Ultrastable millimeter-wave kinetic inductance detectors

Microwave kinetic inductance detectors (MKIDs) are a leading low-temperature detector technology that provide high sensitivity, inherently scale to large-sensor-count arrays, and are well-suited to millimeter/submillimeter/FIR photon detection.^1,2 Since their initial conception nearly 20 years ago, MKID maturity has steadily increased. The NIKA2 camera coupled to the IRAM 30 m telescope is equipped with MKID focal planes regularly used for astronomical observations at millimeter wavelengths.³ Focal planes with detector counts $≳104$ exist^4,5 or are under development^6,7 for multiple experiments. In early MKID work, photon-noise limited sensitivity (also referred to as background-limited performance or BLIP) was hampered by unexpected noise sources, such as contributions from two-level systems (TLS).^8,9 Through advances in materials science, understanding TLS noise scaling, and boosting device responsitivity with engineering choices, MKID sensitivity has rapidly improved. BLIP has been demonstrated by many research groups, in a number of MKID architectures, in both the frequency and dissipation readout quadratures, and by the use of several superconducting materials.^10–13 These demonstrations, however, focused on signal frequencies > 1 Hz. Many millimeter-wave instruments, particularly those mapping large angular fields, require stability on much longer time scales (⁠$τ≳10 s$⁠), and therefore, it is critical to demonstrate suitable performance in the subhertz regime for any millimeter wave detector technology. Ultrastable detectors are particularly important for Cosmic Microwave Background (CMB) polarimeters. Interest in applying MKIDs to CMB measurements has increased due to the integration simplicity and multiplexing advantages relative to other superconducting detector technologies. These advantages are substantial when considering the number of sensors needed for in-development and planned imagers such as the Simons Observatory¹⁴ (∼60 000 superconducting sensors), CCAT-prime¹⁵ (∼200 000 sensors), and CMB Stage IV¹⁶ (⁠$≥500 000$ sensors).

In this Letter, we demonstrate ultrastable photon-noise limited sensitivity down to 50 mHz at $λ=2 mm$ using feedhorn coupled, polarization-sensitive MKIDs made from hybrid TiN and Al films. The design of millimeter-wave MKIDs used in this work has some heritage from the feedhorn coupled, polarization-sensitive submillimeter-wave MKIDs developed for the BLAST-TNG project,¹⁷ which is illustrated in Fig. 1 and has been described in several publications.^12,18,19 Two orthogonal but noncrossing absorber strips, serving also as inductors, are connected to the two interdigitated capacitors (IDCs) forming X and Y polarization-sensitive MKIDs. In BLAST-TNG, the active regions of both the inductive absorber and the capacitor were formed from a $∼1.5 K$ multilayer of stoichiometric TiN and Ti. However, the millimeter-wave MKIDs in this work are hybrid resonators: the IDCs are made from 50 nm stoichiometric TiN, and the inductors/absorbers are made from 30 nm Al films.

The TiN-Al hybrid MKID architecture offers several advantages. First, for efficient optical coupling, the absorber resistance must match the waveguide impedance. The sheet resistance of 30 nm Al is ∼1 $Ω/□$⁠, which is too conductive for coupling at submillimeter wavelengths where the waveguide diameter is small, but is suitable at millimeter wavelengths. Simulation shows that the optimal total series resistance of the absorber distributed across the waveguide aperture lies within the range $rabs*=1−2 kΩ$⁠. A single $1 μm$-wide Al absorber spanning a length of the BLAST-TNG $λ=250 μm$ band waveguide (a diameter of $170 μm$⁠) results in $rabs=170 Ω$⁠, far from the optimal value. The use of narrower or thinner Al strips could in principle improve impedance matching at the expense of fabrication ease, wafer uniformity, and sensitivity to surface oxidation.²⁰ In comparison, however, a $1 μm$ wide Al absorber for λ = 2 mm band (with a waveguide diameter of 1.6 mm) has $rabs=1.6 kΩ$⁠, right in the optimal resistance range. In this work, we have designed 1.5 μm wide Al absorbers and achieved widths of 1.2 μm after wet etch, which produces an effective $rabs≈700 Ω$⁠, after accounting for the two 1.4 kΩ parallel strips (see Fig. 1). Second, the TiN-Si substrate interface has low TLS density,²¹ as evidenced by the high internal quality factor of TiN resonators measured at single-photon power²² and long qubit lifetime measured in a hybrid qubit made from TiN IDCs and Al junctions.²³ Third, stoichiometric TiN has a superconducting transition temperature much higher than that of thin Al (T_c = 4.5 K as compared to 1.5 K), which forms a natural quasiparticle trap to confine the Al quasiparticles to the sensitive absorber/inductor part of the circuit. Fourth, unlike Al, TiN does not form a surface oxide, and therefore, TLS noise is not expected to increase over time.

The MKID devices are fabricated on Silicon on Insulator (SOI) wafers. The $146 μm$ device layer creates a quarter-wave backshort at 150 GHz. Hydrogen fluoride (HF) is used to remove the native oxide,²⁴ and then 50 nm of stoichiometric TiN is deposited via reactive sputtering.²² We etch pockets in the TiN for the Al absorber/inductor with a sloped reactive ion etch that does not aggressively etch the Si and leaves a smooth surface for the Al inductors. After a second HF etch, we sputter 30 nm of Al and use a wet-etch to define the inductors. We then etch the remaining TiN to create the IDCs. At this point in fabrication, the inductor and capacitor are not electrically connected. A 200 nm Al lift-off layer is used to connect these 2 ideal components, which ensures good step coverage and provides a much more robust electrical contact than direct overlapping of the 30 nm Al with the 50 nm TiN film in the connection area. Zoom-in views of this connection area, showing the liftoff patch and the central area of noncrossing X and Y absorbers, may be seen in Fig. 1(c). Next, a 50 nm amorphous-Si (α-Si) passivation layer is deposited by PECVD across the entire wafer to protect Al from oxidation. Vias are etched into the α-Si to access the feedline bondpads. We choose α-Si because it is known to have much lower TLS loss tangent (⁠$∼2×10−4$⁠) as compared to other deposited dielectrics²⁵ available in our cleanroom. Then, the handle wafer is etched from the backside by deep reactive ion etching to the buried oxide layer. The buried oxide is removed beneath the inductor and capacitor to lessen adverse effects from TLS. Finally, Al is sputter-deposited on the backside of the wafer to complete the backshort and provide a ground for the resonator circuit. Figure 1(d) shows a cross-sectional view (not-to-scale) of the layers in the final yielded device with the layer thicknesses noted.

The device package and cryogenic optical measurement setup are similar to those described in Ref. 12 and are shown in Fig. 2(a). The MKID device package is mounted to the 50 mK stage of an adiabatic demagnetization refrigerator (ADR) cryostat. The feedhorns view a beam-filling, temperature controlled blackbody source whose temperature varies between 3.4 K and 20 K. The optical passband is defined by the 120 GHz waveguide cut-off of the feedhorn and a well-characterized 185 GHz low-pass metal-mesh filter²⁶ mounted in front of the feedhorn.

To fully characterize the MKIDs, we first made dark measurements by blanking off the feedhorn in a separate cooldown. Subsequently, we opened the feedhorn to the blackbody for optical-coupling and noise characterizations. The parameters of the 4 resonators on the chip, measured using a vector network analyzer (VNA) in the dark environment and under 3.8 pW optical loading (⁠$Tbb=7.3K$⁠), are listed in Table I. The X-MKID and Y-MKID are located under the feedhorn and are sensitive to X and Y polarizations, respectively. The D-MKID is identical to the X-MKID, but it is not illuminated by the feedhorn, i.e., dark. The N-MKID is another dark resonator that was designed with the same IDC finger/gap but a much wider (10 μm) inductor for measuring the TLS noise contribution (photon noise diluted by the large inductor).

For optical testing, we first measured the complex transmission $S21(f)$ of the X, Y, and D-MKIDs as a function of blackbody temperature (3.4 K $<Tbb<10.4 K$⁠, which produces single-mode optical loads in the range of 0.8 pW $<Popt<6.5$ pW) keeping the bath temperature fixed at $Tbath=150 mK$⁠. The fitted fractional frequency shift $δfr/fr$ response of a detector to the changing optical load is shown in Fig. 2(b). As expected, the dark D-MKID shows very little optical response, approximately 5% of the X-MKID. The Y-MKID shows an $∼20%$ less response than the X-MKID, which can be explained by the smaller kinetic inductance fraction due to the additional geometric inductance from the semicircle leads to the Y-absorbers [see Fig. 1(a)].

For each optical load, we measure noise at the microwave frequency, which maximizes $δS21/δfr$ using the standard homodyne measurement scheme.²⁷ A SiGe low-noise amplifier with an $∼5$ K noise temperature mounted at 3 K is used to amplify the MKID signals. The power on the feedline is $∼−95$ dBm, chosen to be at least 3 dB below bifurcation, thus avoiding strong nonlinear effects in the resonator.²⁸ Time domain data are digitized at 2.5 Ms/s with an antialiasing low pass filter at 1 MHz, and a linear drift is removed from the time-stream. Next, we project the raw in-phase and quadrature components of the data into the frequency and dissipation quadratures and examine the noise in the frequency quadrature. The noise analysis procedure is described in Refs. 27 and 29.

Representative fractional frequency noise spectra measured under 3.8 pW optical load at $Tbath=150$ mK are plotted in Fig. 3(a). The spectral shape is white with a Lorentzian roll-off, as expected from photon noise. For both X and Y-MKIDs, the white noise is flat even at 50 mHz (the minimum frequency of the plot), demonstrating high stability and BLIP well below 1 Hz; no common mode subtraction has been applied to the data. Furthermore, we have measured “1/f-noise free” spectra similar to Fig. 3(a) for $Popt≤$ 4 pW and $150 mK≤$ $Tbath≤$ 200 mK without applying common subtraction to the data. Similar spectra are also measured even when the detector is only illuminated by the stray light present in the cryostat. However, at lower $Tbath$⁠, TLS noise begins to contaminate the low frequency end of the spectrum. At higher $Popt$ and/or $Tbath$⁠, the measurement requires better temperature control stability (for both the bath and the blackbody) than our current setup can provide. We plan to improve temperature stability in the future.

We attribute the superior photon-noise limited performance at millihertz frequencies to the implementation of four TLS noise reduction strategies. First, the TiN IDC takes advantage of the low-TLS TiN-Si interface. A similar strategy was adopted by Janssen et al.¹¹ They reported a factor of $∼10$ reduction of TLS noise in a hybrid NbTiN/Al MKID as compared to an all-Al nonhybrid device. Second, we operate at a relatively high bath temperature of 150 mK to take advantage of the temperature dependent TLS noise effect.³⁰ To demonstrate the effectiveness of this strategy, we measured the noise levels of the N-MKIDs in a bath temperature sweep, and the result is plotted in Fig. 3(b). All resonators show a factor of $∼5$ reduction in noise as $Tbath$ increases from 75 mK to 150 mK. Third, we use a wide IDC finger/gap of 10 μm to take advantage of the geometric dependence of TLS noise.^8,31 In Fig. 3(b), the noise from the 10 μm-IDC device is a factor of $∼ 2$ lower than the 5 μm-IDC device, consistent with the $S−1.6$ width dependence of TLS noise found in CPW resonators.⁸ With the above 3 strategies (10 μm TiN IDC at 150 mK), the TLS noise contribution in the N-MKID has been aggressively suppressed to lower than $10−18/Hz$⁠, as shown by the red spectrum in Fig. 3(a). In the fourth strategy, we have further maximized the IDC area (1.5 mm × 2.5 mm) and capacitance (9 pF) in the X and Y-MKID designs. This has two effects. On the one hand, because the noise contribution of TLS fluctuators is expected to be spatially uncorrelated, the total noise of the capacitor should scale as 1/A, where A is the area of the capacitor. On the other hand, the large capacitance drives down the resonance frequency, which also helps to reduce TLS noise because the TLS noise is expected to have a generalized frequency-temperature dependence on $hfr/kBT$^2,30 according to TLS physics.²⁷ This dependence has not, however, been quantitatively studied. Because the capacitor area and value of the X and Y-MKIDs are a factor of 3 larger than the N-MKID [see Fig. 1(b)] and the frequencies are a factor of 2 lower, we expect the true TLS noise contributions in the IDCs of the X and Y-MKIDs to be at least an extra factor of 3 below the plotted red spectrum in Fig. 3(a), which corresponds to a factor of 10 below the photon noise level at 50 mHz. Additionally, the amplifier noise contribution is also over a factor of 10 lower than the photon-noise level, as indicated by the tails above 100 kHz in Fig. 3.

To evaluate the effect of the α-Si passivation layer, samples of N-MKIDs fabricated with and without α-Si coating were measured. As shown in Table I, all the passivated devices exhibit $Qi>300 000$⁠, substantially higher than the Q_i under optical load. Surprisingly, we find that the coated resonators show lower noise than the bare resonators. The cleaning step before the α-Si deposition may have played a role or the α-Si layer may have pushed surface contaminants 50 nm further from the sharp edge of IDC fingers, where the noise is most sensitive to TLS. We plan to investigate this in the future.

With the measured optical response shown in Fig. 2(b), and the noise levels under different optical loads, we have obtained the measured noise equivalent power, $NEPmea2$⁠, which is plotted in Fig. 4. The photon-noise limited NEP for our millimeter-wave MKIDs, including quasiparticle recombination noise, is³² 

where ν is the mean photon frequency, $Popt$ is the calculated single-mode power in a top hat band over the frequencies of 120 GHz–185 GHz from a thermal source at temperature T, η is the optical efficiency, and B is the 65 GHz optical bandwidth. In the derivation of Eq. (1), a pair breaking efficiency of $ηpb=2Δ/hν$ is assumed because the entire optical band falls with the range of $2Δ/h$ and $4Δ/h$⁠.³³ In comparison, the “photon-only” NEP without recombination noise contribution is

which is smaller than Eq. (1) by the recombination noise contribution of $2hνPopt/η$⁠.

By fitting the measured NEP to Eq. (1), we determine that the optical efficiency of the X-MKID (Y-MKID) is 28% (38%). This difference mainly arises from the different absorber geometry in the design [Fig. 1(a)] and is consistent with EM simulations results. These values are lower than previously published feedhorn-coupled submillimeter-MKIDs (⁠$∼70%−80%$⁠)^12,18 and result from a combination of factors. The 43% fractional bandwidth (dictated by the available feedhorn/waveguide and free-space low pass filter) is larger than our submillimeter MKID demonstrations, and the absorber was not optimized for this larger band. The realized absorber impedance (⁠$rabs∼700 Ω$⁠) is a factor of ∼2 lower than optimal. Finally, this detector packaging lacks a choke at the waveguide exit. Increasing the optical efficiency is the subject of future research. We plan to implement narrower absorber strips (⁠$∼0.8μm$ width using optical lithography) or investigate meandering absorber structures as others have done.³² 

Figure 4 also shows the calculated photon-limited noise levels with perfect optical efficiency η = 1 with (black) and without (red) recombination noise contribution. The former is the best achievable sensitivity of pair-breaking detectors (appropriate for MKIDs), and the latter is the best achievable sensitivity for any detector. One way to suppress the recombination noise is to use a smaller superconducting gap, an important future research direction for CMB applications of MKIDs.³⁴ 

In conclusion, we have demonstrated ultrastable photon-noise limited sensitivity down to 50 mHz at millimeter-wave wavelengths using feedhorn coupled, polarization-sensitive MKIDs made of TiN IDCs and Al inductors covered by a thin layer of amorphous-Si. The superior noise performance is achieved by the implementation of several TLS noise reduction strategies, including wide and large area TiN IDCs as well as operating at relatively high bath temperatures. These measures take advantage of the material, geometry, temperature, and frequency dependence of TLS noise. This suppression of TLS noise also benefits other superconducting high-Q resonators such as in quantum computing.

We acknowledge funding through the NASA Astrophysics Research and Analysis Program Solicitation Number: NH17ZDA001N-APRA. These devices were fabricated in the NIST-Boulder microfabrication facility.