Disentangling Losses in Tantalum Superconducting Circuits

Superconducting qubits are a leading system for realizing large-scale quantum processors, but overall gate fidelities suffer from coherence times limited by microwave dielectric loss. Recently discovered tantalum-based qubits exhibit record lifetimes exceeding 0.3 ms. Here, we perform systematic, detailed measurements of superconducting tantalum resonators in order to disentangle sources of loss that limit state-of-the-art tantalum devices. By studying the dependence of loss on temperature, microwave photon number, and device geometry, we quantify materials-related losses and observe that the losses are dominated by several types of saturable two-level systems (TLSs), with evidence that both surface and bulk related TLSs contribute to loss. Moreover, we show that surface TLSs can be altered with chemical processing. With four different surface conditions, we quantitatively extract the linear absorption associated with different surface TLS sources. Finally, we quantify the impact of the chemical processing at single-photon powers, the relevant conditions for qubit device performance. In this regime, we measure resonators with internal quality factors ranging from 5 to $15\times {10}^6$, comparable to the best qubits reported. In these devices, the surface and bulk TLS contributions to loss are comparable, showing that systematic improvements in materials on both fronts are necessary to improve qubit coherence further.

Popular Summary

Superconducting qubits are one of the most successful quantum platforms, and they have been integrated into some of the largest processors to date. Building large-scale systems that are robust to computational errors will require improvements in the underlying hardware to extend the quantum coherence of individual qubits. Recent work has shown a marked improvement in qubit lifetime and coherence by employing tantalum as the superconducting metal in the capacitor of a superconducting qubit. Here, we identify key sources of loss and noise in this new material system.

In this work, we perform systematic measurements of over 100 microwave resonators made from tantalum patterned on sapphire. By studying the losses as a function of temperature and microwave power, we quantitatively extract different components of loss, such as radiation into uncontrolled electromagnetic modes and resistive losses arising from broken Cooper pairs.

We find that the dominant source of loss is “two-level systems,” which are absorbers that lead to increased loss at the low temperatures and microwave powers required for qubit operation. By varying the device geometry, we observe at least two different sources of two-level systems, at the surface and in the substrate. Using chemical processing to controllably change the tantalum oxide surface, along with our loss model, we extract different material components of the loss.

Our results indicate state-of-the-art tantalum qubits will require material improvements on at least three fronts: mitigating bulk losses in sapphire, processing or removing the tantalum oxide, and avoiding hydrocarbon contamination at the device surface. The measurement protocols described here isolate and identify the material-related loss, thereby enabling quantitative comparisons among different material systems.

Figure 1

Measuring superconducting resonators. (a) Optical microscope image of a CPW resonator chip, consisting of eight resonators with varying pitch capacitively coupled to a single rf feedline. The scale bar represents 1 mm. (b) Optical microscope image of an LE resonator chip, consisting of four resonators with varying capacitor spacing inductively coupled to a single rf feedline. The scale bar represents 1 mm. Scanning electron microscope images of representative devices are shown in Fig. 1. (c) Transmission spectrum of a single resonator, centered about the resonance frequency $f_0=4.484501\mathrm{GHz}$. The solid line indicates a fit to the data from which $Q_{\mathrm{int}}$, $f_0$, and the coupling losses are extracted. (d) $Q_{\mathrm{int}}$ as a function of the applied microwave power, expressed in terms of the average intracavity photon number. The solid line indicates a fit to the data based on saturation of TLSs and an additional power-independent loss.

Figure 2

Parametrizing losses. (a) Internal quality factor $Q_{\mathrm{int}}$ as a function of applied microwave power and temperature for a characteristic resonator. The traces are well separated at low temperatures and then collapse together and fall exponentially at high temperatures. The characteristic shape of the curves is fit to a model incorporating TLS loss and equilibrium quasiparticles. Solid lines show the best fit to the dataset. (b) Shift in the resonant frequency with temperature relative to the base temperature center frequency for a representative device. The solid line represents a fit to the data. (c) Comparison between estimates of $Q_{\mathrm{TLS},0}$ extracted from two independent measurements: the power and temperature dependence of $Q_{\mathrm{int}}$ and the temperature dependence of the frequency. The dashed line is a guide to the eye showing the case where $Q_{\mathrm{TLS},0}$ is equal for both measurements. Only 26 devices are shown in this plot, because we optimize our measurements to measure $Q_{\mathrm{int}}$ across temperature and power, with a sparser temperature sampling than is required to extract $Q_{\mathrm{TLS},0}$ from the fractional frequency shift with high confidence.

Figure 3

Dependence of loss on SPR. (a) Cartoon cross section illustrating the dependence of SPR on device geometry. As the distance between capacitor pads (gray) increases, the fraction of the electric field (black arrows) energy overlapping with a thin layer at the three interfaces [metal-air (yellow), metal-substrate (purple), and substrate-air (green)] decreases. The fraction of the electric field energy in the sapphire substrate (blue) does not strongly depend on the distance between capacitor pads. (b) Dependence of the extracted $Q_{\mathrm{TLS},0}$ from $Q_{\mathrm{int}}$ measurements on SPR. For the highest SPR devices $Q_{\mathrm{TLS},0}$ exhibits linear scaling with SPR, but for lower SPR the $Q_{\mathrm{TLS},0}$ saturates, indicating that there are both surface and bulk TLS baths. Comparing the data for four different surface conditions allows for the estimate of surface loss tangents for each surface as well as the bulk substrate loss tangent. An inset is included in the bottom right showing the lowest SPR data plotted on a log-linear scale, which reveals the scale of the observed plateau for the lowest SPR devices. (c) Histogram of surface loss tangents for native, BOE, and long BOE CPW devices, showing that BOE and long BOE treatments result in surface loss tangents that are a factor of 1.96 times and 2.02 times, respectively, lower than the native surface on average.

Figure 4

Dependence of $Q_{\mathrm{TLS}}(\overline{n}=1)$ on SPR. $Q_{\mathrm{TLS}}(\overline{n}=1)$ is calculated at base temperature. Data from four different surface conditions are shown. While $Q_{\mathrm{TLS}}$ is a nonlinear function of $\overline{n}$, we nevertheless observe a roughly linear dependence between $Q_{\mathrm{TLS}}(\overline{n}=1)$ and SPR. We fit an apparent loss tangent to each surface condition, as well as the bulk substrate loss tangent. Data are calculated from Eq. (7) with errors propagated from errors in fit parameters. The error bars are truncated at the lower end by $Q_{\mathrm{TLS},0}$.

Figure 5

Scanning electron microscope images of (a) a wet-etched device before piranha treatment, (b) a wet-etched device after piranha treatment, and (c) a chlorine-etched device after piranha treatment.

Figure 6

Wiring diagram for each of our measurement lines. Ranges of attenuation are given where the attenuation varies from line to line. The magnetic shields in our experiments vary between a QCan supplied by qdevil and a custom-made mu-metal can. A traveling wave parametric amplifier (TWPA) is sometimes used on the output line in our experiments and is placed in a separate magnetic shield and wired after the second isolator.

Figure 7

Wide frequency transmission sweep of a chip with four resonators coupled to a single feedline. The four sharp dips correspond to the location of the four resonators.

Figure 8

Fitted $Q_c$ parameters for a power and temperature sweep. This dataset corresponds to the same power and temperature sweep shown in Fig. 2 in the main text. Colors correspond to power applied at the input, with the highest power being the darkest shade and the lowest power being the lightest shade. All powers are spaced 10 dB apart.

Figure 9

$Q_{\mathrm{TLS},0}$ and $Q_{\text{other}}$ versus $Q_C$. The value and uncertainty for $Q_C$ plotted is the mean and standard deviation of fitted $Q_C$ values for all $|S_{21}|$ traces of a given resonator.

Figure 10

(a) An example of high-power resonator transmission trace with observable nonlinearity. The best fit line to the data using Eq. (a1) is shown in orange. This trace is excluded from our analysis. (b) Power sweep showing $Q_{\mathrm{int}}$ for the nonlinear trace in (a) at the maximum $\overline{n}$. The orange line is a fit to the data with the nonlinear data point excluded.

Figure 11

Plots of $T_c$ estimates provided by the frequency shift and $Q_{\mathrm{int}}$ fitting methods for the three different quasiparticle frequency shift regimes.

Figure 12

$Q_{\mathrm{TLS},0}$ extracted from a full temperature and power sweep (blue) and a base temperature power sweep (orange) for a random selection of devices. The base temperature power sweep systematically overestimates $Q_{\mathrm{TLS},0}$.

Figure 13

Plot of extracted quantities versus chosen interface and assumed sidewall angle. Small horizontal perturbations are added to points that share the same horizontal coordinate in order to increase readability of the figure.

Figure 14

Fit to data using a model for loss that includes only a contribution from surfaces.

Figure 15

XPS data of the surface of tantalum films after various surface treatments. Scans are of the $\mathrm{Ta}4f$ (a), $\mathrm{O}1s$ (b), and $\mathrm{C}1s$ (c) spectra. The “no treatment” data are taken after photoresist is stripped from a sample. “Piranha,” “$\mathrm{Piranha}+\mathrm{BOE}$,” and “Triacid” correspond to the “Native,” “BOE,” and “Triacid” surface conditions, respectively. $\mathrm{Ta}4f$ and $\mathrm{O}1s$ data have a Shirley background subtracted [59], and all $\mathrm{C}1s$ data have a linear background subtracted. All data are normalized to the total $\mathrm{Ta}4f$ intensity measured on the sample.

Figure 16

A model for hydrocarbon losses in which BOE and triacid treatments remove residual hydrocarbons left over from photoresist. The native samples suffer from losses from both the native oxide and the hydrocarbons on the MA interface. In the above cartoon, the pink layer is hydrocarbons, and the orange, green, and purple layers are the MA, SA, and MS interfaces, respectively. The BOE diagram corresponds to both the BOE and long BOE treatments, with the difference being the thickness of the oxide layer. This model assumes that piranha cleaning is effective at removing hydrocarbons on the sapphire but not on the oxide surface.

Figure 17

Model estimates provided by the three possible combinations of hydrocarbon-free species. Blue is BOE and triacid, orange is long BOE and triacid, and green is BOE and long BOE. The best fit value is shown in red, with a shaded box to distinguish it from the different extracted estimates. (a) Estimates from $Q_{\mathrm{TLS},0}$ data. (a) Estimates from $Q_{\mathrm{TLS}}(\overline{n}=1)$ data.

Figure 18

An example of a model excluded by our data. Since BOE does not etch sapphire and does not etch hydrocarbons, one possibility is that hydrocarbons reside on the MA and SA interfaces of the native samples and the SA interface of the BOE and long BOE. This model could be achieved if piranha cleaning is ineffective at removing hydrocarbons from the sapphire surface, while the triacid treatment is highly effective. We continue to assume that hydrocarbons are lifted off from tantalum with BOE etching of the oxide. The BOE diagram corresponds to both the BOE and long BOE treatments, with the difference being only the thickness of the oxide layer. The parameter values we extract from this model given our data are unphysical.

Figure 19

(a) $\mathrm{Ta}4f$ spectra for native (blue), 20 min BOE treated (red), 40 min BOE treated (green), and 120 min BOE treated (orange) samples. Data are Shirley background corrected [59] and normalized so the peak height of the ${\mathrm{Ta}}_{7/2}$ metallic peak is unity. (b) Fit to the XPS peaks for the 20 min BOE treated sample. The peaks used to fit the spectrum are doublets of ${\mathrm{Ta}}^0$ (dark blue), ${\mathrm{Ta}}_{\mathrm{int}}^0$ (cyan), ${\mathrm{Ta}}^{1+}$ (green), ${\mathrm{Ta}}^{3+}$ (yellow), and ${\mathrm{Ta}}^{5+}$ (pink). ${\mathrm{Ta}}^0$ and ${\mathrm{Ta}}_{\mathrm{int}}^0$ peaks are fit with asymmetric Voigt profiles; others are fit with symmetric Gaussians. The lower binding energy peak in each doublet corresponds to the ${\mathrm{Ta}}_{7/2}$ spin state and the higher to the ${\mathrm{Ta}}_{7/2}$ spin state [61]. (c) Correlation of oxide photoelectron intensity fit to our lab-based XPS data to the oxide thickness measured in VEXPS [19]. Data (blue) are available from VEXPS for native, 20 min BOE treated, and 40 min BOE treated samples. Green is the best fit line to these data points, extrapolated to the oxide photoelectron intensity fraction of the 120 min BOE treated sample (gray dashed line) to give an estimate of the oxide thickness after a 120 min BOE treatment (orange). Photoelectron intensity fractions are normalized so that the native intensity fraction is unity.

Figure 20

Correlations between all seven fitted parameters used in Eqs. (1)–(3) in the main text. Lower uncertainty bounds in $Q_{\text{other}}$ are truncated to $Q_{\mathrm{TLS},0}$.

Figure 21

Data from a power-temperature sweep that exhibits an exponential decrease in $Q_{\mathrm{int}}$ with temperature across three orders of magnitude, implying the origin of excess thermal quasiparticles is a low $T_c$.

Figure 22

Fitted parameters from Eqs. (1)–(3) in the main text versus surface participation ratio. $Q_{\mathrm{TLS},0}$ is not shown here, as it is shown in Fig. 3 in the main text.

Figure 23

Critical photon number ($n_{\mathrm{sat}}$) at $T=20\mathrm{mK}$ versus surface participation ratio. $n_{\mathrm{sat}}$ is defined in Eq. (h2).

Figure 24

Critical photon number ($n_{\mathrm{sat}}$) at $T=20\mathrm{mK}$ versus fit parameters from Eqs. (1)–(3). $n_{\mathrm{sat}}$ is defined in Eq. (h2).

Figure 25

(a) XRD data from the center and edge of a single tantalum deposition. XRD data taken on a bare sapphire wafer included for comparison. All data taken on a Bruker D8 Discover diffractometer. Solid gray vertical lines are crystallographic planes for tantalum which match our data for the primary copper $\mathrm{K}\text{−}\alpha$ XRD wavelength [64]. Dotted lines are XRD peaks corresponding to the $\alpha \mathrm{Ta}\text{−}(222)$ plane and the copper $\mathrm{K}\text{−}\beta$, tungsten $\mathrm{L}\text{−}\alpha 1$, and tungsten $\mathrm{L}\text{−}\alpha 2$ wavelengths. These wavelengths are also emitted from our x-ray source with less intensity and cause visible secondary peaks offset from primary primary peaks. (b) Power and temperature sweep of a resonator fabricated from the center of the wafer measured in (a). A suppressed $T_C$ is observed despite no $\beta$ phase tantalum being visible in the XRD.

Figure 26

Dependence of $Q_{\mathrm{TLS},0}$ on SPR separated by etch type.

Figure 27

Dependence of extracted $Q_{\text{other}}$ on SPR, separated into devices packaged into the puck and penny assembly, the qcage.24 with bare copper surfaces, and the qcage.24 with aluminum-flashed surfaces. Lower error bars are truncated to the value of $Q_{\mathrm{TLS},0}$.

Figure 28

(a) Dependence of extracted $Q_{\mathrm{TLS},0}$ on SPR, separated into devices fabricated on annealed substrates and those fabricated on unannealed substrates. All devices are treated in BOE for 20 min. No significant difference in performance is seen. (b) AFM image of annealed sapphire surface. Scanned in 512 lines with a 1 Hz scan rate and a 7 mm tip.

Figure 29

Effect of surface morphology on device performance. Tantalum films used in our experiment are deposited by our group or by Star Cryoelectronics, and films from the two different sources show qualitatively different surface morphologies. (a),(b) Example temperature sweeps from devices fabricated with tantalum deposited by our group (a) or Star Cryoelectronics (b). Both devices are BOE treated and have surface participation ratios of approximately ${10}^{-3}$. The color represents input power, with the darkest shade being the highest power. The spacing between powers is 10 dB. (c) Histogram of surface loss tangents from devices fabricated on films deposited by our group (blue) and Star Cryoelectronics (orange). Only devices with a BOE treatment are included. (d),(e) Example atomic force microscopy images showing surface morphology on a film deposited by our group (d) and by Star Cryoelectronics (e). The color scale represents depth.

Figure 30

(a) Results from temperature sweep fitted to a device treated with a rapid thermal anneal followed by a BOE treatment. The calculated surface participation ratio is approximately $2.6\times {10}^{-3}$. The fitted value of $Q_{\mathrm{TLS},0}$ is $(6.97\pm 0.36)\times {10}^5$. (b),(c) XPS data and fits for the $\mathrm{Ta}4f$ peaks performed on native films without (b) and with (c) the RTA process. All data are Shirley background corrected [59] and normalized so the total intensity for the spectrum is unity. The peaks used to fit the spectrum are doublets of ${\mathrm{Ta}}^0$ (dark blue), ${\mathrm{Ta}}_{\mathrm{int}}^0$ (cyan), ${\mathrm{Ta}}^{1+}$ (green), ${\mathrm{Ta}}^{3+}$ (yellow), and ${\mathrm{Ta}}^{5+}$ (pink). ${\mathrm{Ta}}^0$ and ${\mathrm{Ta}}_{\mathrm{int}}^0$ peaks are fit with asymmetric Voigt profiles; others are fit with symmetric Gaussians. The lower binding energy peak in each doublet corresponds to the ${\mathrm{Ta}}_{7/2}$ spin state and the higher to the ${\mathrm{Ta}}_{7/2}$ spin state [61]. There is an approximately 20% decrease in the fitted intensity of the ${\mathrm{Ta}}_{\mathrm{int}}^0$ peaks. Data are taken at the Spectroscopy Soft and Tender 2 (SST-2) end station at the National Synchrotron Light Source II at Brookhaven National Lab with X-ray energy 2000 eV. Data are collected with the same methodology described in Ref. [19].

Figure 31

Examples of representative fits to temperature sweep data. Data are taken from a variety of LE and CPW devices, as well as from native, BOE treated, long BOE treated, and triacid-treated surfaces. Colors indicate circulating power in the feedline, with the darkest shade representing the highest power and the lightest shade the lowest power. All traces are spaced 10 dB apart.

Figure 32

Dephasing experiments on low SPR resonators. (a) Example incoherently (upper) and coherently (lower) averaged signals from a ring down experiment. Solid lines are fits to exponential decays. The fit to incoherently averaged data includes a constant offset to capture the squared noise. (b) Comparison of $Q_{\mathrm{tot}}$ fit to the incoherently and coherently averaged signals for four different resonators. (c) Fitted resonator center frequencies for measurements taken across different times. The vertical axis is the deviation of each data point from the mean. Each panel represents a different resonator.