Figure 4.11: Photon count rate measurement at different photon wavelengths. Wavelengths shorter than 800 nm are not plotted as our electronic readout scheme used at the time limits the discrimination of small signal amplitudes when biasing the detector below 2µA.
4.6 Temperature dependence
The temperature at which a detector can operate in an optimal way is closely related to the material Tc, as discussed in Section 2.2 of Chapter 2. The material sensibility is also related to theTcin such a way that a saturated detection efficiency at 1550 nm is difficult to obtain at temperature higher than 2 K, independently of the material. Recently, Dane et al. [12] optimized the deposition condition of NbN and obtained saturated efficiency at 2.5 K for 1550 nm wavelength photons. However, it is experimentally known that detectors behave better in every aspect (efficiency saturation, jitter, DCR, and maximum count rate) when operated colder. In the case of MoSi, the temperature dependence for the first device generation is shown in Fig. 4.12. The bias range in which the detector can be operated optimally is defined between the saturation current Isat (current at which the count rate reaches 90% of the plateau) andIDCR (current at which the dark count rate starts to rise up), it is illustrated by the grey area in Fig. 4.12a and 4.12b. As the detectors exhibit better performance at 0.8 K, no further investigations were performed.
Isat IDCR Ic
10 12
8 6
4 14
10 20 40 60 80
(a)
T (K)
(b)
Figure 4.12: Temperature dependence of the first generation device. (a) Photon count rate and dark count rate. (b) Temperature dependence of the device shown in (a). The optimal bias range is illustrated by the grey area. Isat is the bias current at which the count rate reaches 90% of the one of the plateau, while IDCR is the bias current at which the dark count rate starts to rise up and make the detector not practically optimal.
5 Timing jitter
The timing jitter is defined as the timing variation of the arrival time of the detection pulses. The jitter is a crucial characteristic for time-resolved measurements such as light detection and ranging (LIDAR), high-speed quantum communication [67], and lifetime measurement of single-photon sources. Despite showing the highest SDE ever reported with SNSPDs, amorphous materials typically lead to lower critical currents, which impacts on their jitter performance and combining a very low jitter and a high SDE remains a challenge. This chapter is composed of two parts. Section 5.2 focuses on detectors combining high efficiency and low jitter, while Section 5.3 details the experiment partially performed at NASA Jet Propulsion Laboratory (USA), with which we could reach the fundamental limits of MoSi material, and quantify the intrinsic component of the timing jiiter. This is also referred in Appendix A.3. While the core of this chapter is already presented in details in the appendices, this chapter intends to add precisions on the experimental methods and discuss the results in more details. The reader who looks for specific details should refer to Appendix A.2 for meandered devices, and Appendix A.3 for intrinsic jitter study.
Amorphous materials operate at low bias currents and hence showed until now a timing jitter rather high compared to what can be achieved with NbN and NbTiN. A wide range of values have been reported for different geometries and materials, typically from tens to hundreds of picoseconds, depending on the nanowire design. Two different nanowire designs have to be differentiated: (i) the conventional meander design, which is necessary to reach high efficiency, and (ii) the short nanowire design, which by its design reduces the geometric jitter and makes extremely low jitter value possible [5]. However, the efficiency is limited by the fact that the nanowire cannot cover the entire area corresponding to the fibre optical mode.
Some recently reported values with meandered detector range between ∼15 ps (NbN [68]
and NbTiN [69]) and 76 ps for the amorphous material (MoSi) [70]. A record value of 2.7 ps at 400 nm wavelength have been recently achieved with the short nanowire
design NbN device [5]. Despite recent theoretical studies [71, 72], the lowest experimental jitter achievable with SNSPDs is still not clear, and some of the fundamental limits were unknown before the work presented in this chapter. Understanding its intrinsic behaviour and limits is a mandatory step toward improvements.
5.1 Measurement setup
Typically, for a Gaussian distribution, the jitter is quantified using the full width at half maximum (FWHM) of the distribution. Assuming independent contributions [73, 74], the total measured jitter can be written as the following:
jsystem2 =j2setup+jnoise2 +j2intrinsic+jgeometric2 (5.1) where jsetup includes the laser pulse width and measurement imprecisions,jnoise is the contribution from the amplification and electronic parts, jintrinsic includes the timing variation of the hotspot itself, and jgeometric is related to the path the signal has to propagate depending on the photon absorption location in the nanowire [74]. The jitter induced by the gaussian noise of the amplification chain can be estimated by [21, 73]:
jnoise= 2√
2 ln 2σRM S
SR (5.2)
whereσRM S is the amplifier RMS noise and SR is the slew rate of the detection signal.
To measure the jitter, the SNSPDs and the short pulse laser synchronization signals are acquired simultaneously on a time counting module (either a high sampling rate oscilloscope or a time-correlated single-photon counting (TCSPC) module). The jitter is then obtained by extracting the FWHM of the time arrival distribution. Fig. 5.1 represents a typical jitter measurement setup.
Start
Figure 5.1: Schematic representing the jitter measurement setup.
5.2. Combining high efficiency and low jitter
5.2 Combining high efficiency and low jitter
Despite showing the highest SDE ever reported with SNSPDs, amorphous materials operate at low bias currents and hence showed until now a time jitter rather high.
Following Eq. 5.1, the system jitter was limited by the noise component jnoise. There are different ways to reduce it but in our case, the idea is the following: by making the device thicker, while maintaining a saturated efficiency and taking care of the latching effect (see Section 5.3), jnoise dramatically drops.
The kinetic inductance in a superconductor is given by [75, 76, 77]:
Lk = m nse2
l
σ (5.3)
where m is the electron mass, ns the superconducting electron density, lis the length, and σ=t·w is the nanowire cross-section.
Thicker device leads to: (i) a lower kinetic inductance, and (ii) larger critical current. A lower kinetic inductance affects in a positive way the rising edge of the detection signal, and consequently jnoise, see Eq. 5.2. The lower Lk, the larger SR. On the other side, the detection signal amplitude is directly related to the current at which the detector is operated at, which means that the larger the bias current Ib, the larger the signal amplitude. Details on the way to reduce jnoise is presented in Section 5.3.
The detectors were fabricated out of a 7 nm-thick film of amorphous Mo0.8Si0.2, as explained in Chapter 2. The detectors are patterned as a meandered wire covering a total surface area of 16×16µm2 and a self-aligning technique is used to ensure optimal coupling to the optical fibre [26]. The room temperature resistance of the devices is typically a few MΩ, depending on the geometry of the nanowire and of the meander.
The current density atIsat is typically around 3 MA/cm2 and is similar for all devices.
The detectors are mounted in a sorption cryostat reaching 0.8 K. For measuring the jitter of the SNSPDs, as explained in Section 5.1, a TCSPC module (Becker & Hickl, SPC-130) with a constant fraction discriminator (CFD) was set up and a 6 ps (FWHM) pulse width fibre laser (Nuphoton Technologies) at 1560 nm was used as the photon source. The power of the source was attenuated to the single photon level by variable attenuators. The single-photon response voltage pulse is amplified by a custom low-noise amplifier cooled to 40 K and by a secondary amplifier at room temperature. The input light polarization was set to optimize the number of counts, the measured jitter of the TCSPC module itself was 9 ps.
During this thesis, a lot of devices have been tested and only a few (but representative) are presented here. At the operating temperature of 0.8 K and for 1550 nm, devices typically exhibited a plateau region and very similar performances according to their
designs. Table 5.1 presents a list of selected devices, and Fig. 5.2b shows their system jitter behaviour as a function of the relative bias current. In this case, Isat is defined as the bias current at which the efficiency reaches 90% of the plateau.
Table 5.1: List of selected devices with their characteristics.
Detector width (nm) fill factor SDE (%) Jitter (ps)
#1 150 0.7 85.8 44.2
#2 150 0.7 82.3 35.4
#3 160 0.6 80.2 32.7
#4 150 0.6 76.5 28.5
#5 160 0.5 80.1 26.1
#6 150 0.5 74.6 28.6
(a) (b)
Figure 5.2: (a) System jitter, the blue and red lines indicate the data and the Gaussian fit, respectively. The system jitter measured is 26 ps (FWHM) and is indicated by the double arrow. (b) Jitter (FWHM) as a function of Ib relative to the saturation current (Isat) for different devices shown in Table I. Here, Isat is defined as the bias current at
which the SDE reaches 90% of its maximum. Error bars are too small to be seen.
We obtained a device combining a system jitter as low as 26 ps for a SDE of 80.1%±0.9%, see Fig.5.2a. Another one combined a SDE of 85.8% ±0.9% and a system jitter of 44 ps. To cover a given area, a larger fill-factor means a longer nanowire and hence a larger kinetic inductance. Thus, one can expect that for larger fill-factor, jnoise would be bigger.
That is exactly the tendency that can be seen in the Table 5.1. In addition to the length of the nanowire, larger fill-factor also means a larger geometric effect. This effect has been the subject of study in the literature for NbN meandered detector [74]. From Fig. 5.2b, the following points can be highlighted: i) jsystem is constant for low bias currents, ii) jsystem exhibits the same inflexion point close to∼0.92Isat, iii) by increasing the bias current above the inflexion point, the system and intrinsic jitters decrease significantly, iv) the jitter flattens close to ∼1.2Isat and could potentially reach an optimal value.
5.2. Combining high efficiency and low jitter Points iii) and iv) have implications for SNSPDs performances, namely that operation well into the plateau (Ib > Isat) is necessary to reach an optimal jitter value.
The jitter FWHM is indicative of the distribution spread to a certain extent. In practice, for QKD experiment for example, the QBER (qubit error rate) dramatically depends on the tail of the distribution: while the majority of the photon arrives in the center of each time bin, photons arriving in the wrong time bin because of a large tail increase significantly the QBER. As the SNSPD technology progressed, it was always assumed that the timing histogram was gaussian but this is not entirely correct. Interestingly, the jitter histogram of the tested devices was asymmetric and non-gaussian in the vicinity of Isat. Fig. 5.3a shows such a distribution measured at Ib =Isat. The asymmetry consists of a long exponentially decaying tail after the maxima of the histogram. This is the transition region between the probabilistic regime, where the absorption of a photon leads to a resistive region with a small probability, and the deterministic regime (the plateau), where photon absorption leads to a resistive region with almost certainty. The asymmetry however mostly disappears outside of the transition region, where it tends to be much more gaussian. The upper plot of Fig. 5.3b shows the system jitter jsystem(−20 dB)at 20 dB below the maxima of the histogram, while the lower plot shows the residue from what is expected with a Gaussian distribution. Given that the setup (jsetup) and noise (jnoise) jitter distributions are gaussian, the evolution of the asymmetry can only be explained by an intrinsic or geometric contribution. From an application point of view, it is clear here too that the optimal SNSPD operation (jsystem(FWHM)and jsystem(−20 dB)) is reached but also when the bias current is greater than ∼ 1.1Isat. This means that a detector with a very large deterministic region will show intrinsically better performances in term of both jsystem(−20 dB)andjsystem(FWHM). This point is particularly relevant for applications where a low jsystem(−20 dB) is mandatory, such as QKD experiments.
Jitter -20 dB
Occurrence
(a) (b)
Figure 5.3: (a) System jitter distribution on a logarithmic scale at a bias current equal to Isat. The blue and red lines represent the data and the Gaussian fit, respectively. (b) Up:
jsystem(−20dB), down: residues from what is expected with a Gaussian distribution.
5.3 Intrinsically-limited jitter
As mentioned above, a record value of 2.7 ps at 400 nm wavelength have been recently achieved with the short nanowire design NbN device [5]. This results is a great im-provement and show the extreme timing performances of SNSPDs. However, the lowest experimental jitter achievable with SNSPDs is still not completely clear as well as the fundamental limits. The motivation behind this work was to reach the intrinsic jitter of MoSi device and experimentally point out the fundamental limits. Understanding the intrinsic jitter behaviour and limits is a mandatory step toward improvements.
Setup
The devices were fabricated out of 5, 7 and 9 nm-thick films of Mo0.8Si0.2 deposited by co-sputtering, as explained in Chapter 2. A total of 80 different devices were measured for this study. The devices consist of a single 5 µm-long nanowire connected to a contact pad, through an meandered inductor, as illustrated in Fig. 5.4. This nanowire design minimizes the geometric jitter component (jgeometric), while the series inductor is used to prevent the latching effect [5]. To probe the nanowire cross-section dependence of the intrinsic jitter (jintrinsic), the nanowire width was varied from 60 nm to 200 nm, depending on the thickness. When the cross-section of the nanowire increases, the bias current needed to operate the detector increases as well, and eventually gets larger than Ilatch, which prevents its operation. To cope with this problem, the devices are tested with different series inductances ranging from 100 nH to 3500 nH.
2 !m
100 !m
GND
Ibias
GND 1 !m
(a)
(b)
Figure 5.4: (a) Scanning electron microscope image of the device composed of a contact pad (in red), an inductor (in blue), and a nanowire connected to the ground. (b) Zoom of the 5 µm long MoSi nanowire.
The experiment was carried out using a pulse-tube cryocooler with a 4He sorption refrigerator reaching a base temperature just under 1 K. The signal from the detector
5.3. Intrinsically-limited jitter was amplified with SiGe cryogenic amplifiers from Cosmic Microwave. For the slew rate versus the kinetic inductance characterisation and the energy-dependence measurements, the CITLF3 and the CITLF1 were used, respectively. The SNSPDs were biased with a low-noise current source through a 5 kΩresistive bias-T at the input of the AC-coupled amplifier. In order to get higher latching currents, a shunt inductance of 1.2 µH was connected to the ground through a 50 Ω resistance, similarly to [27]. To investigate the photon-energy dependence of the jitter, we used two second harmonic generation (SHG) crystals to frequency double the mode-locked lasers from 1064 nm and 1550 nm to 532 nm and 775 nm, respectively. After the crystal, the light was collimated and free-space coupled into the cryostat through a series of glass windows in the vacuum chamber and the heat shields at 40 K and 4 K, flood illuminating the device under test.
The optical intensity was controlled with a circular metallic variable neutral-density filter.
This configuration ensured that the converted and unconverted light co-propagated via the same path through the optical setup. After generation, filters were used to select 532, 775, 1064, and 1550 nm wavelength illumination. The SNSPDs and laser synchronization signals were acquired simultaneously on a digital real-time oscilloscope with a sampling rate of 40 GS/s and a bandwidth of 12 GHz. The time delay between the two pulses was recorded for each acquisition. Histograms of 5000 detection delays were collected for each jitter measurement, which typically required a collection time of approximately 5 minutes.
Slew rate, kinetic inductance, and latching effect
The first part of this work consisted in understanding the latching current and noise jitter dependence on the electronic readout and device kinetic inductance. The desired mode of operation for SNSPDs is achieved only when the electric feedback is slower than the nanowire cooling time, which happens naturally if its kinetic inductance is large enough [78]. If this feedback is sped up by decreasing the kinetic inductance, the device will suffer from the latching effect where it is locked in a resistive state and can no longer detect photons. Practically, Ilatch is defined as the current at which the count rate of the detector drops down to zero. A large kinetic inductance is necessary to slow down the electric feedback and prevents latching. However, if Lk is too large, two problems arise:
(i) the maximum count rate of the SNSPD is reduced, and (ii) the electrical signal coming out of the nanowire after a detection is affected, meaning a lower slew rate (SR) and consequently a larger noise jitter. The last point is crucial to reach intrinsically-limited jitter.
A representative dataset for 120 nm wide, 7 nm thick nanowires, is shown in Fig. 5.5. The slew rate is extracted from the oscilloscope trace derivative and is plotted as a function of the bias current in Fig. 5.5b. Fig. 5.5c represents the slope of SR(Ib) as a function ofLk. Finally, Fig. 5.5d shows the corresponding estimated jitter induced by the electrical noise as described in Eq. 5.2 as a function of the bias current, for different Lk. A compromise
between Lk, Ilatch, SR and consequently jsystem has to be found. Regarding Fig. 5.5d, it is clear that the best compromise is to reduce as much as possible Lk, while satisfying Ilatch > Isw. The lowest noise jitter we could achieve was estimated to be 5 ps. We performed this characterization for the three thicknesses, and obtained quantitatively the same results. The only way left to reduce the noise jitter is by decreasing the kinetic inductance of the device, which is incompatible with the latching effect, as explained above.
(a) (b)
(c) (d)
Figure 5.5: Dataset for 120 nm wide, 7 nm thick nanowires, with different kinetic inductances. (a) Oscilloscope trace of a typical signal pulse, and its derivative. (b) Slew rate of the signal rising edge for devices with different kinetic inductance. The slew rate was calculated from the maximum of the derivative shown in (a). (c) Slope of SR(Ib) as a function of Lk. (d) Estimated jitter induced by the electrical noise (described in Eq. 5.2) as a function of the bias current. The stars indicate the latching current for the corresponding devices.
5.3. Intrinsically-limited jitter Intrinsic jitter
Once the latching current for a given Lk is known, we selected devices with the lowestLk possible that still satisfiedIlatch> Iswto ensure optimal performances. We experimentally observed higher latching currents when using the CITLF1 amplifier, this allowed us to pick lower kinetic inductances resulting in lower system jitter. The impedance mismatch between the resistive SNSPD and the amplifier most probably results in electrical reflec-tions and oscillareflec-tions. Depending on the amplifier design, the oscillareflec-tions might actually help the detector to recover from its resistive state, and hence increase the latching current. However, further investigations have to be done to confirm this conclusion.
The jitter energy dependence of the 100 nm wide, 7 nm thick nanowire is plotted in Fig. 5.6 together with the photon count rate curves. Fig. 5.7a shows its timing histogram measured for a bias current of 17.9µA. The FWHM of the distributions are 6.0± 0.2 ps and 10.6±0.2 ps at 532 nm and 1550 nm wavelength, respectively. A non-gaussian tail is clearly observed, which becomes more apparent for long wavelengths and low bias currents, this behaviour has also been reported in many studies [71, 21, 5], but its origin remains unclear. The 5 nm and 9 nm-thick devices exhibit qualitatively the same behaviour.
The best detectors for each thickness selected for energy-dependence measurements are summarized in Table 5.2. One notable difference between cross-sections is that we could obtain a jitter of 14.5 ps at 1550 nm for the 9 nm-thick device, while the 5 and 7 nm-thick devices showed values close to 10 ps.
0 10 20 30 40 50
Systemjitter(ps)
532 nm 775 nm 1064 nm 1550 nm
2 4 6 8 10 12 14 16 18
Bias current (µA)
0.0 0.2 0.4 0.6 0.8 1.0
Relativephotoncountrate
Figure 5.6: Dataset for the 100 nm wide, 7 nm thick nanowire. Jitter FWHM as a function of the bias current, for different wavelengths, and the corresponding photon
Figure 5.6: Dataset for the 100 nm wide, 7 nm thick nanowire. Jitter FWHM as a function of the bias current, for different wavelengths, and the corresponding photon