Low kinetic inductance superconducting $MgB_{2}$ nanowire photon detectors with a 100 picosecond relaxation time

Properties of superconducting nanowires set the performance level for Superconducting Nanowire Single Photon Detectors (SNSPD). Reset time in commonly employed large area SNSPDs,5-10ns,is known to be limited by the nanowires kinetic inductance.On the other hand, reduction of the kinetic inductance in small area (waveguide integrated) SNSPDs prevents biasing them close to the critical current due to latching into a permanent resistive state.In order to reduce the reset time in SNSPDs, superconducting nanowires with both low kinetic inductance and fast electron energy relaxation are required. In this paper, we report on narrow (15-100nm) and long (up to 120 $\mu$m) superconducting $MgB_{2}$ nanowires offering such combination of properties.In 5 nm-thick $MgB_{2}$ films, grown using Hybrid Physical Chemical Vapor Deposition, the electron relaxation time was 12ps, the critical temperature was 32K, and the critical current density was 5x$10^{7}$ A/$cm^{2}$ (at 4.8K). Using microwave reflectometry, we measured a kinetic inductance of Lk0(4.8K)=1.3-1.6 pH/sqr regardless of the nanowire width, which results in a magnetic field penetration depth of 90 nm. These values are very close to those in pristine $MgB_{2}$. For 120 $\mu$m long nanowires the response time was only 100ps, i.e. 1/80 of that in previously reported NbN nanowire photon detectors of similar dimensions.

NbN nanowires, large kinetic inductivity (Lk0(4.8K)=90 pH/□) (inductance per square of the nanowire, l=w) leads to a significantly slower current return (restoration of the superconducting state), resulting in a much larger reset time τ 13 : τ=Lk/RL >>τ0, where Lk = Lk0×l/w is the total kinetic inductance of the nanowire and RL is the impedance of the read-out circuit (∼50 Ω). This is particularly critical in large area SNSPDs, with a kinetic inductance as large as hundreds of nH, leading to a reset time of a few tens of ns. On the other hand, large kinetic inductance delays current return from the load RL back into the SNSPD, prior to the hot-spot cooling down, hence preventing the SNSPD from latching into a permanent normal (non-sensitive) state. 14 To a certain extent, the reset time can be reduced by choosing a high-impedance load. However, much increased RL leads to a reduction of the maximum non-latching bias currents, hence precluding SNSPDs from reaching high detection efficiencies. 15 This problem is particularly pronounced in short SNSPD, where shunting resistors of small values or extra inductors in series are required to avoid latching, which does not altogether allow reaching short reset times. 16,17 Apart from low-Tc superconductors (NbN, Nb, NbTiN, TaN, MoN,WSi, etc.) 10,14,18,19 , magnesium diboride (MgB2) nanowires have also shown ability for single photon detection in both visible 20 and IR 21 ranges. However, the reset time in MgB2 SNSPDs was reported to be 2-3 ns, i.e. close to that for NbN SNSPDs. Previously it has been shown that in clean MgB2 (attainable in 50-200nm thick films) the magnetic field penetration depth λ is at least an order of magnitude shorter than that in NbN, 22 which should lead to a small kinetic inductivity (Lk0=µ0λ 2 /d). Moreover, we recently reported that 5nm-thick MgB2 films could be made with a critical temperature >30K and a normal state resistivity comparable to that in thick films. In such films, a quasiparticle relaxation time is τ0=12ps 23 , and which all together suggests that MgB2 nanowires might provide a solution for high speed photon detection.
In this work, we report on the successful demonstration of MgB2 nanowires made from clean and ultra-thin (5nm) films. We study both kinetic inductance and response rate in the devices within a large variety of widths (15 nm -900 nm) and lengths (3 µm -120 µm), and show that a 100 ps voltage relaxation time can be achieved in 120 µmlong devices with a standard 50 Ω readout without latching.
MgB2 films were grown on 6H-SiC substrates using a custom-built Hybrid Physical Chemical Vapor Deposition (HPCVD) system. 24,25 The system was designed for a low deposition rate (∼2.5-3 nm/min) with a diborane gas flow of 2 sscm (5 % B2H6 in H2) and a deposition temperature of 700°C. As a result, continuous MgB2 films could be routinely obtained as thin as 5 nm, as shown by Transmission Electron Microscopy (TEM) (Fig.1a), with a critical temperature of 32-34 K (Fig.3a). Film growth on the SiC substrate is epitaxial, which ensures that bulk properties of MgB2 are preserved in the thin films as manifested in a fairly low normal-state (residual) resistivity of ρn=10-15 µΩ×cm, a high critical current density of Jc∼5×10 7 A/cm 2 , and a small magnetic field penetration depth of λ=90nm (see further in the text). Nanowires ( Fig.1 b,c) were fabricated using e-beam lithography and Ar + ion milling through a negative resist mask. 26 Nanowires were from ∼15 nm to 900 nm in width (determined from Scanning Electron Microscope (SEM) images), and from 3 µm up to 120 µm in length.
All experiments were conducted in a cryogen-free probe station (base temperature 4.8 K) with an optical view port and microwave ground-signal-ground (GSG) probes (Fig.2). Kinetic inductance was obtained from the imaginary part of the microwave impedance (Z(ω)=jωLk), which was measured using a (10MHz-67GHz) Vector Network Analyzer. Voltage response was registered with a real-time digital oscilloscope Infiniium 54854, with nanowires being dcvoltage-biased through a set of low-pass filters and a bias-T (see also Supplementary Material).
As measured in a large variety of samples (width and length), the kinetic inductivity in thin MgB2 nanowires was 1.35-1.60 pH/□ at 4.8K (Fig.3b). In the case of defect-free uniform films, the total kinetic inductance = 0 = 0 is expected to be proportional to the length-towidth ratio (l/w) and hence to the total resistance R in the normal state (40K). This trend was indeed observed (Fig.3c), which confirms scalability of thin-film transport properties from the micron-to the nano-scales.
Kinetic inductance (and its temperature dependence) is a sensitive indicator for superfluid (Cooper pairs) density, hence providing the value for the superconducting energy gap. In MgB2, πand σ-sheets of the Fermi surface display quite dissimilar energy gaps, with temperature dependences following: 27 Previously, in the frame of double-band modeling 28 , it has been shown that electrodynamic properties in MgB2 can be analyzed by considering two quasi-layers (electrons of both πand σbands) in parallel, with a finite (yet, weak) interband scattering. In particular, partial contribution from each band to both the condensate energy and the superfluid density varies according to temperature and magnetic field. E.g. at zero magnetic field, the π-band is expected to contribute about a>70% to the superfluid density (∝1/λ 2 ) at T<(Tc-2K). The exact value of the coefficient a depends on the interband scattering rate, and has to be evaluated for each particular case. However, the general trend seems to be correct, as in Ref. 22 , where it was shown that λ(0) vs the mean free path can be modeled considering predominantly the π-band. In Ref. 29 , a satisfactory agreement with experimental λ(T) was demonstrated for thick films, considering two bands with an interband coefficient a= 0.8. For a general case of two conduction bands, the kinetic inductivity can be calculated from the imaginary part of the BCS conductivity 30 as: By fitting Eq (2) to the experimental Lk0(T) data (Fig. 4a), we obtained the superconductor energy gaps at T=0. Our results showed that Eq (1)  with a filling factor of 50% (∼500 µm long) has a similar L/w ratio to our longest MgB2 samples. For such NbN devices, a voltage fall time of ∼8ns has previously been reported 13 , i.e. a factor of 80 longer than that in MgB2.
Fast quasiparticles relaxation (12 ps in MgB2 vs 50ps in NbN) is a positive factor and reduces the effect of latching in small kinetic inductance samples. We were able to register multiple photon detection events (i.e. no lathing took place) for short MgB2 samples biased directly at the critical current. By increasing laser intensity, the number of pulses on the oscilloscope increases yet preserves fast voltage relaxation.
In conclusion, our results show that fabrication of narrow and long nanowires is feasible using MgB2 superconducting ultra-thin films made by a low deposition rate HPCVD process.
With the preserved high quality of films manifested in a high critical temperature (>30K), a high critical current density (∼5×10 7 A/cm 2 ) and a small magnetic penetration depth (∼90 nm), MgB2 nanowires have a high potential for fast response rate photon (as well as particle)