High-Q trenched aluminum coplanar resonators with an ultrasonic edge microcutting for superconducting quantum devices

Dielectric losses are one of the key factors limiting the coherence of superconducting qubits. The impact of materials and fabrication steps on dielectric losses can be evaluated using coplanar waveguide (CPW) microwave resonators. Here, we report on superconducting CPW microwave resonators with internal quality factors systematically exceeding 5 × 106 at high powers and 2 × 106 (with the best value of 4.4 × 106) at low power. Such performance is demonstrated for 100-nm-thick aluminum resonators with 7–10.5 um center trace on high-resistivity silicon substrates commonly used in Josephson-junction based quantum circuit. We investigate internal quality factors of the resonators with both dry and wet aluminum etching, as well as deep and isotropic reactive ion etching of silicon substrate. Josephson junction compatible CPW resonators fabrication process with both airbridges and silicon substrate etching is proposed. Finally, we demonstrate the effect of airbridges’ positions and extra process steps on the overall dielectric losses. The best quality factors are obtained for the wet etched aluminum resonators and isotropically removed substrate with the proposed ultrasonic metal edge microcutting.

Superconducting CPW microwave resonators are the basic elements of superconducting circuits: quantum processors, 1 quantum-limited parametric amplifiers, 2 quantum memory, 3 photon detectors, 4 and artificial atoms. 33There are many applications where resonators operating in a single-photon regime are characterized by a significant internal quality factor (Qi) decrease due to dielectric losses in bulk dielectrics and thin interfaces containing two-level systems (TLS) 5,6 .Dielectric losses directly affect the performance of superconducting devices, for example, the relaxation times of qubits. 5,7CPW resonators internal quality factor at low microwave power (QiLP) depends dominantly on dielectric losses in interfaces: metal-substrate (MS), metal-vacuum (MA) and substrate-vacuum (SA) interfaces. 8,28It is well known, that the MS interface is dominant 28 and it is generally determined by the choice of metal deposition and substrate cleaning procedures 31 .High QiLP values approaching 2.0x10 6 were obtained for TiN 8 and NbTiN 10 CPW resonators.However, thick metal films up to 300 nm and 750 nm respectively were used, which are not applicable for qubits fabrication.The best QiLP reaching 2.0-3.0×10 6in case of 100 nm thick aluminum film were demonstrated 13 for large footprint CPW resonators (center trace of 24 μm).A silicon substrate etching with Al resonators was implemented in Ref. 29, but with 250 nm thick aluminum the best QiLP up to 1.8x10 6 was achieved.Internal quality factor of CPW resonators itself can be increased using new materials compatible with aggressive treatment, thicker superconducting films and larger footprint of resonators leading to lower field intensity.However, it is very hard to integrate them into superconducting qubit circuits fabrication processes.Aluminum technology is still one of the leading platforms for superconducting qubits, 11,12 which requires base sub-150 nm thick Al layer 12,14,16 with optimized footprint resonators (center trace up to 10 μm 17 ).Improving aluminum CPW resonators quality requires further technology investigation: ultra-high vacuum Al deposition, 13 advanced substrate cleaning 14 , substrate etching, 8,10 and etc.
In this paper, we report on high QiLP aluminum 100 nm thick compact resonators on etched silicon substrates compatible with superconducting qubits fabrication.We investigate Al metal and Si substrate etching, as well as post treatment steps, in order to reduce the loss on the MA and SA interfaces.Using the proposed technology, we demonstrate internal TABLE I. CPW resonators comparison; w is the resonator center trace width, gap is the gap between resonator center trace and the ground, f0 is the resonant frequency, Qc is the coupling quality factors between feedline and resonators, and QiLP are the internal quality factors at low power.quality factors at low QiLP and high QiHP power exceeding 2.0x10 6 and 5.0x10 6 respectively for identical resonators at frequencies ranging from 4.0 to 5.0 GHz.It is fabricated using isotropic substrate etching of optimized footprint compact resonators (10.5 μm center trace and 3.5 μm gap) with both airbridges and without them.The best internal quality factors obtained for the 2.91 GHz resonator are QiLP = 4.4x10 6 and QiHP = 1.9x10 7 .We achieve it by introducing isotropic silicon substrate etching with subsequent ultrasonic resonators edge microcutting after aluminum wet etching.After resonators patterning, we fabricate airbridges to suppress parasitic slotline modes 18 .In order to evaluated airbridges influence on QiLP, we measured identical resonators without airbridges, with airbridges over feedline only, and over both resonators and feedline.Using the proposed technology, we are able to reach the highest internal quality factor at low power for compact aluminum CPW resonators 8,10,13,14,29,30 compatibles with superconducting qubit circuits fabrication process (Table 1).
To evaluate the effects of the Al film and Si substrate etching, airbridges fabrication, additional ultrasonic microcutting on QiLP of the resonators, we fabricated quarter-wave resonators according to the frequency multiplexing scheme 19 on 25x25 mm silicon substrates with further cutting to 5x10 mm chips.There are 12 resonators on each chip with frequencies ranging from 4.0 to 7.0 GHz for devices without substrate etching and 6 resonators with frequencies ranging from 2.5 to 5.0 GHz for devices with substrate etching.All the resonators were designed to have 50 Ohm impedance (center trace widths/gap): 7.0/4.0μm for resonators without substrate etching and 10.5/3.5 μm for resonators with substrate etching.The widths of the etched resonators are corrected to take into account the change in the effective dielectric permittivity (εeff 20 ) during substrate etching.The coupling quality factor Qc was designed to be 3.0x10 5 , but the experimental values are in the range of 2x10 5 to 4x10 5 due to simulation and design issues.A script 16 based on a conformal mapping method was used to evaluate Qc and impedance of the resonators.In order to eliminate frequency dependence, we selected and compared the internal quality factors of the resonators with frequencies ranging from 4.0 to 5.0 GHz only.
For airbridges influence evaluation we used two designs: the first one with 9 airbridges over the feedline only; the second one with both 9 airbridges over the feedline and 4 airbridges evenly spaced over each resonator, which should be enough to eliminate the slotline modes. 18Optical images of the chips can be found in the supplementary materials.
Figure 1(a) shows the fabrication sequence scheme of resonator chips.We used high-resistivity Si(100) substrates (>10kOhm-cm) for all the samples.Al films were deposited by ultrahighvacuum electron-beam deposition system under a base pressure lower than 10 -10 Torr.Before deposition substrates were cleaned in RCA1 solution, followed by HF treatment to remove native oxide and terminate the Si surface with hydrogen.Then we installed Si substrates in the load lock as quickly as possible after cleaning, typically within 10 min.Al films with a thickness of 100 nm were deposited according to the regime used in Ref. 21 and Ref. 32  to form the base metal layer.After photoresist mask spincoating and patterning, Al films were etched either by wet etching in an industrial Aluminum Etching Type A solution (Fig. 1(b) or by dry etching in a BCl3/Cl2 gas mixture (Fig. 1(c).Then we dry etched the silicon substrate either by Bosch DRIE process 22 with 90 cycles (Fig. 1(d)) or by isotropic RIE process in SF6 gas mixture.During Al etching process the edges of resonators center trace are usually damaged (Fig. 1  get the desired undercut, then by using strong ultrasonic microcutting in isopropyl alcohol, we cut them to obtain high-quality metal edges (Fig. 1(e)).At the final stage, airbridges were formed for a group of resonators according to the technology used in superconducting qubit circuits fabrication. 17fter dicing, the chips were mounted in copper sample holders made in according to the recommendations given in Ref. 23, and mounted in a 10 mK stage in the dilution fridge.We used infrared and magnetic shielding to protect our samples against quasiparticles generations 24 and magnetic vortices.We measured the transmission coefficient S21 of the resonators with a vector network analyzer (VNA) according to the method described in Ref. 25.A total attenuation of 90 dB was installed on cryostat stages, all the measurements are performed under the temperatures below 50 mK.The input and output lines were equipped with powder infrared filterseccosorb, as well as low-pass filters.At the output line at 4 K stage, there is an amplifier on a high electron mobility transistor (HEMT).The wiring diagram of a measurement setup for the samples can be found in supplementary materials.We varied the drive power so that the photon population ⟨np⟩ in the resonator ranged from the single-photon levels up to 10 7 photons.We experimentally observed, that at the lowest power QiLP can fluctuate by more than 34% over several hours period due to fluctuations in TLS populations. 9Here, we present the time-averaged QiLP values instead of maximum values.One can notice the systematic dependence of QiLP on the metal and substrate etching processes.We found that the QiLP of resonators fabricated by wet etching is twice higher compared to our dry etching.We attribute this dependence to the metal-vacuum (MA) and substrate-vacuum (SA) interfaces having significantly lower loss tangents after wet etching than after dry etching.It could be definitely observed, that the surface of resonator center trace is damaged 27 at a distance of about 200 nm from the edge (Fig. 1(c)), which is the area with the highest field intensity.At the same time, it was demonstrated by simulation 28 that the substrate etching by only 10 nm reduces the participation ratio of the metal-airsubstrate corners by 50%, while preserving the other participation ratios, which should have a positive effect on the QiLP level.In our case, we have dry etched the substrate to 80 nm depth, but the QiLP level is still much lower than in the case of wet etching, where no etching of the substrate took place.We suppose that the reason is a very high concentration of TLS in the damaged region together with the high field intensity.
Bosch DRIE substrate etching allowed the fabrication of resonators with low QiLP values.The most possible reason is a high TLS concentration in the MA and SA interfaces as a result of incomplete removal of specific Bosch process polymer residues, which could be further cleaned.Isotropic etching of the Si substrate allowed a slight increase in QiLP compared to the level of wet-etched Al resonators (from 1.18x10 6 to 1.21x10 6 ), but the standard deviation in the group increased significantly.The possible reason is a non-reproducibility of metal edge geometry, which turns out to be "suspended" after etching, which negatively affects MA interface, resonator impedance and resonant frequency.We confirm this assumption by introducing an additional treatment in isopropyl alcohol with ultrasound: the "suspended" metal edge is broken off and the geometry of the resonators is reproduced exactly.With the width of the removed metal being of 600 nm, which is 3 times the width of the Al section damaged during etching, resulting in an almost twofold increase in the average QiLP to 2x10 6 while the standard deviation value decreases.
Figure 2(e) shows the QiLP dependences of resonators with wet Al etching and isotropic Si substrate etching with airbridges over the feedline (Fig. 2(f), (h), blue lines), with airbridges over the feedline and resonators (Fig. 2(g), yellow lines), and without airbridges (red lines) on the average photon population in the resonator.The average photons number was determined based on applied power, Qc and the loaded quality factor Ql according to the recommendations from Ref. 26.For the group of resonators without airbridges, only the results with the highest and lowest QiLP are shown.Figure 2(e) also shows Qi of our best resonators without air bridges at the frequencies 2.91 GHz and 3.25 GHz and QiLP equal to 4.4x10 6 and 3.4x10 6 , respectively (violet line).One can notice, that airbridges location directly affects resonator QiLP (Fig. 2(e)), which is in a good agreement with Ref. 18.The airbridges placed over the feedline does not affect the resonators internal quality factor (it is within the variation of QiLP for resonators without airbridges).
In summary, we have measured the internal quality factors of 100 nm thick aluminum compact CPW resonators which are compatible with superconducting qubits fabrication route for various base metal and silicon substrate etching processes, as well as post treatment technological step.Wet Al film etching with isotropic Si substrate dry etching followed by the proposed ultrasonic resonators edge microcutting leads to the average QiLP above 2.0x10 6 , achieved resonators with w = 10.5 μm and f0 = 4.0 -5.0 GHz.The highest achieved QiLP value is 4.4x10 6 for the resonator with w = 10.5 μm and f0 = 2.91 GHz.Finaly, we fabricate high quality factor superconducting CPW resonators with Si substrate etching and airbridges showing that the additional fabrication steps do not result in overall circuit Supplement to: High-Q trenched aluminum coplanar resonators with an ultrasonic edge microcutting for superconducting quantum devices E.V. Zikiy, 1,2 A.I. Ivanov, 1,2 N.S.Smirnov, 1,2 D.O.Moskalev, 1,2 V.I.Polozov, 1 A.R. Matanin, 1,2 E.I. Malevannaya, 1 V.V. Echeistov, 1 T.G.Konstantinova 1 and I.A. Rodionov This supplement provides experimental details and data sets to support the claims made in the main text.First, we present the design and fabrication details for the two types of devices we investigated: a resonator circuit without substrate etching and a resonator circuit with deep substrate etching.We then describe a several technical details of the measurement system: the measurement setup and device shielding and the fitting of the complexvalued transmission spectra.Next, we present the measurement results for the type 1 and type 2 devices.S1 shows the fabrication parameters of all devices presented in this work.

MEASUREMENT SETUP
To minimize resonator losses induced by non-equilibrium quasiparticles and magnetic vortex displacement, we mount the samples inside several layers of shielding (Fig. S2).Specifically, we anchor the PCBmounted sample directly to a copper cold finger connected to the mixing chamber of the dilution refrigerator.The sample is then enclosed in a copper can, the inner surface of which is coated in a mixture of Stycast 2850 FT and silicon carbide granules with diameter 1000 µm.This can is enclosed in a second aluminum can.This is finally enclosed in one layer of cryogenic magnetic shielding (1-mm-thick Cryoperm).Coaxial cables entering the sample holder were pasted into the lid of the inner layer of IR shielding to reduce the impact of open holes on the shielding effectiveness.Extra radiation shielding is provided by in-house inline Eccosorb infrared filters in the input coaxial line mounted outside the magnetic shields at the mixing chamber stage.

FIG 1 .
FIG 1.(a) Fabrication sequence of resonator chips with different Al film and Si substrate treatment.SEM images of the resonators center trace edges: (b) Al wet etching; (c) Al dry etching; (d) Si substrate Bosch DRIE; the sagging edges of the thin film can be observed; (e) Si substrate isotropic etching followed by ultrasonic microcutting.

Figure 2 (
a) shows QiLP measurements for the CPW resonators grouped by different Al film and Si substrate etching technology.Groups 1a and 1b with the average QiLP of 6.0x10 5 and 1.18x10 6 include resonators obtained by RIE and wet Al etching, respectively, without Si substrate etching.Group 2a with the average QiLP of 6.1x10 5 includes resonators obtained by wet Al etching with Si substrate Bosch DRIE.Groups 2b and 2c with the average QiLP of 1.21x10 6 and 2.05x10 6 contain resonators obtained by wet Al etching with Si substrate isotropic etching without ultrasonic edge microcutting and with it, respectively.Figures 2(b), (c), (d) show SEM images of the structure specifics for groups 2a, 2b, 2c.The measurement results of all our samples are shown in the supplementary materials.

FIG 2 .
FIG 2. (a) Internal quality factor in single-photon regime of resonators grouped by fabrication technological features into groups.Group 1a -RIE Al, without substrate etching; group 1b -wet etching Al, without substrate etching; group 2a -wet etching Al, DRIE Bosch substrate; group 2b -wet etching Al, isotropic substrate etching; group 2c -wet etching Al, isotropic substrate etching, additional ultrasonic microcutting (crosses indicate the average value of QiLP for each resonator, whereas the error bars indicate the standard deviations and mean value).SEM images of the cross section of the resonators: (b) group 2a, (c) group 2b, (d) group 2c.(e) Dependence of internal quality factor in single-photon regime of resonators with wet etching Al and isotropic etching of substrate with airbridges over feedline (blue lines), with airbridges over feedline and resonators (yellow lines), without airbridges (red lines) in 4 -5 GHz range and outside this range (violet line) on average photon population in resonator.Lines were added for better visibility.(f) SEM image of the feedline section with bridges; (g) SEM image of the feedline and resonator section with bridges; (h) SEM image of a single bridge on resonator with etching of the substrate in the gap.
FIG. S1: (a) Optical image of a 12-resonators circuit with frequencies from 4.0 to 7.0 GHz without substrate etching (type 1).(b) Optical image of a 6-resonators circuit with frequencies from 2.5 to 5.0 GHz with isotropic substrate etching (type 2).Both resonator circuits are fabricated using wet etching in an industrial Aluminum Etching Type A solution.Resonator circuits with airbridges over feedline and resonators are presented.On the chip without substrate etching (Fig.S1(a)) there are 12 resonators with frequencies: 4.0, 4.4, 4.6, 4.8, 5.0, 5.4, 5.6, 6.0, 6.4, 6.6, 6.8, 7.0 GHz and on the chip with isotropic substrate etching (Fig.S1(b)) there are 6 resonators with frequencies: 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 GHz.For silicon isotropic etching we use hight-density plasma etching at RF power of 700 W and bias power of 40 W, a SF6 with 35 sccm flow rates, and 40 mTorr pressure.TableS1shows the fabrication parameters of all devices presented in this work.

FIG. S2 :
FIG. S2: Wiring diagram of a measurement setup for the samples

TABLE SI .
Device fabrication parameters