Fabrication and Characterization of Superconducting Resonators

Podsumowanie

Superconducting microwave resonators are of interest for detection of light, quantum computing applications and materials characterization. This work presents a detailed procedure for fabrication and characterization of superconducting microwave resonator scattering parameters.

Streszczenie

Superconducting microwave resonators are of interest for a wide range of applications, including for their use as microwave kinetic inductance detectors (MKIDs) for the detection of faint astrophysical signatures, as well as for quantum computing applications and materials characterization. In this paper, procedures are presented for the fabrication and characterization of thin-film superconducting microwave resonators. The fabrication methodology allows for the realization of superconducting transmission-line resonators with features on both sides of an atomically smooth single-crystal silicon dielectric. This work describes the procedure for the installation of resonator devices into a cryogenic microwave testbed and for cool-down below the superconducting transition temperature. The set-up of the cryogenic microwave testbed allows one to do careful measurements of the complex microwave transmission of these resonator devices, enabling the extraction of the properties of the superconducting lines and dielectric substrate (e.g., internal quality factors, loss and kinetic inductance fractions), which are important for device design and performance.

Wprowadzenie

Advances in astrophysical instrumentation have recently introduced superconducting microwave resonators for the detection of infrared light.^1-4 A superconducting resonator will respond to infrared radiation of energy E = hv > 2Δ (where h is Planck's constant, v is the radiation frequency and Δ is the superconducting gap energy). When the resonator is cooled to a temperature well below the superconductor critical temperature, this incident radiation breaks Cooper pairs in the resonator volume and generates quasiparticle excitations. The increase in the density of quasiparticle excitations changes the kinetic inductance, and thus the complex surface impedance of the superconductor. This optical response is observed as a shift in the resonance frequency to lower frequency and a reduction in the quality factor of the resonator. In the canonical read-out scheme for a microwave kinetic inductance detector (MKID), the resonator is coupled to a microwave feedline and one monitors the complex transmission through this feedline at a single microwave frequency tone on resonance. Here, the optical response is observed as a change in both the amplitude and phase of transmission⁵ (Figure 1). Frequency-domain multiplexing schemes are capable of reading out arrays of thousands of resonators.^6-7

To successfully design and implement superconducting-resonator-based instrumentation, the properties of these resonant structures need to be characterized accurately and efficiently. For example, precision measurements of the noise properties, quality factors Q, resonance frequencies (including their temperature dependence) and optical response properties of superconducting resonators are desired in the context of MKID device physics,⁸ quantum computing,⁹ and the determination of low-temperature materials properties.¹⁰

In all of these cases, the measurement of the circuit's complex transmission scattering parameters is desired. This work concentrates on the determination of the resonator's complex transmission coefficient, S₂₁, whose amplitude and phase can be measured with a vector network analyzer (VNA). Ideally, the VNA reference plane (or test port) would be directly connected to the device under test (DUT), but a cryogenic setting normally requires the use of additional transmission line structures to realize a thermal break between RT (~300 K) and the cold stage (~0.3 K in this work; see Figure 2). Additional microwave components such as directional couplers, circulators, isolators, amplifiers, attenuators, and associated interconnecting cables may be needed to appropriately prepare, excite, read out and bias the device of interest. The phase velocities and dimensions of these components vary when cooling from room to cryogenic temperatures, and therefore they affect the observed response at the device calibration plane. These intervening components between the instrument and the device calibration plane influence the complex gain and need to be appropriately accounted for in the interpretation of the measured response.¹¹

In theory, a scheme is needed that sets the measurement reference plane, identical to the one employed during calibration, at the DUT. To reach this target, one could measure the calibration standards over multiple cool-downs; however, this poses constraints on the stability of the VNA and the repeatability of the cryogenic instrument, which are difficult to attain. To mitigate these concerns, one could place the necessary standards in the cooled test environment and switch between them. This is, for example, similar to what is found in microwave probe stations, where the sample and calibration standards are cooled to 4 K by a continuous liquid helium flow or a closed-cycle refrigeration system.¹² This method was demonstrated at sub-kelvin temperatures but requires a low-power, high-performance microwave switch in the test band of interest.¹³

An in-situ calibration procedure is therefore desired which accounts for the instrumental transmission response between the VNA reference plane and the device calibration plane (Figure 2) and which overcomes the limitations of the methods described above. This cryogenic calibration method, presented and discussed in detail in Cataldo et al.¹¹, allows one to characterize multiple resonators over a frequency range wide compared to the resonator line width and inter-resonator spacing with an accuracy of ~1%. This paper will focus on the details of the sample fabrication and preparation processes, experimental test set-up and measurement procedures used to characterize superconducting microwave resonators with planar line geometries.¹¹

Protokół

1. Microstrip Line Resonator Fabrication¹⁴ (Figure 3)

1. Clean a silicon-on-insulator (SOI) wafer, which has a 0.45-µm-thick silicon device layer, with freshly mixed H₂SO₄:H₂O₂ (3:1) for 10 min. Then rinse the wafer in deionized water for 10 min and dry with a nitrogen gun. Immediately prior to subsequently processing, dip the wafer in H₂O:HF (10:1) for 10 sec and rinse in deionized water for 5 min.
2. Fabricate a lift-off mask, which consists of a germanium (Ge)/positive photoresist such as S-1811.¹⁵
   1. Spin-coat the wafer with thinned positive photoresist bilayer (2 parts thinner-P : 1 part positive photoresist) at 4,000 rpm for 30 sec and then electron-beam deposit Ge.
   2. Pattern Ge using photo-lithography by first applying hexamethyldisilazane (HMDS) on the wafer for 1 min and then spin off the excess at 3,000 rpm for 30 sec.
   3. Spin on thinned positive photoresist (2 parts thinner-P : 1 part positive photoresist) at 2,000 rpm for 30 sec and bake it on a hot plate for 1 min at 110 °C. Use a mask aligner to expose photoresist and spray develop resist with a tetramethyl ammonium hydroxide-based solution.
   4. Reactive-ion etch the Ge with an SF₆/O₂ plasma at 70 W. Ash underlying photoresist with O₂ plasma to achieve undercut of photoresist.
   5. DC-magnetron sputter-deposit niobium (Nb) ground plane with 3.7 mT of argon (Ar) at 500 W and lift it off by placing the wafer inside an acetone-filled beaker for 4 hr.
3. Spin-coat bisbenzocyclobutene (BCB) at 4,000 rpm for 30 sec on the Nb-coated surface of the SOI wafer and to one surface of another silicon wafer. Bond the two BCB-coated surfaces together with 3 bar of pressure at 200 °C.
4. Manually flip wafer stack upside down to begin processing the backside of the SOI wafer.
5. Etch the silicon handle wafer by mechanical lapping using Al₂O₃ slurry, followed by deep reactive ion etching using the Bosch process.¹⁶ Etch the buried SiO₂ layer with H₂O:HF (10:1) for 20 min.
6. Deposit molybdenum nitride (Mo₂N) using DC magnetron reactive sputtering at 700 W and 3.3 mT (Ar:N₂ partial pressure = 7:1). Pattern resonators by spinning at 2,000 rpm for 30 sec and baking it at 180 °C for 2 min followed by spinning thinned positive photoresist (2 parts thinner-P : 1 part positive photoresist) at 2,000 rpm for 30 sec. Develop photoresist in a tetramethyl ammonium hydroxide-based solution and ash in a reactive ion etcher. Etch Mo₂N with a phosphoric acid-based solution.
7. Fabricate a lift-off mask consisting of a Ge/PMMA bilayer by spinning on the polymethylmethacrylate (PMMA) at 5,000 rpm for 30 sec and baking it at 180 °C for 2 min followed by electron-beam deposition of Ge. Sputter-deposit Nb transmission lines and lift off in acetone (refer to step 1.2 with the exception that the positive photoresist is substituted with PMMA).
8. In some embodiments, radio-frequency (RF) sputter-deposit SiO₂, pattern it by spinning with positive photoresist and etch in a hydrofluoric-acid based solution. Then, lift off a sputter-deposited Nb thin film using a germanium/positive photoresist liftoff mask as detailed in step 1.2.

2. Procedure for Installation of Microwave Resonator Chip in Test Package

1. Design and machine a test package consisting of gold (Au)-coated copper cavity (with a base and lid) which matches resonator chip dimensions, feedline input and output locations. NOTE: The cavity size of the housing should be specified to support a single-mode operation with minimal parasitic coupling over the band of interest.
2. Design and fabricate a controlled impedance microwave fan-out board¹⁷ to route the signals between the chip and Sub-Miniature version A (SMA) connectors.
3. Insert the SMA connectors into the input and output of the test package so that the center conductor pin is aligned over the corresponding fan-out board contact pad. Apply a solder mask to protect against shorting, and apply solder in the region of the center conductor pin. Place the package on a hot plate and heat to 200 °C for ~5 min to melt the solder. Let cool and then remove the solder mask.
4. Mount the resonator chip into the Au-coated copper package cavity such that the on-chip feedline output and input pads are close and aligned to the corresponding fan-out board coplanar waveguide (CPW) lines. Secure the chip with copper clips which make contact at the edges of the corners of the chip.
5. Place superconducting Al wire bonds between the fan-out board and on-chip contact pads. Place a maximum number (~4 in the case presented here — see Figure 4) of ~500-600-μm-long, ~250-µm-in-height wire bonds, to provide impedance match between the SMA connector input and outputs and the on-chip CPW feedline.
6. After wire-bonding, with a multimeter check the DC resistance between the center pins of the input and output connectors, and between a center pin and ground, to confirm there is an electrical connection across the two center pins and an open connection between the center line and ground.

3. Procedure for Installation of Microwave Resonator in a Cryogenic Helium-3 Microwave Testbed

1. Assemble the testbed as in the configuration shown in Figure 2, in which a series of SMA cables are routed from RT to the 0.3-K cold stage where the device will be mounted.
2. Install copper (Cu) and superconducting niobium-titanium (NbTi) cables as shown in Figure 2 to provide low microwave loss and, in the case of the NbTi cables, a low thermal conductance. Use the NbTi cables as a thermal break between the 2-K and 0.3-K stages.
3. Mount a cryogenic high electron mobility transistor (HEMT) amplifier at the 2-K stage on the output line for low-noise amplification in the band of the resonator device and install a circulator.
4. Insert a cryogenic circulator on the output line at the input to this amplifier.
5. Mount the packaged resonator devices onto a bracket bolted to the 0.3-K cold stage.
6. Connect a microwave attenuator on the input side of the package to provide for matched termination and connect the appropriate SMA cables to this attenuator input and package output. Ensure that these controlled impedance terminations are well matched and are as close to the device under test as possible — they define the "device calibration plane" (see Figure 2).
7. Close up the cryostat. Follow standard procedure to cool the devices to 0.3 K.

4. Procedure for Microwave Resonator Measurements

1. Set the VNA to scan over a wide frequency band (10 MHz - 8 GHz, for the device considered here) at the device-under-test design frequencies. Adjust the power levels on the VNA to suitable levels for the device under test (~-30 dBm, for the device considered here).  
   NOTE: Ensure that the input RF power level is low enough so as not to exceed the critical current of the superconducting microwave resonator and superconducting feedline. Ensure that the power level is high enough to provide an adequate signal-to-noise ratio.
2. Calibrate the flexible RF cables following standard Short-Open-Load-Thru (SOLT) procedure, following VNA software directions found in the VNA manual. Insert in shorted, open, terminated and thru standards at the output of each of the flexible cables, which route from the vector network analyzer and which will later be connected to the input of the cryostat for measurements. This calibration defines the "instrument reference plane" (e.g., see Figure 2).
3. Following this SOLT calibration, verify the fidelity of the calibration by confirming that the transmission, S₂₁, with the thru line connected measured with the VNA, has low residual errors (i.e., the response is at ~0 dB level and S₁₁ and S₂₂ are low, e.g., ≤ -50 dB).
4. Connect the flexible cables to the input and output lines of the cryostat.
5. Turn on the cryogenic microwave amplifier by applying the required DC bias voltage as specified in the company-provided documentation for the microwave amplifier.
6. First, complete a wideband scan of VNA (10 MHz - 8 GHz, for the device considered here) to observe the S₂₁ baseline structure and to look for any sharp high-Q structures indicative of microwave resonators.
7. Then, narrow the frequency range (to ~2 - 4 GHz, for the device considered here) and adjust the number of data points (~30,000 for the device considered here) of the VNA to scan over the resonator band. Use a frequency band wide enough to provide an adequate baseline span for later fits to this baseline to carry out an in-situ calibration (see discussion in Introduction).
   NOTE: Depending on the noise level, increase the number of averages, or reduce the IF bandwidth to improve signal-to-noise.
8. Save these VNA data scans of the complex transmission data to file for post-measurement in-situ calibration, and analysis and extraction of quality factors and resonance frequencies.¹¹

Wyniki

The response of a half-wave Mo₂N resonator (Figure 5) fabricated on a 0.45-µm single-crystal silicon dielectric was validated with this methodology. In this instance, coupling to a Nb coplanar waveguide (CPW) feedline for read-out is achieved via capacitive coupling through a sputter-deposited SiO₂ dielectric, in the "H" shaped region at one of the open ends of the resonator (see Protocol section 1.6). In other instances, capacitive coup...

Dyskusje

The single-flip fabrication process provides a means for realizing superconducting resonators on both sides of a thin 0.45-µm single-crystal Si substrate. One may be motivated to use a single-crystal Si dielectric because it has more than an order of magnitude lower loss than deposited dielectrics (such as Si₃N₄) with loss tangents in the 4.0-6.5-GHz range < 1 x 10^-5. ^23-24 The ability to pattern features on both sides of this substrate allows one to employ a microstri...

Materiały

Name	Company	Catalog Number	Comments
Protocol Section 1
Microposit S-1811 Photoresist	Shipley
BCB	Dow		3022-35
SOI wafers	SOITec		Fabricated with SmartCutTM process
Mo	Kamis		99.99%
Nb	Kamis		99.95% (excludes Ta)
E-6 metal etch w/AES	Fujifilm		CPG Grade
Acetone	JT Baker	9005-05	CMOS Grade
HF dip (1:10)	JT Baker	5397-03
PMMA	Microchem		950 PMMA A2
Protocol Section 2
GE 7031	General Electric		Low-temperature adhesive
Protocol Sections 3-4
Cryogenic Microwave Amplifier	MITEQ	AF S3-02000400-08-CR-4	2-4 GHz, gain ~30 dB
NbTi Semi-rigid SMA cables	Coax. Co.	SC-086/50-NbTi-NbTi
Circulator	PamTech	CTD1229K	return loss > -20 dB from 2-4 GHz
RF attenuator	Weinschel	Model-4M	7 dB attenuation
Flexible SMA cables	Teledyne-Storm	R94-240	ACCU-TEST
Vector Network Analyzer	Agilent	N5242A PNA-X
Liquid He-4 cryogen	Praxair
Liquid N2 cryogen	Praxair