Improving magnetic-field resilience of NbTiN planar resonators using a hard-mask fabrication technique

Superconducting circuits are promising candidates for quantum information processing (QIP) as well as high-precision sensing. Recently, the interest in circuits able to operate under magnetic fields has increased to enable hybrid QIP platforms^1,2 or quantum sensing applications, such as magnetic resonance detection.^3,4 These applications require developing high-quality factor superconducting resonators resilient to magnetic fields. Detrimental effects for microwave superconducting resonators have been largely studied,⁵ with evidence that obtaining high-quality factors at zero magnetic field requires shielding from quasi-particles,⁶ preventing vortex nucleation,⁷ using low-loss dielectric substrates,^8,9 and mitigating microscopic defects.¹⁰ A well-identified symptom of the last effect is that these defects can be saturated to recover a higher quality factor at high power.¹¹ They can have different origins, such as charge states and spurious spin systems.⁹ For the latter, when the spin Larmor frequency is tuned on resonance by the application of a magnetic field, an increase in losses can be observed which allowed to identify these spin systems partly as hydrogen and oxygen adsorbates on sapphire substrates.^12,13 In addition to representing a source of losses when operating under magnetic field, these spins are also believed to contribute to frequency noise as well as flux noise¹¹ limiting, for example, the sensitivity of SQUID magnetometers^14,15 or the coherence of flux qubits.^12,16,17 Here, we evidence similar field-dependent losses for superconducting resonators deposited on sapphire and show that a hard-mask nanofabrication technique mitigates the contribution of some of these spurious spin systems.

Depending on their nature, these microscopic defects can be represented as electric dipoles [commonly identified as two-level-system (TLS) in the literature] and/or spin systems whose interaction strength with the resonator field depends on their location¹⁰ and range from weak to strong coupling.¹⁸ They can be located in the substrate or at the surfaces of the substrate and superconducting electrodes. TLS can be, for instance, trapped charges, dangling bonds, or tunneling atoms located either on the substrate or in an oxide layer capping the superconductor. Many works have now demonstrated that surface dielectric losses are far more detrimental than dielectric bulk losses^8,19 and shown that the impact of these TLS can be minimized by improving materials and fabrication techniques as well as optimizing the design to reduce their contribution.^5,10,20

Spurious spins comprise both nuclear and electronic spins lying at the surfaces or in the bulk of the substrate, such as spin donors for silicon²¹ or metal contaminants in sapphire.²² Their contribution to the resonator intrinsic loss and flux noise is maximum when their transitions are brought to resonance by the application of a magnetic field. Several superconductors, such as Nb,²³ NbN,^13,24 NbTi,²⁵ NbTiN,^26,27 GrAl,²⁸ and YBCO,²⁹ have proven able to yield high-quality factor resonators (⁠ $Q > 10 5$⁠) at moderate (<1T) and large magnetic fields (6T). Yet, in most works reporting resonators resilient to magnetic fields, a drop in their intrinsic quality factors appears at specific magnetic fields. Using resonators of various frequencies fabricated in NbTiN on Si, NbN on SiO₂, and granular Al on sapphire, previous works^24,26,28 observed losses corresponding to a near perfect spin 1/2 bath with a g-value $g = ℏ γ eff / μ B = 2.0 ± 0.3$⁠, where $γ eff = ∂ ω s / ∂ B 0$ is the effective gyromagnetic ratio governing the measured spin frequency ω_s dependence on the applied magnetic field B₀. In addition, Kroll and co-workers³⁰ also observed a similar effect for NbTiN on sapphire, but at a value slightly lower than 2 (about g = 1.9). For NbN on sapphire,¹³ a spin 1/2 absorption line $ω s ( B 0 )$ was observed, along with satellite lines corresponding to hydrogen physiosorbed on the surface, which creates a spin system with a signature hydrogen hyperfine splitting of $A / ( 2 π ) =$ 1.42 GHz. These hydrogen atoms absorbed on the surface are also thought to contribute significantly to flux noise in Ref. 12 in superconducting circuits. Additionally, contribution from O₂ adsorbates and superoxide systems embedded into the surface of the sapphire lattice was reported,¹³ further confirmed by high-field EPR studies³¹ and DFT calculations.³² They show that spin systems, respectively, create a broad absorption at $g ≈ 2.04$ and constant losses occurring for $g ∈ [ 1.5 , 4 ]$⁠. Here, we show that using an aluminum mask instead of a photoresist mask when patterning NbTiN thin films prevents the appearance of most of these spurious spins, except for a signal we attribute to defects within the NbTiN films.

We pattern NbTiN resonators using a dry etching process [Fig. 1(a)] by starting from a 50-nm-thick NbTiN film sputtered on a 2″ sapphire wafer. The wafer is either an edge-defined-grown wafer (EFG, University Wafers) or grown by a heat-exchanger method (HEM, Crystec). The wafer is then diced in rectangular dies of 5 × 7 mm², protected using either photoresist (EFG wafers), or a 50-nm-thick Al layer covered in photoresist (HEM wafers). For each die, we pattern using optical lithography either a photoresist mask (Shipley S1813) or an aluminum mask. The latter is patterned using either the Al layer deposited pre-dicing if it exists or a fresh 50-nm Al layer deposited after cleaning the photoresist off the die post-dicing. The pattern is created by etching the Al through a photoresist mask using an acid etchant (Transene Type A), the photoresist is then stripped off. Using either the resist or Al mask, the NbTiN layer is etched using an ICP-RIE tool (Sentech) using CHF₃/Ar/N₂/O₂ atmosphere (30/100/10/3  sccm). If an Al mask is present, it is then wet etched with the same etch as above. A final cleaning is then performed using N-Methyl-2-pyrrolidone (NMP) followed by isopropanol rinsing. On some devices, to remove the identified contribution of the physiosorbed hydrogen, we performed an annealing at 300 or 600 °C in N₂ atmosphere. On one die, we performed a buffered oxide etch (BOE) of 20 min at room-temperature to remove the oxides formed on top of the NbTiN layer before performing an annealing in Ar atmosphere. In total, we prepared nine dies, with various preparation conditions summarized in the supplementary material. Out of these two dies, two were subjected to open air aging and were measured twice.

We have used two types of resonator geometry: low impedance resonators (⁠ $Z c ≈ 20 − 40 Ω$⁠) targeted for electron spin resonance (ESR) sensing (circle design) and higher impedance (⁠ $Z c ≈ 200 Ω$⁠) resonators targeted for resilience to magnetic field (microwire design) see Fig. 1(b). The first geometry comprises a circular interdigitated capacitor with a pitch of 20 μm surrounding an inductive loop or a short microwire. The second is an inductive ribbon of width 10 μm whose ends are capacitively coupled. The resonators are capacitively or inductively coupled to a coplanar waveguide (CPW). The measurement is done either in hanger geometry with the CPW running through the chip or in reflection with the CPW terminated on chip. The width of the ground plane surrounding the CPW is reduced to 70 μm so that all resonators are free floating and not encased in a superconducting ground plane. This is done to minimize the nucleation of magnetic vortices nearby the resonators⁷ and prevent vortices induced losses when applying a dc magnetic field.

On each die, six to eight resonators were patterned. Using well-established fitting procedures,^33–35 we extract for each resonance its frequency $ω r / 2 π$⁠, and its intrinsic and coupling quality factors Q_i and Q_c at low intra-resonator photon number (⁠ $n ¯ ∼ 1 − 10$⁠). The intrinsic quality factors $Q i 0$ obtained at zero magnetic-field for the different fabrication techniques are shown in Fig. 1(c) and range from 10⁴ to 10⁶. All fabrication techniques exhibit at least a few resonators with Q_i exceeding $5 × 10 5$⁠. All devices fabricated using HEM wafers, and whose NbTiN layer was not in contact with resist, obtain Q_i consistently larger than 10⁵ at zero magnetic fields. With annealing, the intrinsic quality factors improve slightly.

We next study the behavior of each resonator under magnetic field. To isolate the dependence of the resonator intrinsic decay rate $κ s$ on the magnetic field, we subtract the loss rate $ω r / Q i 0$ observed at zero-field and the additional loss rate $ω r / Q i w b$ occurring when the Al wire bonds connecting the die to the sample holder transit from superconducting to normal state at $B 0 ∼$ 10 mT. We plot $κ s ( B ̃ 0 )$ in Fig. 2(a) for resonators made with different fabrication techniques, using a re-scaled x-axis $B ̃ 0 = B 0 ω ̃ r / ω r$ with $ω ̃ r / 2 π =$ 8 GHz for easier comparison. Focusing first on a NbTiN resonator patterned on an EFG wafer using a photoresist mask (green), we observe four different peaks, as well as the onset of a large plateau at $B ̃ 0 =$ 50 mT. To identify these features, we build their frequency-field diagram using all the resonators we have measured [see Fig. 2(b)]. We find that the absorption peak frequency of each feature depends linearly on the magnetic field, allowing us to extract a zero-field splitting $Δ 0$ and an effective g value for each feature: $ω r = Δ 0 + g μ B ℏ B 0$⁠.

The first peak lying at $B ̃ 0 =$ 100 mT is very sharp compared to the others and corresponds to a g-value of 4.7 [gray, Fig. 2(b)]. We attribute it to a response from the sapphire substrate. Indeed, while this effective g-value does not correspond to typical contaminants (Fe, Cr), less typical impurities (V, Mo, Mn, Ti, Gd) or known defects in sapphire which are magnetically active (V and F₂ centers), this line has already been observed without being identified in other studies using HEMEX sapphire²² and Verneuil grown sapphire.³⁶ We, thus, note that it cannot be tied to a particular growth technique. We nevertheless observe its disappearance when switching from EFG to HEM-grown sapphire. Note that we also observe a faint line at g = 3.3 that also disappears and that we cannot identify.

Next, we turn to the spin 1/2 line surrounded by an upper and lower satellite peaks [blue markers in Fig. 2(b)]. These three lines have been observed in Ref. 13 and have been attributed to water adsorption on the sapphire surface resulting in imperfect hydroxylation of the surface and the creation of radicals and unpaired hydrogens. The radicals create the central spin 1/2 line (g = 2), and the coupling of a large part of these radicals to atomic hydrogen gives rise to a hyperfine splitting of strength $A / ( 2 π ) = 1.45$ GHz leading to the appearance of the satellite peaks. These features can be removed by desorbing the sapphire surface, which was successfully done in the previous work³¹ by annealing at 300 °C under vacuum. We observe a similar disappearance using an annealing at the same temperature under both N₂ or Ar atmosphere in our measurements. Using the relative amplitude of the two satellite peaks, we can infer the polarization of the probed spin ensemble and deduce a spin temperature of 80 mK. This value is reasonable considering the limited attenuation we have placed on the input probe line (see the supplementary material).

We now move to two correlated features linked to the adsorption of O₂ and H₂O on the sample surface: the peak at $B ̃ 0 =$ 270 mT and the plateau appearing at $B ̃ 0 =$ 50 mT. Imperfect hydroxylation and defect sites in the sapphire located near the surface leads to the production of superoxides (O $2 −$ and HO $2 −$⁠) contributing to the broad peak at g = 1.77 [black markers in Fig. 2(b)].^13,31 For O₂ molecules which are not reduced by interaction with the surface (either the sapphire or the NbTiN surface), they are expected to respond to ESR probing according to their triplet state nature i.e., as a broad plateau resonance extending from g = 4.0 to low values. We see both features in our experiment, with the superoxide peak appearing more strongly for aged samples which were left in open air for 3 days.

The last feature lies at g = 1.85, with an extracted zero-field splitting $Δ 0 = 0.28 ± 0.12$ GHz [red markers in Fig. 2(b)]. The absorption feature has an asymmetric shape and has not been previously reported, though it may have been identified as a spin 1/2 line in a similar study of NbTiN resonators on sapphire.³⁰ To identify its origin, we calculated for each resonator geometry the participation ratio p_i of each surface Σ_i to the total mode energy using finite-elements microwave simulations (see the supplementary material).⁸ Namely, we wish to distinguish between two hypotheses: whether this spin system is located on the sapphire free surface Σ_f or on the superconductor surface $Σ sc$ [see Fig. 1(a)]. Using a multipeak fitting routine, we have calculated for each resonator the integrated absorption loss $∫ κ s / ω 0 d B 0$⁠. In Fig. 3, we plot this peak area vs $p f$ and $p sc$ for various fabrication protocols. Concentrating on the fabrication without annealing (green markers) for both a resist or an aluminum mask, we see that the peak area is proportional to $p sc$⁠, while its dependence on $p f$ is non-linear. We, thus, conclude that the defect is more likely to emanate from the NbTiN surface. From this linear fit, we can extract that the surface spin concentration is $3.1 ± 0.2 × 10 12 cm − 2$ (see the supplementary material). Note that since we cannot determine the origin of these spurious spins, we do not know whether they are located in a thin oxide layer on top of the NbTiN or across the full thickness of the NbTiN film, leading to an unknown overall factor on $p sc$⁠. In addition, we have checked experimentally that the absorption does not depend on the in-plane orientation of the magnetic field so that the spins are either isotropic or randomly orientated. We can explore a few hypotheses on the origin of these spins. The fluorine etch could leave paramagnetic residues on the edge of the superconducting electrodes.^37,38 For instance, TiF₃ has a paramagnetic response, yet its g-value is anisotropic and would give rise to a broad line extending from 2 to 1.85,³⁹ which does not agree with our measurements. Some electronic states of niobium and titanium exhibit a paramagnetic response; for instance, electronic states Nb $2 +$ and Nb $4 +$ have a paramagnetic response with g-values around 1.85,^40,41 while Ti $3 +$ is anisotropic, with principal g -values lying between 1.9 and 2. Yet, we note that the feature does not appear in Nb or NbN resonators,^13,23 so a contribution from Nb donor states seems unlikely or deeply linked to the presence of Ti in the film.

These features contribute to a background signal strongly dependent on the magnetic field, which complicates the identification of an ESR signal and that also limits the overall achievable quality factor. We now review the impact of different fabrication processes on the different features to elaborate a mitigation strategy. We plot on Fig. 4 the peak height $κ s f$ for each feature, depending on the fabrication protocol. The contribution for each feature was isolated using a multi-peak fit. (1) We note that similarly to measurements on NbN resonators on sapphire, annealing removes the hydrogen peaks (blue) as well as the central OH⁻ peak, independently of the annealing gas. (2) Avoiding contact between photoresist and NbTiN suppresses the plateau resulting from the contribution of triplet O₂: indeed for HEM wafers where only Al was in contact with NbTiN, the plateau is absent, but for EFG wafers, even when an Al mask is used, contact with the protective photoresist layer during dicing is enough for the plateau to be observed. (3) When cleaning the wafer with a long buffered oxide etch after removing the mask, the plateau reappears, with a reduced height. It also gives rise to a small g = 2 feature which is not removed by annealing. Putting aside the NbTiN feature, it, thus, looks like the optimal fabrication technique among those explored here is etching through an aluminum mask followed by an annealing.

The NbTiN feature at g = 1.85, however, shows a strong increase when the sample is annealed: for samples whose NbTiN was never covered by resist, we observe a factor 6 increase for a 300 °C annealing under N₂ or Ar atmosphere (red), and a factor 45 increase for 600 °C annealing under N₂ (see Fig. 3). Note that we observe that when heating NbTiN under N₂ atmosphere at higher temperature, the film swells and gets enriched in nitrogen, moving away from a balanced two atoms face cubic-centered lattice with half of the lattice occupied by nitrogen atoms and the other occupied by Nb and Ti atoms.⁴² It could, thus, be that enrichment of the films in nitrogen and/or a depletion of the film in Ti creates donor niobium sites that give rise to the feature. Remarkably, the sample which was covered by resist for dicing but etched with an aluminum mask does not show the same increase so that we postulate that an oxide passivation layer is sufficient to counteract the effect of annealing on the NbTiN feature.

Nevertheless, avoiding putting photoresist into contact with NbTiN for dicing and etching through an aluminum mask followed by an annealing results in the best combination to remove all magnetic field dependent features. It also ensures that we reach reproducible quality factors above $Q > 10 5$ at zero magnetic field, in particular, for our low-impedance geometry resonator. Considering all sources of losses, including the contribution from aluminum wire bonds (⁠ $∼ 3 × 10 5$⁠) and of the NbTiN feature (⁠ $∼ 2 × 10 5$⁠), we can maintain a total quality factor above $Q > 10 5$ in the 0 to 0.3 T range, an important step to develop an ESR spectrometer based on superconducting microwave resonators. Straightforward improvements to our setup could help reduce the length of the wire bonds so that their contribution is minimized (⁠ $> 2 × 10 6$⁠). The behavior of the NbTiN feature also makes clear that developing a capping layer that acts as a barrier during the annealing without contributing to the oxygen features would help us reach higher quality factors. Interesting avenues to explore regarding this point are to deposit the Al mask in the same tool as the NbTiN or test a different material. Broader perspectives would be to probe the origin of the NbTiN feature by varying the stoichiometry of the NbTi sputtering target or comparing to TiN resonators. Nevertheless, avoiding putting photoresist into contact with NbTiN for dicing and etching through an aluminum mask followed by an annealing results in the best combination to remove all magnetic field dependent features. It also ensures that we reach reproducible quality factors above $Q > 10 5$ at zero magnetic field, in particular, for our low-impedance geometry resonator. Considering all sources of losses, including the contribution from aluminum wire bonds (⁠ $∼ 3 × 10 5$⁠) and of the NbTiN feature (⁠ $∼ 2 × 10 5$⁠), we can maintain a total quality factor above $Q > 10 5$ in the 0–0.3 T range, an important step to develop an ESR spectrometer based on superconducting microwave resonators. Straightforward improvements to our setup could help reduce the length of the wire bonds so that their contribution is minimized (⁠ $> 2 × 10 6$⁠). The behavior of the NbTiN feature also makes clear that developing a capping layer that acts as a barrier during the annealing without contributing to the oxygen features would help us reach higher quality factors. Interesting avenues to explore regarding this point are to deposit the Al mask in the same tool as the NbTiN or test a different material. Broader perspectives would be to probe the origin of the NbTiN feature by varying the stoichiometry of the NbTi sputtering target or comparing to TiN resonators.

See the supplementary material for details on a list of the measured devices and their variation in fabrication steps, as well as additional details on the experiment and data analysis.

This work was supported by the LABEX iMUST (No. ANR-10-LABX-0064) and the project IDEXLYON of Université de Lyon, within the program “Investissementsd'Avenir” (Nos. ANR-11-IDEX-0007 and ANR-16-IDEX-0005) operated by the French National Research Agency (ANR) and by the European Union (ERC, INDIGO, 101039953). We acknowledge IARPA and Lincoln Labs for providing a Josephson Traveling-Wave Parametric Amplifier. The NbTiN films were etched using the ICP-RIE tool of the Nanolyon platform. We thank the cleanroom of the SPEC at CEA-Saclay and Pief Orfila for sputtering NbTiN on our wafers.

The authors have no conflicts to disclose.

A. Bahr: Data curation (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal). M. Boselli: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). B. Huard: Funding acquisition (supporting); Investigation (supporting); Methodology (supporting); Writing – original draft (supporting). A. Bienfait: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.