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REVIEW 2 major objections 4 minor 37 references

Low two-level-system noise in hydrogenated amorphous silicon

T0 review · 2 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Hydrogenated amorphous silicon capacitors show TLS noise comparable to crystalline substrates, beating prior amorphous dielectrics by a factor of 5 or more.

desk verdict New a-Si:H TLS noise result is likely a real advance, but the >5 improvement claim depends on a faulty extrapolation of the a-SiC:H comparison point. read the letter →

arxiv 2412.09693 v1 pith:IULICXUB submitted 2024-12-12 physics.ins-det astro-ph.IM

Fabien Defrance , Andrew D. Beyer , Jordan Wheeler , Jack Sayers , Sunil R. Golwala This is my paper · ORCID
classification physics.ins-detastro-ph.IM
keywords two-levelsystemsTLSnoisehydrogenatedamorphoussiliconparallel-platecapacitorssuperconductingresonatorskineticinductancedetectorsPECVDfrequency
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

The paper reports measurements of two-level-system (TLS) noise in superconducting lumped-element resonators whose capacitors are made from hydrogenated amorphous silicon (a-Si:H) deposited by PECVD. The authors claim that the TLS noise of two a-Si:H recipes is more than five times lower than the best previously reported values for a-Si:H and other amorphous dielectrics, and is comparable to noise levels seen on crystalline substrates. If correct, this removes a key obstacle to using parallel-plate capacitors in kinetic inductance detectors and other superconducting circuits, enabling multilayer architectures without the noise penalty of amorphous dielectrics. The claim is based on fractional-frequency noise measurements between 200 Hz and 2 kHz, fit to a sum of TLS noise with spectral slope −0.5 and white noise.

What carries the argument

The measurement chain: each device is a 50 Ω coplanar-waveguide feedline inductively coupled to six lumped-element LC resonators, each made of niobium with an inductor and two a-Si:H parallel-plate capacitors in series. Noise time-streams are rotated to the frequency-dissipation basis using a two-tone calibration, and fractional-frequency noise power spectral densities are fit to a model $a\nu^{\alpha} + b$ with $\alpha$ fixed to −0.5. The extracted amplitude $a$ at 1 kHz is the TLS noise level, compared across stored power (photon number) and against literature values by overlaying the measurement envelope on a reproduced figure from a review.

What would settle it

A direct measurement of the fractional-frequency noise power spectral density below 100 Hz on these same a-Si:H resonators would test the fixed-slope assumption: if the noise rises above the extrapolated −0.5 slope line, the reported $S_{\mathrm{TLS}}$ at 1 kHz would still stand but the integrated noise below 100 Hz would be higher than modeled. Alternatively, fabricating the same a-Si:H film into an interdigitated capacitor resonator and comparing $S_{\mathrm{TLS}}$ at fixed photon number would test whether the low noise is intrinsic to the film or an artifact of the parallel-plate geometry.

Watch

Extended reading notes

Core claim

The two-level-system (TLS) fractional-frequency noise measured at 1 kHz in niobium lumped-element resonators with a-Si:H parallel-plate capacitors is 8–80 times lower than previous a-Si:H microstrip results, 5–50 times lower than a-SiC:H, more than 100 times lower than silicon nitride, and comparable to resonators on crystalline silicon and sapphire. These results were obtained with two PECVD a-Si:H recipes, and the low noise is consistent with the previously reported low loss tangent of the same films. The authors conclude that a-Si:H PPCs are a viable low-noise alternative to coplanar-waveguide and interdigitated-capacitor architectures for superconducting resonators.

Load-bearing premise

The analysis assumes that between 200 Hz and 2 kHz the measured frequency noise is exactly a TLS component with spectral slope −0.5 plus white noise, so that a single amplitude extracted from each fit represents the TLS level.

Editorial extensions

If this is right

  • Parallel-plate-capacitor kinetic inductance detectors can be built with a-Si:H without the previously expected TLS noise penalty, shrinking detector footprint and reducing stray-light sensitivity.
  • Multilayer superconducting circuits, including microstrip resonators and qubit architectures, become feasible with a deposited dielectric that approaches crystalline noise levels.
  • The factor-of-5-plus improvement over the best prior amorphous dielectrics warrants revisiting applications where amorphous dielectrics were ruled out by TLS noise.
  • The result strengthens the connection between low loss tangent and low TLS noise in a-Si:H, supporting the tunneling model's fluctuation-dissipation predictions.

Reading between the lines

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

  • If the a-Si:H TLS noise is set by the film's intrinsic defect density, further reduction might be possible by tuning deposition temperature or hydrogen content, potentially approaching single-crystal limits.
  • The fixed-slope fitting assumption ($\alpha = -0.5$) should be tested at audio frequencies below 100 Hz, where recent measurements on other amorphous dielectrics show a transition to a steeper slope.
  • A direct side-by-side measurement of the same a-Si:H film in both parallel-plate and interdigitated capacitor geometries on one setup would confirm that the low noise is intrinsic to the film rather than a geometric effect.
  • The comparison to literature relies on one dataset extrapolated from 10 Hz to 1 kHz; a direct measurement at 1 kHz on that same material would sharpen the claimed improvement.
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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

2 major / 4 minor

Summary. This paper reports measurements of two-level-system (TLS) frequency noise in hydrogenated amorphous silicon (a-Si:H) deposited by two PECVD variants and integrated into niobium lumped-element resonators with parallel-plate capacitors. The authors measure fractional-frequency noise PSDs for 18 resonances across five devices at 230 mK, fit a sum of white noise and a TLS term with spectral slope α fixed to −0.5 over 200 Hz to 2 kHz, and extract TLS noise amplitudes at 1 kHz as a function of stored photon number. They cross-check two devices at NIST at 20 mK, finding agreement within about a factor of two, and compare their results to a literature compilation. The central claim is that their a-Si:H resonators improve on the best previous amorphous-dielectric TLS noise by a factor >5 and approach crystalline-dielectric performance.

Significance. If validated, the quantitative claim would establish PPC-based superconducting resonators with a-Si:H as a practical low-noise alternative to CPW and IDC devices, with potential impact on KID design and multi-layer qubit architectures. The paper's strengths include systematic power and temperature sweeps, a cross-laboratory check on the same devices, the use of a well-established readout and calibration procedure, and explicit acknowledgment of limitations such as the 2–3 dBm power calibration uncertainty. The main weakness is an internal inconsistency in the literature comparison, which undermines the abstract's '>5' factor for 'other amorphous dielectrics' as currently presented.

major comments (2)
  1. [Figure 5 and the paragraph beginning 'In order to compare our a-Si:H TLS noise results...'] The comparison point K (a-SiC:H from Kouwenhoven et al.) is extrapolated from 10 Hz to 1 kHz using α = −1, but the same reference, as described earlier in this paper, reports α ≈ −1 only below 100 Hz and α ≈ −0.5 above 100 Hz to 1 kHz. Using the correct piecewise extrapolation raises the K point by a factor of 100/(10*sqrt(10)) ≈ 3.16, changing the claimed 5–50× improvement over K to roughly 1.6–16×. The abstract's claim of '>5' improvement over other amorphous dielectrics is therefore not established by the presented comparison. The authors should either use the piecewise slope or rephrase the claim to be specific to a-Si:H (point H), which is unaffected by this issue.
  2. [Figure 3 and the paragraph defining the red envelope] The red envelope in Figure 3 is defined by eye, and three outlier datasets are excluded without a stated quantitative criterion. Since the factor '>5' in the abstract is derived from the lower edge of this envelope in the Figure 5 overlay, the authors should provide a reproducible definition of the envelope (for example, a fixed percentile of the datasets or the range containing a stated fraction of resonator datasets) and report how the lower edge and the comparison factors change if the outliers are included.
minor comments (4)
  1. [Figure 2 and the fitting procedure] The fixed slope α = −0.5 is motivated by fits at high feedline readout power, but the paper does not quantify the scatter in α across the different resonators or powers used to set this fixed value. A brief sensitivity check of the extracted amplitude a to plausible variations in α would strengthen the robustness of the reported STLS values.
  2. [Figure 4 and the Caltech–NIST comparison] The 2–3 dBm power calibration uncertainty is invoked to explain the Caltech–NIST discrepancy. Since the photon-number axis in Figures 3–5 depends directly on the feedline power, the authors should state how this uncertainty propagates to N and whether it affects the placement of the red envelope relative to the literature points plotted at nominal powers.
  3. [Figure 1 and calibration description] The sentence 'The direction − − − →B1B2 corresponds to the frequency direction' uses a malformed arrow that is difficult to read; please typeset the vector notation properly.
  4. [Results section, the comparison paragraph] The phrase 'We see that the STLS(ν = 1 kHz) results presented in this article are 8 – 80 times lower than previous measurements for a-Si:H (H)' would benefit from specifying whether the range reflects the full spread of the red envelope or a single representative value, given the envelope's finite width.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: measured TLS noise compared to independent literature; the only self-citations are supporting, not load-bearing.

full rationale

The paper reports a direct measurement rather than a model-derived prediction. The central claim that the a-Si:H PPC resonators achieve TLS noise '>5' times lower than prior amorphous dielectrics is obtained by fitting each measured fractional-frequency PSD to a * nu^alpha + b, plotting the fitted amplitude a at 1 kHz against photon number, and overlaying the resulting envelope on independent literature data from Zmuidzinas' review plus the a-SiC:H, SiNx, and Si3N4 points. Fixing alpha = -0.5 from high-power fits is an empirical constraint on the measurement model, not a parameter fitted to the target quantity and then renamed as a prediction: the reported S_TLS values are the fitted amplitudes themselves, not outputs of a theory that already contains the answer. The only self-citations are to Defrance et al. 2024 for fabrication details, device geometry, and the photon-number conversion formula; these support the apparatus and calibration but do not determine the noise results. The potential issue of extrapolating the a-SiC:H literature point from 10 Hz to 1 kHz using alpha = -1 while the same reference reports a two-slope spectrum is an internal-consistency and accuracy concern about the literature comparison, not circularity: even if the comparison factor is overstated, the authors' measured noise levels are not equal to their inputs by construction. No equation is defined in terms of the claim, no fitted parameter is presented as a prediction, and no load-bearing argument reduces to a self-citation. Score 1 reflects only the minor, non-load-bearing self-citations to the prior loss-tangent paper.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on extracting a noise amplitude from fits and comparing it to literature at similar photon numbers. The key inputs are the fixed spectral slope, the absolute power calibration, and the hand-drawn envelope.

free parameters (2)
  • TLS spectral slope alpha = -0.5 (fixed from high-power fits)
    Used to extract the TLS noise amplitude from each PSD; the fixed slope is a modeling choice that affects the reported STLS at 1 kHz.
  • Comparison envelope (red envelope) = Hand-drawn; excludes three outlier datasets
    This envelope represents the a-Si:H noise level in the headline comparison with literature; excluding outliers makes the comparison more favorable.
assumptions (4)
  • domain assumption Frequency-noise PSD is modeled as a*nu^alpha + b with alpha = -0.5 over 200 Hz to 2 kHz.
    Used to extract the TLS noise amplitude; low-frequency PSDs are considered less reliable and are excluded from fits.
  • domain assumption TLS noise scales as T^-beta, P^-0.5, and nu^alpha.
    Used to compare measurements at different temperatures and stored powers and to extrapolate one literature point from 10 Hz to 1 kHz.
  • domain assumption Stored photon number N follows Eq. (1) using fitted Q factors and feedline power.
    Absolute N calibration places the data on the comparison axes; the authors state a 2-3 dBm power uncertainty.
  • domain assumption Measured frequency noise originates in the a-Si:H film TLS, not interface or readout effects.
    No control resonator without a-Si:H is measured for noise; the PPC geometry is assumed to concentrate the field in the film.

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Cite this review

Pith. "Pith review of Low two-level-system noise in hydrogenated amorphous silicon." pith.science (2026). https://pith.science/paper/IULICXUB

@misc{pith2026241209693,
  author       = {Pith},
  title        = {Pith review of: Low two-level-system noise in hydrogenated amorphous silicon},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IULICXUB}},
  note         = {Machine review of arXiv:2412.09693}
}
read the original abstract

At sub-Kelvin temperatures, two-level systems (TLS) present in amorphous dielectrics source a permittivity noise, degrading the performance of a wide range of devices using superconductive resonators such as qubits or kinetic inductance detectors. We report here on measurements of TLS noise in hydrogenated amorphous silicon (a-Si:H) films deposited by plasma-enhanced chemical vapor deposition (PECVD) in superconductive lumped-element resonators using parallel-plate capacitors (PPCs). The TLS noise results presented in this article for two recipes of a-Si:H improve on the best achieved in the literature by a factor >5 for a-Si:H and other amorphous dielectrics and are comparable to those observed for resonators deposited on crystalline dielectrics.

Figures

Figures reproduced from arXiv: 2412.09693 by the authors.

Figure 1
Figure 1. FIG. 1. After removal of the cable delay component, the complex [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Fractional-frequency noise PSD ( [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. TLS fractional-frequency noise PSD measured at 1 kHz as [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. TLS fractional-frequency noise PSD measured at 1 kHz as [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 11, 2026 · model on record in the stance chip above.