verlag, 452 p. (2003)

    2003

  3. [2]

    = 0.333nm between atomic rows of the1×1lattice (see Eq. (2))

  4. [3]

    N., Kirakosian A., Lin J.- L., Petrovykh D

    Losio R., Altmann K. N., Kirakosian A., Lin J.- L., Petrovykh D. Y., Himpsel F. J.Band splitting for Si(557)-Au: Is it spin-charge separation? Phys. Rev. Lett., vol. 86, 4632 (2001); doi: 10.1103/PhysRevLett.86.4632

    work page doi:10.1103/physrevlett.86.4632 2001

  5. [4]

    A global plane subtraction, frequently used for the analysis of Si(ℎ ℎ 𝑚) SPM data [13–20], can provide misaligned topography images with tilted terraces

    and Si(7710) surfaces [13] corresponds to four rows of adatoms of the Si(111)7×7reconstruction (or 9 atomic rows of the Si(111)1×1lattice). A global plane subtraction, frequently used for the analysis of Si(ℎ ℎ 𝑚) SPM data [13–20], can provide misaligned topography images with tilted terraces. As a result, such partially aligned images cannot be adequatel...

  6. [5]

    A., Mark A

    Lipton-Duffin J. A., Mark A. G., MacLeod J. M., McLean A. B.,Si(557)-Ag: A metallic quasi-one-dimensional system// Phys. Rev. B, vol. 77, 125419 (2008); doi: 10.1103/PhysRevB.77.125419

    work page doi:10.1103/physrevb.77.125419 2008

  7. [6]

    Tegenkamp C., Kallassy Z., Pfn¨ ur H., G¨ unter H.-L., Zielasek V., Henzler M.Switching between one and two dimensions: Conductivity of Pb-induced chain structures on Si(557).Phys. Rev. Lett., vol. 95, 176804 (2005); doi: 10.1103/PhysRevLett.95.176804

    work page doi:10.1103/physrevlett.95.176804 2005

  8. [7]

    C., Himpsel F

    Erwin S. C., Himpsel F. J.Intrinsic magnetism at silicon surfaces. Nat. Commun., vol. 1, 58 (2010); doi: 10.1038/ncomms1056

    work page doi:10.1038/ncomms1056 2010

Show all 43 references
  1. [8]

    H., Das T., Tegenkamp C.Observation of correlated spin–orbit orderinastronglyanisotropicquantumwiresystem.Nat

    Brand C., Pfn¨ ur H., Landolt G., Muff S., Dil J. H., Das T., Tegenkamp C.Observation of correlated spin–orbit orderinastronglyanisotropicquantumwiresystem.Nat. Commun., vol. 6, 8118 (2015); doi: 10.1038/ncomms9118

    2015 doi

  2. [9]

    R., Yeom H

    Ahn J. R., Yeom H. W., Yoon H. S., Lyo I.-W.Metal- insulator transition in Au atomic chains on Si with two proximal bands.Phys. Rev. Lett., vol. 91, 196403 (2003); doi: 10.1103/PhysRevLett.91.196403

    2003 doi

  3. [10]

    Nita P., Dachniewicz M., Ja lochowski M., Palotas K., Krawiec M.Template driven self-assembly of the pentacene structure on the Si(553)-Pb surface.J. Phys. Chem. C, vol. 126, 17738-17745 (2022); doi: 10.1021/acs.jpcc.2c05308

    2022 doi

  4. [11]

    However, both these findings and the detailed atomic structure of the triple steps have been disputed in several subsequent studies [12– 23]

    identified the period and local surface orientation of the regular triple-step staircase as 5.73 nm and Si(557), respectively. However, both these findings and the detailed atomic structure of the triple steps have been disputed in several subsequent studies [12– 23]. Scanning...

    2026 arXiv

  5. [12]

    S., Kitaoka Y., Hirahara T., Hasegawa S., Yeom H

    Morikawa H., Kim K. S., Kitaoka Y., Hirahara T., Hasegawa S., Yeom H. W.Conductance transition and interwire ordering of Pb nanowires on Si(557).Phys. Rev. B, vol. 82, 045423 (2010); doi: 10.1103/PhysRevB.82.045423

    2010 doi

  6. [13]

    A., Romanyuk K

    Teys S. A., Romanyuk K. N., Zhachuk R. A., Olshanetsky B. Z.Orientation and structure of triple step staircase on vicinal Si(111) surfaces.Surf. Sci., vol. 600, 4878 (2006); doi: 10.1016/j.susc.2006.08.009

    2006 doi

  7. [14]

    T., Pfn¨ ur H

    Quentin M., Nhung Nguyen T. T., Pfn¨ ur H. , Tegenkamp C.Electronic correlation effects in Pb quantum wires on Si(557).Phys. Rev. B, vol. 102, 035438 (2020); doi: 10.1103/PhysRevB.102.035438

    2020 doi

  8. [15]

    J., Briddon P

    Zhachuk R., Teys S., Coutinho J., Rayson M. J., Briddon P. R.Static and dynamic buckling of reconstructions at triple steps on Si(111) surfaces.Appl. Phys. Lett., vol. 105, 171602 (2014); doi: 10.1063/1.4900783

    2014 doi

  9. [16]

    N., Fauster Th., Lin J.-L., Petrovykh D

    Kirakosian A., Bennewitz R., Crain J. N., Fauster Th., Lin J.-L., Petrovykh D. Y., Himpsel F. J.Atomically accurate Si grating with 5.73 nm period.Appl. Phys. Lett., vol. 79, 1608 (2001); doi: 10.1063/1.1401788

    2001 doi

  10. [17]

    Chaika A. N., V. N. Semenov V. N., Glebovskiy V. G., Bozhko S. I.Scanning tunneling microscopy with single crystalline W[001] tips: High resolution studies of Si(557)5×5surface.Appl. Phys. Lett., vol. 95, 173107 (2009); doi: 10.1063/1.3254240

    2009 doi

  11. [18]

    M., Marz M., Hoffmann-Vogel R.Atomic-scale imaging of the surface 10 dipole distribution of stepped surfaces.J

    P´ erez Le´ on C., Drees H., Wippermann S. M., Marz M., Hoffmann-Vogel R.Atomic-scale imaging of the surface 10 dipole distribution of stepped surfaces.J. Phys. Chem. Lett., vol. 7, 426 (2016); doi: 10.1021/acs.jpclett.5b02650

    2016 doi

  12. [19]

    Zhachuk R., Pereira S.Comment on ’Atomic structure model of the reconstructed Si(557) surface with a triple step structure: Adatom-parallel dimer model’.Phys. Rev. B, vol. 79, 077401 (2009); doi: 10.1103/PhysRevB.79.077401

    2009 doi

  13. [20]

    K., Nam J

    Oh D.-H., Kim M. K., Nam J. H., Song I., Park C.- Y., Woo S. H., Hwang H.-N., Hwang C. C., Ahn J. R. Atomic structure model of the reconstructed Si(557) surface with a triple step structure: Adatom-parallel dimer model.Phys. Rev. B, vol. 77, 155430 (2008); 10.1103/PhysRevB.77.155430

    2008 doi

  14. [21]

    N., Fokin D

    Chaika A. N., Fokin D. A., Bozhko S. I., Ionov A. M., Debontridder F., Cren T., Roditchev D.Atomic structure of a regular Si(223) triple step staircase.Surf. Sci., vol. 603, 752 (2009); doi: 10.1016/j.susc.2009.01.007

    2009 doi

  15. [22]

    K., Oh D.-H., Baik J., Jeon C., Song I., Nam J

    Kim M. K., Oh D.-H., Baik J., Jeon C., Song I., Nam J. H., Woo S. H., Park C.-Y., Ahn J. R.Control of a quasi- one-dimensional phase of a Si nanostructure: Vicinal Si(557) surfaces.Phys. Rev. B, vol. 81, 085312 (2010); doi: 10.1103/PhysRevB.81.085312

    2010 doi

  16. [23]

    428, 129 (2003); 10.1016/S0040-6090(02)01236-1

    Henzler M., Zhachuk R.The step structure of the Si(557) surface.Thin Solid Films, vol. 428, 129 (2003); 10.1016/S0040-6090(02)01236-1

    2003 doi

  17. [24]

    M., Marz M., Hoffmann-Vogel R.Atomically resolved scanning force studies of vicinal Si(111).Phys

    P´ erez Le´ on C., Drees H., Wippermann S. M., Marz M., Hoffmann-Vogel R.Atomically resolved scanning force studies of vicinal Si(111).Phys. Rev. B, vol. 95, 245412 (2017); doi: 10.1103/PhysRevB.95.245412

    2017 doi

  18. [26]

    N., Fokin D

    Chaika A. N., Fokin D. A., Bozhko S. I., Ionov A. M., Debontridder F., Dubost V., Cren T., Roditchev D.Regular stepped structures on clean Si(ℎ ℎ 𝑚)7×7 surfaces.J. Appl. Phys., vol. 105, 034304 (2009); doi: 10.1063/1.3072667

    2009 doi

  19. [27]

    606, 209-216 (2012); doi: 10.1016/j.susc.2011.09.019

    Pr´ evot G., Leroy F., Croset B., Garreau Y., Coati A., M¨ uller P.Step-induced elastic relaxation and surface structure of the Si(7710) surface.Surface Science, vol. 606, 209-216 (2012); doi: 10.1016/j.susc.2011.09.019

    2012 doi

  20. [28]

    C., Woods R

    Gonlases R. C., Woods R. E., Eddins S. L.Digital image processing using MATLAB, 2𝑛𝑑 ed., Tata McGraw Hill Education Private Limited, New Delhi, 728 p. (2010)

    2010

  21. [29]

    The angle𝜃between two planes, characterized by the Miller indices (ℎ 1,𝑘 1,𝑙 1) and (ℎ 2,𝑘 2,𝑙 2), can be determited from the relationship 𝜃= arccos (︃ ℎ1ℎ2 +𝑘 1𝑘2 +𝑙 1𝑙2√︀ ℎ2 1 +𝑘 2 1 +𝑙 2 1 √︀ ℎ2 2 +𝑘 2 2 +𝑙 2 2 )︃

  22. [30]

    Marr D., Hildreth E.Theory of Edge Detection. Proc. R. Soc. Lond. B, vol. 207, 187-217 (1980); doi: 10.1098/rspb.1980.0020

    1980

  23. [31]

    Yu., Chaika A

    Aladyshkin A. Yu., Chaika A. N., Semenov V. N., Aladyshkina A. S., Bozhko S. I., Ionov A. M.Visualization of Atomic Structures on Faceted and Nonflat Surfaces by the Difference-of-Gaussians Approach.Journal of Physical Chemistry C, vol. 128, 16143-16153 (2024); doi: 10.1021/ac...

    2024 doi

  24. [32]

    indicate the triple-step spacings normalized to the distance 𝑏= √ 3𝑐/(2 √

  25. [33]

    Yu., Chaika A

    Aladyshkin A. Yu., Chaika A. N., Semenov V. N., Ionov A. M., Bozhko S. I.Effective removal of global tilt from atomically-resolved topography images of vicinal surfaces with narrow terraces.Ultramicroscopy, vol. 267, 114053 (2024); doi: 10.1016/j.ultramic.2024.114053

    2024

  26. [34]

    Kovasznayl I. S. G., Joseph H. M.,Processing of Two-Dimensional Patterns by Scanning Techniques.Science, vol. 118, 475-477 (1953); doi: 10.1126/science.118.3069.47

    1953 doi

  27. [35]

    N., Nazin S

    Chaika A. N., Nazin S. S., Semenov V. N., Bozhko S. I., L¨ ubben O., Krasnikov S. A., Radican K., Shvets I. V.Selecting the tip electron orbital for scanning tunneling microscopy imaging with sub-Angstr¨ om lateral resolution. EPL 92, 46003 (2010); doi 10.1209/0295- 5075/92/46003

    2010 doi

  28. [36]

    Si samples with typical dimensions of0.5×3×8mm 3 were fabricated from polished𝑛-type single-crystal wafers (P-doped, resistivity of the order of25 Ω·cm at 300K)

    and our own code written in Matlab. Si samples with typical dimensions of0.5×3×8mm 3 were fabricated from polished𝑛-type single-crystal wafers (P-doped, resistivity of the order of25 Ω·cm at 300K). These crystals were cut at an angle of either 9.45∘ or 5.05∘ relative to the (1...

    2024

  29. [37]

    A.The Gaussian derivative model for spatial vision: I

    Young R. A.The Gaussian derivative model for spatial vision: I. Retinal mechanisms.Spatial Vision, v. 2, 273–293 (1987); doi: 10.1163/156856887x00222

    1987 doi

  30. [38]

    Lindeberg T.Image matching using generalized scale- space interest points.J. Math. Imaging Vis., v. 52, 3-36 (2015); doi: 10.1007/s10851-014-0541-0

    2015 doi

  31. [39]

    R., Berton L., Lopes A

    Assirati L., Silva N. R., Berton L., Lopes A. A., Bruno O. M.Performing edge detection by Difference of Gaussians using𝑞-Gaussian kernels.J. Phys.: Conf. Ser., v. 490, 012020 (2014); doi: 10.1088/1742-6596/490/1/012020

    2014 doi

  32. [40]

    N., Orlova N

    Chaika A. N., Orlova N. N., Semenov V. N., Postnova E. Yu., Krasnikov S. A., Lazarev M. G., Chekmazov S. V., Aristov V. Yu., Glebovsky V. G., Bozhko S. I., Shvets I. V.Fabrication of [001]-oriented tungsten tips for high resolution scanning tunneling microscopy. Sci. Rep., vol...

    2014 doi

  33. [41]

    M., Colchero J., Gomez-Herrero J., Baro A

    Horcas I., Fernandez R., Gomez-Rodriguez J. M., Colchero J., Gomez-Herrero J., Baro A. M.WSXM: A software for scanning probe microscopy and a tool for nanotechnology. Rev. Sci. Instrum. vol. 78, 013705 (2007); doi: 10.1063/1.2432410; http://wsxm.eu

    2007 doi

  34. [42]

    N., Bozhko S

    Chaika A. N., Bozhko S. I., Ionov A. M., Myagkov A. N., Abrosimov N. V.STM and LEED studies of atomically ordered terraced Si(557) surfaces.Semiconductors, vol. 41, 431-435 (2007); doi: 10.1134/S1063782607040136

    2007 doi

  35. [43]

    G.,Molecular Configuration in Sodium Thymonucleate.Nature, vol

    Franklin R., Gosling P. G.,Molecular Configuration in Sodium Thymonucleate.Nature, vol. 171, 740–741 (1953); doi: 10.1038/171740a0. 11

    1953 doi

Pith tools

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