Pith. sign in

REVIEW 3 major objections 5 minor 37 references

A 10 nm tantalum buffer layer inserted between silicon and a TaN seed raises the internal quality factor of TaN/Ta superconducting resonators from about 1.5×10^5 to 5.9×10^5 at single-photon power.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-01 05:10 UTC pith:DOCV27QC

load-bearing objection Plausible and useful buffer-layer result for TaN resonators, but without error bars the headline 4x Qi gain is a call for replication, not a demonstrated effect. the 3 major comments →

arxiv 2607.22294 v3 pith:DOCV27QC submitted 2026-07-24 cond-mat.mtrl-sci cond-mat.supr-conquant-ph

Substrate-metal interface engineering enhances TaN/Ta thin film superconducting resonator performance

classification cond-mat.mtrl-sci cond-mat.supr-conquant-ph
keywords tantalum nitridesuperconducting resonatorscoplanar waveguideinternal quality factortwo-level system lossesinterface engineeringreactive sputteringtransmission electron microscopy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to show that the dominant microwave loss in reactively sputtered tantalum-nitride-on-silicon resonators sits at the metal–substrate interface, not in the bulk film. It reports that a standalone superconducting TaN film and a 200 nm Ta film grown on a 5 nm TaN seed both reach internal quality factors Qi ≈ 1.5×10^5 at 100 mK and single-photon power. Inserting an extra 10 nm Ta layer between the Si substrate and the TaN seed raises Qi to 5.9×10^5, roughly four times higher. Cross-sectional TEM and EELS show nitrogen at the Si boundary and a disordered lattice in the un-buffered stacks, while the buffered stack has a clean interface. A sympathetic reading: this is evidence that controlling the substrate–metal interface—specifically keeping nitrogen away from silicon—is a lever for reducing two-level-system loss in superconducting qubit circuitry.

Core claim

The central claim is that nitrogen-related disorder at the TaN–Si interface, not the superconducting film itself, limits the internal quality factor. TaN-only and Ta-on-TaN-seed resonators both have Qi ≈ 1.4–1.5×10^5; adding a 10 nm Ta buffer under the TaN seed raises this to 5.9×10^5 (TLS-limited QTLS,0 from ~1.6×10^5 to ~9×10^5). TEM and EELS correlate the gain with the absence of nitrogen at the silicon boundary and the disappearance of the disordered interface layer. The paper frames the result as strong support for the hypothesis that substrate–metal interface engineering is pivotal for superconducting qubit performance.

What carries the argument

The mechanism is substrate–metal interface engineering by a few-nanometer tantalum buffer. In a coplanar waveguide resonator, the highest electric fields sit at the metal edges, so the loss contribution from the thin interfacial region is amplified. The paper's structural evidence—cross-sectional TEM and EELS—shows that the buffer separates the nitrogen-containing TaN from silicon and removes the disordered interface layer. The electrical evidence is the TLS model fit (Equation 1), which extracts the zero-power TLS-limited quality factor QTLS,0 and the critical photon number nc; the buffer raises QTLS,0 almost sixfold and lowers nc from ~2.6×10^3 to ~4, consistent with a different, more stro

Load-bearing premise

The paper's explanation assumes the 10 nm Ta buffer changes only the metal–substrate interface; the measurements show correlation between a cleaner interface and higher Qi, but the authors do not control for changes in stress, grain structure, or the metal-air interface that the buffer could also introduce.

What would settle it

Deposit the same resonators with Ta buffer thicknesses of 0, 2, 5, 10, and 20 nm under otherwise identical sputter conditions. If Qi does not rise monotonically and saturate once the buffer is thick enough to separate TaN from Si, or if TEM shows no nitrogen at the Si interface even in a 0 nm buffer repeat, the central claim is falsified. A complementary check: grow TaN with the nitrogen flow turned on only after an initial few-nm Ta layer (so Si never sees reactive nitrogen) and compare Qi with the standard TaN-on-Si stack.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • TaN can serve as a useful seed or superconducting base without being a dominant loss source, as long as the substrate interface is controlled.
  • Reactively sputtered nitride films deposited directly on silicon are likely to carry the same nitrogen-related interfacial loss; buffer layers may benefit other nitride-on-Si stacks.
  • In the buffered stack the remaining loss is probably at the metal-air interface or elsewhere, since high-power Qi only reaches just above 10^6.
  • The drop in critical photon number from ~2.6×10^3 to ~4 implies that the residual TLSs in the buffered stack saturate at much lower power, matching a surface-TLS distribution rather than a distributed interface layer.

Where Pith is reading between the lines

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

  • If the nitrogen-interface interpretation is right, a buffer-thickness series (e.g., 0, 2, 5, 10, 20 nm) should show Qi rising and then saturating once the buffer fully separates nitrogen from silicon; this is a direct test the paper does not report.
  • The same buffer logic may transfer to other reactively sputtered nitrides (NbN, TiN) used in superconducting circuits, where nitrogen reaching the substrate could be a hidden loss channel.
  • Since the buffered stack retains a lower high-power ceiling (~10^6), combining the substrate buffer with metal-air surface passivation could plausibly push Qi toward the >10^6 values seen in the best pure alpha-Ta resonators; this is an extrapolation, not a paper claim.
  • An alternative explanation remains live: the 10 nm Ta buffer changes film stress or grain structure, and those changes—not nitrogen suppression—could be responsible for the higher Qi. A buffer-thickness series with structural characterization would distinguish the two.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports on three thin-film stacks on Si substrates: 200 nm TaN, 5 nm TaN / 200 nm Ta, and 10 nm Ta / 5 nm TaN / 200 nm Ta, all fabricated by reactive RF magnetron sputtering. CPW resonators are fabricated from each stack and measured at 100 mK with varying photon number. The authors report single-photon internal quality factors of QiTaN = 1.53×10^5, QiTaN/Ta = 1.41×10^5, and QiTa/TaN/Ta = 5.88×10^5, and conclude that inserting a thin Ta buffer layer between Si and the TaN seed layer significantly improves resonator performance. TEM and EELS show nitrogen accumulation and lattice disorder at the TaN–Si interface in the non-buffered stacks, while the buffered stack shows a clean Si interface. The authors attribute the Q-factor improvement to suppression of interface-related two-level-system (TLS) losses.

Significance. If the reported enhancement is reproducible, the paper describes a simple and effective interface-engineering step for tantalum-based superconducting circuits: a 10 nm Ta buffer layer under a TaN seed layer improves the single-photon internal quality factor by roughly a factor of four. The work is also one of few systematic studies of TaN as a superconducting resonator material, and it adds supporting structural evidence (TEM/EELS) for the role of the substrate–metal interface in TLS losses. The paper ships standard TLS-model fits and shows a clear trend across the full power range. The main limitation is that the central quantitative claim rests on a single Qi value per stack, with no error bars, no repeated-chip statistics, and no statistical significance test; the TEM/EELS evidence is also qualitative and appears to come from a single lamella per stack. These issues currently prevent the result from being regarded as airtight.

major comments (3)
  1. [Section III-B, Fig. 2] The central claim that the Ta/TaN/Ta stack 'significantly' outperforms the other two stacks rests on single Qi values (1.53×10^5, 1.41×10^5, 5.88×10^5). The manuscript does not report the number of resonators measured per stack, the standard deviation across equivalent devices, or the uncertainty from the circle fits. In superconducting resonators, device-to-device scatter can easily exceed a factor of two, so the reported ~4× enhancement cannot be distinguished from sample-to-sample variation without repetition. Please provide per-stack statistics, at least for the single-photon Qi values, or explicitly reframe the claim as a single-device observation.
  2. [Section III-C] The TEM/EELS analysis is presented as the key structural evidence linking the Qi increase to suppression of nitrogen-related interfacial disorder. It is not stated how many lamellae were prepared per stack, and the figures appear to show one representative cross-section. If the image is from a single lamella, it is not clear that the observed 'structural disorder' is uniformly present in the non-buffered stacks or absent in the buffered stack. Moreover, the buffered stack also differs in film stress, grain structure, and possibly impurity distribution; the paper does not control for these alternatives. The correlation is acknowledged as not direct proof, but the conclusion in Section IV states the causal link more strongly than the data support. Please quantify the TEM evidence (e.g., number of lamellae, extent of disorder) and discuss or rule out alternative mechanisms, or soften the ca
  3. [Section III-B, Eq. (1)] The TLS model fits yield QTLS,0 = 1.64×10^5 (TaN), 1.36×10^5 (TaN/Ta), and 9.06×10^5 (Ta/TaN/Ta), which are used to support the claim that the buffer layer reduces TLS losses. No uncertainties or goodness-of-fit metrics are reported for these fit parameters, and the fit itself has two free parameters (Fδ_TLS^0 and n_c). Without confidence intervals or a comparison of fit quality across stacks, the difference between QTLS,0 = 1.36×10^5 and QTLS,0 = 9.06×10^5 cannot be assessed as statistically meaningful. Please report fit uncertainties and, ideally, the number of resonators used for each fit.
minor comments (5)
  1. [Fig. 2 caption] The caption has a typo: 'Circle symbols: measured data points.. Dashed lines:' contains a double period. Also, use consistent capitalization and punctuation in captions throughout.
  2. [Section II-A] Typo: 'in a n RF-magnetron sputter tool' should be 'in an RF-magnetron sputter tool'.
  3. [Section II-C] The text uses 'λ/4' with a literal Greek lambda; for clarity, use 'quarter-wave' or 'λ/4' with a proper math font. Also, 'S21' is not consistently formatted (should be S21 or S21 parameter).
  4. [Section III-A] The paper reports RRR values but does not define 'RRR' (residual resistance ratio) explicitly. Consider defining it as the ratio of room-temperature resistance to resistance just above the superconducting transition.
  5. [References] Reference [35] is to an apparently closely related prior study ('Interfacial Strain and Structural Defects Govern the Performance of Tantalum Superconducting Waveguide Resonators'). The connection to the current work is not discussed in the text; a brief comparison would help the reader place the new result.

Circularity Check

0 steps flagged

No significant circularity: the Qi comparison is a direct measurement and the TLS fit/TEM evidence are used as interpretation, not as a derived prediction.

full rationale

The paper's central claim is an experimental comparison of measured internal quality factors for three sputtered stacks: TaN-only, TaN/Ta, and Ta/TaN/Ta. The reported Qi values (1.53e5, 1.41e5, 5.88e5) come from resonator measurements and circle fits, not from a derivation that reduces to fitted parameters renamed as predictions. Equation (1) is a standard TLS model used to extract QTLS,0 and nc from the power-dependent Qi data; these extracted quantities are reported as fit outputs, not presented as an independent prediction of the buffer-layer improvement. The TEM/EELS observations are independent structural evidence: they show disorder/nitrogen at the TaN-Si interface in the low-Qi stacks and its suppression in the high-Qi stack. The paper explicitly labels the causal link as a hypothesis ('consistent with', 'strongly supports', 'does not provide direct proof'), so the conclusion does not assert a derivation from the model. The self-citations are not load-bearing in a circular sense: [24] (alpha-Ta growth on TaN seed) is independently corroborated in this paper by GI-XRD showing exclusively alpha-Ta peaks; [35] (prior pure alpha-Ta Qi) is used only as external context and is not an input to the buffer-layer comparison; [34] (Qc range) is a design justification, not the result. The absence of error bars or repeated measurements is a statistical robustness concern, not a circularity concern under the specified rules. Thus no step in the claimed chain is equivalent to its own input by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central claim does not introduce new free parameters beyond the standard TLS fit; however, the fit itself adds two parameters per stack. No new entities.

free parameters (2)
  • F*delta_TLS^0 (intrinsic TLS loss) = 1/QTLS,0 = 6.1e-6, 7.35e-6, 1.10e-6 for TaN, TaN/Ta, Ta/TaN/Ta respectively
    Fitted to TLS model Eq. (1) for each resonator power sweep.
  • n_c (critical photon number) = 1.71e3, 2.58e3, 4.08 for TaN, TaN/Ta, Ta/TaN/Ta respectively
    Fitted to TLS model Eq. (1).
axioms (3)
  • standard math TLS model (Eq. 1) describes power-dependent loss in superconducting resonators
    Taken from cited reference [31]; standard in the field.
  • domain assumption Sputtered TaN film is superconducting delta-TaN and the Ta top layer is alpha-Ta
    Supported by GI-XRD and Tc measurements in Section III-A.
  • domain assumption Internal quality factor Qi extracted via circle fit [25] reflects material loss
    Standard resonator analysis; no independent validation of fit uncertainty.

pith-pipeline@v1.3.0-alltime-deepseek · 10216 in / 7027 out tokens · 55685 ms · 2026-08-01T05:10:23.542506+00:00 · methodology

0 comments
read the original abstract

Tantalum has been demonstrated as a promising material for superconducting qubits. However, comparatively little attention has been given to its nitrides. Tantalum nitride exhibits a range of stoichiometries, resulting in a variety of material properties, including both superconducting and non-superconducting phases. Owing to this versatility, tantalum nitrides can serve multiple purposes in superconducting qubits: as seed layers for alpha-Ta growth, as a superconducting base material and as a non-superconducting barrier in the Josephson junction. In this study, we explore the performance of superconducting TaN and Ta thin film combinations on silicon substrates in terms of internal quality factor Qi. We find that standalone TaN films exhibit Qi values of about 1.5x10^5 at 100mK in the single-photon regime. Surprisingly, a resonator made from Ta grown on a few-nanometers-thick TaN seed layer yields largely the same performance. However, adding an additional, few-nanometers-thick Ta buffer layer between the Si substrate and this TaN seed layer enhances Qi significantly up to 5.9x10^5. Supporting transmission electron microscopy measurements reveal nitrogen accumulation and structural disorder at the TaN-Si interface, while this interfacial modification is suppressed when the Ta buffer layer is introduced. The observed improvement in resonator performance is consistent with a reduction of interface-related two-level system losses and strongly supports the hypothesis that controlling the substrate-metal interface is pivotal for the performance of superconducting qubit circuitry.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

37 extracted references · 22 canonical work pages · 2 internal anchors

  1. [1]

    Superconducting Qubits: Current State of Play,

    M. Kjaergaard et al., “Superconducting Qubits: Current State of Play,” Annu. Rev. Condens. Matter Phys. , vol. 11, no. 1, pp. 369 –395, Mar. 2020, doi: 10.1146/annurev-conmatphys-031119-050605

  2. [2]

    Superconducting quantum computing: a review,

    H.-L. Huang, D. Wu, D. Fan, and X. Zhu, “Superconducting quantum computing: a review,” Sci. China Inf. Sci., vol. 63, no. 8, p. 180501, Aug. 2020, doi: 10.1007/s11432-020-2881-9

  3. [3]

    A Quantum Engineer’s Guide to Superconducting Qubits,

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, “A Quantum Engineer’s Guide to Superconducting Qubits,” Appl. Phys. Rev. , vol. 6, no. 2, p. 021318, Jun. 2019, doi: 10.1063/1.5089550

  4. [4]

    A Review of Developments in Superconducting Quantum Processors,

    A. Mamgain et al. , “A Review of Developments in Superconducting Quantum Processors,” J. Indian Inst. Sci., vol. 103, no. 2, pp. 633 -669, Oct. 202 3, doi: 10.1007/s41745-022-00330-z

  5. [5]

    The Physics of Superconducting Microwave Resonators,

    J. Gao, “The Physics of Superconducting Microwave Resonators,” Ph.D. thesis, California Institute of Technology, 2008

  6. [6]

    Materials challenges and opportunities for quantum computing hardware,

    N. P. de Leon et al. , “Materials challenges and opportunities for quantum computing hardware,” Science, vol. 372, no. 6539, p. eabb2823, Apr. 2021, doi: 10.1126/science.abb2823

  7. [7]

    Materials in superconducting quantum bits,

    W. D. Oliver and P. B. Welander, “Materials in superconducting quantum bits,” MRS Bull., vol. 38, no. 10, pp. 816–825, Oct. 2013, doi: 10.1557/mrs.2013.229

  8. [8]

    Localization and Mitigation of Loss in Niobium Superconducting Circuits,

    M. V. P. Altoé et al. , “Localization and Mitigation of Loss in Niobium Superconducting Circuits,” PRX Quantum, vol. 3, no. 2, p. 020312, Apr. 2022, doi: 10.1103/PRXQuantum.3.020312

  9. [9]

    Nitrogen plasma passivated niobium resonators for superconducting quantum circuits,

    K. Zheng et al., “Nitrogen plasma passivated niobium resonators for superconducting quantum circuits,” Appl. Phys. Lett., vol. 120, no. 10, p. 102601, Mar. 2022, doi: 10.1063/5.0082755

  10. [10]

    High temporal stability of niobium superconducting resonators by surface passivation with organophosphonate self -assembled monolayers,

    H. Gupta et al. , “High temporal stability of niobium superconducting resonators by surface passivation with organophosphonate self -assembled monolayers,” Commun. Mater. , vol. 7, no. 1, p. 58, Jan. 2026, doi: 10.1038/s43246-025-01068-8

  11. [11]

    New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds,

    A. P. M. Place et al. , “New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds,” Nat. Comm., vol. 12, no. 1, p. 1779, Dec. 2021, doi: 10.1038/s41467-021-22030-5

  12. [12]

    Microwave characterization of tantalum superconducting resonators on silicon substrate with niobium buffer layer,

    Y. Urade et al. , “Microwave characterization of tantalum superconducting resonators on silicon substrate with niobium buffer layer,” APL Mater., vol. 12, no. 2, p. 021132, Feb. 2024, doi: 10.1063/5.0165137

  13. [13]

    Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds,

    C. Wang et al., “Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds,” Npj Quantum Inf., vol. 8, no. 1, p. 3, Jan. 2022, doi: 10.1038/s41534-021-00510-2

  14. [14]

    Mitigation of interfacial dielectric loss in aluminum -on-silicon superconducting qubits,

    J. Biznárová et al., “Mitigation of interfacial dielectric loss in aluminum -on-silicon superconducting qubits,” Npj Quantum Inf. , vol. 10, no. 78, Aug. 2024, doi: 10.1038/s41534-024-00868-z

  15. [15]

    Aluminum Josephson Junction Formation on 200mm Wafers Using Different Oxidation Techniques,

    S. Lang, A. Schewski, I. Eisele, C. Kutter, and W. Lerch, “Aluminum Josephson Junction Formation on 200mm Wafers Using Different Oxidation Techniques,” ECS Trans., vol. 111, no. 1, pp. 41 –52, May 2023, doi: 10.1149/11101.0041ecst

  16. [16]

    Enhanced coherence of all -nitride superconducting qubits epitaxially grown on silicon substrate,

    S. Kim et al. , “Enhanced coherence of all -nitride superconducting qubits epitaxially grown on silicon substrate,” Commun. Mater. , vol. 2, no. 1, p. 98, Dec. 2021, doi: 10.1038/s43246-021-00204-4

  17. [17]

    Optimizing CMOS-compatible, superconducting titanium nitride resonators: Deposition conditions and structuring processes

    S. J. K. Lang et al. , “Optimizing CMOS -compatible, superconducting Titanium Nitride Resonators: Deposition Conditions and Structuring Processes,” 2026, arXiv. doi: 10.48550/ARXIV.2603.00441

  18. [19]

    Structure of Tantalum Nitrides,

    N. Terao, “Structure of Tantalum Nitrides,” Jpn. J. Appl. Phys., vol. 10, no. 2, p p. 248 -259, Feb. 1971, doi: 10.1143/JJAP.10.248

  19. [20]

    Structural and electrical properties of tantalum nitride thin films fabricated by using reactive radio-frequency magnetron sputtering:,

    H. B. Nie et al., “Structural and electrical properties of tantalum nitride thin films fabricated by using reactive radio-frequency magnetron sputtering:,” Appl. Phys. A Mater. Sci. Process. , vol. 73, no. 2, pp. 229 –236, Aug. 2001, doi: 10.1007/s003390000691

  20. [21]

    Superconducting transition temperatures of reactively sputtered films of tantalum nitride and tungsten nitride,

    F. M. Kilbane and P. S. Habig, “Superconducting transition temperatures of reactively sputtered films of tantalum nitride and tungsten nitride,” J. Vac. Sci. Technol., vol. 12, no. 1, pp. 107 –109, Jan. 1975, doi: 10.1116/1.568734

  21. [22]

    Stable and metastable structures of the multiphase tantalum nitride system,

    C. Stampfl and A. J. Freeman, “Stable and metastable structures of the multiphase tantalum nitride system,” Phys. Rev. B , vol. 71, no. 2, p. 024111, Jan. 2005, doi: 10.1103/PhysRevB.71.024111

  22. [23]

    Fabrication and characterization of NbN/(TaN/NbN)N stacked Josephson junctions,

    L. Zhang et al. , “Fabrication and characterization of NbN/(TaN/NbN)N stacked Josephson junctions,” Supercond. Sci. Technol. , vol. 35, no. 12, p. 125010, Dec. 2022, doi: 10.1088/1361-6668/ac9f83

  23. [24]

    Tantalum Thin Films Sputtered on Silicon and on Different Seed Layers: Material Characterization and Coplanar Waveguide Resonator Performance,

    M. Singer, B. Schoof, H. Gupta, D. Zahn, J. Weber, and M. Tornow, “Tantalum Thin Films Sputtered on Silicon and on Different Seed Layers: Material Characterization and Coplanar Waveguide Resonator Performance,” in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) , Montreal, QC, Canada: IEEE, Sep. 2024, pp. 1197 –1202. doi: 10....

  24. [25]

    Circle fit optimization for resonator quality factor measurements: Point redistribution for maximal accuracy,

    P. G. Baity et al., “Circle fit optimization for resonator quality factor measurements: Point redistribution for maximal accuracy,” Phys. Rev. Res. , vol. 6, no. 1, p. 013329, Mar. 2024, doi: 10.1103/PhysRevResearch.6.013329

  25. [26]

    Magnetron sputter deposited tantalum and tantalum nitride thin films: An analysis of phase, hardness and composition,

    D. Bernoulli, U. Müller, M. Schwarzenberger, R. Hauert, and R. Spolenak, “Magnetron sputter deposited tantalum and tantalum nitride thin films: An analysis of phase, hardness and composition,” Thin Solid Films, vol. 548, pp. 157 –161, Dec. 2013, doi: 10.1016/j.tsf.2013.09.055

  26. [27]

    Deposition of tantalum nitride thin films by D.C. magnetron sputtering,

    S. K. Kim and B. C. Cha, “Deposition of tantalum nitride thin films by D.C. magnetron sputtering,” Thin Solid Films, vol. 475, no. 1 –2, pp. 202 –207, Mar. 2005, doi: 10.1016/j.tsf.2004.08.059

  27. [28]

    Growth optimization of TaN for superconducting spintronics,

    M. Müller et al. , “Growth optimization of TaN for superconducting spintronics,” Mater. Quantum Technol., vol. 1, no. 4, p. 045001, Dec. 2021, doi: 10.1088/2633-4356/ac2e14

  28. [29]

    High - temperature epitaxial growth of tantalum nitride thin films on MgO: structural evolution and potential for SQUID applications,

    M. Cedillo Rosillo, O. Contreras López, J. A. Díaz, A. Conde Gallardo, and H. A. Castillo Cuero, “High - temperature epitaxial growth of tantalum nitride thin films on MgO: structural evolution and potential for SQUID applications,” Beilstein J. Nanotechnol., vol. 16, pp. 690–699, May 2025, doi: 10.3762/bjnano.16.53

  29. [30]

    Microstructure and Mechanical Properties of TaN Thin Films Prepared by Reactive Magnetron Sputtering,

    A. Zaman and E. Meletis, “Microstructure and Mechanical Properties of TaN Thin Films Prepared by Reactive Magnetron Sputtering,” Coatings, vol. 7, no. 12, p. 209, Nov. 2017, doi: 10.3390/coatings7120209

  30. [31]

    Materials loss measurements using superconducting microwave resonators,

    C. R. H. McRae et al. , “Materials loss measurements using superconducting microwave resonators,” Rev. Sci. Instrum., vol. 91, no. 9, p. 091101, Sep. 2020, doi: 10.1063/5.0017378

  31. [32]

    Anomalous Loss Reduction Below Two‐Level System Saturation in Aluminum Superconducting Resonators,

    T. Tai, J. Cai, and S. M. Anlage, “Anomalous Loss Reduction Below Two‐Level System Saturation in Aluminum Superconducting Resonators,” Adv. Quantum Technol., vol. 7, no. 2, p. 2200145, Feb. 2024, doi: 10.1002/qute.202200145

  32. [33]

    Single crystal silicon capacitors with low microwave loss in the single photon regime,

    S. J. Weber, K. W. Murch, D. H. Slichter, R. Vijay, and I. Siddiqi, “Single crystal silicon capacitors with low microwave loss in the single photon regime,” Appl. Phys. Lett., vol. 98, no. 17, p. 172510, Apr. 2011, doi: 10.1063/1.3583449

  33. [34]

    Enhanced Tantalum Superconducting Resonator Performance via All‐Surface Organic Monolayer Passivation,

    H. Gupta et al., “Enhanced Tantalum Superconducting Resonator Performance via All‐Surface Organic Monolayer Passivation,” Adv. Funct. Mater., p. e77131, Jul. 2026, doi: 10.1002/adfm.77131

  34. [35]

    Interfacial Strain and Structural Defects Govern the Performance of Tantalum Superconducting Waveguide Resonators

    M. Singer, H. Gupta, B. Schoof, E. Willinger, A. Orekhov, and M. Tornow, “Interfacial Strain and Structural Defects Govern the Performance of Tantalum Superconducting Waveguide Resonators,” Jul. 02, 2026, arXiv:2607.02238. doi: 10.48550/arXiv.2607.02238

  35. [36]

    Coplanar waveguide resonators for circuit quantum electrodynamics,

    M. Göppl et al. , “Coplanar waveguide resonators for circuit quantum electrodynamics,” J. Appl. Phys. , vol. 104, no. 11, p. 113904, Dec. 2008, doi: 10.1063/1.3010859

  36. [37]

    Experimental evidence for a surface distribution of two -level systems in superconducting lithographed microwave resonators,

    J. Gao et al. , “Experimental evidence for a surface distribution of two -level systems in superconducting lithographed microwave resonators,” Appl. Phys. Lett. , vol. 92, no. 15, p. 152505, Apr. 2008, doi: 10.1063/1.2906373

  37. [38]

    Surface loss simulations of superconducting coplanar waveguide resonators,

    J. Wenner et al. , “Surface loss simulations of superconducting coplanar waveguide resonators,” Appl. Phys. Lett., vol. 99, no. 11, p. 113513, Sep. 2011, doi: 10.1063/1.3637047