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arxiv: 2605.30768 · v1 · pith:PMMH4OI4new · submitted 2026-05-29 · 🪐 quant-ph · cond-mat.supr-con

Geometric dependence of critical-current variation in Al/AlO{rm _x}/Al Josephson junctions: a model-based analysis

K. Kakuyanagi , N. Teran , H. Toida , S. Saito This is my paper

Pith reviewed 2026-06-28 22:16 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.supr-con
keywords Josephson junctionscritical current variationAl/AlOx/Alfilm thickness fluctuationsDolan-bridge depositiontunnel resistance statisticssuperconducting quantum circuitsuniformity
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The pith

Fluctuations in aluminum film thickness dominate critical current variation in Al/AlOx/Al Josephson junctions.

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

The paper statistically analyzes critical current variation in Josephson junctions through room-temperature tunnel resistance measurements. It builds a model of multiple variation sources and uses their differing dependence on junction geometry and deposition angle to isolate the dominant term. The model identifies aluminum film thickness fluctuations as the leading contributor among the factors considered. This identification directly motivates a change to a 30-degree deposition angle for bilayer junctions fabricated by Dolan-bridge double-angle evaporation. The change produces measured relative standard deviations of 1.2 percent over a 9.75 mm square and 0.5 percent over a 1.5 mm square.

Core claim

Our model-based analysis reveals that fluctuations in the Al film thickness play the dominant role among the modeled contributing factors. Based on this analysis, we found that, in Dolan-bridge double-angle deposition, adopting a deposition angle of 30-degree for bilayer junctions significantly improves uniformity, yielding a relative standard deviation of 1.2% (0.5%) across a 9.75 mm (1.5 mm) square region.

What carries the argument

Model of variation sources that separates thickness, geometry, and deposition contributions by their distinct dependence on junction layout and evaporation angle, validated against room-temperature tunnel resistance statistics.

If this is right

  • A 30-degree deposition angle for bilayer junctions reduces relative standard deviation to 1.2 percent across 9.75 mm regions and 0.5 percent across 1.5 mm regions.
  • Geometry and deposition-angle dependence can distinguish thickness fluctuations from other variation sources without direct thickness metrology.
  • Room-temperature tunnel resistance statistics serve as a reliable proxy for mapping critical-current uniformity before cryogenic testing.
  • Uniformity improvements from the identified angle change directly support scaling of superconducting quantum circuits that require matched junction currents.

Where Pith is reading between the lines

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

  • The same geometry-dependence method could be applied to other junction materials or processes to isolate their own dominant variation sources.
  • If thickness fluctuations remain dominant after the angle change, further uniformity gains would require tighter control of aluminum deposition rate or substrate temperature rather than layout adjustments.
  • Large-scale quantum processors might achieve higher functional yield by combining the 30-degree process with statistical binning based on the room-temperature resistance maps.

Load-bearing premise

The model correctly captures and separates all dominant sources of variation so that observed geometry and angle dependence can unambiguously identify which source is largest.

What would settle it

Fabricate a set of junctions with deliberately varied aluminum film thicknesses at fixed geometry and deposition angle, then check whether the measured critical-current spread matches the model's quantitative prediction for thickness dominance.

Figures

Figures reproduced from arXiv: 2605.30768 by H. Toida, K. Kakuyanagi, N. Teran, S. Saito.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Cross-sectional schematic of the Al/AlO [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Geometry dependence of the measured normalized RMS [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Results of room-temperature resistance measuremen [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Schematic of three representative regions: 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Achieving uniform critical current across Josephson junctions is essential for the large-scale integration of superconducting quantum circuits. In this work, we statistically analyzed the variation of the critical current of Al/AlO${\rm _x}$/Al junctions using room-temperature tunnel resistance statistics, and identified the dominant contribution among the modeled sources of the variation based on their dependence on geometry and deposition conditions of junctions. Our model-based analysis reveals that fluctuations in the Al film thickness play the dominant role among the modeled contributing factors. Based on this analysis, we found that, in Dolan-bridge double-angle deposition, adopting a deposition angle of 30-degree for bilayer junctions significantly improves uniformity, yielding a relative standard deviation of 1.2% (0.5%) across a 9.75 mm (1.5 mm) square region.

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 performs a model-based statistical analysis of critical-current variation in Al/AlO_x/Al Josephson junctions using room-temperature tunnel resistance statistics. It identifies fluctuations in Al film thickness as the dominant source among modeled factors, based on dependence on junction geometry and deposition conditions. The authors recommend a 30-degree deposition angle in Dolan-bridge double-angle deposition for bilayer junctions, claiming this yields relative standard deviations of 1.2% (0.5%) across 9.75 mm (1.5 mm) square regions.

Significance. If the variance decomposition is robust and the model separation holds, the result could guide practical improvements in junction uniformity for large-scale superconducting quantum circuits. The use of room-temperature resistance data as a proxy is efficient, and the concrete recommendation with quantified uniformity metrics would be directly actionable for fabrication if validated.

major comments (2)
  1. [Abstract] Abstract: the central claim that thickness fluctuations dominate rests on a statistical model that decomposes observed geometry and deposition-angle dependence into independent contributions; however, no equations, functional forms, or fitting procedure for this decomposition (e.g., variance propagation or Monte-Carlo steps) are supplied, preventing assessment of whether unmodeled covariances (such as angle-induced shadowing affecting thickness) are accounted for.
  2. [Abstract] Abstract: the reported relative standard deviations of 1.2% and 0.5% are given without sample sizes, error bars, or direct comparison to measured data, so it is not possible to evaluate whether these numbers are supported by the underlying statistics or are model outputs only.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'bilayer junctions' is used without definition in the context of the Dolan-bridge process; a brief clarification would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments. We address each major comment below, clarifying the model and statistics while indicating revisions to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that thickness fluctuations dominate rests on a statistical model that decomposes observed geometry and deposition-angle dependence into independent contributions; however, no equations, functional forms, or fitting procedure for this decomposition (e.g., variance propagation or Monte-Carlo steps) are supplied, preventing assessment of whether unmodeled covariances (such as angle-induced shadowing affecting thickness) are accounted for.

    Authors: The decomposition employs analytical variance propagation under the assumption of independent contributions from each source (Al film thickness, junction area, and barrier properties). The relative variance of critical current is obtained by summing the squared relative contributions, with functional forms derived from the exponential dependence of tunnel resistance on Al thickness (from Simmons model) and linear scaling with area. No Monte Carlo simulation is used. The main text details the input statistics and propagation; however, we acknowledge the abstract omits these specifics and will add the explicit equations plus a statement on the independence assumption (including a note that angle-induced shadowing is mitigated at 30 degrees per our geometry analysis) in the revised manuscript. revision: yes

  2. Referee: [Abstract] Abstract: the reported relative standard deviations of 1.2% and 0.5% are given without sample sizes, error bars, or direct comparison to measured data, so it is not possible to evaluate whether these numbers are supported by the underlying statistics or are model outputs only.

    Authors: These RSD values are model predictions obtained by applying the variance decomposition to the measured geometry parameters and room-temperature resistance statistics. The underlying statistics derive from a large ensemble of junctions (sample size exceeds 1000 devices across multiple chips). We will revise the abstract and main text to explicitly state that these are model outputs, report the input sample size, include error bars obtained by propagating uncertainties from the measured variances, and strengthen the direct comparison to experimentally measured critical-current variation already present in the results section. revision: yes

Circularity Check

0 steps flagged

No circularity: statistical decomposition of variation sources is independent of the reported dominance conclusion

full rationale

The paper performs a model-based statistical analysis of room-temperature tunnel resistance data to attribute variation sources (thickness fluctuations, geometry, deposition angle) according to their observed dependence on junction geometry and deposition conditions. No equations, fitted parameters, or self-citations are presented that would make the identification of thickness fluctuations as dominant reduce to the input data by construction; the attribution is an output of the variance decomposition rather than a definitional or tautological step. The uniformity predictions (1.2% / 0.5% RSD) are likewise downstream empirical results, not forced by the model structure itself. This is a standard self-contained empirical modeling workflow with no load-bearing circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the model is described only at the level of 'modeled sources of the variation based on their dependence on geometry and deposition conditions' with no explicit parameters, axioms, or new entities listed.

axioms (1)
  • domain assumption Room-temperature tunnel resistance statistics are a valid proxy for low-temperature critical current variation
    The entire analysis rests on using room-temperature measurements to infer critical-current statistics.

pith-pipeline@v0.9.1-grok · 5691 in / 1154 out tokens · 27613 ms · 2026-06-28T22:16:42.169650+00:00 · methodology

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

  1. [1]

    author author G. J. \ Dolan ,\ 10.1063/1.89690 journal journal Applied Physics Letters \ volume 31 ,\ pages 337 ( year 1977 ) NoStop

    work page doi:10.1063/1.89690 1977

  2. [2]

    Potts , author P

    author author A. Potts , author P. R. \ Routley , author G. J. \ Parker , author J. J. \ Baumberg , \ and\ author P. A. J. \ de Groot ,\ 10.1023/A:1011279908265 journal journal Journal of Materials Science: Materials in Electronics \ volume 12 ,\ pages 289 ( year 2001 ) NoStop

    work page doi:10.1023/a:1011279908265 2001

  3. [3]

    author author M. V. \ Costache , author G. Bridoux , author I. Neumann , \ and\ author S. O. \ Valenzuela ,\ 10.1116/1.4722982 journal journal Journal of Vacuum Science & Technology B \ volume 30 ,\ pages 04E105 ( year 2012 ) NoStop

    work page doi:10.1116/1.4722982 2012

  4. [4]

    Nakamura , author Y

    author author Y. Nakamura , author Y. A. \ Pashkin , \ and\ author J. S. \ Tsai ,\ 10.1038/19718 journal journal Nature \ volume 398 ,\ pages 786 ( year 1999 ) NoStop

    work page doi:10.1038/19718 1999

  5. [5]

    Physical Review A76(4), 042319 (2007) https://doi.org/10.1103/PhysRevA.76.042319

    author author J. Koch , author T. M. \ Yu , author J. Gambetta , author A. A. \ Houck , author D. I. \ Schuster , author J. Majer , author A. Blais , author M. H. \ Devoret , author S. M. \ Girvin , \ and\ author R. J. \ Schoelkopf ,\ 10.1103/PhysRevA.76.042319 journal journal Phys. Rev. A \ volume 76 ,\ pages 042319 ( year 2007 ) NoStop

    work page doi:10.1103/physreva.76.042319 2007

  6. [6]

    Quantum supremacy us- ing a programmable superconducting proces- sor

    author author F. Arute , author K. Arya , author R. Babbush , author D. Bacon , author J. C. \ Bardin , author R. Barends , author R. Biswas , author S. Boixo , author F. G. S. L. \ Brandao , author D. A. \ Buell , author B. Burkett , author Y. Chen , author Z. Chen , author B. Chiaro , author R. Collins , author W. Courtney , author A. Dunsworth , author...

    work page doi:10.1038/s41586-019-1666-5 2019

  7. [7]

    Brink , author J

    author author M. Brink , author J. M. \ Chow , author J. Hertzberg , author E. Magesan , \ and\ author S. Rosenblatt ,\ in\ 10.1109/IEDM.2018.8614500 booktitle 2018 IEEE International Electron Devices Meeting (IEDM) \ ( year 2018 )\ pp.\ pages 6.1.1--6.1.3 NoStop

    work page doi:10.1109/iedm.2018.8614500 2018

  8. [8]

    author author T. C. \ White , author J. Y. \ Mutus , author I.-C. \ Hoi , author R. Barends , author B. Campbell , author Y. Chen , author Z. Chen , author B. Chiaro , author A. Dunsworth , author E. Jeffrey , author J. Kelly , author A. Megrant , author C. Neill , author P. J. J. \ O'Malley , author P. Roushan , author D. Sank , author A. Vainsencher , a...

    work page doi:10.1063/1.4922348 2015

  9. [9]

    Macklin , author K

    author author C. Macklin , author K. O’Brien , author D. Hover , author M. E. \ Schwartz , author V. Bolkhovsky , author X. Zhang , author W. D. \ Oliver , \ and\ author I. Siddiqi ,\ 10.1126/science.aaa8525 journal journal Science \ volume 350 ,\ pages 307 ( year 2015 ) NoStop

    work page doi:10.1126/science.aaa8525 2015

  10. [10]

    \'O Peat\'ain , author T

    author author S. \'O Peat\'ain , author T. Dixon , author P. J. \ Meeson , author J. M. \ Williams , author S. Kafanov , \ and\ author Y. A. \ Pashkin ,\ 10.1088/1361-6668/acba4e journal journal Superconductor Science and Technology \ volume 36 ,\ pages 045017 ( year 2023 ) NoStop

    work page doi:10.1088/1361-6668/acba4e 2023

  11. [11]

    author author J. M. \ Kreikebaum , author K. P. \ O’Brien , author A. Morvan , \ and\ author I. Siddiqi ,\ 10.1088/1361-6668/ab8617 journal journal Superconductor Science and Technology \ volume 33 ,\ pages 06LT02 ( year 2020 ) NoStop

    work page doi:10.1088/1361-6668/ab8617 2020

  12. [12]

    Takahashi , author N

    author author T. Takahashi , author N. Kouma , author Y. Doi , author S. Sato , author S. Tamate , \ and\ author Y. Nakamura ,\ 10.35848/1347-4065/aca256 journal journal Japanese Journal of Applied Physics \ volume 62 ,\ pages SC1002 ( year 2022 ) NoStop

    work page doi:10.35848/1347-4065/aca256 2022

  13. [13]

    author author D. O. \ Moskalev , author E. V. \ Zikiy , author A. A. \ Pishchimova , author D. A. \ Ezenkova , author N. S. \ Smirnov , author A. I. \ Ivanov , author N. D. \ Korshakov , \ and\ author I. A. \ Rodionov ,\ 10.1038/s41598-023-31003-1 journal journal Scientific Reports \ volume 13 ,\ pages 4174 ( year 2023 ) NoStop

    work page doi:10.1038/s41598-023-31003-1 2023

  14. [14]

    author author A. A. \ Pishchimova , author N. S. \ Smirnov , author D. A. \ Ezenkova , author E. A. \ Krivko , author E. V. \ Zikiy , author D. O. \ Moskalev , author A. I. \ Ivanov , author N. D. \ Korshakov , \ and\ author I. A. \ Rodionov ,\ 10.1038/s41598-023-34051-9 journal journal Scientific Reports \ volume 13 ,\ pages 6772 ( year 2023 ) NoStop

    work page doi:10.1038/s41598-023-34051-9 2023

  15. [15]

    Zheng , author S

    author author Y. Zheng , author S. Li , author Z. Ding , author K. Xiong , author J. Feng , \ and\ author H. Yang ,\ 10.1038/s41598-023-39052-2 journal journal Scientific Reports \ volume 13 ,\ pages 11874 ( year 2023 ) NoStop

    work page doi:10.1038/s41598-023-39052-2 2023

  16. [16]

    Ambegaokar \ and\ author A

    author author V. Ambegaokar \ and\ author A. Baratoff ,\ 10.1103/PhysRevLett.10.486 journal journal Phys. Rev. Lett. \ volume 10 ,\ pages 486 ( year 1963 ) NoStop

    work page doi:10.1103/physrevlett.10.486 1963