At the present time, ultrahigh performance superconducting nanowire single-photon detectors are the key elements in a variety of devices from biological research to quantum communications and computing. Accurate tuning of superconducting material properties is a powerful resource for fabricating single-photon detectors with desired properties. Here, we report on the major theoretical relations between ultrathin niobium nitride (NbN) film properties and superconducting nanowire single-photon detector characteristics, as well as the dependence of ultrathin NbN film properties on reactive magnetron sputtering recipes. Based on this study, we formulate the exact requirements for ultrathin NbN films for ultrahigh performance superconducting nanowire single-photon detectors. Then, we experimentally studied the properties of ultrathin NbN films (morphology, crystalline structure, critical temperature, and sheet resistance) on silicon, sapphire, silicon dioxide, and silicon nitride substrates sputtered with various recipes. We demonstrate ultrathin NbN films (obtained with more than 100 films deposition) with a wide range of critical temperature from 2.5 to 12.1 K and sheet resistance from 285 to 2000 Ω/sq and report a sheet resistance evolution of more than 40% within two years. Finally, we found out that one should use ultrathin NbN films with a specific critical temperature near 9.5 K and a sheet resistance of about 350 Ω/sq for ultrahigh performance state-of-the-art superconducting nanowire single-photon detectors at 1550 nm wavelength.

State-of-the-art superconducting nanowire single-photon detectors (SNSPDs) show better performance compared to other single-photon detectors, including a quantum efficiency up to 99%,1–3 a counting rate higher than 1 GHz,4,5 a jitter less than 3 ps,6 and a dark count rate around 10−3 Hz.7 The next innovation step makes it possible to create high-performance waveguide superconducting single-photon detectors8 for low-loss photonic integrated circuits.9 In combination with efficient single-photon sources10,11 and low-loss integrated optical modulators,12 these are the key elements for an integrated photonic quantum computing platform.13 Nevertheless, developing superconducting single-photon detectors that combine all of the above-mentioned characteristics is still a difficult problem. Many recent studies demonstrate a strong dependence of SNSPD characteristics on nanowire material parameters.14–16 However, a proper choice of niobium nitride (NbN) ultrathin film properties and its deposition recipe is still a nonobvious everyday task for many scientific groups. In this paper, we report on the theoretical relations between SNSPD characteristics and niobium nitride (NbN) ultrathin film properties and propose several approaches for getting the required SNSPD characteristics based on various film properties, including a high detection efficiency, a high count rate, and a low dark count rate. Niobium nitride is one of the well-known materials for high performance SNSPD as it has a high enough critical temperature Tc to allow the use of cryocoolers for operation. We experimentally investigate ultrathin NbN films deposited by reactive magnetron sputtering at different temperatures with various stoichiometries on silicon, sapphire, silicon dioxide, and silicon nitride substrates. Then, the critical temperature Tc and the sheet resistance Rs of each deposited film were carefully measured. We investigated Tc and Rs dependencies on nitrogen concentration in the chamber and substrate temperature during deposition for different substrates. In addition, it is well known that thin film properties could significantly change over time.17 To study this effect, we routinely measured the Rs degradation over two years due to NbN ultrathin film oxidation. More than 100 samples were investigated in the paper, providing a wide range of experimentally measured NbN ultrathin film properties.

The most important parameters of superconducting films in terms of future SNSPD applications are the critical temperature Tc and sheet resistance at room temperature, Rs. First, one chooses them for ultrathin NbN film characterization as they can be measured using an easy-to-implement four probe method. Second, they characterize superconducting films quite completely, reflecting the change in other film parameters, such as diffusion coefficient D, quasiparticle thermalization time tth, etc. It is important to note that Tc and Rs are often related to each other in accordance with the universal scaling law,18 which means that the lower the sheet resistance, the higher the critical temperature. In conjunction with the universal scaling law, our results allow the evaluation of the suitability of NbN films for high-performance SNSPD fabrication using easy-to-measure room temperature film sheet resistance. However, in some cases, it is possible to get ultrathin NbN films with high Tc and high Rs.19 One of the key characteristics of superconducting nanowire single-photon detectors is system detection efficiency (SDE), which determines the probability that single photons that are sent to SNSPD will be detected. This parameter value is calculated by the following equation:
(1)
where ηOCE is an efficiency of optical coupling between an incident light and an active area of SNSPD, which does not depend on film properties and is determined by a nanowire area,20 optical fiber, and measuring setup parameters;1,21 ηABS is an absorption efficiency, which depends on a film thickness and its properties,22 nanowire fill factor,23 optical cavities,24 photon polarization,20 and wavelength;25 and ηIDE is an intrinsic detection efficiency, which depends on film properties, which directly determine detector sensitivity to single photons,26 as well as a nanowire geometry,27 bias current, bath temperature,28 photon wavelength,29 and flux.1 Another characteristic of SNSPD is a dark count rate (DCR), which describes the frequency of detector false counts. This undesirable effect can occur for a variety of reasons, including a current crowding effect,27 thermal fluctuations in superconductors,30 and phase slips,31 and depends on a bias current, bath temperature,29 external noise, and photon flux.32 DCR can be reduced by both selecting optimal operating conditions for the SNSPD23,26,32,33 and determining the most appropriate film properties26 together with nanowire geometry.34–37 

In the case of quantum communications applications, for example, the most important SNSPD characteristics are count rate (CR) and jitter. The count rate is limited primarily by nanowire geometry26 and is also dependent on nanowire material,38 measurement setup,39 photon wavelength,40 and flux.1 Jitter depends primarily on a cryogenic measurement setup and bias current,41 but is also determined by nanowire geometry,42 bath temperature,43 external noise,44 and film properties.38 However, the nature of jitter remains a poorly explored topic. Figure 1 shows the impact of superconducting film properties, nanowire geometry, measurement setup, and light properties on SNSPD characteristics. As one can see, nanowire film properties significantly influence the most important SNSPD characteristics. Here, we use some previously proposed approaches to evaluate the influence of ultrathin film properties on SNSPD absorption efficiency, counting rate, and cut-off wavelength. We also propose a new model to link together the critical temperature and sheet resistance of NbN films, as well as SNSPD operating parameters, with their dark counts due to thermal fluctuations.

FIG. 1.

SNSPD performance vs measurement setup, nanowire design, light, and superconducting film properties. “High” indicates a strong impact of the parameter, “Low” indicates a weak impact, and “No” indicates no information about the impact.

FIG. 1.

SNSPD performance vs measurement setup, nanowire design, light, and superconducting film properties. “High” indicates a strong impact of the parameter, “Low” indicates a weak impact, and “No” indicates no information about the impact.

Close modal
Achieving high absorption efficiency is one of the biggest challenges in SNSPD development. One way to increase absorption is to form optical cavities under the nanowire, such as distributed Bragg reflectors45 and quarter-wave resonators.46 In addition, nanowire film thickness has a great influence on absorption.45 A high absorption efficiency is observed in thick superconducting films, but increased film thickness leads to decreased intrinsic efficiency of the SNSPD;47 therefore, the film thickness usually does not exceed 10 nm. High absorption efficiencies without compromising other SNSPD characteristics can be achieved by optimizing superconducting film properties. The absorption of a thin metal film can be calculated as follows:48,
(2)
where Z0 = 377 Ω is an impedance of free space and nsub is the substrate refractive index. To evaluate the absorption in a meander-shaped nanowire, the calculated value must be multiplied by a fill factor. The calculated absorption efficiency for NbN films depending on their sheet resistance and substrate refractive index is shown in Fig. 2(a), and the calculated ηABS for films on silicon, sapphire, silicon dioxide, and silicon nitride substrates is shown in Fig. 2(b). The substrate's refractive indices are taken for the 1550 nm wavelength. It is worth noticing that in this chapter we are talking about nanowires fabricated on substrates without optical cavities. Equation (2) can be accurately applied in the case of a metal film deposited on a homogeneous substrate that is far thicker than the optical wavelength, so that the optical reflection at the bottom surface of the substrate can be neglected. Therefore, the absorption values for SNSPD on a silicon substrate with thin SiO2 and Si3N4 layers (3.5 μm and 150 nm thick, respectively) are somewhat underestimated. One should take into account that for these two cases, Eq. (2) can only be used to assess the effect of superconducting material properties on the absorption efficiency, not to predict it quantitatively. One can conclude that NbN film absorption can be increased either by using low refractive index substrates or with a certain sheet resistance at the extremum. The choice of a substrate material is often impossible due to technological route limitations for integrated devices. For example, SNSPD with self-alignment coupling49 requires a silicon substrate as it is fabricated through Si etching.50 Conversely, tuning the film sheet resistance can be done for every substrate and technology, either by changing the film thickness or the deposition recipe. The figure shows an absorption extremum at certain Rs, but it is extremely difficult to achieve such low resistance for sub-10 nm NbN films. Summarizing the above, in order to achieve the highest absorption efficiency for ultrathin NbN films, their sheet resistance should be minimized.
FIG. 2.

Calculated dependencies of SNSPD characteristics on ultrathin NbN film properties. The blue and orange areas show the ranges of film properties shown in (g) for wavelengths of 1550 and 925 nm, respectively. (a) Absorption efficiency for ultrathin NbN films with various sheet resistances on substrates with a different refractive index (nsub). (b) Absorption efficiency vs NbN film sheet resistance for silicon (Si), sapphire (Sap), silicon nitride (Si3N4), and silicon dioxide (SiO2) substrates. (c) SNSPD count rate vs NbN film critical temperature and sheet resistance. (d) SNSPD Berezinsky–Kosterlitz–Thouless transition temperature vs NbN film critical temperatures and bias currents (with constant Rs = 400 Ω/sq). The horizontal surface corresponds to the bath temperature. (e) Intersection curve of the calculated TBKT surface (d) and horizontal planes corresponded to 0.8, 1.2, 2.5, and 4.2 K. (f) SNSPD cut-off wavelength vs NbN film sheet resistance and critical temperature. (g) Intersection curve of the calculated λc surface (f) and horizontal planes corresponded to 925 and 1550 nm. The blue dots show the experimentally measured properties of the sputtered ultrathin NbN films. The areas highlighted with blue and orange dotted lines correspond to the film properties necessary for high-performance SNSPD at wavelengths of 1550 and 925 nm, respectively.

FIG. 2.

Calculated dependencies of SNSPD characteristics on ultrathin NbN film properties. The blue and orange areas show the ranges of film properties shown in (g) for wavelengths of 1550 and 925 nm, respectively. (a) Absorption efficiency for ultrathin NbN films with various sheet resistances on substrates with a different refractive index (nsub). (b) Absorption efficiency vs NbN film sheet resistance for silicon (Si), sapphire (Sap), silicon nitride (Si3N4), and silicon dioxide (SiO2) substrates. (c) SNSPD count rate vs NbN film critical temperature and sheet resistance. (d) SNSPD Berezinsky–Kosterlitz–Thouless transition temperature vs NbN film critical temperatures and bias currents (with constant Rs = 400 Ω/sq). The horizontal surface corresponds to the bath temperature. (e) Intersection curve of the calculated TBKT surface (d) and horizontal planes corresponded to 0.8, 1.2, 2.5, and 4.2 K. (f) SNSPD cut-off wavelength vs NbN film sheet resistance and critical temperature. (g) Intersection curve of the calculated λc surface (f) and horizontal planes corresponded to 925 and 1550 nm. The blue dots show the experimentally measured properties of the sputtered ultrathin NbN films. The areas highlighted with blue and orange dotted lines correspond to the film properties necessary for high-performance SNSPD at wavelengths of 1550 and 925 nm, respectively.

Close modal

The count rate (CR) of the SNSPD is limited by the duration of the pulse resulting from photon counting. After the photon is absorbed, the nanowire transits from the superconducting state to the normal one for time τrise, followed by a voltage pulse and its decay for time τfall. Thus, if the next photon arrives before the voltage pulse has completely decayed, it may not be detected, and the count rate of the SNSPD can be determined from the sum of the rise and fall times.51 

Since the rise and fall times depend on the kinetic inductance of the nanowire, which is determined by its geometry and material properties, the count rate can be calculated as follows:52 
(3)
where kB is the Boltzmann constant, w and l are the width and length of the nanowire, respectively, T is the bath temperature, is the reduced Planck constant, RN is the resistance of the nanowire that occurs when a photon is detected, and RL is the impedance of the coaxial electrical lines. RN is usually about 1 kΩ,53 and RL is taken to be equal to 50 Ω. For further calculations, the film thickness was taken to be equal to 5 nm, the width of the nanowire was 100 nm, and its length was 1 mm. The count rate calculation results for SNSPD based on NbN films with different properties are shown in Fig. 2(c).

It can be seen that the count rate increases with an increase in the critical temperature and with a decrease in the sheet resistance of the film. The behavior of a superconductor, when a decrease in Tc is associated with an increase in Rs, is typical and is well described by a universal scaling law.18 In addition, a decrease in sheet resistance can also positively affect absorption efficiency, as shown earlier. However, to achieve the best performance of the SNSPD, it is not preferable to take a film with the highest critical temperature and the smallest sheet resistance, since this could reduce the detection efficiency, as will be discussed below.

The most significant contribution to the total number of dark counts of the SNSPD is made by the unbinding of vortices from pinning centers as well as thermal fluctuations in a superconducting nanowire.54 The unbinding of vortices from pinning centers due to an increase in the Lorentz force with increasing bias current can be prevented by optimizing the geometry of the SNSPD nanowire. Thermal fluctuations are the main source of dark counts at high bias currents and are associated, in particular, with the Berezinsky–Kosterlitz–Thouless (BKT) transition, which can occur at temperatures above TBKT.55–57 The impact of thermal fluctuations on the characteristics of the SNSPD depends both on the bath temperature in the cryostat and on the properties of the nanowire thin film.

Based on the fact that TBKT can be determined from the sheet resistance of the film and its transition temperature Tc0, we took into account the effect of the bias current Ibias on Tc0 and derived an equation to estimate TBKT for a superconducting film with critical temperature Tc and sheet resistance Rs, biased by current Ibias/Ic (the derivation is given in the supplementary),
(4)
where e is an elementary charge and Ic is a critical current.

The results of the TBKT calculation using Eq. (4) are shown in Fig. 2(d). The horizontal surface shows the bath temperature in the cryostat T. From the equation, it can be seen that the effect of sheet resistance on TBKT is negligible compared to the influence of Tc and Ibias. Based on this, we present the surface plot at a constant sheet resistance of 400 Ω/sq. Figure 2(e) shows the curve of the intersection of the calculated surface and the horizontal planes corresponding to widely occurring bath temperatures of 0.8, 1.2, 2.5, and 4.2 K.

Thus, to ensure the minimum number of dark counts associated with thermal fluctuations, it is necessary to use ultrathin NbN films with a high critical temperature, which will weaken the influence of the bias current on the decrease in the energy gap. In addition, lowering the bath temperature can also greatly reduce the probability of thermal fluctuations occurring at high bias currents. At this calculation stage, the requirements for the properties of the NbN film to minimize DCR do not contradict the requirements for increasing the count rate and absorption efficiency of the SNSPD.

The intrinsic detection efficiency ηIDE of the SNSPD is determined both by the properties of the nanowire film and by the photon wavelength. As the wavelength increases, the photon energy decreases. At a certain wavelength, λc, this energy becomes insufficient to effectively suppress superconductivity in a nanowire. This wavelength is called the cut-off wavelength.27 Thus, at wavelengths less than λc, unity intrinsic efficiency is observed, and at larger wavelengths, the efficiency is significantly reduced. When developing SNSPD, it is necessary to ensure that the cut-off wavelength is higher than the operating wavelength, which in our case is taken to be 1550 nm. This can be achieved by changing the geometry of the nanowire and reducing its width, but the limiting factors are the kinetic inductance, as shown above, and the technological capabilities of electron beam lithography. Further in this section, we aim to specify the properties of the NbN film to achieve unity intrinsic detection efficiency at a wavelength of 1550 nm.

Based on the assumption that unity intrinsic detection efficiency is achieved when the order parameter in the hotspot is fully suppressed, the cut-off wavelength could be calculated as follows:52 
(5)
where h is a Planck constant, tth is the thermalization time of quasiparticles, Cph and Ce are the phonon and electron heat capacities of the film, respectively, and T is the bath temperature. For further calculation, the thermalization time was taken to be equal to 7 ps, and the ratio of phonon and electron heat capacities was taken to be equal to 4.08.58 Assuming a bath temperature of 2.5 K, we plotted the dependence of the cut-off wavelength on the properties of the NbN film shown in Fig. 2(f). For the cut-off wavelengths equal to 925 and 1550 nm, we obtain the curves shown in Fig. 2(g), where films located above the curve will provide unity intrinsic detection efficiency at the considered wavelength, while films located below do not. Looking ahead, the dots show the properties of our ultrathin NbN films, the deposition of which is discussed later in this paper.

To ensure a guaranteed high cut-off wavelength, it is possible to use a film with a low critical temperature and high sheet resistance, but this contradicts the requirements presented earlier for achieving low DCR, high CR, and high ηABS. In order to obtain a specific ratio of SNSPD characteristics, one can use the given dependencies and achieve an improvement in one characteristic at the expense of a deterioration in another. However, in order to achieve the complex characteristics of SNSPD, we propose the following approach: In order to ensure unity in intrinsic detection efficiency together with high absorption, high count rate, and low dark count rate, one should use NbN films with the properties located in the areas highlighted by the blue and orange dotted lines [Fig. 2(g)] for wavelengths 1550 and 925 nm, respectively, which lie above the curves but as close to them as possible. For the wavelength of 1550 nm, it is a region with Tc of about 9.5 K and Rs of about 350 Ω/sq, and for the wavelength of 925 nm, it is Tc between 11 and 12 K and Rs of about 300 Ω/sq. In Figs. 2(b), 2(c), 2(e), and 2(f), these specific ranges are shown with blue and orange areas, so one can choose a film that allows for high SNSPD performance. For example, SNSPD based on such a film on a silicon substrate is capable of achieving unity intrinsic detection efficiency at 1550 nm wavelength, a counting rate from 84 to more than 100 MHz, an absorption efficiency from 12.8 to 16.7%, and dark counts due to fluctuations at a bath temperature of 2.5 K will appear at bias currents greater than 0.9Ic. Thus, the possibility for NbN film with specific properties deposition is necessary to create SNSPDs with predetermined characteristics. The remainder of this paper is devoted specifically to recipes of NbN films deposition in a wide range of properties to enable the fabrication of SNSPDs with a wide range of characteristic ratios.

All thin films were deposited by ultrahigh vacuum reactive magnetron sputtering. The schematic layout of the sputtering system vacuum chamber is shown in Fig. 3(a). The vacuum chamber is pumped out by a cryogenic pump, which ensures the base ultrahigh vacuum conditions before deposition processes. In all the experiments described below, the sputtering current, argon flow, sputtering angle, distance between samples and magnetron source, and operating pressure remained constant. The deposition angle was chosen to ensure the best uniformity of film thickness over the substrates.59,60 The nitrogen flow was controlled by a mass flow controller and varied to obtain NbN films with different stoichiometry. The substrate temperature was varied to obtain films with different crystalline structures. The temperature was set using infrared heaters located above the sample holder and monitored using a temperature sensor located nearby. More detailed information on the deposition and characterization methods for NbN films can be found in the supplementary material.

FIG. 3.

Experimentally measured properties of sputtered NbN thin films. (a) Vacuum chamber of the magnetron sputtering system. Fixed parameters are shown in navy, and variable parameters are shown in green. (b) SEM images of 50 nm-thick NbN film surfaces on silicon substrates with various substrate temperatures and nitrogen concentrations during sputtering. (c) SEM images of 50 nm-thick NbN film surfaces on sapphire substrates with various substrate temperatures and nitrogen concentrations during sputtering. (d) Critical temperature and sheet resistance of 5 nm-thick NbN films on various substrates depending on the nitrogen concentration (sputtered at 800 °C substrate temperature). (e) 5 nm-thick NbN films sheet resistance vs nitrogen concentration for various substrates and deposition temperatures. (f) 5 nm-thick NbN films critical temperatures on silicon and sapphire substrates vs nitrogen concentration (sputtered at 800 °C substrate temperature). The relations between 5 nm-thick films and 50 nm-thick films sputtered with the same recipes, critical temperatures, and morphology are demonstrated.

FIG. 3.

Experimentally measured properties of sputtered NbN thin films. (a) Vacuum chamber of the magnetron sputtering system. Fixed parameters are shown in navy, and variable parameters are shown in green. (b) SEM images of 50 nm-thick NbN film surfaces on silicon substrates with various substrate temperatures and nitrogen concentrations during sputtering. (c) SEM images of 50 nm-thick NbN film surfaces on sapphire substrates with various substrate temperatures and nitrogen concentrations during sputtering. (d) Critical temperature and sheet resistance of 5 nm-thick NbN films on various substrates depending on the nitrogen concentration (sputtered at 800 °C substrate temperature). (e) 5 nm-thick NbN films sheet resistance vs nitrogen concentration for various substrates and deposition temperatures. (f) 5 nm-thick NbN films critical temperatures on silicon and sapphire substrates vs nitrogen concentration (sputtered at 800 °C substrate temperature). The relations between 5 nm-thick films and 50 nm-thick films sputtered with the same recipes, critical temperatures, and morphology are demonstrated.

Close modal

We chose four types of substrates: high-resistivity silicon (10 000 Ω cm), sapphire, silicon dioxide on silicon, and silicon nitride on silicon. We varied the nitrogen flow to achieve its concentration in the vacuum chamber during deposition from 10 to 40%, and the substrate temperature was varied from 21 to 800 °C. 5 nm-thick NbN films were chosen for SNSPD fabrication. However, it is very difficult in some cases to use quartz crystal thickness control for accurate ultrathin film deposition, as the deposition rate also depends on the substrate temperature (quartz crystal cannot be heated and controlled correctly at high deposition temperatures). Therefore, to deposit 5 nm-thick NbN films with various recipes, we first deposited the films with a thickness of 50 to 100 nm using the same deposition parameters, hereinafter referred to as thin films. First, it allowed us to accurately measure the film thickness using a scanning electron microscope (SEM) and carefully calculate the deposition time for 5 nm-thick films. Second, the thicker films allowed us to precisely characterize the film's surface and particular features of growth using SEM. SEM images of the 50 nm-thick NbN films deposited in characteristic regimes on silicon and sapphire substrates are shown in Figs. 3(b) and 3(c), respectively. For films deposited on silicon dioxide and silicon nitride substrates, the surface is very similar to that shown for silicon, so these images are provided in the supplementary material.

One can conclude that 50 nm-thick films surface on the silicon substrate obtained at room temperature and 400 °C look almost the same at any nitrogen concentration. The surface is represented by multiple small grains, which do not have a specific direction of growth or clustering. However, the morphology of the film sputtered at 800 °C differs dramatically. The film deposited at a 10% nitrogen concentration has a transitional structure with multiple individual grains of much larger size. Films obtained at 20 and 35% nitrogen concentrations consist of individual grain clusters with characteristic dimensions of tens/hundreds of nanometers, which in turn makes it possible to achieve superconducting properties close to those previously required. Here, we demonstrated, together with the well-known effect of grain sizes increasing at elevated substrate temperature,61 that nitrogen promotes the formation of larger grain cluster. For the films on sapphire substrates, the effect of the nitrogen concentration on the morphology is noticeable even at low temperatures. At room temperature, with the increased nitrogen concentration, a larger grain size is observed, which becomes elongated but does not have a clear direction of growth. By increasing the nitrogen concentration at 400 °C, one can observe the same character of morphology modification. However, at higher nitrogen concentrations, the grains acquire several characteristic growth directions, which are mixed over the substrate area. At 800 °C, the growth behavior is almost the same as for silicon substrates, while nitrogen also promotes larger cluster formation, but on sapphire substrates, they have several micrometer scale dimensions. We observed elongated grains with a strict direction inside these clusters.

Based on these data, we sputtered 5 nm-thick NbN films on the same substrates at room temperatures, 400, 600, and 800 °C, with various nitrogen concentrations, hereinafter referred to as ultrathin films. We investigated the nitrogen fraction in 5 nm-thick NbN films dependence on the nitrogen concentration in the chamber during sputtering (for details, see the supplementary material). The deposition of ultrathin NbN films at room temperature did not allow us to obtain sheet resistances less than 1000 Ω/sq at high critical temperatures; therefore, we did not consider these films for further SNSPD fabrication. With an elevated temperature of up to 800 °C, we obtained films with higher critical temperatures and lower sheet resistances. The dependence of critical temperature and sheet resistance on nitrogen concentration, for ultrathin NbN films deposited at 800 °C is shown in Fig. 3(d). One can notice that at 35% nitrogen concentration an extremum of the critical temperature is observed, while the sheet resistance tends to decrease with nitrogen concentration increasing. However, we found that at a 30% nitrogen concentration, the sheet resistance shows a slight local increase. For the films deposited at lower temperatures, the local increase in Rs was much more significant, as can be seen in Fig. 3(e). One can observe a dependence between local sheet resistance peaks at specific nitrogen concentrations and film crystalline structure (over-100 nm size grains start growing); we suppose that these peaks may be due to changes in film structure, such as changes in the NbN phase due to changes in film stoichiometry. At all the considered substrate temperatures and nitrogen concentrations, ultrathin NbN films on the sapphire substrates showed the highest critical temperatures and the lowest sheet resistances, while films on silicon, on the contrary, tended to have the lowest critical temperatures and the highest sheet resistances. The ultrathin NbN films on the silicon nitride and silicon dioxide substrates properties were close to each other and were found between the values for the films on the silicon and sapphire substrates. We deposited ultrathin NbN films on various substrates at 800 °C temperature and 30–40% nitrogen concentration, which show properties that can theoretically ensure SNSPD with high performance (high detection efficiency, high count rate, and low dark count rate), as it is presented earlier in this paper.

Another interesting thing is the relationship between the film morphology and its superconducting properties, since it is widely known that the properties of a film are largely determined by its structure.62 The SEM method does not allow us to evaluate the morphology of ultrathin NbN films; however, indirectly, the trends in morphology variation with different deposition recipes can be assessed on thicker films. Figure 3(f) demonstrates the correspondence between the critical temperatures and morphology of 5 nm-thick films and 50 nm-thick films at the same parameters. We found out that with increased nitrogen concentration (up to a certain value), both the grain size of 50 nm-thick film and the critical temperature of 5 nm-thick film increase. When 50 nm-thick films reach the maximum grain size (at 35% nitrogen concentration), the extremum of Tc is observed for 5 nm-thick films. With the following increase in nitrogen concentration from 35 to 45%, the grain cluster size does not grow; however, multiple crystallites appear that protrude above the film surface. Thus, we found out that the maximum critical temperature of 5 nm-thick films corresponds to 50 nm-thick film morphology with the largest grain clusters, but multiple inclusions with individual out-of-plane growth directions are not observed for them.

It is critical for high performance SNSPD fabrication that ultrathin NbN films change their properties over time due to oxidation.63 Having examined several samples, we did not see a change in the critical temperature or changes in the film surface over time, but the change in sheet resistance was significant. To study the degradation of NbN film properties over time, we deposited identical ultrathin NbN films on various substrates and measured their sheet resistances over time. Figure 4(a) shows the sheet resistance of NbN films on various substrates depending on the time after exposure to the atmosphere after deposition. We found that the dependencies of Rs in time are well fitted by power-law functions, the derivatives of which are also shown for various substrates in Fig. 4(a) in dashed lines to demonstrate the change in the rate of sheet resistance growth with time. It should be noted that the lines for Si and Si3N4 substrates overlap each other, so only the curve for Si substrate is shown. The resulting dependence shows a significant decrease in the growth rate of Rs over time. Thus, already a day after deposition, the growth rate of Rs is about 1 Ω/(sq h), vs several hundred Ω/(sq h) in the first minutes of the film study, which is the result of film surface oxidation over time.

FIG. 4.

NbN sheet resistance experimental analyses over time. (a) Sheet resistance of 5 nm-thick NbN films on various substrates over time after exposure to atmosphere. (b) Sheet resistance of three NbN films sputtered in a single process over time, which were removed from the vacuum chamber at various times after deposition.

FIG. 4.

NbN sheet resistance experimental analyses over time. (a) Sheet resistance of 5 nm-thick NbN films on various substrates over time after exposure to atmosphere. (b) Sheet resistance of three NbN films sputtered in a single process over time, which were removed from the vacuum chamber at various times after deposition.

Close modal

In order to determine whether the properties of NbN films change due to interaction with the atmosphere or relaxation processes in the film, an additional experiment was carried out. We sputtered three identical 5 nm-thick NbN films on silicon substrates in the same process, and then each of them was removed from the vacuum chamber after a different delay time [Fig. 4(b)]. After the unloading of each film, their sheet resistances were measured immediately. The first film unloading time moment was taken as zero; however, it was several hours after deposition, so the samples were guaranteed to cool down and their temperature did not affect the result. One can see that the time in the vacuum does not affect a permanent increase or decrease in the Rs. A slight increase in sheet resistance immediately after unloading for the second and third films compared to the first can be explained by a short time in the load lock at atmospheric pressure (when the first sample escaped). We conclude from this experiment that oxidation is the key process in sheet resistance degradation over time.

In conclusion, based on the theoretical model, we demonstrated that SNSPDs can be achieve a low dark count rate, high count rate, and high absorption by reducing NbN nanowire ultrathin film sheet resistance and increasing its critical temperature; however, this contradicts achieving high intrinsic detection efficiency. We found out that in order to create high performance SNSPDs (high intrinsic detection efficiency, high absorption efficiency, high count rate, and low dark count rate) at 1550 nm wavelength, one should use ultrathin NbN films with Tc near 9.5 K and Rs of about 350 Ω/sq. We experimentally demonstrated the films with the desired properties in this paper. We investigated several batches of NbN thin films deposited by reactive magnetron sputtering on Si, Al2O3, SiO2, and SiN substrates at different temperatures and nitrogen concentrations. For all the sputtered films on different substrates, we noticed the following trends: (1) as the substrate temperature increases, the critical temperature increases, but the sheet resistance decreases, and (2) by increasing nitrogen concentration, Tc shows a parabolic dependence with an extremum at a certain nitrogen concentration, and the sheet resistance tends to decrease. We found that at 30% nitrogen concentration, the sheet resistance shows a local maximum together with polycrystalline film structure formation for the films deposited at all studied temperatures. We concluded that in order to deposit 5 nm-thick NbN films with the highest possible Tc and low Rs, that is, to achieve a high absorption, a high count rate, and a low dark count rate, one should use a high substrate temperature and a certain nitrogen concentration (35% for our deposition tool). On the contrary, to get low Tc and high Rs, regardless of the nitrogen concentration, the substrate must be cooled down to room temperature. Finally, we experimentally deposited and analyzed superconducting NbN thin films with a wide range of properties, including Tc from 2.5 to 12.1 K and Rs from 285 to more than 2000 Ω/sq. We investigated the dependence of ultrathin NbN film sheet resistance over time and demonstrated that it could increase by more than 40% within two years for some samples.

Additional data and characterization relevant to this article and referenced in the main text are provided in the supplementary material.

The samples were fabricated and studied at the BMSTU Nanofabrication Facility (FMN Laboratory, FMNS REC, ID 74300).

The authors have no conflicts to disclose.

Ilya A. Stepanov: Conceptualization (lead); Formal analysis (equal); Investigation (lead); Methodology (lead); Project administration (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Aleksandr S. Baburin: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Danil V. Kushnev: Formal analysis (supporting); Investigation (supporting); Methodology (equal). Evgeniy V. Sergeev: Investigation (supporting); Methodology (equal). Oksana I. Shmonina: Formal analysis (supporting); Visualization (equal). Aleksey R. Matanin: Investigation (equal); Methodology (supporting). Vladimir V. Echeistov: Investigation (supporting); Methodology (equal). Ilya A. Ryzhikov: Conceptualization (equal); Formal analysis (equal); Writing – review & editing (equal). Yuri V. Panfilov: Conceptualization (equal); Formal analysis (equal). Ilya A. Rodionov: Conceptualization (equal); Formal analysis (equal); Project administration (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are available within the article and its supplementary material and from the corresponding author upon reasonable request.

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Supplementary Material