Epitaxial Al 2 O 3 capacitors for low microwave loss superconducting quantum circuits

We have characterized the microwave loss of high-Q parallel plate capacitors fabricated from thin-film Al/Al2O3/Re heterostructures on (0001) Al2O3 substrates. The superconductor-insulator-superconductor trilayers were grown in situ in a hybrid deposition system: the epitaxial Re base and polycrystalline Al counterelectrode layers were grown by sputtering, while the epitaxial Al2O3 layer was grown by pulsed laser deposition. Structural analysis indicates a highly crystalline epitaxial Al2O3 layer and sharp interfaces. The measured intrinsic (low-power, low-temperature) quality factor of the resonators is as high as 3 × 104. These results indicate that low-loss grown Al2O3 is an attractive candidate dielectric for high-fidelity superconducting qubit circuits.

2][3][4][5][6] The phase qubit has achieved several notable milestones, including realization of high-fidelity entangling gates in two and three qubit circuits, 3 quantum state tomography of two and three qubits, 3,4 and full characterization of highly non-classical states in linear microwave resonators. 5,6 owever, qubit gate fidelity is limited by relatively short energy relaxation times of order hundreds of ns. 7It has been shown that the energy relaxation rate is dominated by spurious coupling of the qubit to low-energy two-level state (TLS) defects in the amorphous dielectrics of the qubit circuit. 8These defects are believed to arise from atomic scale structural imperfections 9 and are known to exist in the surface oxides of the superconductors, at the superconductor-insulator interface, and in the bulk of the amorphous dielectrics of the circuit. 10,11 here are ongoing efforts to develop improved low-loss amorphous dielectric materials for superconducting qubits, 12,13 and it is expected that the incorporation of defect-free, crystalline dielectrics into qubit circuits will lead to dramatic improvements in energy relaxation times.There have been prior efforts to realize Josephson tunnel barriers from grown epitaxial Al 2 O 3 and phase qubits incorporating crystalline junctions display a factor 5 reduction in the density of resonant TLS junction defects. 14Furthermore, there have been efforts to incorporate epitaxial Josephson junctions into the transmon qubit. 15,16 wever, this approach to qubit realization requires excellent control over the grown tunnel barrier thickness, which determines the junction critical current.An alternative approach is to fabricate a submicrometer Josephson junction and to shunt the junction with a low-loss external capacitance. 17n this approach, qubit T 1 is very simply related to the loss tangent of the capacitor dielectric: T 1 = 1/ω 10 tan δ, where ω 10 is the qubit transition frequency.Here, we report the development of crystalline Al/Al 2 O 3 /Re trilayers for potential applications as qubit shunt capacitors.As has been shown previously, rhenium (Re) is an attractive candidate for epitaxial qubit applications since it has a low free energy of oxidation, a high melting temperature, and an excellent lattice match to sapphire, factors that are crucial to the realization of a highquality metal-dielectric interface. 14,18 oreover, optimized Re films have very low microwave loss. 19he epitaxial trilayers were grown in a custom hybrid deposition system incorporating both pulsed laser deposition (PLD) and planar magnetron sputtering sources, switchable by a simple ∼180 • rotation of the substrate heater. 20The hybrid system was further equipped with high-pressure reflection high-energy electron diffraction (RHEED), 21 which enabled in situ surface monitoring during the growth.The trilayers were grown on single crystal c-plane Al 2 O 3 substrates (Crystec GmbH Berlin, Germany).Prior to Re deposition, the Al 2 O 3 substrates were annealed in a flowing O 2 environment at 1100 • C for 4 h.The 100 nm-thick epitaxial Re base layers were deposited at 900 • C via dc magnetron sputtering from a 1.33 diameter Re target (purity > 99.99%); following growth, the films were annealed in vacuum at 900 • C for 2 h.Next, the Al 2 O 3 dielectric layers were grown by PLD from a 1 diameter, 1/8 thick ceramic target; the PLD system employed a KrF excimer laser (λ = 248 nm) operating at 5 Hz with a fluence of 1.2 J/cm 2 .We investigated two different processes for Al 2 O 3 growth.In the first approach (the "one-step" process), a 20 nm-thick Al 2 O 3 film was deposited at 850 • C in a single step.In the second approach (the "two-step" process), we first grew 2 nm of amorphous AlO x at room temperature; we then annealed the sample in vacuum at 850 • C to form a seed layer for Al 2 O 3 homoepitaxy and deposited an additional 18 nm of Al 2 O 3 at that temperature.To complete the trilayer, a 100 nm-thick Al layer was grown by dc magnetron sputtering at room temperature.
The crystalline quality and epitaxial arrangement of the thin films was investigated by conventional four-circle XRD using CuK α 1 radiation (Bruker D8).The one-step grown Al 2 O 3 layers on Re are aligned epitaxially and show no sign of a second phase.In Fig. 1(a), the 2θ -θ scan shows that both the Re and the one-step deposited Al 2 O 3 layers grow with the c-axis normal to the substrate.From the measurements, Re lattice parameters a 0 = 2.77 Å and c 0 = 4.47 Å were determined, indicating full relaxation with the same unit cell volume as bulk Re. 22 The full width at half maximum (FWHM) value in (0002) Re rocking curve is 0.2 • , which is narrower than any previously reported value to the best of our knowledge [Fig. 1 We have used TEM analysis to confirm the epitaxial growth of the trilayer heterostructure.In order to evaluate the dependence of dielectric quality on the growth parameters of the Al 2 O 3 films, we fabricated lumped element LC resonators from the Al/Al 2 O 3 /Re stack.Here, the singleturn inductor was fabricated from the Re base layer, and the parallel-plate capacitor incorporated the grown Al 2 O 3 layer as the dielectric.The LC tank circuits were coupled to a common feedline via overlap coupling capacitors comprising an ex situ PECVD deposited amorphous SiN x dielectric as shown in Fig. 4(a).The resonance frequencies of the fabricated resonators were in the range from 4 to 5 GHz.The samples were cooled down in an adiabatic demagnetization refrigerator (ADR) with a base temperature around 50 mK.From the measured frequency-dependent transmission across the resonator we extracted both the loaded and internal quality factors Q c and Q i , respectively. 12igure 4(d) shows the internal quality factors of several devices grown under a variety of conditions.The low-power internal quality factor of the resonator incorporating the two-step grown Al 2 O 3 is 2 × 10 4 , while the internal Q of the resonator comprising the one-step grown Al 2 O 3 is 3 × 10 4 .The measured quality of the one-step grown Al 2 O 3 is thus comparable to the intrinsic Q of the best demonstrated amorphous a-Si:H dielectrics. 12According to the theory of dielectric loss induced by low-energy TLS defects, the dielectric quality factor is expected to scale linearly with the rms voltage across the resonator at high drive power. 24The extremely weak power dependence observed here suggests that resonator loss is not dominated by low-energy defects in the grown Al 2 O 3 films; indeed, separate measurements reveal comparable internal quality factors in single-layer coplanar waveguide resonators (CPW) fabricated from the grown Re layer.It is possible that the low-angle grain boundaries contribute significantly to the loss in both resonator structures; and that the intrinsic quality of the grown Al 2 O 3 is significantly higher than the measured internal Q of the LC resonators.We anticipate that it will be possible to suppress the loss of the Re thin films in future work.
In summary, we have grown high quality epitaxial Al 2 O 3 /Re heterostructures on (0001) Al 2 O 3 substrates in a hybrid thin film deposition system incorporating both pulsed laser deposition and sputtering.We have investigated the low-temperature, low-power microwave loss properties of the grown trilayers and demonstrated internal quality factors comparable to the best intrinsic Q yet demonstrated for grown dielectric thin films.Our grown epitaxial Al 2 O 3 shows promise as a high-quality capacitor dielectric for Josephson phase qubit circuits.The incorporation of low-loss, defect-free crystalline dielectrics into the phase qubit will yield a substantial improvement in qubit energy relaxation time.

FIG. 2 .
FIG. 2. AFM image and RHEED pattern of the grown Re and Al 2 O 3 layers: (a) Epitaxial Re on Al 2 O 3 substrate and (b) STM image of 100 nm-thick Re film showing single unit cell steps.The line scan of STM image of Re film.(c) AFM image and RHEED pattern of epitaxial Al 2 O 3 layer on Re/Al 2 O 3 substrate.
(b)].Fig. 1(c) shows azimuthal φ-scans of the off-axis (11 26) Al 2 O 3 substrate and (11 24) Re reflections, which exhibit a 30 • in-plane rotation of the Re with respect to Al 2 O 3 . 23The schematic diagram of the in-plane relationship between Re and Al 2 O 3 layer is shown in Fig. 1(d).We grew a 20 nm-thick Al 2 O 3 layer on top of the Re/Al 2 O 3 substrate while maintaining the same in-and out-of-plane epitaxial alignment with the Al 2 O 3 substrate and without any sign of peak separation in 2θ -θ and φ-scans (not shown).Figs. 2(a) and 2(c) show AFM images and RHEED patterns of the epitaxial Re and onestep grown Al 2 O 3 films, respectively.The films display island growth with characteristic lateral dimensions from 100 to 150 nm.The rms roughness of the Re and Al 2 O 3 thin films are 0.7 nm and 1.6 nm, respectively.The RHEED patterns of the Re and the Al 2 O 3 thin film show bright streaks, indicating that the heteroepitaxy proceeds in a Frank-Van der Merwe (FV) growth mode, yielding a high degree of crystallinity.We see hexagonal islands comprising single unit cell steps centered on screw dislocations.The hexagonal islands in the Re films have screw dislocations at the center as revealed by the STM image shown in Fig. 2(b).This indicates that the growth proceeds in a spiral mode with the screw dislocation as the growth flow axis.As shown in Fig. 2(b), observed step is 0.3 nm high.The line scan covers two single steps and three double steps, showing a height of ∼2.4 nm.

Fig. 3 (
a) shows a low magnification bright-field TEM image.In Fig. 3(b), the high-resolution TEM image shows an atomically sharp interface between the Re and Al 2 O 3 layers; the epitaxial match between the layers is clear.Fig. 3(c) shows the selected area electron diffraction pattern (SAED) of the Al 2 O 3 thin film on Re from a planar view.The diffraction pattern shows only one set of Al 2 O 3 spots, which overlap with the Re spots.The elongation of the diffraction spots indicates small angular mosaic spread (<7 • ) between Al 2 O 3 grains.The in-plane epitaxial relationship between the various layers appears to be Al 2 O 3 thin film [ 2110]//Re [ 1010]//Al 2 O 3 substrate [ 2110]; these relative orientations are also supported by the XRD data.

FIG. 3 .
FIG. 3. (a) Low magnification cross-sectional TEM images of Al/Al 2 O 3 /Re trilayer on (0001) Al 2 O 3 substrate.(b) The cross-sectional HRTEM image near the interface between Al 2 O 3 thin film and Re layer.(c) Planar view selected area electron diffraction (SAED) pattern of Al 2 O 3 thin film and Re layer.

FIG. 4 .
FIG. 4. (a) Layer stack of the lumped element LC resonator device showing epitaxial trilayer and SiN x overlap coupling capacitor connected to the measurement feedline.The thicknesses for trilayer stack were 100 nm, 20 nm, and 100 nm for Re, Al 2 O 3 , and Al, respectively.(b) Resonator CAD layout.(c) Electrical circuit schematic of the resonator.(d) Internal loss 1/Q i of epitaxial Re/Al 2 O 3 /Al LC resonators and CPW Re resonators ver sus rms voltage across the resonator.The LC resonators incorporate trilayers grown according to both the one-step and two-step processes described in the text; the multiple datasets for the one-step growth and for the CPW Re represent different growth and fabrication runs with nominally identical parameters.