key: cord-0666414-abfzavwu
authors: Yu, C'ecile Xinqing; Zihlmann, Simon; Fern'andez-Bada, Gonzalo Troncoso; Thomassin, Jean-Luc; Gustavo, Fr'ed'eric; Dumur, 'Etienne; Maurand, Romain
title: Magnetic field resilient high kinetic inductance superconducting niobiumnitride coplanar waveguide resonators
date: 2020-12-08
journal: nan
DOI: nan
sha: 88380a1082699ce29335cd8356e646cc00cfdeb1
doc_id: 666414
cord_uid: abfzavwu

We characterize niobium nitride $lambda/2$ coplanar waveguide resonators, which were fabricated from a 10nm thick film on silicon dioxide grown by sputter deposition. For films grown at 120{deg}C we report a superconducting critical temperature of 7.4K associated with a normal square resistance of 1k$Omega$ leading to a kinetic inductance of 192pH/$Box$. We fabricated resonators with a characteristic impedance up to 4.1k$Omega$ and internal quality factors $Q_mathrm{i}>10^4$ in the single photon regime at zero magnetic field. Moreover, in the many photons regime, the resonators present high magnetic field resilience with $Q_mathrm{i}>10^4$ in a 6T in-plane magnetic field as well as in a 300mT out-of-plane magnetic field. These findings make such resonators a compelling choice for cQED experiments involving quantum systems with small electric dipole moments operated in finite magnetic fields.

We characterize niobium nitride λ /2 coplanar waveguide resonators, which were fabricated from a 10 nm thick film on silicon dioxide grown by sputter deposition. For films grown at 120°C we report a superconducting critical temperature of 7.4 K associated with a normal square resistance of 1 kΩ leading to a kinetic inductance of 192 pH/ . We fabricated resonators with a characteristic impedance up to 4.1 kΩ and internal quality factors Q i > 10 4 in the single photon regime at zero magnetic field. Moreover, in the many photons regime, the resonators present high magnetic field resilience with Q i > 10 4 in a 6 T in-plane magnetic field as well as in a 300 mT out-of-plane magnetic field. These findings make such resonators a compelling choice for cQED experiments involving quantum systems with small electric dipole moments operated in finite magnetic fields.

High quality superconducting microwave resonators are at the heart of circuit quantum electrodynamics (cQED) experiments 1-3 . In recent years, high-impedance superconducting microwave resonators (HISMRs) have emerged as a new component [4] [5] [6] allowing to explore regimes previously unattained 5, [7] [8] [9] . Such resonators are characterized by their characteristic impedance Z c = L /C , L -C being the inductance-capacitance per unit of length, close or even higher than the quantum of resistance h/(2e) 2 ≈ 6.5 kΩ. To reach such a high impedance, the resonators need low stray capacitance and extremely high inductance 10, 11 . A large inductance can be achieved either with Josephson meta-materials 12, 13 or thanks to the kinetic inductance of disordered superconductors like TiN 14 , NbTiN 4 or granular aluminium 5 . Through their large inductance, HISMRs generate large zero-point voltage fluctuations V ZPF ∝ f 0 √ Z c with f 0 the resonator fundamental frequency. This large V ZPF enables the coupling of microwave photons to small electrical dipole moments like polar molecules 15 or charges in semiconductor quantum dots [16] [17] [18] . Moreover, using disordered superconductors with a high critical magnetic field, it is possible for HISMRs to maintain their high quality factors up to several teslas 4 opening cQED type experiments to quantum systems requiring magnetic field like spin 7, 19, 20 or majorana fermion qubits [21] [22] [23] .

In this prospect, we present superconducting microwave λ /2 coplanar waveguide (CPW) resonators made from 10 nm thick films of NbN. We first study the kinetic inductance of the films by four probe DC measurement and by two-tone spectroscopy on long resonators. We show that the substrate temperature during the film growth is a viable control knob to achieve a desired kinetic inductance value. We fabricate, in one etching step, resonators of different characteristic impedances ranging from 110 Ω to 4.1 kΩ, just by varying the geometry of the CPW. We characterize the internal quality factor of the resonators as a function of the average photon number occupancy. Then we extend the investigation by a) Electronic mail: cecile.yu@cea.fr b) Electronic mail: romain.maurand@cea.fr studying the resilience of the resonators to in-plane and outof-plane magnetic fields. Finally, we pinpoint that the 4.1 kΩ resonators, which induce the highest zero-point voltage fluctuations, show Q i > 10 4 in the single photon regime, while preserving a high quality factor in both 300 mT out-of-plane and 6 T in-plane magnetic fields. This makes NbN HISMR a compelling choice for cQED experiments involving quantum systems with small electric dipole moments under sizable magnetic fields. The resonators are fabricated on a 525 ± 25 µm thick p-type silicon wafer (1-15 Ω cm), covered by 400 ± 80 nm of thermally grown SiO 2 . The NbN deposition is performed inside arXiv:2012.04366v1 [cond-mat.mes-hall] 8 Dec 2020 a sputtering chamber where the wafer is first heated during ∼16 h at 120°C at a base pressure of 2 × 10 −9 mbar. Then, we perform a cleaning step of 30 s of Ar milling with a bias voltage of 350 V. The sputtering step lasts for 11 s to deposit 10 nm of NbN at 0.01 mbar with an Ar:N partial gas ratio of [60:40]. Afterwards the resonators are patterned in one e-beam lithography step using ZEP resist, followed by an O 2 /SF 6 plasma etching.

Representative scanning electron microscopy (SEM) images of the resonators obtained after such a process are shown in Fig. 1(a) . We designed arrays of resonators in a hanger type geometry allowing parallel measurement of 5 resonators in one experimental run. In Fig. 1(b) , we show an instance of such a chip inside its sample box. The sample box is placed in a dry dilution refrigerator equipped with a 3D vector magnet (6 -1 -1 T) and connected to a standard microwave setup, see Fig. 1 (c). The chip is then cooled down to a base temperature of 8 mK at zero magnetic field.

We characterize the NbN film by measuring its sheet resistance as a function of temperature, see Fig. 2 (a). The inset shows the high temperature behaviour for which the sheet resistance increases while lowering the temperature from room temperature to ∼ 19 K, typical of weak localization and Coulomb interaction in strongly disordered superconductors 24 . From 19 to 5 K the resistance decreases, until zero resistance marking the superconducting transition. From this curve we extract the sheet resistance R = 1033 ± 1 Ω/ as the maximal value of the curve and the critical temperature T c = 7.4 ± 0.1 K as the temperature at the inflexion point of the curve, see Fig. 2 (a). From the sheet resistance and the critical temperature, we estimate the kinetic inductance of our NbN film 25 as

whereh is the reduced Planck constant and ∆ 0 is the superconducting gap at zero temperature. We assume that the superconducting gap for NbN is given by ∆ 0 = 1.76k B T c where k B the Boltzmann constant 26 . From this DC measurement we obtain a kinetic inductance value of L kin = 192 ± 3 pH/ .

To confirm the kinetic inductance value extracted via DC measurements, we performed an independent RF measurement based on a two-tone spectroscopy 27 . This method relies on measuring the dispersion relation of a resonator whose resonance frequency is set intentionally low, here f 0 = 750 MHz. This allows to probe a large number of its harmonics. To map the dispersion relation, a VNA is set to measure the transmission at a resonant frequency of the resonator f VNA within the 4-8 GHz band of our measurement setup. We then sweep a second tone at a frequency f MW and whenever that second tone matches a harmonic of the resonator, at a frequency f n , the measured resonance at f VNA is dispersively shifted by the cross-Kerr effect 28 and the transmission readout by the VNA is modified. By identifying all f n , the dispersion relation can be reconstructed. In Fig. 2(b) we show the dispersion relation for a probe frequency f VNA = 5.22 GHz, the seventh harmonic of the resonator. Since the angular wavenumber of each resonance is given by k n = πn/ where is the length of the λ /2 resonator and n is the mode index, we can extract the kinetic inductance as follows:

where ω n = 2π f n is the angular resonance frequency, C is the capacitance per unit length and L m , L kin are the geometric and the kinetic inductance per unit length respectively. L m and C are purely geometrical quantities and can be estimated using a microwave simulation software like Sonnet (L m = 2.13 × 10 −7 H/m and C = 2.82 × 10 −10 F/m) or conformal mapping calculations 29 (L m = 2.13 × 10 −7 H/m and C = 3.13 × 10 −10 F/m). From this RF measurement and Sonnet simulations data we obtained a kinetic inductance value L kin = 3.84 × 10 −6 H/m corresponding to L kin = 192 ± 3 pH/ , which is in excellent agreement with the DC measurement extraction. Our kinetic inductance is significantly higher than previous reports of kinetic inductance in NbN: L kin ∈ [4.4, 82]pH/ 6, 30 . Note that the kinetic inductance can be tuned by varying the substrate temperature during the sputter deposition. We find that by tuning the temperature from room temperature to 275°C the kinetic inductance changes from 220 pH/ to 45 pH/ as T c evolves from 5.56 K to 10.5 K. From the NbN layer characterized previously (192 pH/ ) we have designed three sets of resonators with impedances of 110 Ω, 890 Ω and 4.1 kΩ by just varying the central conductor width s from 50 µm to 200 nm while keeping the gap width w = 2 µm, see Tab. I. We study the effect of the impedance FIG. 3. Power dependence of the resonator's internal quality factor. a) Typical normalized S 21 response of a resonator in the many photons regime. b) Parametric plot (dot) and fit (line) of Im(1/ S 21 ) vs Re(1/ S 21 ) (dots) of the same data as in a). c) Power dependence of the internal quality factor for the resonators with different characteristic impedances. At low photon number, the internal quality factor saturates. At high photon number, Q i for the 110 Ω resonator saturates at n ph = 10 5 then decreases, which may be due to the high non-linearity of the material at high power. For the high-impedance resonators, the saturation of Q i is not probed since it happens at very high power which makes the resonance unstable. and the input power on the internal quality factor of the resonators resonating in the 4-8 GHz band of our set-up. A typical normalized transmission spectrum is shown in Fig. 3(a) . The transmission spectrum is normalized by setting the background signal to 0 dB and removing the electronic delay and phase shift of the measurement set-up. Once normalized and close to resonance, the S 21 coefficient can be described by 31

where Q i , Q c are the internal and coupling quality factor respectively, φ is the rotation in the 1/ S 21 complex plane due to an impedance mismatches of the feedline of the resonators and δ x = ( f − f 0 )/ f 0 is the relative frequency to the resonance frequency f 0 . The fit is performed in the 1/ S 21 complex plane to take into account the resonance response in magnitude and in phase simultaneously. A typical result of such a fit is shown in Fig. 3(b) . From a circuit model we derive the average photon number inside the resonator as

where P in is the input power at the resonator and ω 0 = 2π f 0 . Fig. 3(c) shows the internal quality factor as a function of the averaged number of photons. For each impedance, each data point corresponds to the mean value of 4 resonators of the same impedance but with different resonance frequencies.

Before going into detail we precise that the 110 Ω resonators stayed in ambient atmosphere for a few months during the COVID-19 pandemic between its fabrication and the characterization, which may explain its different behaviour from the two other sets of resonators. At low power we observe for the 900 Ω and 4.5 kΩ resonators a clear saturation of the internal quality factor that may be explained by two-level system dynamics 32 . At high photon number, n ph > 10 5 , and for the same set of resonators, self-Kerr non-linearities lead to a strong asymmetry of the measured resonances rendering the analysis of the quality factors beyond the scope of our study. We can only conclude that the internal quality factor saturation usually observed at such input powers 14 was not visible up to the power shown here. For the 110 Ω resonators, whom we suspect had a different aging evolution than the other sets of resonators, we do not observe a saturation in the single photon regime while observing a clear saturation at high power around ∼ 10 4 photons. We now turn to the behaviour of the resonators in a static magnetic field. The internal quality factor and the relative frequency shift as a function of the applied magnetic field have been measured with an average of ≈ 100 photons and the results can be seen in Fig. 4 . For an out-of-plane magnetic field, see Fig. 4(a) and (b) , the internal quality factor drops to 10 2 at 100 mT with an abrupt jump in resonance frequency around 0 T for the 110 Ω and 890 Ω resonators. For the narrowest resonators (4.1 kΩ) Q i stays well above 10 4 up to B ⊥ = 300 mT without any jump or hysteresis in the resonance frequency. We note a dip in Q i around ∼ 150 mT, which can be associated with a coupling of the resonator to magnetic impurities. The quadratic shift of the resonance is explained by the superconducting depairing under magnetic field and can be fitted following the expression 4 

⊥ s 2 with D the electronic diffusion constant. The extracted diffusion constant D ≈ 0.58 cm 2 /s is consistent with previous measurements 33, 34 on NbN thin films.

For the in-plane magnetic field resilience, see Fig. 4 (c) and (d), we find Q i > 10 4 for all resonators from 500 mT to 6 T. Finally, both out-of-plane and in-plane magnetic field studies show that the highest impedance have also the highest magnetic field resilience. As the losses induced in a magnetic field are mainly attributed to the creation of magnetic-flux vortices in the superconducting film, a smaller width of the central conductor minimizes vortices creation and dynamics, thus suppressing the quality factor degradation. For the 4.1 kΩ resonator for example, the central conductor width (200 nm) is shorter than the London penetration depth of NbN 35 . Therefore, vortices are induced only in the ground plane 36 , which explains its high Q i in magnetic fields. The relative reso- nance shift in B in Fig. 4(d) shows that the 100 Ω resonances jump abruptly around 0 T, which is a signature of unstable magnetic-flux vortices in the superconducting film, while the 890 Ω and the 4.1 kΩ resonators show smooth shift of the resonance frequency and no hysteretic behaviour. Thus, even without complex microwave engineering to minimize vortices dynamics, a nanowire CPW design already improves the magnetic resilience by several orders of magnitude for both inplane and out-of-plane magnetic field. In addition, we have verified that the excellent behaviour under a magnetic field of B = 6 T with Q i > 10 4 is preserved in the single photon regime.

Concerning the interaction between the resonator and magnetic impurities, the inset in Fig. 4(c) shows the internal quality factors of four 4.1 kΩ resonators with different resonance frequencies. The observed dip in the internal quality factor is shifting to a higher magnetic field as the resonator frequency is increased as expected for the resonant condition gµ B B = hω 0 with g the Landé g-factor of the magnetic impurities. From all resonator measurements, we extract g = 1.97 ± 0.29, which matches the g-factor of free electrons (g = 2).

In conclusion, we fabricate CPW resonators from a 10 nm thick NbN film in a single e-beam lithography step with a kinetic inductance of 192 pH/ on silicon oxide. The highest impedance reaches 4.1 kΩ, which should induce zero-point voltage fluctuation one order of magnitude higher than for a 50 Ω resonator. The high kinetic inductance enables the fabrication of superinductor with relaxed geometry constraints compared to previous reports 6 . We find, at zero field, an internal quality factor Q i > 10 4 in the single photon regime. The narrow center conductor of the 4.1 kΩ resonator made it highly resilient to magnetic fields with Q i > 10 4 in a 300 mT out-of-plane and in a 6 T in-plane magnetic field without any hysteresis in the resonance frequency. Finally, NbN HISMR is a compelling choice for cQED experiments operating at finite magnetic fields and involving quantum systems with small electric dipole moments. We acknowledge useful discussions with Romain Albert, Franck Balestro, Jérémie Viennot and Nicolas Roch. We also thank Michel Boujard for all mechanics parts to build the setup. This work is supported by the ERC starting grant LONG-PSIN (No.759388). S. Zihlmann acknowledges support by an Early Postdoc.Mobility fellowship (P2BSP2_184387) from the Swiss National Science Foundation. G. Troncoso acknowledges the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No.754303.

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