cavities with indium bump bonding high coherence

Appl. Phys. Lett. 116, 154002 (2020); https://doi.org/10.1063/5.0003907 116, 154002

© 2020 Author(s).

High coherence superconducting microwavecavities with indium bump bondingCite as: Appl. Phys. Lett. 116, 154002 (2020); https://doi.org/10.1063/5.0003907Submitted: 06 February 2020 • Accepted: 26 March 2020 • Published Online: 15 April 2020

Chan U Lei, Lev Krayzman, Suhas Ganjam, et al.

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High coherence superconducting microwavecavities with indium bump bonding

Cite as: Appl. Phys. Lett. 116, 154002 (2020); doi: 10.1063/5.0003907Submitted: 6 February 2020 . Accepted: 26 March 2020 .Published Online: 15 April 2020

Chan U Lei,1,2,a) Lev Krayzman,1,2,b) Suhas Ganjam,1,2 Luigi Frunzio,1,2 and Robert J. Schoelkopf1,2,c)

AFFILIATIONS1Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA2Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA

a)Author to whom correspondence should be addressed: [email protected])Electronic mail: [email protected])Electronic mail: [email protected]

ABSTRACT

Low-loss cavities are important in building high-coherence superconducting quantum computers. Generating high-quality joints betweenparts is crucial for the realization of a scalable quantum computer using the circuit quantum electrodynamics (cQED) framework. In thispaper, we adapt the technique of indium bump bonding to cQED to realize high-quality superconducting microwave joints between chips.We use this technique to fabricate compact superconducting cavities in the multilayer microwave integrated quantum circuit (MMIQC)architecture and achieve single photon quality factors over 300� 106 or single-photon lifetimes approaching 5ms. To quantify the perfor-mance of the resulting seam, we fabricate microwave stripline resonators in multiple sections connected by different numbers of bonds,resulting in a wide range of seam admittances. The measured quality factors combined with the designed seam admittances allow us to boundthe conductance of the seam at gseam � 2� 1010=ðXmÞ. Such a conductance should enable the construction of micromachined supercon-ducting cavities with a quality factor of at least a billion. These results demonstrate the capability to construct very high-quality microwavestructures within the MMIQC architecture.

Published under license by AIP Publishing. https://doi.org/10.1063/5.0003907

Circuit quantum electrodynamics (cQED) is one of the mostpromising platforms for quantum computation. Coherence times havebeen dramatically improved in the past decade.1 Additionally, circuitswith dozens of qubits have been realized and used to demonstratemany interesting results, such as molecular simulations,2–4 condensedmatter simulations,5 and proof-of-principle quantum supremacycalculations.6 However, further scaling up the number of circuit com-ponents while maintaining or even improving their coherence is verychallenging.

In the past several years, techniques from the MEMS industryhave been applied to the cQED framework to construct multilayermicrowave integrated quantum circuits (MMIQCs).7 Tremendousprogress has been achieved in 3D integration of quantum circuitelements while maintaining their coherence.8–11 Micromachinedsuperconducting cavities can be highly useful in the MMIQC architec-ture. Such structures can serve as long-lived quantum memories or asenclosures to suppress radiation loss to the environment and crosstalkbetween quantum circuit elements. A crucial requirement for con-structing high-quality micromachined superconducting cavities is the

fabrication of high-quality microwave joints between layers of theMMIQC.10 The loss associated with joints significantly limits thechoice of geometries, materials, and fabrication processes of the super-conducting cavities, as well as the layout of quantum circuits. To main-tain the performance of superconducting cavities without sacrificingdesign flexibility, a qubit-compatible method to create high qualityjoints between parts is critically important.

In the particle accelerator community, a lot of effort has been puttoward improving the joint quality in superconducting RF cavities.Methods such as diffusion-bonding12 and electron beam welding13

have been used to create high-quality joints. Recently, niobium cavitieswith the quality factor higher than 1010 have been demonstrated atsingle-photon powers.14 Although these methods create high-qualityjoints between metal parts, their application to joining on-chip super-conducting circuits has not been demonstrated. Therefore, integratingqubits into such cavities would require manual assembly with currenttechnology. A better candidate for creating ultra-low loss joints forsuperconducting quantum circuits is indium bump bonding. It is anestablished method that has been used in the field of cryogenic

Appl. Phys. Lett. 116, 154002 (2020); doi: 10.1063/5.0003907 116, 154002-1

Published under license by AIP Publishing

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detectors15 and has several properties that make it suitable for thisapplication. Indium cold-welds to itself and is not brittle at cryogenictemperatures,16 allowing for room-temperature bonding, whichremains robust even with thermal cycling to milli-Kelvin tempera-tures. Additionally, it superconducts at 3.4K and can thus formlow-loss bonds. Finally, it is compatible with standard lithographictechniques, enabling the adaptation of the existing approaches forscaling up quantum circuits. Recently, indium bonding has been usedfor chip hybridization and interconnections.8,17–19

In this work, we adapt indium bump bonding to the cQED archi-tecture. Using this technique, we create superconducting joints withvery low loss at microwave frequencies. We quantify the loss of theresulting joint by fabricating bump-bonded indium stripline resona-tors and measuring their internal quality factors. We then apply thisindium bump-bonding technique to realize high-quality microma-chined cavities and show devices with a low-power quality factor ofover 300� 106.

Building superconducting cavities requires joining together atleast two different parts. However, the seam at the joint may limit thecoherence of a cavity resonator. In an ideal joint, the contact surfacesparticipating in the seam would be identical to the bulk material thatcomprises the remainder of the cavity; there would be no extra lossassociated with the seam. In a realistic joint, imperfections such as

lattice defects, metal oxides, or organic residue on the surfaces canreduce the electrical conductivity across the seam and degrade thequality of the resonator. The loss of the seam can be quantified withthe following phenomenological model from Ref. 10:

1Qseam

¼ 1gseam

�

ðseamj~Js � l̂ j2dl

xðtot

lj~H j2dV� 1

gseam� yseam; (1)

where l̂ is a unit vector along the seam and the integral in the denomi-nator is taken over the entire volume of the mode (see Fig. S1 in thesupplementary material). The conductance per unit length gseam is anempirical value, and the admittance per unit length yseam is a geometricfactor that can be calculated analytically or numerically.

Previous studies10 have shown that seam loss can be dominant ina cavity, depending on the cavity geometry and location as well asquality of the seam, as shown in Fig. 1(c). Series A (black circles, datafrom Brecht et al.10) represents the TE110 modes of a set of rectangu-lar cavity resonators machined out of bulk 6061 aluminum. Eachdevice is nominally identical, except for the location of its seam. Thedifferent seam positions result in different values of yseam, with higheryseam corresponding to lower Q. The internal quality factors of thesedevices lie on a diagonal line corresponding to a gseam � 103=ðXmÞ.

FIG. 1. (a) Schematic of the bump-bonded stripline resonator. The two chips are depicted separately, with sapphire in teal and indium in blue. The multi-section stripline is visi-ble, with bumps on the daughter chip making the connections. Additionally, mechanical support bumps can be seen on the edges of the stripline. (b) False-colored opticalmicrograph of the daughter chip, with the interrupted stripline together with the bumps visible. The inset shows an SEM image of a bump. (c) Plot of measured internal Q vssimulated yseam for four series of devices. Dashed diagonal lines are lines of constant gseam. Series A (black circles) represents the TE101 modes of traditionally machined alu-minum 6061 cavities with seams placed at varying locations. The green lines in the accompanying diagram show the locations of the seams: either along the dashed line (withvarying horizontal positions) or along the solid line (with varying depths d). The arrow on the plot indicates that the device has an yseam value of nominally 0 although machiningimprecision can give it a non-zero yseam, indicated by the position of the circle. Series B (red squares) represents micromachined cavities of differing depths. Although thepoints seem to lie along a line of constant gseam, we note that several other loss mechanisms (metal–air interface, conductor loss) scale with the depth in the same way asyseam, meaning that the cavity could be limited by any or several of these mechanisms. Series C (blue diamonds) represents the bump-bonded stripline resonators, with varyingnumbers of bumps. One device has an yseam value of precisely 0 (indicated by a break in the x-axis), as it is a control device with the entire stripline on one chip. We generallyobserve a device-to-device variation of around a factor of two in the Q values of our stripline resonators, which is represented here as a blue band around the control device. Ifthe striplines were limited by seam loss, we would expect a consistent deviation from this band. The blue line of gseam ¼ 2� 1010=ðXmÞ is a lower bound on the seam con-ductance that is representative of the several devices with very large seam admittance. Finally, the green triangles represent the TM010 mode of niobium TESLA cavities,14

with published Qint values and yseam that we estimated by simulated the mode structure for the published dimensions.




Since the geometries of the devices are nominally identical, the energyparticipation in other loss mechanisms remains fixed, while yseamvaries. This is consistent with their Q values being limited by seamloss. For micromachined cavities made by bonding two waferstogether, the location of the joint is necessarily at the worst locationfor the fundamental mode, with yseam � 1=ðXmÞ. In order to improveits coherence time, it is, therefore, necessary to increase gseam by devel-oping better joints.

As mentioned above, indium bump bonding is a promisingmethod for improving the joint quality of superconducting microwavecircuits. We fabricate indium bumps at the location of the joint using avariant of the standard process (see the supplementary material).Photolithography is used to lift off thermally evaporated indium,forming approximately 15 lm� 15lm� 10 lm bumps [see the insetin Fig. 1(b)]. For the other side of the joint, we leave a uniform layer ofevaporated indium. Before bonding, we treat both chips using aplasma surface treatment in order to remove oxide and passivate thesurface. Finally, we bond the two chips in a commercial wafer bonderat room temperature. As the bumps are compressed, they deform,breaking through the surface oxide and forming metal-to-metal bonds,which results in a low-loss seam.

In order to characterize the quality of the resulting joint, we cre-ate indium stripline resonators in multiple sections connected byvarying numbers of bump bonds [see Fig. 1(a)]. By varying the num-ber of bumps, we can change yseam of the devices. The highest yseam isachieved when there are a maximum number of bumps given fabrica-tion constraints [see Fig. 1(b)]. These devices can attain much higheryseam than micromachined cavities without too much of a decrease inQ, allowing us to place a tighter lower bound on gseam. A controldevice is also created by placing the entire stripline on one chip, whichis still bonded to the second chip by the mechanical support bumps onthe edge. Since such a device has no seam at all, its yseam should beprecisely 0.

We measure the stripline resonators in a multiplexed package inthe hanger configuration at the base of a dilution refrigerator, withtemperature around 15 mK.20 Series C (blue diamonds) in Fig. 1(c)represents these devices. The control device was measured to haveQint � 106, which is set by seam-independent losses. A shaded blueband is drawn around the control device with the width set by the nor-mal device-to-device variation observed in stripline resonators. If theresonators are not seam-limited, we expect their Q values to consis-tently lie within the band. We note that this is the case for most devicesexcept for two with lower Q, which could be caused by some imperfec-tion in the device or the bond. This suggests that the measured Qvalues of the bump-bonded resonators are not limited by seam lossbut rather by other mechanisms, such as dielectric or conductor losses.With these data, we place a lower bound on gseam � 2� 1010=ðXmÞ,which is representative of the distribution of several points around ourhighest yseam. A seam with such a conductance would enable a micro-machined cavity to have a Q value of 1 to 10 billion, depending on thedepth.

We additionally plot two green triangles representing theTM010 mode of niobium TESLA cavities14 for comparison. TheQint values are as reported in this paper, and the yseam valuesare obtained by simulating the mode structure of cavities withthe shape and dimensions as well as the seam location set as pub-lished. It is interesting to note that lower bound on gseam obtained

in this manner is similar to the lower bound obtained in this workalthough the techniques and materials are quite different. In eithercase, the seam quality enables cavities with a Qint value of 109–1010.However, the particular methods used in Romaneko et al. requirespecialized processing and cannot be easily applied to creating goodjoints between bonded chips.14

The high-quality indium joint described above is, thus, a goodcandidate for application to enhance the lifetime of micromachinedcavities, which have so far been limited by seam loss.10 These cavitiesare composed of two silicon chips that are metallized with 1:2lm ofthermally evaporated indium [Fig. 2(a)]. The bottom chip contains arectangular recess area made using a potassium hydroxide anisotropicsilicon etch, resulting in a 54:7� sidewall [Fig. 2(b)]. The top chipis patterned with a coupling aperture for the measurement [inset inFig. 2(a)]. In order to improve the seam quality, indium bump arraysare fabricated along the contact region on the top chip [dashed line onthe top chip in Fig. 2(a)]. The two chips are bonded together with acommercial wafer bonder with a force of 2 kN in ambient conditionsto form a micromachined cavity, which is mounted on a sampleholder to be measured in a reflection configuration (see the supple-mentary material).

The internal loss of the micromachined cavity consists of theconductive loss of the indium, the dielectric loss of the indium oxide,and the loss from the seam formed at the contact of the two chips,

1Qint¼ aRs

xl0k0þ pdiel tan dþ yseam

gseam: (2)

Here, x is the frequency of the cavity resonance, l0 is the vacuum per-meability, and k0 is the penetration depth of indium. The kineticinductance fraction a, the surface dielectric participation ratio pdiel,and the seam admittance per unit length yseam are geometrical parame-ters that can be calculated analytically or numerically. The surfaceresistance Rs of the superconductor, the loss tangent tan d of the sur-face dielectric, and the seam conductance per unit length gseam repre-sent the intrinsic loss of each respective loss mechanism.

For the TE110 mode of the micromachined cavity, we observethat the internal quality factor increases linearly with d, as shown inFig. 2(d). However, a, pdiel, and yseam are all inversely proportional tothe depth of the cavity d for this mode. Therefore, we cannot deter-mine which loss mechanisms are dominant based on this set of mea-surements. Nevertheless, by attributing the total loss to a single lossmechanism, we can place bounds on the corresponding intrinsicloss, which gives Rs � 261 nX; tand � 1:2� 10�2, and gseam � 3:4�108=ðXmÞ. The highest internal quality factor we have achieved inthis study is 3:4� 108 with a cavity depth of d ¼ 1:5mm. The life-times of these cavities are independent of whether a phase-sensitiveheterodyne measurement [Fig. 2(e)] or a phase-insensitive powerringdown measurement [Fig. 2(f)] is used, i.e., T2 ’ 2T1.Additionally, their internal quality factors depend very weakly on theaverage photon number ð�nÞ as compared to typical coplanar wave-guide (CPW) resonators. This is consistent with the fact that themode volume of the micromachined cavities is several million timeslarger than that of CPW resonators (see the supplementary material).No apparent degradation in the internal quality factor has beenobserved after the samples have been exposed to air for over3months.




In conclusion, we have demonstrated techniques to fabricateand characterize high-quality superconducting joints. We have usedthe bump-bonding technique to construct high-quality indium micro-machined cavities using industry standard methods that do notrequire manual assembly. Using this technique, we have achieved alow-power internal quality factor of over 300� 106 corresponding toan intrinsic T1 approaching 5ms, which is comparable to the perfor-mance of conventionally machined cavities used for quantum memo-ries in cQED. This result together with the ability to make low-lossjoints shows that indium is a good superconductor for making high-quality quantum circuits.

Coupling a qubit to a micromachined cavity requires a slightlydifferent design11,21 than in other 3D circuit QED experiments usingconventional machined cavities.22 A correctly designed qubit struc-ture on the top chip of the micromachined cavity has been shown tohave adequate dipole coupling to the cavity.11 To incorporate a qubitinto the high-Q indium micromachined cavity developed in thiswork, the qubit is first fabricated on the top chip using e-beamlithography and double-angle aluminum evaporation. After that, theindium ground plane (which also serves as the roof of the cavity) isfabricated on the top chip using a standard photolithographyprocess. Finally, indium bumps can be fabricated on the indiumground plane with an additional lithography step, and the indiumbump-bonding technique developed in this work can be applied toimprove the lifetime of a MMIQC-based quantum memory to themillisecond level.

The desire to build 3D cavities either to serve as quantummemo-ries or to provide electromagnetic shielding highlights the fact thatseam losses are very important for the 3D integration of quantumcircuits. Since the scaling of superconducting circuits for quantuminformation processing will likely require multilayer circuits and inter-connects,8,11 the improved performance of the superconducting jointsdemonstrated here can be a key enabler for enhancing coherence in awide range of devices. It also allows the realization of low-loss compactmultilayer circuits including flip-chip resonators and lumped-elementmicrowave networks. This work, thus, provides an important steptoward building a more complicated MMIQC while improving itsperformance.

See the supplementary material for the fabrication process andthe measurement setup, the calculation of the participation factors, aswell as the temperature and power dependence of the micromachinedcavities.

AUTHOR’S CONTRIBUTIONS

C.U.L. and L.K. contributed equally to this work.

We thank Harvey Moseley, Ari Brown, Nicholas Costen,Timothy Miller, Luke Burkhart, and Gianluigi Catelani for usefulconversations; Jan Schroers and Teresa Brecht for assistance withwafer bonding; Charles Ahn, Frederick Walker, and Cristina Visanifor assistance with DC measurements; Philip Reinhold and

FIG. 2. (a) The top chip and the bottom chip of a micromachined cavity before bonding; the dashed line on the top chip indicates the location of the indium bumps, and theinset shows the optical micrograph of the coupling aperture on the top chip. (b) Side wall of the bottom chip. (c) Electron micrograph of the indium bumps. (d) Internal qualityfactor of micromachined cavities with the cavity depth equal to 100 lm (blue), 300lm (orange), 650lm (green), 900 lm (red), 1200lm (purple), and 1500 lm (brown).Squares (circles) represent devices from batch 1 (2). Opened and filled symbols represent data from two cooldowns that are separated by more than 3 months. The solid lineis a linear fit for devices from batch 2. (e) Transmission spectrum of a micromachined cavity with d ¼ 1500 lm at 4 photons (blue) and 1010 photons (black). (f) Power decaymeasurement data (blue) and exponential fit (red).




Christopher Axline for experimental assistance; and Michael Power,Michael Rooks, Christopher Tillinghast, James Agresta, Yong Sun,Sean Rinehart, and Kelley Woods for assistance with devicefabrication. This research was supported by U.S. Army ResearchOffice Grant No. W911NF-18-1-0212. S.G. was supported by a MaxPlanck Research Award from the Alexander von HumboldtFoundation. Facility use was supported by the Yale Universitycleanroom and YINQE. R.J.S. and L.F. are founders andshareholders of Quantum Circuits Inc.

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cavities with indium bump bonding high coherence

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