Development of an Array of Kinetic Inductance Magnetometers (KIMs)
Sasha Sypkens, Farzad Faramarzi, Marco Colangelo, Adrian Sinclair, Ryan Stephenson, Jacob Glasby, Peter Day, Karl Berggren, Philip Mauskopf
DDevelopment of an Array of Kinetic Inductance Magnetometers(KIMs)
Sasha Sypkens , Farzad Faramarzi , Marco Colangelo , Adrian Sinclair , RyanStephenson , Jacob Glasby , Peter Day , Karl Berggren , and Philip Mauskopf School of Earth and Space Exploration, Arizona State University Department of Physics, Arizona State University Department of Electrical Engineering and Computer Science, Massachusetts Institute ofTechnology School of Electrical, Computer, and Energy Engineering, Arizona State University Jet Propulsion Laboratory
Abstract
We describe optimization of a cryogenic magnetometer that uses nonlinear kinetic inductancein superconducting nanowires as the sensitive element instead of a superconducting quantuminterference device (SQUID). The circuit design consists of a loop geometry with two nanowiresin parallel, serving as the inductive section of a lumped LC resonator similar to a kinetic induc-tance detector (KID). This device takes advantage of the multiplexing capability of the KID,allowing for a natural frequency multiplexed readout. The Kinetic Inductance Magnetometer(KIM) is biased with a DC magnetic flux through the inductive loop. A perturbing signal willcause a flux change through the loop, and thus a change in the induced current, which alters thekinetic inductance of the nanowires, causing the resonant frequency of the KIM to shift. Thistechnology has applications in astrophysics, material science, and the medical field for read-out of Metallic Magnetic Calorimeters (MMCs), axion detection, and magnetoencephalography(MEG). a r X i v : . [ phy s i c s . i n s - d e t ] J a n ntroduction Highly sensitive magnetic sensors are useful in many fields, particularly inastronomy, medicine, and geology. [1, 2, 3] Currently, the SuperconductingQUantum Interference Device (SQUID) is the most sensitive magnetometer,with a sensitivity of f T / √ H z [3]. Arrays of SQUIDs have been used for timedivision multiplexing (TDM) of superconducting detectors for over a decade[4]. However, scaling to the increasing number of detectors used in moderninstruments is challenging partly because the SQUID requires multiple layersduring fabrication, which increases time and cost to make arrays [5]. A recentdevelopment called µ MUX attempts to couple each SQUID to a correspondingtransmission line resonator to achieve frequency domain multiplexing (FDM)with a high multiplexing factor. This uses an RF SQUID coupled to a modu-lation coil to counteract the periodic nature of the device, and a load inductorto couple to the resonator for readout. Each resonator has a unique resonantfrequency, and is shifted by the change in inductance in the RF SQUID [6] [7][8].In addition to improving SQUID readout, there has been some publication onusing Dayem bridges instead of Josephson Junctions. [9] Using a Dayem bridgeand a small SQUID diameter, one group was able to achieve 50 n Φ / √ H z [10]Furthermore, it has been shown that kinetic inductance rather than magneticinductance can modulate nanoSQUIDs, effectively reducing the size of the de-vice by an order of magnitude. [11]Alternatively, two groups independently developed a superconducting mag-netic sensor that uses nanowires with high kinetic inductance instead of Joseph-son Junctions as the sensing component [5] [12]. These devices are similar tothe Lumped Element Kinetic Inductance Detector (LEKID) in that they areplanar lumped element devices and use superconductors which have high non-linear kinetic inductance. However, they have not been able to achieve SQUIDsensitivity or develop an array of magnetometers. This paper aims to demon-strate an array of KIMs read out using FDM and a discussion on its sensitivity.The KIM can be used for magnetic field sensing, direct readout of magneticx-ray detectors, and current-coupled readout. [5] [12] [13]
Operating Principles
The kinetic inductance of a nonlinear superconducting thin film in which thethickness, t is much less than the penetration depth, λ can be expressed by k = L k (0) (cid:18) I b I ∗ + ... (cid:19) , (1)where I ∗ is the characteristic current dependent on the material and geometry ofthe film that sets the nonlinearity of the film, and L k (0) is the kinetic inductanceof the superconductor with no bias current, I b . The superconductor is at itspeak nonlinearity when biased close to I ∗ .When formed into a loop, the superconductor obeys the following expression: Φ b − LI s = n Φ , (2)in which I s is the shielding current induced by the bias field, the total induc-tance, L = L k + L g includes the geometric term and the kinetic inductance ofthe material, Φ b is the bias flux, and n is an integer multiple of Φ , the fluxquantum. When the loop is biased with a magnetic flux perpendicular to itsplane, the superconductor generates an opposing shielding current, which fromlooking at Eq. 1, determines the kinetic inductance. If there is a perturbationin the flux, the kinetic inductance of the loop will change. When the loop isincorporated into a resonator, the change in kinetic inductance can be seen asa shift in resonance, ω r = 1 / √ LC . [5] [12] [13] TL TL C c C r NWNW - Φ b + Z Z L Figure 1: Circuit diagram of a KIM
Experiment
Design
The KIM is a microwave resonator cou-pled to a CPW transmission line via an in-terdigitated coupling capacitor. The res-onator consists of two nanowires acting as in-ductors in parallel with an interdigitated res-onant capacitor. Both capacitors are inter-digitated to reduce two-level system (TLS)noise and the geometry of the nanowires arekept small ( w ≈ t ≈ α , the kinetic inductance fraction of thedevice. TLS noise originates from couplingbetween the resonator and electric dipolemoments on the substrate/superconductorinterface. [14] [15] There are four chips, each with an array of 8 resonators, where theresonant capacitor varies in each device. NbN was chosen to be the device material due toits high kinetic inductance. The nanowire length for each array was chosen to be 250nm,500nm, 750nm, and 1 µ m. a) optical micrograph
200 μm 56 nm (b) SEM of one resonator
Figure 2: Optical and scanning electron micro-graphs of the fabricated device. The dark portionin b) is NbN and the light portion is the substrate.The nanowire is also highlighted in white in thesecond SEM image.
Fabrication
The KIM arrays were fabricated from a ≈ . -thick niobium nitride (NbN) film.NbN was reactively sputtered at room tem-perature on a high-resistivity silicon wafer[16]. The room-temperature sheet resistancewas R s ≈
165 Ω per square, the critical tem-perature was T c = 8 .
74 K , and the criti-cal current was roughly 50 µ A. The arrayswere patterned using
125 kV -electron beamlithography with ZEP530A positive tone re-sist. The patterns were transferred into NbNwith CF reactive ion etching (more fabrica-tion details are reported in previous publi-cations on superconducting nanowire singlephoton detectors [17, 18]). Fig. 2 shows op-tical and scanning electron micrographs ofthe fabricated device. Test Setup
An in-house Helmholtz coil made withsuperconducting wire and calibrated with acommercial hall sensor was used to bias the
Coax DUT CoaxCoaxDC BlockCoax CoaxDC BlockCoaxVNA300K40K4KMagnetic Shield Φ b Figure 3: Test Setup of the DUT with a magneticflux bias, Φ b . The coaxial cables use a combina-tion of stainless steel (300K to 3K stages) and cop-per (outside of the cryostat and at the 3K stage)cables. The cold amplifier is a lab made LNA with10K noise temperature and 30dB of gain, and theroom temperature amplifier is from mini-circuits. resonators. The Helmholtz coil and devicewere wrapped with Nb foil on the 3K testbedto shield them from environmental magneticfields. The magnetic bias and shield are indi-cated next to the DUT in Fig. 3. To read outthe KIM array, an attenuator and low noiseamplifier (LNA) are placed on either side ofthe DUT, with coax cables leading on eitherend to the VNA. The DC blocks shown inthe same figure are inner/outer blocks to actas thermal breaks. Results and Discussion
Temperature Response
Fig. 4 shows the temperature responseof a resonator from the 1 µ m array with a -85dBm input power at the device. [19] Thisbehavior is expected because it is seen frommeasurements taken from a typical LEKIDarchitecture. At the lowest temperature(3K), the internal quality factor for all ofthe resonator arrays was around 4,000 withthe total quality factor heavily dominated µm -long array as a function of temperaturegoing from 3K to 5K. The top image shows S and the lower image shows the response in phasespace. by the coupling. Magnetic Response
The responsivity of a KIM is how muchthe resonant frequency shifts with a mag-netic field bias, df /f dB . As stated pre-viously, the resonant frequency shifts as afunction of inductance, and so (cid:18) f dfdB (cid:19) ∝ − δLL = − α δL k L k , (3)where α is the kinetic inductance fraction, L k / ( L k + L g ) . The kinetic inductance termcan be seen as the kinetic energy divided bythe pairing energy [20], E k E p = L k I N ∆ V , (4)in which N is the single-spin density ofstates, ∆ is the band gap energy of the su-perconductor at T=0, and V is the volumeof the nanowires. Solving for I s in equa-tion (2), taking into account there being twonanowires, and plugging it in to the equationabove, the responsivity becomes R = αL k N ∆ V (cid:18) Φ b − n Φ L k (cid:19) . (5)Doing some simple term cancellation showsthat L k should be high enough for α ≈ but not more than necessary because it isinversely proportional to responsivity.The above equation also shows that once Φ b = n Φ , responsivity goes to 0, indicating that the nanowires have turned normal and atthat point in time, 174 flux quanta enter the loop before the nanowires turn superconductingagain. This behavior is periodic in that the response starts over after each nanowire-turn-normal event.The magnetic response of one resonator and a comparison of responsivity and calculatedflux noise based on nanowire length are plotted in Fig. 5. In image (a), the resonant frequencywith no magnetic field bias is 2.045GHz, and the resonant frequency shifts downward as themagnetic field is increased. At 1.25 µ T, the resonant frequency shifts maximally, and if biasedfurther would shift back up to the original value, indicating the nanowires turn normal andlet in some flux quanta before turning superconducting, again. Based on the geometry ofthe loop, 174 flux quanta enter the loop at each period. a) Magnetic Response Fit: 1 µ m long nanowire (b) Calculated Responsivity and Flux Noise Figure 5: KIM data. a) magnetic response with fit of resonator 3 in the 1- µm -long array, b) calculated responsivity when biased near I ∗ (red + sign) and flux noise (blue dot) for allarrays (250nm, 500nm, 750nm, 1 µ m long nanowires). The magnetic response fit equation in image (a) is f r = − B a − B b , (6)where a = 9 . nT /GHz and b = 1 . nT /GHz are the fit parameters and f r is the resultantresonant frequency from the magnetic field bias. [5] The nonlinearity from Eq. 1 can be seenin the responsivity at higher applied magnetic field.In Fig. 5, image (b) compares the response of all four arrays, one being for calculated fluxnoise and the other for responsivity. It can be seen that flux noise is inversely proportionaland responsivity is directly proportional to nanowire length. This is because the nanowire’szero-bias kinetic inductance increases with length, thereby decreasing responsivity. This inturn corresponds to lower noise because it is inversely proportional to responsivity, as canbe seen by calculating the equivalent total flux noise power spectral density at the input ofthe KIM, S B = (cid:18) f dfdB (cid:19) − k B T a Q P , (7)where k B is the Boltzmann constant, T a is the amplifier noise temperature, Q is the qualityfactor of the resonator, P is the input power, and dfdB is the responsivity calculated from themagnetic response fit in image (a). One should note that the calculation assumes the systemis dominated by the amplifier noise because other sources such as TLS noise is considerablysmaller from the use of IDCs. [5] The calculations in Fig. 5 (b) for the flux noise used aninput power of -79dB. From there, the flux noise can be easily converted from magnetic fieldnoise. For the 1 µ m array, the flux noise was calculated to be roughly 7.5 µ Φ / √ Hz . Conclusion and Future Work
Noise measurements were taken using the Keysight E5072A VNA by settingthe center frequency to a 0Hz span and the IFBW to 100kHz for a nyquist andwidth of 50 kHz. Unfortunately, the data shows that the system wasdominated by the noise of the VNA. To mitigate this effect from future noisemeasurements, more amplification will be used after the cold amplifier than the13dB warm amplifier that was used for this measurement. Additionally, we willuse a ROACH2 with MUSIC-DAC/ADC readout system [21] and an amplifierwith lower noise temperature than the one that was used for this measurement(10K noise temperature).Of the resonators measured, the highest responsivity was in the 1 µ m arrayat 28MHz/ µ T, corresponding to a calculated flux noise of 7.5 µ Φ / √ H z . Tocompare to a SQUID, its noise would need to be 1 µ Φ / √ H z . [5]In this experiment, the thickness of the entire resonator, both the nanowiresand the remaining components, was the same at roughly 17nm. To ensurethe device is only affected by the nanowires, a different fabrication processneeds to be implemented so that the nanowires are thin and everything elseis either thicker or a different material that does not have high kinetic induc-tance. Optimizing the design in this way will reduce the flux noise to lowerthan 7 µ Φ / √ H z . Furthermore, the average internal quality factor of these res-onators was around 4,000, with the coupling factor reducing the total qualityfactor by an order of magnitude. Although the coupling needs to change fora higher total quality factor, measuring these resonators at 800mK instead of3K would greatly improve their quality. Lastly, the magnetic shield was justNb foil wrapped around the device and Helmholtz coil, which led to large gapsin shielding at the input and output of the DUT. Another goal is to design aproper magnetic shield for the setup.
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