A microwave SQUID multiplexer optimized for bolometric applications

For many scientific applications involving photon-sensing low-temperature detectors, measurement sensitivity is limited by fluctuations intrinsic to the signal of interest. As such, experiments implement arrays of photon-noise-limited sensors to improve the signal-to-noise ratio. The array size is limited by the ability to combine signals into a manageable number of output wires to transmit signals from the cryogenic stage to the room temperature readout electronics. For power-sensing instruments based on transition-edge-sensors (TESs), time-division multiplexing (TDM)¹ and megahertz frequency-division multiplexing (FDM)^2,3 are well-established techniques, which to date have been used in fielded experiments to combine a maximum of 68 sensors into one wiring/amplification chain.^4,5 The many instruments that require thousands to hundreds of thousands of bolometers^6–11 stretch the capability of these established techniques, which are fundamentally limited by their ∼10 MHz output channel bandwidth. To increase the number of sensors per wiring/amplification chain (here referred to as the multiplexing factor) and enable more sensitive bolometric arrays, multiplexing techniques that make use of the microwave readout band are under development. These techniques include microwave kinetic inductance detectors (MKIDs),¹² kinetic inductance parametric upconverters (KPUPs),¹³ and the subject of this Letter, the microwave superconducting quantum interference device (SQUID) multiplexer (μmux).^14–18 Application to calorimetric instruments has been previously described.^19,20 Here, we focus on bolometric applications, with a particular emphasis on measurements of the cosmic microwave background (CMB). Preliminary work has demonstrated the feasibility of the μmux for CMB measurements.²¹ The MUSTANG2²² 90 GHz receiver coupled to the Greenbank Telescope (GBT) operates using a 4 × 64 channel μmux readout. In addition, a Keck Array receiver has been retrofitted with an 8 × 64 channel μmux readout and has spent a season observing the CMB at 150 GHz.²³ In this Letter, we present a μmux100k multiplexer chip that has been optimized for the readout of TES bolometers. Multiple frequency-scaled versions of this chip can be combined to form a nearly 2000 sensor multiplexer within one octave of rf bandwidth.

The principle of operation of the μmux has been described in previous publications.^14,15,19,24 Briefly, an rf-SQUID transduces a dc-biased TES signal into the frequency shift of an approximately gigahertz quarter-wave resonator. Each TES is coupled to its own SQUID-coupled resonator that has a unique resonant frequency. All resonances are coupled to a common co-planar waveguide (CPW) microwave readout line. An additional source of SQUID flux is ramped to linearize the SQUID response under the paradigm of flux-ramp modulation.²⁴ 

The μmux100k multiplexer represents a significant departure from previous work^15,19,21 and has been influenced by its application to the Simons Observatory,⁶ a set of CMB imagers sensitive to a broad range of angular scales. In general, the multiplexer architecture achieves an 1820 multiplexing factor within a 4–8 GHz readout band. All components are designed to fit within a two-dimensional plane behind a 150 mm detector wafer, which aids in tiling multiple wafers into a single focal plane.²⁵ The readout contributes <5% to the overall noise of the detectors, which translates to an input-referred current noise of 45 pA/$Hz$⁠. The maximum crosstalk between readout channels is < 0.3%. Finally, the absolute frequency placement of the resonators is designed to match the usable rf bandwidth of the room temperature electronics.²⁸ 

Figure 1 shows the μmux100k multiplexer chip, which satisfies the criteria stated in the previous paragraph. Each 4 × 20 mm² chip has 65 readout channels plus one resonator without a SQUID. Multiple frequency-scaled versions of the μmux100k chip may be connected in series (“daisy-chained”) via aluminum wirebonds to create a larger multiplexer. The resonator without a SQUID is intended to track the two-level system (TLS) noise of the resonators. The user may opt to leave one of the 65 readout channels disconnected to track both the readout noise of the system and magnetic pickup in the SQUIDs.

Table I summarizes the chip specifications. A key distinction relative to previous multiplexers is the reduced resonator bandwidth (BW = 100 kHz), which lends the multiplexer version its name (μmux100k). The BW is controlled by adjusting the capacitive coupling (Q_c) to the CPW feedline and has been chosen to maximize the number of channels within one octave of readout bandwidth while considering both the signal bandwidth and the flux ramp rate needed to overcome sources of 1/f noise. Q_c is set by varying the length of the three fingers, which define the interdigitated capacitor (IDC). A four-lobe gradiometric SQUID²⁶ is utilized to reduce sensitivity to external magnetic fields. The TES input mutual inductance (M_in) is set by a loop winding through all four lobes, while the flux ramp mutual inductance (M_fr) is set by a smaller loop winding through the lower two SQUID lobes. The resonant frequency (f_o) is periodic with applied flux, and the peak-to-peak frequency swing (df_pp) is set to match the resonator BW by tuning the SQUID-to-resonator coupling (M_res). This is tuned by varying the size of a coil, which winds through the upper two SQUID lobes.

The resonant frequencies and spatial resonator layout are designed to achieve high spatial density while suppressing several sources of crosstalk. The design principle is to distribute resonators such that spatial neighbors are largely separated in frequency space, and frequency neighbors are largely separated in spatial distance.²⁷ We include several frequency gaps that guard against frequency collisions, which may arise due to intra-wafer variation. Additionally, there are 38 MHz wide frequency gaps every 500 MHz to accommodate the input quadruplexers of the SLAC Microresonator Radio Frequency (SMuRF) room-temperature electronics.²⁸ These choices lead to a non-uniform resonator frequency schedule, which repeats every 500 MHz and spans 3.5 chips. Each of the 66 channels comprising a single multiplexer band is split into two halves and placed into upper and lower rows of resonators to maximize spatial density of the channels (see Fig. 1). In each half band, the 33 channels are grouped into two additional subbands of 17 and 16 channels that are interleaved in spatial distance on the chip. Within a subband, resonators are spaced by $Δf$ =1.8 MHz, the minimum designed frequency spacing. Between subbands, half-bands, and bands, there are additional fixed gaps of 3.06 MHz, 4.5 MHz, and 6.3 MHz, respectively. This grouping results in either a 32.0 MHz or 65.7 MHz space between nearest spatial neighbors and > 31.7 MHz for next-nearest neighbors. Frequency adjacent channels are spaced 1 mm apart. With this configuration, we simulate in Microwave Office a maximum crosstalk of 0.2%, dominated by nearest-frequency-neighbor resonator-to-resonator crosstalk. Other sources of crosstalk contribute less than <0.1%.

As with all FDM systems, resonator frequency collisions or omissions complicate mapping resonant frequencies to optical pixels, which is required in most instruments. The chips measured in this Letter demonstrate no collisions or resonant frequency swapping and only four missing resonators. The limited number of missing resonators, coupled with the resonance grouping technique outlined here, limits these concerns to a manageable level for the demonstrated frequency density. Full screening of multiplexer chips before integration in larger instruments can also aid frequency to pixel mapping.

Device fabrication largely follows the description in the work of Mates.¹⁵ In brief, these devices are fabricated on 3 in. diameter high-resistivity silicon wafers, which are covered with a minimal layer (20 nm) of $SiO2$ in an effort to reduce its TLS noise contribution. First, the Josephson junction process begins with depositing a trilayer of niobium (200 nm), aluminum (∼7 nm), which is partially oxidized to form the insulating barrier, and niobium (120 nm). The top two layers are etched away to form the 2.5 × 2.5 $μm2$ junction pillars, with the bottom constituting the first wiring layer where the majority of the circuitry is defined. Next, a $SiO2$ insulating layer (350 nm) is deposited. Etching holes through this layer allows for the creation of vias. An additional niobium layer (300 nm) is deposited to connect the junctions to the first wiring layer and to create the CPW feedline ground-straps. In the penultimate step, all $SiO2$ is etched away wherever possible to reduce TLS noise. The CPW resonators are etched in the final step of fabrication so that no other process can contaminate the resonant cavity. To efficiently microfabricate ∼2000 unique resonant frequency cells, we employ a lithographic stepper-based fabrication technique, similar to the tile-and-trim approach for fabricating MKIDs.²⁹ With reference to the schematic in Fig. 1, all CPW resonators within a half-band are flashed by a single image that consists of w CPW meander turns and s unexposed turns. Resonant frequencies are subsequently defined by shooting a second image, which completes the s turns with a reduced turn length δ, that realizes a unique CPW length. There is a factor of ∼6 reduction in nearest-neighbor frequency scatter when employing this technique relative to shooting all resonators on a chip with a single, large mask. Additionally, re-configuring the frequency schedule to optimize from one fabrication round to the next, or even to meet the needs of an entirely different experiment, requires only a new stepper job file. New mask generation is not required.

To test this architecture, we assembled a seven-chip multiplexer spanning 4–5 GHz into a copper device box¹⁹ and installed the package into a $He3$-backed adiabatic demagnetization refrigerator (ADR) cooled to 100 mK. The experimental setup detailing the rf wiring is shown in Fig. 2. We used a commercial vector network analyzer (VNA) for microwave transmission measurements. For noise and crosstalk measurements, we operated the SMuRF room-temperature electronics with a 20 kHz SQUID modulation rate and utilized resonator tone-tracking.²⁸ This resulted in a 4 kHz effective sampling rate, which we further down-sampled to 200 Hz. Resonances were interrogated with microwave probe tone powers near –73 dBm (referred to the input of the multiplexer chip feedline), which is near optimal for noise performance.

Figure 3 presents a frequency survey and the channel statistics based on these data. We fit the complex transmission of each resonance to a model³⁰ and determine the resonator parameters f_o, internal quality factor (Q_i), and BW. We identified 458 resonances out of a possible 462. The mean resonator spacing is 1.9 MHz, which is close to the design goal. All resonator pairs are separated by >3 $×BW$⁠, which we deem collision-free. The mean Q_i = 128 348 is generally consistent with our experience in multiple rounds of μmux100k fabrication. The mean BW = 115 kHz is 15% higher than the designed value and is a result of the coupling quality factors (Q_c) being chosen with the assumption that $Qi=200 000$⁠. In summary, we expect >99% initial multiplexer channel yield from these measurements, which is typical of these devices.

To determine the noise performance of the multiplexer, the TES inputs were left open and 800 s of data were simultaneously streamed from the channels within the first 500 MHz of rf bandwidth. Of the possible 227 channels, the electronics successfully tone-tracked 205, for a yield of 90.3%. The remaining 22 channels were disabled by the SMuRF due to improper automatic resonator calibration. Several of these channels may be recoverable with better resonator tuning parameters. A linear drift subtraction was the only time-domain data processing step. For each resonator, we compute the amplitude power spectral density using multiple Welch periodograms at several frequency resolutions. The SMuRF tracking algorithm natively returns the flux-ramp demodulated phase (⁠$ϕ$⁠) in radians. We convert the demodulated phase noise (⁠$Sϕ$⁠) to input current noise (S_I) [or equivalently noise equivalent current (NEI)] by use of the relation

where $Φo$ is the magnetic flux quantum and M_in is the mutual inductance between the rf SQUID and the TES. Figure 4 presents the results. The median white-noise level is 45 pA/$Hz$⁠. The 1/f knee, defined as the frequency at which the noise is twice the white-noise level (evaluated between 50 and 100 Hz), is 64 ± 31 mHz. When subtracting one readout channel's timestream from all others (a naive form of common-mode subtraction) and computing the power spectral densities, the peak in the 1/f knee histogram reduces to ∼20 mHz. The true value may be lower still because the measurement is limited by the 800 s measurement time. We note the naive common-mode subtraction is valid in the limit that all channels have the same gain. Equation (1) shows that M_in is the single parameter that governs the gain. Variation of this parameter is geometry-dependent and set by micro-lithography. We simulate via FastHenry the maximum over-etch possible during lithography (100 nm), which produces <0.8% deviation from the designed value. The absence of the 60 Hz line in the common-mode subtracted power spectrum suggests that this assumption is true.

These measured noise characteristics are highly favorable for measurements of the cosmic microwave background. The expected photon noise of a 150 GHz channel in a ground-based⁸ CMB experiment with a 3.10 pW photon load is 30.5 aW/$Hz$⁠. Similarly, the expected photon noise for a satellite-based³¹ experiment with a 0.46 pW load is 9.77 aW/$Hz$⁠. To put the noise equivalent power (NEP) of these experiments in context of the current noise of the multiplexer, we use the following equation:

which assumes an ideal bolometer in the high-loop gain limit with the electrical power (P_e) equal to 1.5 times the optical power and the bolometer operating resistance R_o = 4 mΩ. Significant deviations in sensor resistance from 4 mΩ may require changing M_in in order to maintain the stated performance. The measured multiplexer white-noise level is one fifth and one fourth of the expected current noise for the ground and satellite-based experiments. Therefore, the multiplexer decreases the sensitivity to photon noise by only 2% and 3%, respectively, for the ground and satellite cases. Furthermore, the low 1/f knee provides access to large angular scale measurements, which are required for CMB B-mode polarization searches.

As in any multiplexer, combining multiple signals into one wiring/amplification chain may lead to unwanted sources of crosstalk between signal channels. Sources of crosstalk particular to the microwave SQUID multiplexer are discussed by Mates et al.²⁷ To quantify the crosstalk of the μmux100k multiplexer, a single chip was packaged in a device box and installed in a separate ADR cryostat with rf wiring similar to that shown in Fig. 2 and readout with tone-tracking via SMuRF. The sum of a dc and sinusoidal current was injected into a single channel's input (referred to as the “perpetrator” channel), and the response of the 64 “victim” channels was observed. The amplitude of the sinusoidal signal was chosen to produce $∼Φ0/10$⁠, so as to measure the differential crosstalk at a single dc current level. The fractional crosstalk response for a given channel was calculated using a lock-in demodulation technique relative to the perpetrator response. The measurement was repeated as the dc current level was stepped in $Φ0/10$ intervals across several $Φ0$⁠, as crosstalk arising from resonator hybridization is expected to vary sinusoidally with the SQUID dc flux offset.²⁷ The largest fractional crosstalk across all dc current levels for each channel is reported in Fig. 5. The highest measured crosstalk was 0.3% which corresponds to channels closest in frequency to the perpetrator. Spatial neighbors of the perpetrator channel display the next-highest level of crosstalk (⁠$<0.1%$⁠), and all other victim channels show crosstalk at or below one part in 10⁴. While these results come from measurements on a single chip, we expect the results to hold for higher channel-count multiplexers with the exception of crosstalk that results from intermodulation products, which scale with the number of microwave tones. Tone-tracking and careful selection of linear amplifiers ameliorate this source of crosstalk. These results are less than or equal to the crosstalk in TDM systems¹ that have been deployed in tens of TES-based instruments.

Large-sensor-count bolometric experiments pose a significant readout challenge. To meet these demands, we developed the μmux100k multiplexer. We have presented the μmux100k chip design as well as the topology to construct a 1820-channel multiplexer within the 4–8 GHz readout band. Key metrics of yield, noise, and crosstalk have been quantified on resonators that span more than the fundamental repeating unit of the multiplexer, and these metrics meet or exceed the requirements of large-scale bolometric instruments currently under development. The multiplexer is scalable in sensor count and rf bandwidth and flexible in defining a resonant frequency schedule. As such, the design may be tailored to other applications in a straightforward manner.

The authors acknowledge the support of the Simons Foundation (Award No. 457687, B.K.), the NIST Innovations in Measurement Science program, and the NASA APRA program. The effort at SLAC was supported by the Department of Energy, Contract No. DE-AC02-76SF00515.