Flux flow velocity instability and quasiparticle relaxation time in nanocrystalline β-W thin films
Introduction
The development of thin films superconducting technologies has generated multiple low current electronic devices, including superconducting nanowire single-photon detectors (SNSPD) [1], quantum bits [2], and microwave resonators [3]. The SNSPD consist of a superconducting nanowire or microwire biased by a dc current slightly below the critical value (IC) [4]. When a photon interacts with the nanowire, it produces a resistive “hotspot”, which in turn disrupts the superconductivity across the wire, resulting in a voltage pulse [1,5]. Usually, SNSPDs can detect visible and near-infrared photons with energies less than the work function of the superconducting material [6]. The relevant parameters for the design of SNSPD are the resistivity (ρ), the superconducting transition temperature (Tc), the relaxation time of quasiparticles (τe), and the uniformity of patterned wires [1,6,7]. The most common materials used in these devices are amorphous tungsten and WSi [8,9], NbN [[10], [11], [12], [13], [14]], NbTiN [15], TaN [16], MoNx [17], and MoSi [18], among others. All of them preserve superconductivity with uniform properties in films with thicknesses of a few nanometers.
The intrinsic efficiency of a SNSPD depends on the superconducting quality, geometry, design, and fabrication precision of the superconducting nanowire. The design of a SNSPD starts with the synthesis of smooth thin films. Amorphous materials such as MoSi [18] and WSi [19] are particularly desirable due to their high degree of homogeneity and uniformity over large areas. Moreover, SNSPD with WSi are characterized by high detection efficiency and operation temperatures up to 2.5 K. The efficiency has been related to the generation of big hot spots due to its small energy gap and low carrier density [19]. The excellent performance of WSi suggests that materials with similar properties may provide an alternative to develop SNSPD. Indeed, nanocrystalline β-W thin films with Tc≈ 4.7 K can be grown by sputtering using an Ar/N2 mixture [20]. This Tcvalue is between the 6.2 K reported for amorphous W by the focused ion beam induced technique [21] and the 3.4 - 4 K reported for W1-xSix [19,22]. The fabrication process of β-W thin films uses a unique W target and a reactive atmosphere (Ar/N2) at room temperature. Moreover, the method can be applied to develop devices on flexible substrates [23]. Nitrogen impurities reduce the grain size and avoid the crystallization of α-W with a Tc = 12 mK [24]. The films are very homogeneous, and their Tc is thickness independent for films thicker than ~17 nm. Below this thickness, the Tc value decreases systematically, being 3.1 K for 4 nm thick films. Considering that the operation of SNSPD involves excitation and relaxation of quasiparticles, an essential parameter for applying β-W thin films in SNSPD is the τe. This value relates to the time involved in recovering the equilibrium state after photon absorption. It occurs through electron-electron scattering, electron-phonon scattering, and recombination of quasiparticles into Cooper pairs [25]. Reported values for materials like NbN and WSi range from tens of ps to the ns [10,19,22,26].
In this work, we extend our previous finding on the characterization of superconducting β-W thin films' properties [20]. The study is performed on a 23 nm thick β-W thin film. Considering the little changes in the superconducting properties with thickness, it is expected that the results of this work be representative of thin films as thinner as 8 nm [20]. The mechanisms for vortex dissipation are identified by measuring current-voltage (IV) curves as a function of temperature (T) and magnetic field (B). The value of τe is estimated from the analysis of Larkin and Ovchinnikov (LO) instability, which manifests as a discontinuous jump to the normal state as current increases [27]. Both vortex pinning mechanisms and absolute values of critical current densities Jc are discussed.
Section snippets
Experimental method
The W film was grown by sputtering at room temperature on (100) Si according to the description provided in reference [20]. The β-W phase is stabilized by nitrogen impurities. During the deposition, the substrate is positioned at 5.5 cm directly over a W target (99.99 % purity), operating at 50 watts. The total pressure during the growth of the film was kept constant at 0.67 Pa. The nitrogen partial pressure was 8 %. The deposition rate is ≈ 23 nm/min. This work is performed using a 23 nm thick
Results and discussion
Fig. 1a shows the XRD pattern for a 23 nm thick β-W film. A broad peak corresponding to the (210)β reflection is observed at 2Θ ≈ 39°. Fig. 1b shows low angle XRR and the corresponding fit for the film. The high amplitude of the oscillations indicates a very low roughness. The thickness is 22.8 nm, and the fluctuations from the fit are 0.3 nm. The estimation of the grain size average using the equation of Scherrer is around 8 nm (see the peak deconvolution in Fig. 1a), being smaller than the
Conclusion
We have experimentally studied the vortex dissipation mechanisms in β-W thin films. The results show that a nanocrystalline 23 nm thick β-W film displays a Tc = 4.6 K, ξ (0) = 6.4 nm and λ (0) ≈ 1300 nm, and a small electron diffusion coefficient D ≈ 0.4 cm2/s. The films display weak pinning, as manifest in a fast drop in Jc (B). The Jc values at SF are similar to the estimated depairing current J0. Using the LO instability at small magnetic fields, we estimate a quasiparticle relaxation time ≈
Author contributions
J. A. H. and N. H. contributed equally to this work
Declaration of Competing Interest
None.
Acknowledgment
The authors acknowledge J Schmidt for the careful reading of the manuscript. This work was partially supported by the ANPCYT PICT2018-1597, CONICET PIP 2015-0100575CO and U. N. de Cuyo 06/C576. NH is member of the INN (CNEA-CONICET).
References (45)
- et al.
Superconductivity in nanocrystalline tungsten thin films growth by sputtering in a nitrogen-argon mixture
Thin Solid Films
(2019) - et al.
Formation and stability of W coating on a flexible polyimide substrate
Thin Solid Films
(2020) - et al.
Effect of self-heating on flux flow instability in a superconductor near Tc
Physica C
(1992) - et al.
Electronic instability during vortex motion in cuprate superconductors regime of low and high magnetic fields
Physica C
(1995) - et al.
Nonlinear flux flow in TiN superconducting thin film
Physica C
(1999) - et al.
Superconducting nanowire single-photon detectors: physics and applications
Supercond. Sci. Technol.
(2012) - et al.
Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles
Nature
(2014) - et al.
High kinetic inductance microwave resonators made by He-Beam assisted deposition of tungsten nanowires
Appl. Phys. Lett.
(2019) - et al.
Different Single-Photon Response of Wide and Narrow Superconducting MoxSi1−x Strips
Phys. Rev. Appl.13
(2020) - et al.
Kinetic-inductance-limited reset time of superconducting nanowire photon counters
Appl. Phys. Lett.
(2006)
Detection mechanism of superconducting nanowire single-photon detectors
Supercond. Sci Technol.
Superconducting nanowire single-photon detectors for quantum information
Nanophotonics
Focused-ion-beam induced deposition of superconducting nanowires
Appl. Phys. Lett.
Superconducting properties of tungsten nanowires fabricated using focussed ion beam technique
Nanotechnology
Characterization of the thin-film NbN superconductor for single-photon detection by transport measurements
Phys. Rev. B
Optical single-photon detection in micrometer-scale NbN bridges
Phys. Rev. Appl.
Optical and transport properties of ultrathin NbN films and nanostructures
Phys. Rev. B
Single-Photon Detectors Based on Ultranarrow Superconducting Nanowires
Nano Lett.
Saturating intrinsic detection efficiency of superconducting nanowire single-photon detectors via defect engineering
Phys. Rev. Appl.
Superconducting nanowire single photon detectors operating at temperature from 4 to 7 K
Opt. Express
Tantalum nitride superconducting single-photon detectors with low cut-off energy
Appl. Phys. Lett.
Comparison of hot Spot formation in NbN and Mon thin superconducting films after photon absorption
IEEE Trans. Appl. Supercond.
Cited by (10)
Role of nitrogen partial pressure, deposition rate and annealing on stability of β-W phase
2023, Applied Physics A: Materials Science and ProcessingVortex Counting and Velocimetry for Slitted Superconducting Thin Strips
2023, Physical Review Applied