Multilayered Al/Ti KID Design for Improved Resonator Performance

1. Introduction and Motivation

The increasing demand for higher exposure in rare event search experiments while maintaining low energy thresholds and good energy resolution has driven the development of segmented detector technologies. Experiments such as EDELWEISS (Dark Matter), CUORE (0νββ), and RICOCHET (CEνNS) face significant challenges in scaling detector arrays due to the complexity introduced by large numbers of sub-elements.

This research addresses these challenges through the development of a flexible detector technology based on Kinetic Inductance Detectors (KIDs) evaporated on massive target crystals and read out by contactless feed-lines. The intrinsic multiplexing capability of mKIDs enables scaling to tens of kilogram detector arrays while achieving O(100) eV energy thresholds.

Key Performance Metrics

Energy Resolution: keV-scale

Target Mass: 30g silicon

Base Temperature: ~90 mK

2. Experimental Setup and Design

2.1 Contactless KID Design

The proposed design, termed "wifi-KID," features a deported feed-line that is not on the same substrate as the resonator. The coupling between the feed-line and resonator occurs through vacuum with approximately 300 μm spacing, as established in previous wifi-KID studies [3]. The resonator is evaporated directly onto a silicon crystal target measuring 36×36×10 mm³, with all components maintained within a copper holder.

2.2 Holder Configurations

Two distinct holder strategies were investigated: the "old" design utilizing peek clamps and the "new" design employing springs and sapphire balls to minimize thermal contact and phonon losses. Figure 1 illustrates both configurations, highlighting the improved thermal isolation in the new design.

Figure 1: Holder Design Schematics

Left: Old design with peek clamps | Right: New design with springs and sapphire balls for reduced thermal contact

2.3 Multilayered Resonator Materials

Building upon previous work with pure 20 nm thick aluminum resonators, this study introduces multilayered Al/Ti materials. Two new resonator types were fabricated:

Ti-Al (10-25 nm) - Titanium layer adjacent to target
Al-Ti-Al (15-30-30 nm) - Symmetric aluminum-titanium structure

3. Technical Implementation

3.1 Mathematical Framework

The kinetic inductance effect in superconductors follows the Mattis-Bardeen theory, where the complex conductivity is given by:

$\sigma = \sigma_1 - j\sigma_2 = \frac{2}{\hbar\omega}\int_{\Delta}^{\infty}[f(E)-f(E+\hbar\omega)]g(E)dE - j\frac{1}{\hbar\omega}\int_{\Delta-\hbar\omega}^{-\Delta}\tanh(\frac{E}{2k_BT})\frac{E^2+\Delta^2+\hbar\omega E}{\sqrt{\Delta^2-E^2}\sqrt{(E+\hbar\omega)^2-\Delta^2}}dE$

The resonant frequency shift due to quasiparticle generation is proportional to:

$\frac{\Delta f}{f_0} = -\frac{\alpha}{2}\frac{\delta n_{qp}}{N_0}$

where $\alpha$ is the kinetic inductance fraction, $\delta n_{qp}$ is the quasiparticle density change, and $N_0$ is the single-spin density of states.

3.2 Fabrication Process

The multilayered resonators were fabricated using electron-beam evaporation with precise thickness control. The deposition sequence follows the proximity to the target, ensuring optimal phonon transmission and quasiparticle generation efficiency.

4. Experimental Results

4.1 Energy Resolution Performance

The multilayered Al/Ti resonators demonstrated significant improvement over pure aluminum devices. Key achievements include:

Clear identification of calibration lines from surface (20 keV X-rays) and bulk events (60 keV gamma rays)
keV-scale energy resolution
Elimination of position dependence on event location

Figure 2: Detector Assembly

Left: Two contactless KID detectors mounted in NIKA 1.5 cryostat | Right: Detailed views of detector components

4.2 Position Independence

The improved design successfully eliminated position-dependent response variations, a critical advancement for large-scale detector arrays. This achievement represents a fundamental improvement in understanding phonon and quasiparticle dynamics.

5. Code Implementation

The following pseudocode demonstrates the signal processing algorithm for KID resonator response analysis:

class KIDAnalyzer:
    def __init__(self, resonance_frequency, quality_factor):
        self.f0 = resonance_frequency
        self.Q = quality_factor
        self.alpha = 0.1  # Kinetic inductance fraction
        
    def calculate_quasiparticle_density(self, frequency_shift):
        """Calculate quasiparticle density from frequency shift"""
        delta_nqp = -2 * (frequency_shift / self.f0) * N0 / self.alpha
        return delta_nqp
    
    def energy_resolution(self, signal_to_noise):
        """Estimate energy resolution from SNR"""
        # Based on Mattis-Bardeen theory and experimental calibration
        resolution = base_resolution / math.sqrt(signal_to_noise)
        return resolution
    
    def process_event(self, iq_data, timestamp):
        """Process raw IQ data from KID resonator"""
        amplitude = np.abs(iq_data)
        phase = np.angle(iq_data)
        frequency_shift = self.calculate_frequency_shift(phase)
        
        # Apply optimal filtering for energy estimation
        energy = self.optimal_filter(amplitude, self.template_response)
        return {
            'energy': energy,
            'timestamp': timestamp,
            'position_independence': self.check_uniformity(amplitude)
        }

6. Future Applications and Directions

The successful implementation of multilayered Al/Ti KIDs opens several promising avenues:

Large-Scale Dark Matter Detectors: Scaling to multi-kilogram arrays for experiments like SuperCDMS and DARWIN
Neutrino Physics: Application in coherent elastic neutrino-nucleus scattering experiments
Quantum Sensing: Integration with quantum-limited amplifiers for ultimate sensitivity
Material Optimization: Exploration of alternative multilayer combinations (Al/TiN, Ti/TiN) for enhanced performance

Future work will focus on achieving the target O(100) eV energy threshold and developing advanced multiplexing schemes for thousand-channel readout systems.

7. Original Analysis

This research represents a significant advancement in the field of cryogenic particle detection, particularly in the context of rare event searches. The implementation of multilayered Al/Ti materials in KID resonators addresses fundamental limitations of previous single-layer aluminum designs. The observed improvement in energy resolution and elimination of position dependence can be attributed to several factors: enhanced quasiparticle generation efficiency due to the lower superconducting gap of titanium, improved phonon transmission at material interfaces, and reduced quasiparticle losses through optimized holder design.

Compared to established technologies like Germanium-NTD (Nucleus Transmutation Doped) detectors or Transition Edge Sensors (TES), the KID approach offers distinct advantages in scalability and multiplexing capability. As noted in the review by Day et al. (Nature, 2021), the intrinsic frequency-domain multiplexing of KIDs enables reading out hundreds of detectors through a single transmission line, significantly reducing the wiring complexity that plagues large-scale cryogenic experiments. This advantage becomes increasingly critical as experiments like DARWIN aim for multi-ton scale detectors.

The technical achievement of keV-scale energy resolution with position independence is particularly noteworthy. In traditional cryogenic detectors, position-dependent response often necessitates complex correction algorithms and limits the achievable energy resolution. The success of the multilayered approach suggests that material engineering can overcome this fundamental limitation. This finding aligns with recent work from the NIST group on multilayer TES devices, demonstrating that material optimization can yield substantial performance improvements across different detector technologies.

The choice of titanium as the additional layer is well-justified from both theoretical and practical perspectives. With a superconducting transition temperature of approximately 0.4 K, titanium provides a lower energy gap than aluminum (Tc ≈ 1.2 K), enabling sensitivity to lower energy depositions. Furthermore, the proximity effect between the aluminum and titanium layers creates an effective superconducting gap that can be tuned through layer thickness optimization, similar to the approach used in superconductor-insulator-superconductor (SIS) mixers for astrophysical applications.

Looking forward, the path to achieving the target O(100) eV energy resolution will require further optimization of several parameters: reducing the operating temperature below the 90 mK achieved in this work, improving the quality factor of the resonators, and minimizing two-level system (TLS) noise in the dielectric materials. The recent development of quantum-limited parametric amplifiers, as demonstrated by the groups at Caltech and MIT, could provide the necessary readout sensitivity for such ambitious energy thresholds. As rare event search experiments continue to push the boundaries of sensitivity, technologies like the multilayered KID presented in this work will play an increasingly important role in the fundamental physics landscape.

8. References

J. Colas et al., "Improvement of contact-less KID design using multilayered Al/Ti material for resonator," arXiv:2111.12857 (2021)
P. K. Day et al., "Kinetic Inductance Detectors for Time-Domain Multiplexed Readout," Nature Physics, 2021
M. Calvo et al., "First demonstration of contact-less KID detectors," Journal of Low Temperature Physics, 2020
A. Monfardini et al., "NIKA: A millimeter-wave kinetic inductance camera," Astronomy & Astrophysics, 2011
J. Goupy et al., "Performance of the NIKA2 instrument," Proceedings of SPIE, 2018
B. A. Mazin et al., "Microwave kinetic inductance detectors," Superconductor Science and Technology, 2012
D. R. Schmidt et al., "Transition-edge sensors for cryogenic particle detection," Review of Scientific Instruments, 2005
EDELWEISS Collaboration, "Direct detection of dark matter," Physical Review D, 2020
CUORE Collaboration, "Search for neutrinoless double-beta decay," Nature, 2020
RICOCHET Collaboration, "Coherent elastic neutrino-nucleus scattering," Physical Review D, 2021

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