Nano-optical photoresponse mapping of superconducting nanowires with enhanced near infrared absorption

Superconducting nanowire single-photon detectors (SNSPDs) play an important role in emerging optical quantum technologies. We report on advanced nanometric characterization of a high efficiency near infrared SNSPD design based on a low roughness tantalum pentoxide (Ta2O5)/silicon dioxide (SiO2) distributed Bragg reflector (DBR) cavity structure. We have performed high resolution transmission electron microscopy analysis to verify the smoothness of the DBR. Optical reflectance measurements show excellent correspondence with DBR simulations. We have carried out precision nano-optical photoresponse mapping studies at 940 nm wavelength at T = 3.5 K, indicating excellent large area device uniformity (peak efficiency 55% at 100 Hz dark count rate (DCR)) with a full width half maximum timing jitter of 60 ps. With manual fibre coupling with single mode fibre, we achieve a system detection efficiency (SDE) of 57.5% at 940 nm wavelength (100 Hz DCR) at T = 2.3 K and a low polarization dependence of 1.20 ± 0.03. For coupling with multimode fibre, we achieve SDE of 90% at 940 nm (200 Hz DCR) at T = 2.3 K. These SNSPD devices are promising candidates for use in quantum dot photoluminescence studies and optical quantum technology applications.


Introduction
Since the pioneering work of Gol'tsman et al demonstrating single-photon detection in niobium nitride (NbN) superconducting nanowires [1], superconducting nanowire single-photon detectors (SNSPDs) have undergone rapid development [2][3][4]. SNSPDs are extremely sensitive devices, capable of registering the arrival of individual infrared photons with low noise and excellent timing resolution, outperforming off-the-shelf technologies such as semiconductor single-photon avalanche photodiodes and photomultipliers [5]. Thus, SNSPDs have emerged as an important enabling technology for quantum key distribution (QKD) [6,7], optical Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. quantum information processing (QIP) [8,9] and fundamental tests of quantum mechanics [10]. SNSPDs are typically based on an ultra-thin (<10 nm) superconducting films deposited onto a substrate and afterwards patterned to nanoscale dimension (100 nm) nanowires using electron-beam lithography (EBL) and etching [3]. The nanowires are patterned in a meander geometry to increase the sensitive area of the device that is then aligned to the core of a single mode optical fibre for efficient optical coupling [2,3]. Cooled below the superconducting transition temperature T c and current-biased just below the critical current I c of the nanowire, upon the absorption of a single photon the SNSPD will generate an electrical pulse [11,12]. The absorption of photons in the nanowires can be enhanced through embedding the SNSPD in an optical cavity [13], photonic waveguide [14] or through nanophotonic structures such as nanoantennas [15]. State-ofthe-art SNSPDs can offer high detection efficiency (>90% at 1550 nm wavelength) [16,17] low intrinsic dark count rates (DCR, mHz) [18], low timing jitter (<18 ps full width at half maximum, FWHM) [19] and short reset times (<5 ns) [20]. Moreover, owing to the small superconducting energy gap of the materials employed [21], SNSPDs can offer a wide spectral range from visible to mid infrared wavelengths [21,22].
Optical QIP requires efficient generation and detection of single-photons [5]. Single-photon source performance is defined by three characteristic properties: firstly, ability to deliver indistinguishable photons, secondly their purity and thirdly their efficiency [23]. The most promising candidates for near infrared (NIR) single-photon generation are InAs/ GaAs quantum dot (QD) single-photon sources. These can achieve extremely high purity (>99.99%) [24] and a photon indistinguishability of up to 97% [25]. These QD singlephoton sources most commonly have an emission wavelength in the region of 940 nm and state-of-the-art QD single-photon sources at this wavelength are on the point of becoming commercially available [26,27]. In the NIR wavelength range, the energy of a single photon is of order 1 eV making detection an extremely challenging task. Off-the-shelf semiconductor photon-counters including single-photon avalanche photodiodes (SPADs) and photomultiplier tubes perform very well in the visible range. However, moving into NIR wavelengths, their performance declines [5]. Particularly close to 940 nm wavelength, there is a gap in performance: the detection efficiency of Si SPADs drops steeply beyond 900 nm, whereas InGaAs SPADs [28,29] typically operate between 1.1-1.6 μm. Therefore, the development of highly efficient detectors with low DCRs and high timing resolution at 940 nm is essential for exploitation of QD sources in secure communications (QKD) [30] and other QIP systems. Most applications with SNSPDs have been focused on telecommunication bands (1310-1550 nm). Nonetheless, to characterise the performance of a QD single-photon source and exploit these sources in QIP applications, highly efficient SNSPDs operating at 940 nm are required. Initial efforts at QD single-photon source characterisation used early generation SNSPDs without an optical cavity and thus with limited efficiency [31,32]. Very recently, a SNSPD based on NbN in an optical cavity with a system detection efficiency (SDE)>80% at 940 nm [33] has been reported and a broadband design (500-1100 nm) with a peak efficiency of 30% at 800 nm [34] has also been reported. Moreover, a design on non-periodic distributed Bragg reflector (DBR) optimized for (650-900 nm) with a peak efficiency of 82.3% at 808 nm [35] has been demonstrated.
In this study we present comprehensive nanometric characterisation of a NbTiN SNSPD design atop a Ta 2 O 5 /SiO 2 DBR tuned for maximum optical absorption at 940 nm. We present and analyse high resolution transmission electron microscopy (TEM) of the device structure. We map the single-photon response of the device using a novel low temperature nano-optical setup. At 3.5 K, the SNSPD under test exhibits uniform photoresponse under perpendicular illumination, corresponding to a maximum SDE of 55% at 940 nm wavelength under 100 Hz DCR and a FWHM) timing jitter of 60 ps. With a view to deploying this SNSPD design in QD single-photon emitter studies we manually couple a device with single mode optical fibre achieving an SDE of 57.5% at 940 nm wavelength at T=2.3 K at 100 Hz DCR. Using multimode optical fibre we achieve SDE of 90.0% at 940 nm wavelength at T =2.3 K at 200 Hz DCR.

Materials and methods
The NbTiN thin films that were used for this work were deposited by DC reactive sputtering at room temperature at the National Institute of Information and Communications Technology (NICT), Japan [36]. The film thickness was controlled by the deposition rate and deposition time. The inclusion of Ti into NbN thin films allows for higher current density and sheet resistance in comparison to NbN films. As a result, the signal to noise ratio is significantly improved during device characterisation. Additionally, NbTiN films are more forgiving with regards lattice mismatched substrates in comparison to NbN films [37]. Prior to the 7.5 nm NbTiN thin film deposition, the deposition conditions were optimized for a relatively thick NbTiN film. NbTiN alloy target (80% Nb and 20% Ti) was sputtered onto a silicon substrate at ambient temperature with a total pressure of 2 mTorr and 3.0 A discharge current. 100 nm thick NbTiN test films were grown at various nitrogen flow rates while other parameters were kept unchanged, and the superconducting transition temperature, T c was measured. As soon as the best conditions were reached for the highest T c for a bulk NbTiN film, the thickness was decreased to below 10 nm by decreasing the deposition time. A critical temperature T c =8 K, defined as the resistancetemperature transition mid-point was measured for the 7.5 nm thick NbTiN on top of a DBR optimised for maximum absorption at 940 nm. The DBR consisted of seven periodic Ta 2 O 5 /SiO 2 bilayers grown via an ion-beam sputtering method [38] on top of a Si substrate as a one-dimensional cavity with a measured reflectance of the bilayers equal to 98% at 940 nm. The number of the bilayer repeats has been carefully chosen as a trade-off between achieving photon absorption in the film above 98% and whilst minimizing mechanical stress/roughness of the top layer where the thin NbTiN film will be grown. This would allow us to maximize the detection efficiency of the device. By taking advantage of this advanced optical structure and using front-side illumination, light absorption in the superconducting NbTiN layer is enhanced. The devices were then patterned and fabricated in the James Watt Nanofabrication Centre at the University of Glasgow. The SNSPD nanowire width was 95 nm and the spacing was 105 nm meandering over a square area of 15×15 μm 2 (fill factor 47.5%).
Two EBL steps were used during the fabrication process. EBL was carried out by a Vistec VB6 UHR EHF EBL tool at 100 keV. The first EBL step used a PMMA bilayer positive tone electron-beam resist to pattern alignment markers and bonding contact pads. After development in MIBK: IPA, 100 nm Au (with 3 nm Ti adhesion layer) markers and contact pads were deposited by ultra-high vacuum electron-gun evaporation and lift-off. The nanowire and a 50 Ω impedance matched coplanar waveguide electrodes were patterned in the second EBL step with the use of 165 nm ZEP 520 A positive tone electron-beam resist. Then the pattern was transferred into the NbTiN film by reactive-ion etching with tetrafluromethane (CF 4 ). The reflectance of the DBR without a NbTiN thin film was measured as a function of wavelength and is illustrated in figure 1(a). The full detector structure from top to bottom was made up from NbTiN/DBR/Si as shown in figure 1(b). A scanning electron micrograph (SEM) of a fabricated NbTiN SNSPD (Device 1) with an active area of 15 x 15 μm 2 is portrayed in figure 1(c) and a magnified SEM image of an area of the nanowire is illustrated in figure 1(d).
The nano-optical characterisation of the NbTiN SNSPD reported in this paper was performed in a cryostat with a base temperature of 3.5 K. Within the cryostat there is a miniature confocal microscope configuration setup [39]. A stack of three piezoelectric stepper motors (Attocube Systems) allow the confocal microscope system to move in x and y-axes over a large area (5×5 mm 2 ). The third piezoelectric motor is used for the focus of the confocal microscope. Additionally, a stack of two independent scanning motors (Attocube Systems) allow for small area 30 μm by 30 μm scanning across the device with sub-nanometre resolution. The three stepper   motors were controlled by an Attocube ANC150 piezo motion controller whereas, the two scanner motors were controlled by an Attocube ANC200 motion controller. The microscope housing is attached via a flexible thermal link to the second stage of a pulse-tube cooler (Cryomech PT-403). Light attenuated to the single-photon level is delivered to the SNSPD through an optical fibre feedthrough into the cryostat with single-mode fibres (Thorlabs 780HP) and a fibre-based confocal microscope [40] as shown in figure 2.
Measurements of the inductance of the SNSPD devices were carried out with the use of a computer-controlled vector network analyser (VIA Bravo), with frequencies ranging from 0.1 to 50 MHz.

Results and discussion
We present results from four devices of the same design from a single wafer fabrication run: device 1 was used for the SEM and TEM studies; device 2 was measured at 3.5 K in our nano-optical mapping setup; devices 3 and 4 were fibre coupled and measured inside a second cryostat with base temperature of 2.3 K.
The structural properties of device 1 have been characterised via high resolution TEM. The TEM facilities available in the School of Physics and Astronomy, University of Glasgow (FEI Tecnai T20 microscope) have been used for this purpose. Before the TEM analysis, electron transparent cross sections have been prepared using a dual beam focussed ion beam system. Figure 3(a) shows a TEM image of the SNSPD cross-section with the DBR substrate. Additionally, in figure 3(b) a zoomed-in TEM image of the SNSPD crosssection active area is shown. During our TEM analysis, we have also examined the thickness variation of each subsequent bilayer at eight different points across the imaged area shown in figure 3 (corresponding to a span of 5 μm) and their mean value was calculated. Additionally, the root-mean-square (rms) roughness of each subsequent layer was extracted, and it was observed that the rms roughness is increasing from the Si substrate interface up to the top SiO 2 layer on which the NbTiN thin film was grown as displayed in table 1. The SiO 2 layers show higher roughness in comparison to the Ta 2 O 5 layers (increasing from 1.2 nm for SiO 2 and 0.6 nm for Ta 2 O 5 for the first bilayer repeat, to 6.02 nm for SiO 2 and 4.50 nm for Ta 2 O 5 in the seventh bilayer repeat). The uppermost SiO 2 layer has rms roughness of 6.4 nm over the lateral length scale of 5 μm sampled, which approaches the thickness of the superconducting NbTiN film (7.5 nm) making up the SNSPD device, indicating that the roughness of the DBR may begin to affect the uniformity of the patterned SNSPD device.
Device 2 was mounted and cooled in the setup shown in figure 2. The NbTiN SNSPD device was characterized in terms of basic superconducting properties that include: transition temperature T c , current-voltage characteristic (I-V curve) and normalized inductance versus normalized bias current (L-I curve). To confirm the uniformity of the nanowires, we analysed the change in inductance while varying the bias current (I b ) [41]. By using this method, is possible to record what happens to the inductance as the SNSPD approaches its I c . The L-I curve was fitted with the aid of Ginzburg-Landau theoretical model that describes the dependence of the kinetic inductance with respect the bias current (I b ). The inductance was normalized at the value of L 0 that represents the inductance of the SNSPD at I b =0 and the During the fitting of the data, we introduced a parameter C=I c /I * c , where I * c is derived from the Ginzburg-Landau theoretical prediction and describes the critical current of nanowires with no constrictions. This parameter C was firstly used to explain the effect of a constriction on the cross-sectional area of nanowires with respect their kinetic inductance and their critical current [41]. The obtained value of C for Die 6a was 0.65, whereas the ideal theoretical value for an entirely uniform nanowire without a constriction is C=1. This method could be refined further by the use of BCS theory to obtain a more accurate fit and a precise inductance value [42]; for the purposes of our study the Ginzburg-Landau based model was useful to give an initial indication of nanowire uniformity prior to single-photon response measurements.
To characterise the local detection efficiency of the SNSPD, we used the low temperature confocal miniature microscope to map the surface of the chip and locate the active area of the device. A 1550 nm wavelength superluminescent diode source was used to illuminate the chip. Light reflected from the chip, while the piezoelectric positioners moved, was measured by an InGaAs detector via a circulator at room temperature to create a reflection map. Figure 5(a) illustrates the output voltage signal of the InGaAs Table 1. Measured thickness of each subsequent bilayer at eight different points across the 5 μm lateral width of the structure of Device 1 imaged in figure 3 and their mean value is presented. Additionally, the rms roughness for each of the SiO 2 and Ta 2 O 5 bilayers is presented. SiO 2 /Ta 2 O 5 bilayer was repeated seven times with a final SiO 2 layer acting as a λ/4 cavity before the NbTiN SNSPD device. The DBR was grown on top of a Si substrate. photodiode versus the relative x-y positions indicating the device active area. We then current-biased the device using a bias tee and through room temperature amplification (56 dB) we measured the DCR of the NbTiN SNSPD using an Agilent 53131 universal counter. The photoresponse uniformity of the SNSPD was confirmed by mapping the device area with a 940 nm calibrated pulsed laser at a repetition rate of 1 MHz. The input photon flux illuminating the device was maintained below 1 photon per pulse. The optical spot was scanned across the same area as the photo reflection map figure 5(b). At the highest responding point, the local SDE of the SNSPD was calculated, while the device was biased at 17.0 μA (95% of I c ) indicating a peak SDE of 55% at 100 DCR. By maintaining the spot of the confocal microscope in the same position used for the SDE measurements, we acquired the timing jitter for that device. A 1550 nm femtosecond fibre laser and an Agilent Infinium DSO80804A 8 GHz oscilloscope were used for the timing jitter measurements illustrated in figure 6. The timing jitter was extracted from the Gaussian fit on the histogram. The FWHM jitter of this device is 60 ps at I/I c =0.85. Device 3 from our batch was manually fibre-coupled with a 4.4 μm core diameter 780HP single-mode fibre and cooled on a two-stage type Gifford-McMahon cryocooler (Sumitomo SHI RDK-101D) [43] with a base temperature of T=2.3 K. In figure 7(a) the SDE is illustrated as a function of I b for this device measured with 940 nm wavelength illumination. Due to the meandering geometry of the nanowire (a) Device resistance versus temperature, the critical temperature T c is 8 K defined as the transition mid-point, (b) current-voltage characteristics of same device without a shunting resistor at 3.5 K using a two-wire measurement, the critical current I c is 18 μA. (c) Normalized inductance for Die 6a versus the variation of the normalized bias current; the inductance was normalized at the value of L o representing the inductance of the SNSPD at bias current (I b =0) and the bias current was normalized at the value of I c of the SNSPD. The black (solid line) represents the theoretical curve for C=1, based on Ginzburg-Landau theory for nanowires with no cross-section constrictions and the red (dotted squares) represent the device Dies 6a with a C=0.65. The data points in all the plots represent the average of repeated measurements and the resulting error bars are comparable or smaller than the data points.  devices, their efficiency depends on the polarisation of the photons that impinge upon the active area of the device [13]. The polarization of the incident light was controlled with a two-paddle manual fibre-coupled polarizer, that was inserted between the programmable attenuators and the SNSPD, which allowed regulation of the photon-counts from the SNSPD. Figure 7(a) shows the maximum (CRmax) count rate, minimum (CRmin) count rate and DCR of the SNSPD with respect to I b . Also, we have extracted a maximum (SDEmax) and a minimum (SDEmin) with respect I b as presented in figure 7(b). A low polarization dependence of 1.20±0.03 was recorded while varying the I b .
Device 4 from our batch was manually fibre coupled with 9 μm core diameter SMF28 fibre and tested alongside Device 3 at 2.3 K. Figure 8 shows SDE and DCR versus I b . We see that multimode fibre coupling further enhances the SDE, reaching 90% for 200 Hz without polarization control.

Conclusion
In this study, we have designed and fabricated a new 15×15 μm 2 SNSPD design atop a DBR cavity comprising seven SiO 2 /Ta 2 O 5 bilayer repeats optimized for 940 nm wavelength. We have employed advanced nanometric characterization and low temperature measurement techniques to gain insight into the device uniformity and performance. Device 2 from the same fabrication run was electrically and optically characterized at T=3.5 K in a novel nano-optical photoresponse mapping setup. The best SNSPD device showed an overall SDE=55% at λ=940 nm (DCR=100 Hz) and a timing jitter of 60 ps at I/I c =0.95. Additionally, devices 3 and 4 from the same fabrication run were manually fibre-coupled and optically characterized at T=2.3 K. Device 3, coupled with single mode fibre (4.4 μm core diameter), showed an overall SDE=57.5% at λ=940 nm (DCR=100 Hz), and a low polarization dependence of 1.20±0.03. Device 4 coupled with multimode fibre (9 μm core diameter) showed a maximum SDE of 90% with unpolarized illumination at 940 nm wavelength. During the manual fibre coupling, it was challenging to minimise the coupling losses and a future direction would be to adopt a self-aligning scheme that will require patterning the devices in a keyhole structure that can fit the ferrule of singlemode fibre and will minimise coupling losses [2,44]. In our device structure, this requires further technological development, as a deep anisotropic etch process has to be developed not just for the Si wafer, but also for the DBR heterostructure. With self-alignment, we would expect high SDE to be consistently achieved. Also, use of anti-reflection coated fibre [32] would allow a modest increase in SDE. Our TEM analysis shows that the DBR roughness increases with the number of bilayer repeats, and the rms roughness of the top (b) System detection efficiency (SDE) versus bias current, I b for maximum and minimum polarization of the light at λ=940 nm and T=2.3 K for device 3. The SDE max (red data points) and SDE max (blue data points) curves were obtained by adjusting the polarization to reach the maximum and minimum count rate of the SNSPD. layer of our DBR stack (6.4 nm) approaches the thickness of the NbTiN superconducting thin film (7.5 nm). Therefore, reducing the number of DBR repeats may achieve the optimal trade-off between optical absorption and SNSPD uniformity. To sum up, high efficiency single-photon detectors are crucial for emerging single-photon quantum technologies using 940 nm wavelength. For example, single-photon purity of emission can be verified by second order correlation functions g 2 (t), which indicate the statistical distribution of photons emitted by the source. High efficiency SNSPDs with low dark counts and low timing jitter will improve the acquisition of g 2 (t) is improved, yielding lower uncertainty in the measured data for a fixed acquisition time.