Nonbolometric bottleneck in electron-phonon relaxation in ultrathin WSi films

Abstract

We developed the model of internal phonon bottleneck to describe the energy exchange between the acoustically soft ultra-thin metal film and acoustically rigid substrate. Discriminating phonons in the film into two groups, escaping and non-escaping, we show that electrons and non-escaping phonons may form a unified subsystem, which is cooled down only due to interactions with escaping phonons, either due to direct phonon conversion or indirect sequential interaction with an electronic system. Using an amplitude-modulated absorption of the sub-THz radiation technique, we studied electron-phonon relaxation in ultra-thin disordered films of tungsten silicide. We found an experimental proof of the internal phonon bottleneck. The experiment and simulation based on the proposed model agree well, resulting in e−ph~ 140-190 ps at C = 3.4 K supporting the results of earlier measurements by independent techniques. downslide, until the excited volume containing highly non-equilibrium quasiparticles and phonons, termed as a hotspot, is formed [15]. The details of this process play an important role in SNSPDs and were the focus of recent work [18], where the dominant role of electron-phonon interactions over electron-electron interactions was emphasized even in strongly disordered NbN and WSi where electron-electron interaction is strongly enhanced. Another aspect of hotspot formation is phonon loss into a substrate, defining energy density and hence equilibration rates [18] and fluctuations [19]. The energy exchange between the film and the substrate controls the nucleation and growth of normal domain, resulting in photon count. The latter is also influenced by the strength of electron-phonon, phonon-electron interactions and phonon escape from the film. For this reason, studying electron-phonon interaction and cooling of non-equilibrium electron and phonon distributions in materials, which are used for radiation detection is one of the central problems for all sensors.A new class of amorphous superconductors for SNSPDs, and in the first instance WSi, attracted immediate attention. Subsequently, electron-phonon interaction in WSi was studied by applying pump probe [20] and magnetoconductance [21] measurements, while the detection mechanism was investigated with quantum detector tomography [22]. The experimental work [20] utilised a time resolved two-photon detection technique to study the evolution of the hotspot in current-carrying nanowire under the conditions that the nanowire remains superconducting. Relaxation times of the order of hundreds of picoseconds were found and interpreted in [23] using the kinetic model of hotspot relaxation, where self-recombination of non-equilibrium quasiparticles plays a dominant role. The characteristic electron-phonon time 0 [24], which depends on material, was found to be 0.84 -1.0 ns [20] for tungsten rich WSi. . Thus, electron-phonon relaxation in WSi turned out to be slow in comparison with conventional SNSPD materials, such as NbN and NbTiN (where the measured time of relaxation of ...

Thermal Properties of NbN Single-Photon Detectors

“…[35,36], along with the typical timescales τ esc d/s, where s is the sound velocity, imply extremely short mean-free paths for acoustic phonons in thin NbN films. Thereby the scenario of full-internal reflection of phonons proposed recently in WSi [21] is not applicable here. The result of our analysis is shown in the inset of Fig.…”

“…The radiation energy is absorbed by the electrons and transfered to the substrate within a time called the energy relaxation time, that can be measured via amplitude-modulated absorption of the THz radiation (AMAR) [15]. This method has been first introduced by Gershenzon et al [16] and since then applied to various superconducting materials with different Tdependences of the relaxation time, for instance T −2 in Nb [16] and in boron-doped diamond [15], T −1.6 in NbN [17,18] and T −3 in TiN [19], in NbC [20] and WSi [21] films.…”

A superconducting thermal switch with ultrahigh impedance for interfacing superconductors to semiconductors

“…To determine χ abs , we estimate τ 0 = 5000 ps based on measurements 24 This calculation leads to a value of χ abs which is between 0.01 and 0.03 over the dissipated power range measured in the turn-on delay experiment, which is the same range needed to match experiment based on the simple fixed χ abs model. The absorption fraction increases as the dissipated power increases due to the increased number of high energy phonons present in the heater radiation.…”

Electron energy relaxation in disordered superconducting NbN films

“…The reduced density of states affects the strength of electron-phonon scattering and modifies its temperature dependence [9,10] while reduced isotropy obstructs phonon escaping. The degree of phonon anisotropy depends not only on the phonon wavelength and phonon mean free path but also on the acoustic mismatch between the film and the substrate [5,9,[11][12][13] via the angle of total internal reflection. Attempts to account explicitly for phonon anisotropy and reduced density of states were made phenomenologically in Refs.…”