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Engineering high-Q superconducting tantalum microwave coplanar waveguide resonators for compact coherent quantum circuits

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Alpha-tantalum resonators on silicon reach Qi above 3 million

desk verdict Useful thickness-dependent data for Ta-on-Si resonators, but the alpha-Ta claim is not backed by any structural characterization; send to review with a request for XRD/TEM or a softened claim. read the letter →

arxiv 2412.16099 v1 pith:GWHUFW5J submitted 2024-12-20 quant-ph cond-mat.supr-concs.SYeess.SYphysics.app-ph

Shima Poorgholam-Khanjari , Valentino Seferai , Paniz Foshat , Calum Rose , Hua Feng , Robert H. Hadfield , Martin Weides , Kaveh Delfanazari This is my paper · ORCID
classification quant-phcond-mat.supr-concs.SYeess.SYphysics.app-ph
keywords alpha-tantalumkineticinductancecoplanarwaveguideresonatorinternalqualityfactorniobiumseedlayertwo-levelsystemlosssuperconductingquantumcircuitsmicrowaveresonators
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 fabrication and measurement of tantalum coplanar waveguide resonators on high-resistivity silicon, using a thin niobium seed layer so the tantalum grows in its low-loss body-centered cubic phase. It shows that internal quality factor and kinetic inductance can be tuned by film thickness: a 100 nm film reaches an internal quality factor around $3.6\times 10^6$ at high microwave power, while a 40 nm film gives an estimated kinetic inductance of $0.6\ \mathrm{pH/sq}$. The authors argue this combination is valuable for compact, high-impedance superconducting quantum circuits where strong coupling and small footprints matter. They fit the power and temperature dependence of the loss to the standard two-level-system and quasiparticle model.

What carries the argument

The load-bearing fabrication step is a 5 nm niobium seed layer sputtered before tantalum; the paper states this seed promotes the $\alpha$ (body-centered cubic) phase on unheated silicon, a phase with low microwave loss. The tantalum film thickness then controls kinetic inductance through the standard relation $L_K \approx \hbar R_s/(\pi \Delta_0)$, estimated from measured normal-state sheet resistance and critical temperature. Performance is evaluated with a notch-type complex $S_{21}$ model to extract quality factors, and the TLS saturation model is used to separate two-level-system loss from quasiparticle loss.

What would settle it

An X-ray diffraction or transmission electron microscopy measurement of the 40 nm film that shows $\beta$-Ta or a mixed phase rather than bcc $\alpha$-Ta would falsify the material attribution; alternatively, a direct kinetic inductance measurement disagreeing strongly with the $0.6\ \mathrm{pH/sq}$ estimate would falsify the electrical interpretation.

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Extended reading notes

Core claim

The central claim is that room-temperature sputtered $\alpha$-Ta films on silicon, seeded by 5 nm niobium, can simultaneously deliver high internal quality factor and high kinetic inductance, and that the two quantities trade off with film thickness. Across 40, 80, and 100 nm films, the maximum internal quality factor at high power rises to about $3.6\times 10^6$ for the 100 nm film, while the estimated kinetic inductance falls from $0.6$ to $0.2\ \mathrm{pH/sq}$ as the film thickens. This thickness-dependent dataset is presented as an engineering curve: choose thin tantalum when kinetic inductance and compact high-impedance circuits matter, and thicker tantalum when low loss matters.

Load-bearing premise

The whole interpretation rests on the 5 nm niobium seed layer actually growing the alpha (body-centered cubic) phase of tantalum, but the paper does not include direct structural characterization such as X-ray diffraction or electron microscopy.

Editorial extensions

If this is right

  • A 100 nm alpha-Ta resonator on silicon reaches $Q_i \sim 3.6\times 10^6$ at high power, confirming Nb-seeded room-temperature tantalum as a viable low-loss material on CMOS-compatible substrates.
  • The 40 nm film's estimated $0.6\ \mathrm{pH/sq}$ kinetic inductance is competitive with other high-kinetic-inductance platforms and enables higher characteristic impedance at fixed geometry.
  • Because kinetic inductance rises as thickness falls, designers can choose a thickness to set the resonator's impedance and frequency without changing lithographic dimensions.
  • The power and temperature dependence of $Q_i$ follows the standard TLS plus quasiparticle model, so further gains should come from reducing interface TLS and quasiparticle generation.

Reading between the lines

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

  • A testable extension is to measure the actual crystallographic phase of the films with X-ray diffraction or transmission electron microscopy; if the seed layer produces mixed-phase or beta-Ta, the thickness-dependent story would need reinterpretation.
  • The kinetic inductance values are inferred from normal-state sheet resistance and the BCS gap, not from a direct microwave kinetic inductance extraction, so a direct measurement would pin down the numbers more firmly.
  • If the tradeoff holds, compact high-impedance resonators could couple more strongly to qubits and enable smaller or more densely integrated quantum processors, though a qubit demonstration remains beyond this paper.
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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

4 major / 6 minor

Summary. The manuscript reports the fabrication and cryogenic microwave characterization of coplanar waveguide (CPW) resonators made from tantalum films of 40, 80, and 100 nm thickness deposited on unheated high-resistivity silicon with a 5 nm niobium seed layer. The authors claim that the Nb seed promotes the growth of the body-centred-cubic alpha-Ta phase, and they measure critical temperatures, sheet resistances, and internal quality factors as functions of microwave power and temperature. They report a maximum internal quality factor Qi of about 3.6e6 at high power for the 100 nm film and a kinetic inductance LK of 0.6 pH/sq for the 40 nm film, estimated from the BCS relation using the measured normal-state sheet resistance. The paper fits the power-dependent Qi data with a standard two-level-system (TLS) model and compares the results with earlier Ta resonator work.

Significance. If the results hold, the thickness-dependent Qi-LK tradeoff for Ta films on unheated silicon would be a useful engineering data point for compact, high-impedance circuit-QED devices, particularly because the process is CMOS-compatible and avoids substrate heating. The paper uses established measurement and fitting techniques, including notch-type S21 fitting and the TLS saturation model, and the reported Qi values at high power are competitive with several prior Ta resonator studies. However, the central material claim that the films are alpha-Ta is not directly verified, and the kinetic inductance values are extracted from a Ta/Nb bilayer, so the attribution of the measured performance specifically to alpha-Ta is not yet established.

major comments (4)
  1. [Fabrication (page 3-4) and Conclusion] The claim that the sputtered Ta films are alpha-Ta rests entirely on the sentence 'Before Ta deposition, a 5 nm Nb seed layer was sputtered to promote the growth of the Ta alpha-phase.' No XRD, TEM, electron diffraction, or resistivity-ratio measurement is shown to confirm the phase. This is load-bearing because the abstract and conclusion attribute the high Qi and high LK to alpha-Ta, and because Eq. (2) uses the normal-state sheet resistance Rs, which differs substantially between alpha-Ta (bcc) and beta-Ta (tetragonal). If the films are beta-Ta or a mixed phase, the quoted LK values and the mechanistic narrative change. Please add structural characterization of the films or explicitly reframe the results as properties of the Ta/Nb bilayer stack without the alpha-Ta attribution.
  2. [Eq. (2) and kinetic inductance values (page 5)] The kinetic inductance is estimated as LK ≈ ħRs/(πΔ0) using the measured normal-state sheet resistance of the full film stack. Since the 5 nm Nb seed layer is metallic and superconducting, its own kinetic-inductance contribution is included in the quoted value of 0.6 pH/sq for the 40 nm film. The paper consistently refers to 'Ta samples' and 'Ta films,' but the measured Rs is that of the Ta/Nb bilayer. Please quantify the Nb seed contribution (e.g., by measuring a Nb-only control film or by estimating its sheet resistance separately), or revise the text so the LK values are not presented as intrinsic properties of the Ta layer alone.
  3. [Table 2, 'This work' rows] Table 2 lists the seed layer as '6 nm Nb seed layer' for all three thicknesses, while the fabrication text states '5 nm Nb seed layer.' Additionally, the single-photon Qi range for the 100 nm film is given as '1.65-4.5 × 106', but Table 1 lists the three measured single-photon Qi values for 100 nm as 2 × 10^5, 1.65 × 10^5, and 4.5 × 10^5 — an order of magnitude lower. This internal inconsistency undermines the reliability of the comparison table and must be corrected.
  4. [Tables 1-2 and Figures 4-6] No fit uncertainties or measurement uncertainties are reported for the headline quantities: Qi, 1/Q_TLS^0, and LK. Figure 4 shows error bars, but the source of those errors (e.g., fit covariance, repeated measurements, systematic power calibration) is not described. Since the central quantitative claims are the maximum Qi of ~3.6e6 and LK of 0.6 pH/sq, confidence intervals or at least a description of how the errors were estimated are needed to assess whether the thickness-dependent trends are significant.
minor comments (6)
  1. [Abstract and Table 2] The abstract states a '5 nm Nb seed layer' while Table 2 lists '6 nm Nb seed layer' for the same devices; please harmonize the reported seed-layer thickness throughout.
  2. [Page 5, Eq. (2) reference] Eq. (2) is attributed to reference [46], a paper on niobium nitride resonators; please verify the citation is appropriate for the BCS-based kinetic-inductance relation as used here.
  3. [Page 6, Figure 3 caption] The caption states 'VNA power = 0 dBm' but the text refers to 'high power'; please clarify whether 0 dBm is the power at the VNA port or at the resonator after accounting for the 80 dB of total attenuation.
  4. [Eq. (4) and Figures 4-5] The TLS model in Eq. (4) uses n_ph, while the text and figures use <n_ph>; please use consistent notation for the average photon number.
  5. [Page 8, Eq. (6) and Eq. (7)] The text labels both the quasi-particle loss in Eq. (6) and the Mattis-Bardeen expression in Eq. (7) as δ_qp; please state explicitly how these two expressions are related and which one is used for the fits shown in Fig. 6.
  6. [Page 12, Eq. (9)] The expression Δf_qp = -(1/2) α f_r (ΔL_k/L_k) uses α, which is defined earlier as the kinetic-inductance fraction; please ensure the same symbol is not confused with the fit parameter α in Eq. (1).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: measured Qi and independently computed LK form the core claims.

full rationale

The paper's central claims are empirical: Qi values are extracted from measured S21 traces via the standard notch resonator model (Eq. 1) and a circle-fit procedure, and the reported LK values are computed from independently measured normal-state sheet resistance and Tc using the textbook relation LK ≈ ħRs/(πΔ0) with Δ0 = 1.76kBTc (Eq. 2). None of these quantities is a prediction generated from a fitted parameter; the TLS parameters (1/Q_TLS^0, β, nc) are fit parameters of Eq. (4) that describe the same power-dependent Qi data, and the temperature-dependent frequency-shift modeling (Eqs. 8-9) uses those parameters and the independently estimated kinetic-inductance ratio as a cross-check, not as an equation equivalent to its input. The citations of the authors' prior work (Refs. 6, 52) are methodological or background material and are not load-bearing for the central results. The main scientific risk—that the α-Ta phase is asserted on the basis of the Nb seed layer without XRD/TEM confirmation—is a missing-evidence/correctness concern, not a circular derivation: no equation in the paper reduces to its own input. Hence the circularity score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced; the analysis uses standard materials and loss models. The main unverified input is the assumed alpha-Ta phase, which is an assumption rather than an invented entity. Several free parameters enter the TLS and notch fits, and the headline values depend on those fits, so the ledger is not parameter-free.

free parameters (4)
  • beta (TLS saturation exponent) = 0.44 for 40 nm Ta at f=3.654 GHz and T=77 mK; other values not reported
    Appears as a free exponent in Eq. (4) and is fitted to each Qi versus photon number curve to capture how fast TLS loss saturates.
  • n_c (critical photon number) = not reported
    Free parameter in Eq. (4) that sets the photon number scale for TLS saturation; fitted from the same power-dependent data.
  • 1/Q_TLS^0 (zero-power, zero-temperature TLS loss per resonator) = values in Table 1, e.g., 6.11e-6 for 40 nm at 3.654 GHz
    Extracted by fitting Eq. (4) to measured Qi versus photon number; these values are then tabulated as the material loss benchmark.
  • Notch model environment parameters (a, alpha, tau, phi) = not reported
    Eq. (1) is fitted to each complex S21 spectrum to separate cable delay, phase, and impedance mismatch from the resonator response; the extracted Ql and Qc depend on these nuisance parameters.
assumptions (5)
  • standard math Delta_0 = 1.76 k_B T_c (BCS weak-coupling gap ratio)
    Invoked in Eq. (2) to convert normal-state sheet resistance and measured T_c into kinetic inductance; standard for conventional superconductors, but no strong-coupling correction for thin films is discussed.
  • domain assumption Mattis-Bardeen quasiparticle surface impedance theory
    Eq. (7) is used to model quasiparticle loss at higher temperatures; assumed applicable to these Ta films without independent verification.
  • domain assumption Two-level-system tunneling model of Eq. (4)
    Used to fit Qi versus photon number and temperature; the tanh temperature factor and power saturation form are standard in the cQED materials literature.
  • ad hoc to paper Nb seed layer nucleates the alpha-Ta phase
    The fabrication section asserts that the Nb seed layer promotes alpha-Ta growth, but no structural characterization appears in the paper.
  • domain assumption Effective permittivity epsilon_eff = (epsilon_r+1)/2 and conformal mapping values
    Used to relate resonator geometry to L_l, C_l, and Z0; the calculation appears to ignore the kinetic inductance contribution to the characteristic impedance, although LK is later added to L_m.

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Cite this review

Pith. "Pith review of Engineering high-Q superconducting tantalum microwave coplanar waveguide resonators for compact coherent quantum circuits." pith.science (2026). https://pith.science/paper/GWHUFW5J

@misc{pith2026241216099,
  author       = {Pith},
  title        = {Pith review of: Engineering high-Q superconducting tantalum microwave coplanar waveguide resonators for compact coherent quantum circuits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GWHUFW5J}},
  note         = {Machine review of arXiv:2412.16099}
}
read the original abstract

Tantalum (Ta) has recently received considerable attention in manufacturing robust superconducting quantum circuits. Ta offers low microwave loss, high kinetic inductance compared to aluminium (Al) and niobium (Nb), and good compatibility with complementary metal-oxide-semiconductor (CMOS) technology, which is essential for quantum computing applications. Here, we demonstrate the fabrication engineering of thickness-dependent high quality factor (high-Q_i) Ta superconducting microwave coplanar waveguide resonators. All films are deposited on high-resistivity silicon substrates at room temperature without additional substrate heating. Before Ta deposition, a niobium (Nb) seed layer is used to ensure a body-centred cubic lattice ({\alpha}-Ta) formation. We further engineer the kinetic inductance (L_K) resonators by varying Ta film thicknesses. High L_K is a key advantage for applications because it facilitates the realisation of high-impedance, compact quantum circuits with enhanced coupling to qubits. The maximum internal quality factor Q_i of ~ 3.6 * 10^6 is achieved at the high power regime for 100 nm Ta, while the highest kinetic inductance is obtained to be 0.6 pH/sq for the thinnest film, which is 40 nm. This combination of high Q_i and high L_K highlights the potential of Ta microwave circuits for high-fidelity operations of compact quantum circuits.

Figures

Figures reproduced from arXiv: 2412.16099 by the authors.

Figure 1
Figure 1. (a) The microwave superconducting coplanar waveguide resonators based on 40 nm thick Ta on silicon chip wire bonded to a copper sample box. (b) The packaged Ta microwave superconducting chip is mounted in the 77 mK stage of a dilution refrigerator. (c) Schematic of the cryogenic setup for sub-Kelvin microwave spectroscopy of the chip. In this work, we use a silicon chip as the substrate and 𝛼-Ta is the superconducti… view at source ↗
Figure 2
Figure 2. (b) shows the calculated 𝐿𝐾 (H/m) for 40 nm, 80 nm and 100 nm Ta film thicknesses. It shows that by decreasing the thickness, the 𝐿𝐾 increases. For the Ta film, the effective penetration depth can be obtained by 𝜆𝑒𝑓𝑓 = 𝜆0 coth ( 𝑑 𝜆0 ) [38, 58]; where 𝜆0 represents the penetration depth of the bulk superconductor which is 𝜆0 =150 nm for Ta [38, 59], and d is the film thickness [PITH_FULL_IMAGE:figures/full_fig_p005… view at source ↗
Figure 3
Figure 3. (a) shows the frequency spectrum of a Ta microwave CPW chip with three resonator s, measured at 𝑇 = 77 mK. The spectrum reveals three resonance frequencies, 𝑓𝑟 , within the 3 -5 GHz range. The fitted and measured amplitude and circle fit for 𝑓𝑟 = 3.654 GHz at high po wer (VNA power = 0 dBm) and extracted 𝑄𝑙 = 4872 and 𝑄𝑐 = 4897 are shown in Fig.3(b) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: (a) Internal quality factor (𝑄𝑖 ) of three CPW resonators on silicon as a function of average photon numbers < 𝑛𝑝ℎ >, the scatter plots are for measurement data, solid lines are fitted data based on Eq. (4) and error bars are depicted with caps at the top and bottom of…
Figure 5
Figure 5. Figure 5: (𝑄𝑖/𝑄𝑐 ) of three CPW resonators on silicon as a function of photon number for (a) 40 nm Ta, at 𝑇 = 77 mK. (b) 40 nm Ta for 𝑓𝑟 = 3.654 at three different temperatures. (c) 80 nm Ta at 𝑇 = 44 mK, and (d) 100 nm Ta at 𝑇 = 40 mK. (a) (b) (c) (d) [PITH_FULL_IMAGE:figures/…

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Low-Loss Superconducting Resonators Fabricated from Tantalum Films Grown at Room Temperature

    physics.app-ph 2025-01 conditional novelty 7.0 of 10

    Room-temperature-grown alpha-tantalum resonators on a niobium seed layer reach state-of-the-art quality factors, matching high-temperature-grown tantalum despite smaller grains and more oxygen-rich grain boundaries.

  2. Fast Recovery of Niobium-based Superconducting Resonators after Laser Illumination

    quant-ph 2025-07 conditional novelty 6.0 of 10

    Superfluid helium-4 immersion shortens the post-laser recovery time of NbN and Nb microwave resonators by roughly three orders of magnitude compared with vacuum.

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Pith tools

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