Design, Fabrication and Characterization of Microwave Multiplexing SQUID Prototype

This paper presents the design, fabrication, and characterization of a 32-channel microwave SQUID multiplexer prototype, demonstrating a measured equivalent noise current of 154 pA/$\sqrt{Hz}$ to address the readout bottlenecks of large-scale TES detector arrays.

The Gist

Imagine you are trying to listen to a massive choir of 1,000 singers (the detectors), but you only have one microphone cable running out of the room. If you try to plug every singer into that single cable, you'd need a thousand wires, which is impossible in the freezing cold of space or a lab.

This is the problem scientists face with Transition Edge Sensors (TES). These are incredibly sensitive detectors used to catch faint signals from the universe (like the afterglow of the Big Bang). They are so quiet that they need to be kept near absolute zero. But, the more detectors you add, the more wires you need to read them, and that creates a "traffic jam" of cables that ruins the experiment.

To solve this, the team at the Institute of High Energy Physics in China built a "Super-Receiver" called a Microwave SQUID Multiplexer. Here is how their new prototype works, explained simply:

1. The Problem: Too Many Voices, One Cable

Think of the detectors as 1,000 people trying to talk to you at once.

• Old Way (Time Division): You ask each person to speak one by one. It works, but it's slow, and if someone has a bad day (a faulty sensor), you lose that data.
• New Way (Frequency Division / µMux): You give every person a different musical note (a specific radio frequency). Now, they can all sing at the same time! You just need one cable to hear the whole choir, and a smart computer to separate the notes.

2. The Solution: The "Radio Tuner" Chip

The team built a tiny chip (the µMux) that acts like a super-advanced radio tuner.

• The Detectors: Each sensor is connected to a tiny loop of wire called an RF-SQUID. Think of this loop as a tiny, invisible drum.
• The Resonators: Connected to each drum is a "resonator," which is like a guitar string tuned to a specific pitch.
• The Magic: When a detector senses a tiny bit of energy (like a photon hitting it), it changes the tension on the "drum." This changes the pitch of the "guitar string" attached to it.
• The Reading: The computer sends a "comb" of radio waves down a single cable. It listens for the specific pitches. If a pitch shifts, the computer knows exactly which detector saw something and how strong the signal was.

3. What They Actually Built

The researchers designed and built a 32-channel prototype.

• The Layout: Imagine a parking lot with 32 spots. Each spot is assigned a specific frequency (like a radio station). They spaced them out carefully so they don't interfere with each other (no cross-talk).
• The Fabrication: Making this chip is like building a microscopic city. They used layers of superconducting metal (Niobium) and created tiny tunnels (Josephson junctions) where electricity flows without resistance. It's like building a highway system where cars never hit traffic jams or friction.
• The Challenge: They had to be incredibly precise. If the "roads" (wires) were too wide or the "tunnels" (junctions) were slightly damaged, the whole system would fail. They used advanced lasers and etching tools to carve these structures out of silicon.

4. The Results: How Well Did It Work?

They tested 8 of the 32 channels in a freezer colder than outer space (60 millikelvin).

• The "Noise" Test: Every electronic device has a background hiss (static). The goal is to make this hiss as quiet as possible. Their chip was incredibly quiet, with a noise level of 154 pA/√Hz. To put that in perspective, it's like being able to hear a whisper in a library while standing next to a jet engine, but the jet engine is actually just the background hum of the universe.
• The "Tuning" Test: They checked if the "guitar strings" (resonators) stayed in tune. They found that the system was very stable and could clearly distinguish between the different channels.
• The Hiccup: A few of the "drums" (Josephson junctions) weren't perfectly identical. Some were a bit louder or quieter than expected. This is like having a few singers in the choir who are slightly off-key. The team knows why this happened (tiny variations in the manufacturing process) and is confident they can fix it in the next version.

5. Why Does This Matter?

This chip is a stepping stone for a massive project called AliCPT, a telescope in Tibet designed to hunt for primordial gravitational waves (ripples in space-time from the birth of the universe).

• Currently, AliCPT has only one module.
• In the future, they want to upgrade it to 19 modules with thousands of detectors.
• Without this "Super-Receiver" chip, reading thousands of detectors would require thousands of wires, which is physically impossible to cool down.

In a nutshell: The team built a tiny, super-cold "radio station" that can listen to thousands of cosmic sensors at once through a single wire. They proved it works with great clarity, and they are now tuning it up to handle the massive scale needed to unlock the secrets of the early universe.

Technical Summary

1. Problem Statement

Large-scale arrays of Transition Edge Sensors (TES) are critical for astronomical observations (e.g., Cosmic Microwave Background, X-ray astronomy) due to their ultra-low noise. However, scaling these arrays creates a bottleneck in readout technology. Conventional readout methods face significant limitations:

• Time Division Multiplexing (TDM): Limited multiplexing ratios (typically ~64:1) and stringent yield requirements.
• Frequency Division Multiplexing (FDM): Constrained by bandwidth, limiting ratios to ~70:1–170:1.
• Code Division Multiplexing (CDM): Theoretically high capacity but suffers from extreme design complexity.

Microwave SQUID Multiplexing ($\mu$Mux) has emerged as a promising solution, capable of achieving ratios up to 2000:1 by utilizing RF-SQUIDs and frequency division. However, to support next-generation Chinese experiments like the AliCPT (Ali CMB Polarization Telescope), which requires upgrading from 1 to 19 detector modules, there is a need for domestically developed, high-performance $\mu$Mux prototypes with high channel counts and low noise.

2. Methodology

A. Design

The team designed a 32-channel microwave SQUID multiplexer at the Institute of High Energy Physics (IHEP), Chinese Academy of Sciences.

• Architecture: Each channel consists of an RF-SQUID coupled to a coplanar waveguide (CPW) quarter-wavelength resonator.
• Frequency Allocation: 32 channels are grouped into four sets of eight. The frequency spacing is 10 MHz within a group and 80 MHz between geometrically adjacent groups to minimize crosstalk.
• Modulation: A common flux ramp line modulates groups of 8 RF-SQUIDs to linearize their response.
• Circuitry:
  • RF-SQUID: Designed as a second-order gradiometric device with 4 octagonal slotted washer loops to reduce magnetic interference and flux trapping.
  • Filters: LR low-pass filters are integrated between the input coil and the TES to prevent microwave excitation signals from disturbing the TES bias state.
  • Inductance: Simulated inductances and mutual inductances were calculated using InductEx software.

B. Fabrication

The prototype was fabricated using a 10-step process on a 4-inch high-resistance silicon substrate:

• Materials: Nb/Al-AlOx/Nb trilayer Josephson junctions (200 nm/8 nm/150 nm) and Nb resonators (200 nm thick).
• Process Steps: Included magnetron sputtering, Inductively Coupled Plasma Reactive Ion Etching (ICP-RIE), Ion Beam Etching (IBE), and low-temperature ICP-CVD for SiO2 isolation.
• Key Features: Narrow linewidths (3 µm) were used for slotted washers and coils to minimize flux trapping.

C. Experimental Setup

• Cryogenics: The device was tested in an Adiabatic Demagnetization Refrigerator (ADR) at temperatures of 45 mK to 60 mK.
• Readout: A hybrid system comprising cryogenic Low-Noise Amplifiers (LNAs) and room-temperature electronics (ADC/DAC boards, IF boards).
• Characterization: Vector Network Analyzer (VNA) was used to measure $S_{21}$ transmission parameters. Flux ramp currents were varied to modulate the magnetic flux through the SQUID loops.

3. Key Contributions

1. Domestic Prototype Development: Successfully designed and fabricated a 32-channel $\mu$Mux chip in China, specifically tailored for the AliCPT upgrade.
2. Process Integration: Demonstrated the integration of high-quality Josephson junction fabrication with superconducting microwave resonator production on a single chip.
3. Comprehensive Characterization: Provided a detailed analysis of resonant frequency shifts, quality factors ($Q_i$, $Q_c$), and noise performance across multiple channels under varying magnetic flux conditions.
4. Noise Benchmarking: Achieved a competitive equivalent noise current (NEI) of 154 pA/$\sqrt{\text{Hz}}$, validating the feasibility of the domestic design for large-scale detector arrays.

4. Results

• Resonance Frequency:

  • Measured 8 channels (labeled ch01–ch07, with one missing).
  • Resonant frequencies ranged from 4.33 GHz to 4.58 GHz.
  • The resonant frequency showed a clear periodic dependence on the flux ramp current, fitting well with the theoretical model (Eq. 2).
  • Mutual Inductance: Measured effective mutual inductance ($M_{mod,eff}$) was consistent across channels (~56.4 pH), deviating from simulations by less than 12%.
  • Critical Current: Derived critical currents ranged from 4.6 to 6.9 µA, showing some variability likely due to wafer-level processing inconsistencies.

• Quality Factors:

  • Internal Quality Factor ($Q_i$): Ranged from ~33,000 to ~137,000.
  • Coupling Quality Factor ($Q_c$): Ranged from ~88,000 to ~161,000.
  • Total Quality Factor ($Q$): Ranged from ~22,000 to ~73,000 (e.g., ch01 achieved 73,000).
  • Sub-gap Resistance ($R_{sg}$): Calculated values (60–1160 $\Omega$) were lower than ideal Nb/Al-AlOx/Nb junctions, suggesting potential issues with sputtering stress or etching damage.

• Noise Performance:

  • The equivalent noise current (NEI) for channel 01 was measured at 154 pA/$\sqrt{\text{Hz}}$ in the 2–20 Hz frequency band.
  • This performance meets the requirements for high-sensitivity TES readout.

5. Significance and Future Work

• Strategic Importance: This work is a critical step toward the upgrade of the AliCPT experiment, which aims to detect primordial gravitational waves. The successful fabrication of a 32-channel prototype paves the way for scaling to 80 channels per chip as the technology matures.
• Current Limitations: The study identified issues with Josephson junction critical current uniformity (likely due to 4-inch wafer processing) and lower-than-expected sub-gap resistance.
• Future Plans: The team intends to optimize etching conditions and film deposition stress to improve junction quality. They plan to fabricate higher-multiplexing prototypes (80 channels) to fully support the next phase of the AliCPT detector array.

In conclusion, this paper validates the design and fabrication capabilities of the IHEP for high-performance microwave SQUID multiplexers, demonstrating noise levels and channel counts suitable for the next generation of cosmological observatories.