Measurements and Simulations of Athermal Phonon Transmission from Silicon Absorbers to Aluminum Sensors

Abstract

Phonon reflection/transmission at the interfaces plays a fundamental role in cryogenic particle detectors, in which the optimization of the phonon signal at the sensor (in case of phonon-mediated detectors) or the minimization of the heat transmission (when the detection occurs in the sensor itself) is of primary importance to improve sensitivity. Nevertheless the mechanisms governing the phonon physics at the interfaces are still not completely understood. The two more successful models, Acoustic Mismatch Model (AMM) and Diffuse Mismatch Model (DMM) are not able to explain all the accumulated experimental data, and the measurement of the transmission coefficients between the materials remains a challenge. Here, we use measurements of the athermal phonon flux in aluminium Kinetic Inductance Detectors (KID) deposited on silicon substrates following a particle interaction to validate a Monte Carlo (MC) phonon simulation. We apply the Mattis-Bardeen theory to derive the phonon pulse energy and timing from the KID signal and compare the results with the MC for both AMM and DMM models, finding a remarkable good agreement for AMM. For an aluminum film of 60 nm and a silicon substrate of 380 µm, we obtain transmission coefficients Si-Al in the range [0.3 -0.55] and Si-Teflon in the range [0.1 -0.15].

Final results of CALDER: kinetic inductance light detectors to search for rare events

“…Figure 4 shows a signal produced by an energy deposition of 1.3 keV in the Si wafer, which is similar to the light signal expected from the 0νDBD of 100 Mo. The average rise time of the signals is 120 µs, dominated by the phonon propagation in the substrate, while the decay time is 550 µs, dominated by the recombination of the Cooper pairs [53]. For the estimation of the signal amplitude, the phase and amplitude waveforms are combined with a bi-dimensional matched filter to maximize the signal to noise ratio [43].…”

“…Figure 6 (right) shows the light-calibrated energy spectrum (black histogram) of the events produced by the 55 Fe Xray source. The reconstructed energy is significantly smaller the nominal one (∼ 6 keV), since these devices are sensitive to the position of the energy release [53] and the source, unlike the fiber that illuminates uniformly the substrate, faces one corner of it far from the KID.…”

DEMETRA: Suppression of the Relaxation Induced by Radioactivity in Superconducting Qubits

“…Finally, it is worth highlighting that the KID community is now actively trying to understand the mechanism that relates radioactivity to phonons, and phonons to quasiparticle variations in the detector [34]. While KIDs developers are trying to enhance the signal-to-noise ratio of the detectors by collecting more phonons, the Fig.…”

Phonon and light read out of a $$\hbox {Li}_{2}\hbox {MoO}_{4}$$ crystal with multiplexed kinetic inductance detectors

“…The KIDs response to instantaneous energy deposition on Si substrate can be modelled exploiting three time constants [32]: the time of arrival of phonons (τ ph ), i.e. the characteristic time in which the athermal phonons produced in an energy deposition on the substrate arrive to the KID, the time constant of the resonator (τ ring = Q/π f 0 ), and the time in which quasiparticles recombine back into Cooper's pairs (τ qp ).…”

“…9) obtaining τ scint = 89 ± 1 µs. The difference between the two values of τ scint can be ascribed to approximations in the KID response model [32] and to a non-perfect pulses alignment in the averaging procedure due to trigger instabilities and noise fluctuations. Nevertheless, we account for these effects as a systematic uncertainty: we average the two time constants and we identified its deviation as the systematic uncertainty of the measurement procedure: τ scint = 84.5 ± 4.5(syst).…”