High kinetic inductance microwave resonatorsmade by He-Beam assisted deposition of tungstennanowires

Cite as: Appl. Phys. Lett. 114, 102601 (2019); doi: 10.1063/1.5080925Submitted: 12 November 2018 . Accepted: 2 March 2019 .Published Online: 13 March 2019

J. Basset,a) D. Watfa, G. Aiello, M. F�echant, A. Morvan, J. Esteve, J. Gabelli, M. Aprili, R. Weil, A. Kasumov,H. Bouchiat, and R. Deblock

AFFILIATIONS

Laboratoire de Physique des Solides, CNRS, Universit�e Paris-Sud, Universit�e Paris Saclay, 91405 Orsay Cedex, France

a)Author to whom correspondence should be addressed: julien.basset@u-psud.fr

ABSTRACT

We evaluate the performance of hybrid microwave resonators made by combining sputtered Nb thin films with Tungsten nanowires grownwith a He-beam induced deposition technique. Depending on growth conditions, the nanowires have a typical width w 2 ½35� 75� nmand thickness t 2 ½5� 40� nm. We observe a high normal state resistance R� 2 ½65� 150�X=� which together with a critical temperatureTc 2 ½4� 6� K ensures a high kinetic inductance making the resonator strongly nonlinear. Both lumped and coplanar waveguide resonatorswere fabricated and measured at low temperature exhibiting internal quality factors up to 3990 at 4.5GHz in the few photon regime.Analyzing the wire length, temperature, and microwave power dependence, we extracted a kinetic inductance for the W nanowire ofLK � 15 pH=�, which is 250 times higher than the geometrical inductance, and a Kerr non-linearity as high as KW;He=2p¼ 2006120Hz=photon at 4.5 GHz. The nanowires made with the helium focused ion beam are thus versatile objects to engineer compact,high impedance, superconducting environments with a mask and resist free direct write process.

Published under license by AIP Publishing. https://doi.org/10.1063/1.5080925

High kinetic inductance superconducting materials are having agrowing impact in the circuit quantum electrodynamics community.Operated in the microwave frequency domain, they allow us to engi-neer high impedance circuits providing an efficient way to increase thelifetime of superconducting quantum bits,1–4 couple electron chargeand spins to microwave photons,5,6 study the coherent quantum phaseslip,7 or generate a high impedance environment in dynamicalCoulomb blockade experiments.8,9 These materials may consist ofarrays of Josephson junctions,2,8 disordered thin films of metallic com-pounds such as NbTi,10 NbN,11,12 NbSi,13 TiN,14,16 NbTiN,15,17 granu-lar aluminium,18 or superconducting semiconductors.19 Their use insuperconducting circuits usually requires etching and/or final sharpen-ing with electron-beam lithography. By contrast, beam-assisted depo-sition of superconducting materials allows us to design and depositextremely narrow superconducting nano-objects with a versatile directwrite process with no templates such as masks or resists. This could bea crucial point to incorporate fragile and delicate samples into a reso-nant structure. Until now, tungsten superconducting nanowires havebeen deposited using Gaþ ions in a Focused Ion Beam (FIB)20–22 orelectrons in an electron scanning microscope (SEM).23 This tungsten

has already been used to connect nanoscale samples such as fuller-enes,20 graphene,24 mesoscopic metallic samples,25 and Bi nano-wires26,27 or study superconductivity in low dimension.28,29 Thefocused helium ion beam from gas field-ion sources30 allows us tofabricate extremely narrow nanowires with potentially bettersuperconducting properties than the ones realized with the elec-tron beam and less damage and contamination than with a Ga-FIB. Connecting nanoscale samples with this technique is possible.However, the high frequency properties, and especially the use ofW nanowire as compact non-linear high impedance supercon-ducting elements for quantum electronics, have not yet beenexplored.

We show here that it is possible to grow superconducting Wnanowires using the He-ion beam induced deposition (He-IBID) tech-nique which present attractive properties for high frequency supercon-ducting circuits. This letter is organized as follows. After detailing thesample fabrication, we report resonator datasets as a function of tem-perature and applied power from which we infer the kinetic induc-tance fraction and the non-linear Kerr parameters. We conclude withpotential applications.

Appl. Phys. Lett. 114, 102601 (2019); doi: 10.1063/1.5080925 114, 102601-1

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Two types of designs were compared: a coplanar waveguide(CPW) resonator [Figs. 1(a) and 1(b)] and a lumped element resona-tor [Fig. 1(d)]. Separate control samples with Titanium/Gold contactswere used to measure the nanowire dc properties. To fabricate thehybrid resonators, a 110nm thick layer of Nb is sputtered on a highresistivity silicon substrate with 500nm thick thermal oxide. We thenuse optical lithography to define a positive mask on top of Nb for reac-tive ion etching with SF6. The W nanowire is then deposited to form aresonator: a long grounded wire capacitively coupled to a transmissionline for the k/4 CPW resonator and in parallel with an interdigitatedcapacitor in the lumped geometry [Figs. 1(c) and 1(d)].

The W nanowires are fabricated using helium beam assisteddeposition in an ORION Nanofab microscope from Zeiss company. Itconsists of an ultra-high brightness gas field ionization source (GFIS).The source is formed by three atoms at the apex of a metallic tip cryo-genically cooled with Nitrogen and submitted to a high voltage(30 kV) in the presence of helium gas. An ionized gas is generated atthe end of the tip and emission originates preferentially from the apex.Only He ions from one atom of the trimer are selected for imagingand nanofabrication. The extracted ions are accelerated by the columnof the microscope to raster scan as in a SEM. Imaging is done via sec-ondary electrons collected into an Everhart-Thornley detector. During

nanodeposition, we use a He-beam current ranging from 10 to 30 pA.The W precursor [tungsten hexacarbonyl W(CO)6] is injected by a gasinjection system OmniGIS II from Oxford Instruments. The targetpressure in the chamber is 4 � 10�6Torr. The patterning geometryand parameters are controlled by the nanofabrication system NPVEfrom Fibics. Table I shows the dimensions and growth conditions ofthe nanowires obtained using the above-described procedure. Heightswere measured by atomic force microscopy and widths by SEM. Forthe lumped element resonator, a W nanowire of 9.8 lm was realized,whereas for the CPW k/4 resonator, a length of 390lm was used.Fabricating such a long nanowire is possible thanks to the very highstability of the He-FIB and He-IBID process compared to previousexperiments with Ga-FIB.20 The quality of the W nanowire growthwas controlled by depositing tungsten nanowires on samples dedicatedto electrical dc measurements. These control samples have been mea-sured at low temperatures (see supplementary material) and the dcproperties of three samples are summarized in Table I. They exhibit asuperconducting transition with critical temperature Tc 2 ½5� 6:5� Kand a critical field Hc2 higher than 5T, similar to the properties of 3DgrownW nanowires.31

The microwave characterization of the resonators allows extract-ing the kinetic inductance fraction of the W nanowire, its kineticinductance per unit length, and finally the non-linear Kerr parameters.The kinetic inductance can be estimated, at very low temperature,from R� and TC

32

LK;� �R�h2p2D0

: (1)

Taking Tc � 5.0K, D0 ¼ 1:76kBTc, and the square resistances fromTable I, we evaluate a kinetic inductance LK;� 2 ½7� 25� pH=�.Using this estimate, we designed microwave resonators resonating inthe 2–6GHz microwave range capacitively coupled to a transmissionline (Fig. 1). Each sample is placed into a copper box equipped with aprinted circuit board and thermally anchored to the 10 mK stage of adry dilution unit. Microwaves are sent via attenuated and thermallyanchored microwave lines. The transmitted wave is amplified and thecomplex transmission spectra S21 through the line are measured witha vectorial network analyzer.

At low temperature, the whole structure is superconducting. Oneprobes the properties of the microwave resonator in a hanger type ofgeometry where the interference of the incident microwave signal andthe one reflected from the resonator lead to a dip in S21. This dip isaccounted theoretically by

FIG. 1. (a) SEM image of a CPW sample. The transmission line runs horizontallywith three k/4 resonators hanging vertically. (b) SEM image of the coupling areabetween the CPW resonator and the transmission line. (c) SEM image of a Wnanowire connected to Nb with a thick W patch at the junction. (d) Optical micros-copy picture of the lumped resonator. The arrow points the nanowire placedhorizontally.

TABLE I. Growth parameters, dimensions, and transport properties of the fabricated W nanowires. With the indicated parameters, the time needed to write the W part of the res-onator “Lumped” is 88 s, whereas for the “k/4” type, it is 40 min.

Sample Current Dose Length Thickness Width Resistance R� q n ð2KÞ k ð0KÞ(pA) (lm) (nm) (nm) (kX) (X) (lX cm) (nm) (nm)

NW1 20 0.178 nC/lm 5.9 40 50 7.75 65.7 266 6.7 674NW2 20 0.06 nC/lm 5.9 5.5 35 25.15 149.2 80.6 7.6 400NW3 10 3 nC/lm2 5.9 20 70 9.1 108.0 216.0 7 449Resonator “Lumped” 20 0.16 nC/lm 9.8 30 35Resonator “k=4” 27 3 nC/lm2 390 12 75Resonator “Lumped2” 27 3nC/lm2 30 25 80

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Appl. Phys. Lett. 114, 102601 (2019); doi: 10.1063/1.5080925 114, 102601-2

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S21 ¼ 1� Qt

Qc

1� 2jQcu1þ 2jQtx

(2)

with x ¼ ðx� x0Þ=x0 the fractional detuning of the readout angularfrequency x relative to the resonance frequency x0. u is a dimension-less parameter taking into account the asymmetry in the transmissionline and is essential to extract reliable quality factors in hanger-coupledresonators.35 It reduces to 0 for a symmetric transmission line. Thecoupling quality factor Qc quantifies the coupling between the trans-mission line and the resonator which has an intrinsic quality factor Qi.These two terms are related to the total (or loaded) quality factor Qt viaQ�1t ¼ Q�1i þ Q�1c . Qi gives information on the quality of the resona-tor independently of the coupling to the measurement line and is a fig-ure of merit of the material quality.

The transmission spectra of the lumped resonator at 10 mK andlow power are shown in Fig. 2(a) with a fit using Eq. (2). We foundx0/2p ¼ 4.4642GHz and Qi ¼ 3990 at low power. For comparison, aresonator entirely made of Nb with a similar design exhibits Qi

¼ 11 000 at T¼ 1.6K. Using a finite element simulation usingSonnetV

R

software, we could extract the parallel capacitance C� 240 fF,the geometrical inductance of the design (corresponding to the wideNb inductive part) Lgeo;D � 0:935 nH, and the kinetic inductance ofthe wire LK ¼ 4.3 nH. The geometrical inductance of the nanowirealone is expected to be Lgeo;W � 17 pH leading to the kinetic induc-tance fraction a ¼ LK=ðLgeo;W þ LKÞ ¼ 0:996 and kinetic overgeometrical inductance ratio b ¼ LK=Lgeo;W ¼ 253 so that the geo-metrical inductance can be neglected. We obtain a kinetic inductanceper unit length LK � 439lH=m and a kinetic inductance per squareLK;� ¼ 15:4 pH=� which falls in the expectation window calculatedearlier. These values are sizeable even compared to state-of-the-artmaterial like NbN (LK;NbN;� 2 ½4:4; 82� pH=�11,32) or NbSi thin films(LK;NbSi;� ¼ 20 pH=�13). The kinetic inductance of the W nanowire

can be increased by reducing the thickness and/or width of the wireand less reliably by changing the growth condition.

The coplanar waveguide (CPW) k/4 resonator gave a smallerquality factor Qi � 710 (supplementary material). In this geometry,the wire length was 390lm long with a resonance frequencyx0=2p ¼ 4:05GHz. From the design, we extracted the lineic capaci-tance to ground to C � 48 pF/m and the lineic geometrical inductanceof the wire Lgeo � 1:7 lH=m. The lineic inductance was thenL ¼ Lgeo þ LK � 512 lH=m. From these numbers, we extracted a

phase velocity c ¼ 1=ffiffiffiffiffiffiLCp

¼ 6:4� 106 m=s and a characteristicimpedance ZC ¼

ffiffiffiffiffiffiffiffiffiL=C

p¼ 3:3 kX. Such a material is therefore highly

suitable for dynamical Coulomb blockade experiments where thecharacteristic impedance ZC must be comparable to the resistancequantum RQ ¼ h=4e2 � 6:5 kX. More specifically, the coupling of,e.g., a tunnel junction to a high impedance microwave resonatoris characterized by the coupling parameter k ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipZC=RQ

p. With k

� 1.26 in our experiment, we would be at the onset of the strong cou-pling regime k � 1 where, e.g., dc-driven single microwave photongeneration could be achieved.33,34

Figure 2(a) shows transmission spectra of the lumped resonatoras a function of temperature with fits using Eq. (2). Decreasing thetemperature leads to an increase in the resonance frequency togetherwith a sharpening of the resonance [Figs. 2(b) and 2(c)]. BelowT¼ 0.9K, the resonance frequency is nearly constant and decreasesstrongly as one raises the temperature.Qi evolves similarly with a max-imum value reaching Qi¼ 3990 at 10mK.

We use the Mattis-Bardeen (MB) theory17,36 (supplementarymaterial) as a minimal model to relate the temperature dependence ofthe resonance frequency and quality factor to the complex conductiv-ity of the material r ¼ r1 � ir2. We make the crude assumption thatonly r of the nanowire is relevant. This is justified by the fact that theac current density is much higher in the nanowire compared to the Nbcircuit which has much larger transverse dimensions and is expectedto exhibit smaller losses. Let us emphasize here that the MB theory isnot directly applicable for very disordered superconductors due torounded BCS density of states and inhomogeneities37–40 but consti-tutes a first attempt to model our samples.

The results are shown along with the experimental data in Figs.2(b) and 2(c). Assuming a zero-temperature superconducting gap D0

� 750 leV, this theory allows us to reasonably tackle the temperaturedependence of the resonance frequency whereas discrepancies arefound regarding the quality factors for which the MB theory predicts adiverging Qi as the temperature is lowered. To reproduce our data, weintroduce extra losses in the internal Qi factor as Q�1i ¼ Q�1MB þ Q�1loss.A temperature independent Qloss ¼ 3990 leads to the yellow trace inFig. 2(c). Whereas the saturation value is fine, the global agreement inthe intermediate temperature regime is unsatisfactory. To best repro-duce our data, a phenomenological linear decay of Qloss with respect totemperature defined as Qloss ¼ 3990ð1� T=3Þ was introduced. Thecorresponding curve is shown in black in Fig. 2(c) demonstratingreasonable agreement. This decay sheds light on the physics of lossesinto the resonator which increases as the temperature is raised. Theseextra losses need to be further understood and may be related topoisoning,18,41–43 TLS,15,44 and/or mobile vortices.45

Because of the high critical fields of both materials used for thisexperiment, Nb and W, the resonator should be rather immune to the

FIG. 2. (a) Temperature dependence of the normalized transmission spectra of thelumped resonator. (b) Temperature dependence of the resonance frequency. (c)Extracted quality factors vs temperature.

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applied magnetic field. We measured the properties of a lumped ele-ment resonator as a function of an applied in-plane magnetic field upto 130mT and observed only small changes (see supplementary mate-rial, <10% in quality factor and <0.05% in resonance frequency.).This makes this hybrid resonator interesting to study mesoscopic devi-ces where the spin degree of freedom needs to be addressed.6,15,46

Increasing the microwave power results in the onset of nonlineareffects due to the nonlinear kinetic inductance of the nanowire. Thisleads to the behaviour of a Duffing oscillator (supplementarymaterial). To quantitatively tackle this non-linear effect, one needsto take into account the shift dx of the resonance frequency dueto the non-linear kinetic inductance. The shifted resonance reads47

xr ¼ x0 þ dx ¼ x0 þ Knph where we have introduced the Kerrparameter K relating the frequency shift to the number of photonsstored in the resonator

nph ¼2Q2

t PQc�hx2

0

1þ 4Q2

cQt

Qc � Qtux

1þ 4Q2t x2

: (3)

P is the power at the input of the resonator and

x ¼ x0 �Knphx0¼ x0 � K

2Q2t P

Qc�hx30

1þ 4Q2

cQt

Qc � Qtux

1þ 4Q2t x2

: (4)

Introducing y ¼ Qtx; y0 ¼ Qtx0; v ¼ Qtu, the non-linear parameter

aNL ¼ �2KQ3

t

Qc�hx30P (5)

and defining c ¼ Q2cQt

Qc�Qt, we can rewrite the expression (4) as

y ¼ y0 þ a½1þ4cvy�1þ4y2 . This expression takes into account the asymmetry

of the transmission line. It consists in a third degree polynomial withthree solutions post-selected to match the measurement sweep direc-tion. By solving this equation, we calculate the power-dependent fre-quency detuning x and fit the experimental data using Eq. (2). Doingso allows one to plot as a function of the applied microwave power Pthe nonlinear term aNL, Qi, Qc, and Qt. As expressed in 5, aNL shouldbe a linear function of the power with a slope s related to the non-

linear Kerr parameter K such that K ¼ � Qc�hx30

2Q3ts.

We have measured the power dependence of the transmissionspectra of the resonator. The data together with the results of the fitare shown in Fig. 3. Figure 3(a) shows that as one increases the micro-wave power, the peak shifts towards smaller frequency, slants, andeventually becomes bistable at high power. From the fit, we observethat the quality factors [Fig. 3(b)] slightly increase from Qi ¼ 3990 to4290 as the power is elevated up to 0.1 pW and remains stable athigher powers. This may indicate the saturation of two-level systemsbut should lead to a much higher increase in quality factor.48 The aNLparameter [Fig. 3(c)] is linear with respect to microwave power P.From the slope s, we extract a Kerr parameter K/2p ¼ 2006 120Hz/photon at 4.465GHz, the uncertainty on K being due to the uncer-tainty on the microwave power P reaching the sample.

To conclude, we evaluated the performance of hybrid microwaveresonators made by combining sputtered Nb thin films with Tungstennanowires grown with a He-beam induced deposition technique. Both

lumped and coplanar waveguide resonators were fabricated and mea-sured at low temperature. They exhibit internal quality factors at highpower up to Qi ¼ 4290 at 4.46GHz for T¼ 10 mK. We extracted alarge kinetic inductance for the W nanowire of LK ¼ 15:4 pH=�, akinetic inductance fraction aW;He ¼ 0:996, and a Kerr non-linearity ofthe resonators KW;He=2p ¼ 2006120 Hz/photon at 4GHz. We alsoverified (supplementary material) that the resonators are immune tothe in-plane magnetic field up to 130mT, the highest field achievablein our experimental setup. As such, this hybrid resonator could beinteresting to study mesoscopic devices where the spin degree of free-dom needs to be addressed.6,46 Finally, this study allowed us to con-clude that nanowires made with the He-FIB are versatile tools toengineer compact, high impedance, superconducting environmentswith a direct-write and resist-free process. It could prove useful todetect optical or plasmonic light or study the dynamical Coulombblockade.

See supplementary material for the dc characterization of thenanowires and microwave data for other resonators including themagnetic field dependence.

We acknowledge valuable discussions with F. Chiodi, H. Lesueur,P. Joyez, and S. Gu�eron. This work was funded by the CNRS, CEA,University Paris-Sud, Paris Ile-de-France Region in the framework ofDIM SIRTEQ and DIM NANOK, Labex PALM (ANR-10-LABX-0039-PALM), Labex NANOSACLAY, Lidex NANODESIGN, the FrenchANR JETS (ANR-16-CE30-0029-01), and ANR INTELPLAN (ANR-15-CE24-0020).

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FIG. 3. (a) Power dependence of the normalized transmission spectra of thelumped resonator at 10 mK.(b) Extracted quality factors vs microwave power. (c)Power dependence of the aNL term (see the text).

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