Superconducting nanowire single-photon detectors: physics and applications

The basic device operation of the superconducting nanowire single-photon detector (SSPD/SNSPD) can be described as follows [7, 19, 20]: the NbN nanowire is maintained well below its superconducting critical temperature T_c and direct current biased just below its critical current (figure 1(a)(i)). Individual infrared photons have enough energy to disrupt hundreds of Cooper pairs in a superconductor thereby forming a hotspot (figure 1(a)(ii)). The hotspot itself is not large enough to span the width of the ∼100 nm nanowire. The hotspot region forces the supercurrent to flow around the resistive region (figure 1(a)(iii)). The local current density in the sidewalks increases beyond the critical current density and forms a resistive barrier across the width of the nanowire. The sudden increase in resistance from zero to a finite value generates a measurable output voltage pulse across the nanowire (figure 1(a)(iv)).

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A simple but elegant phenomenological model can be used to simulate the measurable output voltage pulse from an SNSPD biased at I_bias as shown in figure 1(b) [21, 22]. An inductor L_k and a resistor R_n(t) represent the kinetic inductance of the superconducting nanowire and the time-dependent hotspot resistance respectively. The kinetic inductance is given as L_k = _k∫ds/A(s), where _k is the kinetic inductivity and A is the cross-sectional area. Absorption of a photon forms a resistive barrier, which can be simulated as the instantaneous opening of the switch. Introducing R_n(t) into the circuit diverts the current into the load impedance Z₀ (typically 50 Ω ≪ R_n(t)). The LR circuit imposes a time constant of τ₁ = L_k/(Z₀ + R_n(t)) on the decay of I_bias through the nanowire. This τ₁ limits the rise time of the voltage pulse across Z₀. The simulated voltage pulse is shown in figure 1(c). As the current flowing through the nanowire decays to a return current (I_r), the electro-thermal feedback reduces the Joule heating of the resistive region by the bias current in the nanowire. In this model, the switch closes again to remove R_n(t) from the circuit, representing the initiation of the recovery of supercurrent in the nanowire. The current recovers from I_r to I_bias with a longer time constant τ₂ = L_k/Z₀ due to the reduction of total resistance in the circuit (dashed red curve in figure 1(c)). The SNSPD remains insensitive to photons while the supercurrent decays and eventually recovers to a re-triggerable level. The overall non-sensitive time or dead time of the SNSPD is given by τ = τ₁ + τ₂ ≈ τ₂. τ can be reduced considerably by either reducing the value of L_k (either by the use of a shorter or thicker nanowire) [22] or including a resistance R_s in series to the device, thereby reducing the decay time [20]. The kinetic inductance (L_k) of the nanowire is directly related to its length (l), cross-sectional area (A) and magnetic penetration depth (λ) from simplified one-dimensional Ginzberg–Landau theory [L_k = (μ₀λ²)(l/A)]. The magnetic penetration depth (λ) depends on the critical temperature (T_c), the normal state resistivity (ρ_T>Tc) of the nanowire and the operating temperature—therefore the choice of material (see section 2.3.5) and the operating temperature will influence L_k.

Recently, closer attention has been paid to whether the hotspot resistance is fixed or evolves with time. The measured hotspot resistance is considerably higher than the value predicted by this simple hotspot theory. Growth of the resistive region due to Joule heating accounts for the high resistance of the nanowire (figure 1(a)(v)) [20]. Equation (4) can be modified to include Joule heating as follows:

$$\begin{eqnarray} &&C d\frac{\partial T}{\partial t}={J}^{2}d \rho +\kappa d{\nabla }^{2}T+\alpha ({T}_{0}-T) \end{eqnarray} \tag{ 5 }$$

where J is the current density through the wire and ρ is the electrical resistivity. The hotspot cools down by coupling the energy of the excited electrons to the phonons via electron–phonon scattering, with a time constant τ_e−p (∼10 ps). The phonon–phonon scattering then couples the energy into the substrate with a time constant τ_p−sub. A fraction of the energy is backscattered into the electron system owing to mechanisms such as the lattice mismatch between the superconducting nanowire and the substrate. The substrate acts as a heat sink at temperature T₀ [23]. Then the nanowire recovers its superconducting state (figure 1(a)(vi)). The energy of the incident photon is negligible compared to the energy stored in the kinetic inductance; therefore energy or photon number resolution is lost due to the Joule heating of the hotspot [19, 20].

The phenomenological model described above gives insight into some of the SNSPD performance metrics, namely the device recovery time (τ), timing jitter (Δt) and dark count rates, discussed further in sections 2.3.4 and 2.3.8. The other paramount performance metric is the system detection efficiency η_sde. Equation (1) specifies the factors that must be considered, however the model described only affects the third term, η_registering, the probability that a pulse is emitted from the SNSPD (assuming the associated counting electronics in the system register every pulse from the detector). Improvements in the registering probability are discussed in section 2.3.3.

For the SNSPD, η_coupling describes the challenge of efficiently illuminating the potentially sub-micrometre device area (discussed in sections 2.3.1 and 2.4.2). If the illumination is perpendicular to the device surface, η_absorption describes the probability that the photon is absorbed into the superconducting nanowire as opposed to being transmitted through or reflected by the thin film and any surrounding optical structure. This can be simply modelled as a solution of Fresnel equations for light moving between media of differing refractive indices if the optical properties of the substrate and superconductor are known [24]. Progress in increasing the absorption probability is discussed in section 2.3.2. The sub-100 nm fine structure of the detector (commonly an order of magnitude less than the wavelength of the incident light) is a small perturbation of this result [25], described in section 2.3.7.

Focusing an optical spot at λ = 1550 nm on to a 150–200 nm wide nanowire [26] (figure 2(a)) with η_coupling approaching unity is not feasible. In order to enhance η_coupling, a nanowire meander is written typically across a 10 µm × 10 µm [27, 38] (figure 2(b)) or 20 µm × 20 µm area [33]. These NbN meander devices show system detection efficiencies (η_sde) of about 2–3% at 1550 nm, 1 kHz DCR at T ∼ 3 K (figure 3(a)). As illustrated in figure 3(a), in general for SNSPDs η_sde decreases as the energy of the photon decreases (i.e. at longer wavelength)—pointing to a decrease in η_registering [27, 39]. Figure 3(c) shows typical timing jitter (60 ps FWHM) for a large area SNSPD measured with TCSPC electronics and a femtosecond laser.

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Intrinsic device detection efficiencies (η_dde) of 57% for 1550 nm photons (and 67% at 1064 nm), at 1.8 K, have been demonstrated by embedding a 3 µm × 3 µm nanowire meander SNSPD inside an optical cavity in order to increase η_absorption (figure 2(c)) [28]. This design has been refined further (via a buried oxide and a four pixel layout) to achieve 87% η_dde at 1550 nm [40]. Efficient optical coupling is required to convert these intrinsic values into practical system efficiencies, as discussed in section 2.4.2. Impressive system efficiency results have been reported with η_sde ∼ 24–28% [41, 42], ∼23–40% [36, 41] and ∼46% [43] for 1550, 1310 and 900 nm photons respectively. Recently system detection efficiency as high as η_sde = 73% for a 14 µm diameter four-element detector operating for 1550 nm photons has been presented [44].

Optical coupling via lensed fibre [41, 42] or substrate thinning [45] is required to focus the light to the device active area to minimize the beam divergence in the substrate if a back side coupling regime is implemented. On the other hand, superconducting nanowires can be patterned on top of wavelength specific SiO₂/Si [36, 46] or GaAs/AlGaAs distributed Bragg mirrors [47]. The advantage here is that front side fibre coupling is sufficient to enhance absorption for these devices. The coupling can be further improved by integrating an Au optical antenna with the nanowires [48].

Recently several groups have proposed [49, 50] or demonstrated [31, 51–53] embedding the nanowire in an optical waveguide [31, 49–53] (an example is illustrated in figure 2(f)). A nanowire running along the length of an optical waveguide [31, 52] should give a long interaction length for incident photons, allowing η_absorption to be maximized. An array of nanowires can be used to sample a standing wave in an optical waveguide interferometer for spectroscopy applications [51, 53].

η_registering of the device can be improved by reducing the width of the nanowires. Multiple narrow wires can be placed in parallel to boost the output signal whilst improving long wavelength sensitivity [54]. Ultra-narrow nanowire (20 or 30 nm) devices (figure 2(e)) have been demonstrated to be more responsive to low energy photons than typical nanowire devices (90 nm) [30]. In this work four ultra-narrow nanowire elements are placed in parallel, and the device is referred to as a superconducting nanowire avalanche photodetector (SNAP). Maximum η_registering is observed as η_dde saturates at a lower bias current. Upon absorption of a photon in a single parallel element of the device, the element turns resistive and diverts additional current into the other elements, switching the entire device resistive by exceeding the critical current of the parallel elements [55]. If the bias current is significantly lower than the critical current, the first photon absorption switches the first element but the diverted current may not be enough to trigger the avalanche. In this scenario, the device waits either for a second photon to be absorbed in another element or the occurrence of a dark count in another element to switch the whole device resistive. If this does not occur the device can recover without completing the avalanche and registering a count [55]. The registering probability saturation is also observed when smaller superconducting gap energy materials such as a-W_xSi_1−x [37] (figure 3(d)) are used for fabrication of SNSPDs. These devices exhibit η_dde saturation (and near-unity η_registering) at λ = 1550 nm even when the nanowires are 150 nm wide with 4.5 nm film thickness. This behaviour is most likely a consequence of the smaller size of superconducting energy gap in this material leading to an increased hotspot size for a given photon energy.

Fabricating uniform, large area meanders [27, 33, 38, 56] or meanders with fill factors >50% [57] with high yield remains a challenge. Constrictions in the nanowire do not allow the detector to be biased at a high current, consequently lowering η_dde of the device due to a lower η_registering [58]. Nano-optical studies have been undertaken to confirm that a constricted device is sensitive only at the constriction and is insensitive or less sensitive at the non-constricted regions due to lower current density [59]. For a given defect density, reducing the area of nanowire meander will improve the nanowire uniformity. 3 µm × 3 µm devices have been shown to be highly uniform exhibiting higher η_dde [58]. However, coupling the light efficiently to this small 3 µm × 3 µm area is challenging. L_k is lower for shorter nanowires, resulting in a shorter τ. This makes shorter nanowires highly suitable for high speed applications. The load impedance can also be increased to reduce τ. However, τ suppression has a limitation. If τ is reduced excessively, the current will return to the nanowire too rapidly. Joule heating results in a self-heating hotspot [60]. This self-heating hotspot causes the nanowire to enter into a 'latched' state, preventing further detection of photons without manually reducing I_bias. Alternatively, the inductance of the detector can be reduced by writing a set of parallel nanowires [61–63] or an array of parallel nanowire pixels [64] rather than relying on a single meander nanowire across a given area.

NbN was the first choice material for SNSPDs. Subsequently SNSPDs have also been demonstrated using NbTiN (a superconducting material with very similar properties to NbN) on silicon-based substrates [65, 66]. NbTiN nanowire devices have been shown to possess low L_k due to their low resistivity above the superconducting transition temperature, therefore NbTiN SNSPDs have smaller τ compared to the NbN devices [66]. Similarly Nb SNSPDs have lower resistivity than NbN resulting in shorter τ, but the Nb devices suffer from latching due to their slow energy relaxation process [67]. Fabricating a superconducting nanowire meander using novel or high-T_c superconductors is arguably just a question of technological development. Recently MgB₂ SNSPDs have been fabricated [68] and single-photon sensitivity at visible wavelengths has been demonstrated [69], but new fabrication and film growth techniques have to be developed to increase the active area by patterning uniform meanders without defects. Ultra-thin nanowires have been processed in YBa₂Cu₃O_7−δ thin films but single-photon sensitivity is yet to be demonstrated at visible or infrared wavelengths [70]. Fabrication challenges aside, this result may be expected as high-T_c superconducting materials have a large superconducting gap energy compared to NbN, reducing the sensitivity to photons of a given energy. Single-photon sensitivity has been reported in NbN SNSPDs up to 5 µm wavelength, albeit with a significant reduction in η_dde (and η_registering) as wavelength increases [39]. SNSPDs based on smaller superconducting gap energy materials such as amorphous W_xSi_1−x [37] (see section 2.3.3 and figure 3(d)), NbSi [71] and TaN [72] appear to have better sensitivity than NbN at longer wavelengths. These low energy gap superconducting materials have lower transition temperatures, so the SNSPD operating temperature is reduced (requiring more advanced cooling techniques than those discussed in section 2.4.1).

Multi-element SNSPDs (MESNSPDs) offer another solution to improving the single-photon count rate and achieving photon number resolution (PNR) [64, 73]. MESNSPDs consist of spatially interleaved nanowires meandering across a large active area. In this configuration each element is independently current biased and requires an individual readout [64]. This design reduces the dead time without compromising on L_k or Z₀, with no apparent cross-talk between pixels. When the pixels of the MESNSPDs are broadly illuminated photon number resolution can be achieved [73].

An alternative approach to achieving PNR in SNSPDs is by connecting multiple nanowire elements in parallel, provided the hotspot creation in one element does not affect the superconducting state of the remaining elements. This is achieved by current biasing each nanowire element independently with a single voltage source, by introducing a tailored series resistance in each nanowire element [29] (figure 2(d)). The resistance values are carefully chosen such that the hotspot formation diverts the current into Z₀ instead of flowing into the remaining nanowires. When 'n' individual elements fire simultaneously, current flowing into Z₀ increases by a factor of 'n'. This PNR-SNSPD output results in a 'n' times taller observable voltage pulse providing PNR capability [29, 74].

Another technique to observe multi-photon events using SNSPDs is to reduce the bias current and rely on the absorption of multiple photons to form a resistive barrier across the nanowire [7, 75]. Recently new detector tomography techniques have been employed to examine this regime [76]. However, at low current bias the SNSPD is typically much less efficient, so this multi-photon detection regime is hard to exploit in practical applications.

From an optical standpoint, the meander SNSPD device is essentially a subwavelength grating and is observed to possess noticeable polarization sensitivity that varies with wavelength [25]. The count rate from the detector (and hence η_sde) displays a maximum and a minimum value depending on whether the electric field is either parallel or perpendicular to the nanowire. This polarization dependent variation in η_absorption due to the meander structure can be simulated convincingly [25]. This effect can be mitigated by using spiral and perpendicular device designs [77]. These designs eliminate the SNSPD polarization sensitivity by accepting an intermediate efficiency.

The signal-to-noise ratio, which can be achieved with an SNSPD, is governed not just by the practical efficiency (η_sde) and the dark count rate (DCR) but also timing jitter (Δt) [10]. The DCR of the SNSPD is a crucial factor in the device performance. Empirically, the DCR rate rises exponentially as I_bias approaches I_c (figure 3(a)) [33]. It is clear from these data (from a device with a large area meander with no cavity) at the shorter illumination wavelength (λ = 830 nm) relatively high efficiency can be achieved at negligible dark count rates. The origin of the exponential behaviour of dark count rate with bias is poorly understood. Theoretical explanations centre on the possible transit of flux vortices across the current-carrying superconducting nanowire. Several mechanisms have been put forward: quantum phase-slips, single-vortex crossings and vortex–antivortex pair nucleation [78].

Experimental tests have been far from conclusive [79, 80], owing to the difficulty of differentiating these fundamental mechanisms from prosaic environmental noise owing to the bias and readout configuration. Recent studies of dark counts over a wide temperature range (0.5–4 K) provide valuable fresh data [35] (see figure 3(b)). Furthermore, new theoretical studies also indicate that the device geometry (in particular, tight bends in the meander structure) may play a crucial role in triggering dark counts [81].

The very low timing jitter Δt of SNSPDs makes these detectors very attractive for TCSPC applications. When the arrival time of the photon is known extremely well (using modern ultrafast optical sources) the main timing uncertainty arises from the jitter of the SPD. The lowest timing jitter reported is 18 ps [82], but this result has not been widely reproduced and the dimensions of the device used and photon flux were unclear. 29 ps FWHM has been demonstrated in small area (4 µm × 4.2 µm) single- and multi-pixel SNSPDs [73]. Larger area SNSPDs typically give larger timing jitter when measured with femtosecond laser sources and state-of-the-art TCSPC electronics: for example 10 µm × 10 µm meanders of the type first reported by Verevkin [27] give 68 ps FWHM [83] and 20 µm × 20 µm meander devices [33] give 60 ps FWHM (figure 3(c)). These results indicate that a highly uniform nanowire (most easily achieved with a short wire length) will give lower timing jitter. Higher critical currents have been observed to improve jitter in uniform devices [84] allowing 40 ps FWHM to be demonstrated in 15 µm × 15 µm meander devices [85]. Recently studies using nano-optical techniques to study the local efficiency and timing properties of SNSPDs [86] indicate that different parts of a non-uniform nanowire give different hotspot resistances yielding different pulse rise times, broadening the overall timing jitter.

The most common method for cooling a SNSPD is to immerse it in liquid helium (He) [7] or to mount the device in a cryogenic probe station [28] and reach 4.2 K. Pumping on the He bath [87, 88] can reduce the temperature further (see figure 4(a)(i)). Liquid He is expensive, hazardous and demands trained personnel for correct use. This technique is satisfactory for testing superconducting devices in a low temperature physics laboratory; however if the ultimate goal is to provide a working device for users in other scientific fields or in industrial applications, alternative cooling methods must be sought. Operating SNSPDs in a closed-cycle refrigerator [8, 89] offers a solution to this problem. The circulating fluid is high pressure, high purity He gas which is enclosed inside the refrigerator allowing continuous operation and eliminating repeated cryogenic handling. A recent version of a SNSPD system operating on this principle is shown in figure 4(a)(ii).

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The most obvious way to couple photons to a detector inside a cryostat is via an optical window [7]. This technique has the following disadvantages: (i) it is difficult to focus the optical spot on the 10 µm × 10 µm or 20 µm × 20 µm nanowire meander area, (ii) vibrations in the refrigerator and ambient temperature fluctuations outside the cryostat result in poor alignment stability, (iii) operating multiple SNSPDs in parallel will require separate alignment optics, this will eventually limit the number of simultaneous operating detectors and (iv) the DCR will be higher due to the increase in blackbody radiation and stray light coupling to the device. Delivering the photons through a standard single-mode optical fibre [33, 87–89] (package shown in figure 4(b)(i)) or lensed fibre [41, 42] (package shown in figure 4(b)(ii)) overcomes these issues, and removes the need for an optical window in the cryostat. The fibre-coupled configuration makes the operating environment more favourable for low noise SNSPD operation at low DCR, due to reduction in blackbody radiation and stray light reaching the detector. However, this technique can potentially suffer from optical misalignment, since the fibre is typically aligned to the active area of the SNSPD at room temperature and subsequently cooled down to cryogenic temperatures. New 'self-alignment' schemes [90] cleverly constrain the position of the device relative to the fibre and can be applied to SNSPDs on silicon substrates [91]. Cryogenic piezoelectric nano-positioners have been employed to provide precision in situ optical alignment at low temperatures. This method has helped to improve the system detection efficiency for smaller active area devices [42] (section 2.3.2), but the high cost of the nano-positioners is a barrier to widespread adoption. Cryogenic nano-positioners are also of great benefit in carrying out nano-optical studies of local device properties. Local sections within the SNSPD have been examined with sub-micrometre resolution with the help of a confocal microscopy setup (shown in figure 4(b)(iii)), which can be implemented either in a liquid-He cryostat [59] or a closed-cycle refrigerator [86].

As discussed in section 2.3 important avenues in the advancement of SNSPD technology are the development of multi-pixel SNSPD arrays [29, 64, 73], and integration of SNSPDs with other technologies, such as on-chip optical waveguides [31, 51–53]. More efficient, low noise readout schemes are therefore of paramount importance. Progress has been made on several low noise superconducting readout schemes. Rapid single-flux quantum (RSFQ) technology [92] has been successfully integrated at low temperature with SNSPD single pixel devices and arrays [85, 93–95]. The output pulses from RSFQ circuits to room temperature require further amplification, but nevertheless impressive timing jitter has been achieved (as low as 40 ps FWHM). A promising alternative to RSFQ readout is a recently demonstrated superconducting amplifier/discriminator scheme, which provides large voltage pulses [96] with low timing jitter [97].