Recent progress in the development of superconducting nanowire single-photon detectors (SNSPDs) has delivered excellent performance and has had a great impact on a range of research fields. The timing jitter, which denotes the temporal resolution of the detection, is a crucial parameter for many applications. Despite extensive work since their apparition, the lowest jitter achievable with SNSPDs is still not clear, and the origin of the intrinsic limits is not fully understood. Understanding its intrinsic behavior and limits is a mandatory step toward improvements. Here, we report our experimental study on the intrinsically-limited timing jitter in molybdenum silicide SNSPDs. We show that to reach intrinsic jitter, crucial properties such as the latching current and the kinetic inductance of the devices have to be understood. The dependence on the nanowire thickness and the energy dependence of the intrinsic jitter are quantified, and the origin of the limits is exhibited. System timing jitter of 6.0 ps at 532 nm and 10.6 ps at 1550 nm photon wavelength has been obtained.

Since their first demonstration,1 superconducting nanowire single-photon detectors (SNSPDs) have emerged as a key technology for optical quantum information processing.2 Their low dark count rate, fast response time, small jitter, and high efficiency favor their use in various demanding quantum optics applications such as quantum key distribution,3 quantum networking,4 device-independent quantum information processing,5 deep-space optical communication,6 IR-imaging,7,8 and integration in photonic circuits.9–11 

One advance in the SNSPD field has been the introduction of amorphous superconductors such as tungsten silicide (WSi)12 and molybdenum silicide (MoSi).13–16 SNSPDs based on these materials currently have the highest reported system detection efficiencies (SDEs) (93% for WSi12). Their amorphous properties make them materials of choice for applications where the film quality and yield are crucial, such as multimode coupled SNSPDs or large arrays.17 

The jitter is a crucial characteristic for time-resolved measurements such as light detection and ranging, high-speed quantum communication, and lifetime measurement of single-photon sources. It denotes the timing variation of the arrival time of the detection pulses. Assuming independent contributions,18,19 the total measured jitter can be written as the following: jsystem2=jsetup2+jnoise2+jintrinsic2+jgeometric2, 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 linked to the path the signal has to propagate depending on the photon absorption location in the nanowire.19 

A wide range of values have been reported for different geometries and materials, typically from a few to hundreds of picoseconds.14,18,20,21 A record value of 2.7 ps at 400 nm wavelength has been recently achieved with a NbN device.22 A recent study with MoSi meandered devices showed that a low jitter value (26 ps at 1550 nm) is achievable with amorphous material.16 Despite recent theoretical studies,23,24 the lowest experimental jitter achievable with SNSPDs is still not clear, and the fundamental limits remain unknown. Understanding its intrinsic behavior and limits is a mandatory step toward improvements. This letter addresses this question with MoSi-based devices.

We report on devices with a special design, which reduce significantly the geometric jitter component. They have been fabricated and measured with cryogenic amplifiers and measurement setup that reduces the noise jitter component.22 Reaching the intrinsic jitter level is a challenging task. Amorphous material, which is known to exhibit a lower signal-over-noise ratio and a higher inductivity, is more subject to the latching effect. We show that different crucial parameters have to be understood and optimized, namely, the kinetic inductance (Lk) of the devices and its latching current (Ilatch). After overcoming those issues, we were able to reach and quantify the intrinsic jitter for different photon energies and nanowire thicknesses.

The devices are fabricated out of 5, 7, and 9 nm-thick films of Mo0.8Si0.2 deposited by cosputtering. The film is then patterned by a combination of e-beam lithography and reactive ion etching. 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 a meandered inductor, as illustrated in Fig. 1. This nanowire design minimizes the geometric jitter component (jgeometric), while the series inductor is used to prevent the latching effect.22 To probe the nanowire cross-section dependence of the intrinsic jitter (jintrinsic), the nanowire width is 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.

FIG. 1.

(a) Scanning electron microscope image. The device is 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.

FIG. 1.

(a) Scanning electron microscope image. The device is 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.

Close modal

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 SNSPD was amplified with SiGe cryogenic amplifiers from Cosmic Microwave. For the slew rate vs the kinetic inductance characterization 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 kΩ resistive 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.25 

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 copropagated 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 min. The histograms are fitted with an exponentially modified gaussian (EMG) function, and the jitter was obtained by taking the FWHM of this distribution.

The first part of this work consisted of 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.26 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, we define Ilatch as the current at which the count rate of the detector drops down to zero. Experimentally, we observed that Ilatch does not depend on the nanowire cross section but only on the series inductance. When Ilatch was high enough, oscillations-relaxation phenomenon was observed when operating the device higher than the switching current (Isw). 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 slowed down, meaning a lower slew rate (SR) and consequently a larger noise jitter. The last point is crucial to reach intrinsically-limited jitter. The jitter induced by the gaussian noise of the cryogenic amplifier can be estimated by16,18

jnoise=22ln2σRMSSR,
(1)

where σRMS is the amplifier RMS noise and SR is the slew rate of the detection signal.

Figure 2 shows the slew rate and the jitter induced by the noise for 120 nm wide, 7 nm thick nanowires, with different kinetic inductances ranging from 100 nH to 1000 nH. During the screening process, inductances bigger than 1000 nH yielded very slow slew rates and consequently high noise jitter. For clarity purpose, the data in Fig. 2 were restrained to low series inductances. The slew rate is extracted from oscilloscope traces and is plotted in Fig. 2(a) as a function of the bias current. Figure 2(b) shows the corresponding estimated jitter induced by the electrical noise as described in Eq. (1) as a function of the bias current.

FIG. 2.

Dataset for 120 nm wide, 7 nm thick nanowires, with different kinetic inductances. (a) Slew rate of the signal rising edge for devices with different kinetic inductances (shown in the legend). (b) Estimated jitter induced by the electrical noise [described in Eq. (1)] as a function of the bias current. The stars indicate the latching current for the corresponding devices.

FIG. 2.

Dataset for 120 nm wide, 7 nm thick nanowires, with different kinetic inductances. (a) Slew rate of the signal rising edge for devices with different kinetic inductances (shown in the legend). (b) Estimated jitter induced by the electrical noise [described in Eq. (1)] as a function of the bias current. The stars indicate the latching current for the corresponding devices.

Close modal

A compromise between Lk, Ilatch, SR, and consequently jsystem has to be found. Regarding Fig. 2, 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.

Once the latching current for a given Lk is known, we selected devices with the lowest Lk possible that still satisfied Ilatch>Isw to ensure optimal performances. The best detectors for each thickness were selected for energy-dependence measurements as shown in Table I. 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 reflections and oscillations. Depending on the amplifier design, the oscillations might actually help the detector to recover from its resistive state and hence increase the latching current. The details of this mechanism and the exact explanations are left for future work.

TABLE I.

List of the selected devices for energy-dependence measurements, and their system jitter.

ThicknessWidthLkWavelength (nm)
(nm)(nm)(nH)53277510641550
#1 120 200 6.2 6.5 8.8 10.7 ps 
#2 100 200 6.0 6.4 7.8 10.6 ps 
#3 80 250 7.0 7.3 9.5 14.4 ps 
ThicknessWidthLkWavelength (nm)
(nm)(nm)(nH)53277510641550
#1 120 200 6.2 6.5 8.8 10.7 ps 
#2 100 200 6.0 6.4 7.8 10.6 ps 
#3 80 250 7.0 7.3 9.5 14.4 ps 

Figure 3(a) shows the timing histogram for the 7 nm thick device measured for a bias current of 17.9μA, as indicated by the circles in Fig. 3(b). The FWHMs of the distributions are 6.0±0.2 ps and 10.6±0.2 ps at 532 nm and 1550 nm wavelength, respectively. A nongaussian tail is clearly observed, and it becomes more apparent for long wavelengths and low bias currents; this behavior has also been reported in many studies,16,22,23 but its origin remains unclear. The jitter energy dependence is plotted in Fig. 3(b). The 5 nm and 9 nm-thick devices exhibit qualitatively the same behavior, and the results are summarized in Table I. One notable difference between thicknesses 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.

FIG. 3.

Results for 7 nm-thick and 100 nm-large devices. (a) Jitter histogram at 532 and 1550 nm for a bias current of 17.9μA, as indicated by the circles in (b). The lines represent the exponentially modified gaussian fit. (b) Jitter FWHM as a function of the bias current, for different wavelengths. (c) Photon count rates for the same wavelengths as shown in (b).

FIG. 3.

Results for 7 nm-thick and 100 nm-large devices. (a) Jitter histogram at 532 and 1550 nm for a bias current of 17.9μA, as indicated by the circles in (b). The lines represent the exponentially modified gaussian fit. (b) Jitter FWHM as a function of the bias current, for different wavelengths. (c) Photon count rates for the same wavelengths as shown in (b).

Close modal

The exact value of jintrinsic can be determined precisely only if we know all the other components, which is practically extremely difficult and experimentally imprecise. Instead of trying to determine its absolute value, we can have the following approach: for the same bias current, jsetup, jnoise, and jgeometric are independent of the photon wavelength. One way to quantify jintrinsic is to compare jsystem at a given wavelength relatively to jsystem at 532 nm. By doing so, we can probe the intrinsic component very precisely, and this is well illustrated in Fig. 3(b). The intrinsic behavior becomes clearer for low bias currents and longer wavelengths.

At 532 nm, the system jitter of device #2 is 6.0 ps, while its noise jitter was estimated to be 5 ps. If we subtract the noise jitter to the system jitter, i.e., the noise contribution would be totally negligible, and the remaining jitter goes down to roughly 3.5 ps. While this value seems very close to 2.7 ps of the NbN-based devices,22 the difference appears more clearly for longer wavelengths, where NbN achieved 4.6 ps at 1550 nm, while MoSi achieved 8.6 ps (after subtracting the noise). This shows that MoSi-based devices seem to yield larger jitter, and the fact that this remaining jitter is purely intrinsic seems to point to a material difference for long wavelengths. A full theoretical explanation of this remains to be formulated. We, however, note that in the recently introduced modified time-dependent Ginzburg-Landau model of Allmaras et al.,27 the electron-electron inelastic scattering time τee is the material parameter that has the dominating influence on the value of the intrinsic jitter of NbN. Our observation could indicate that MoSi has a larger τee than NbN. The energy-dependence data sets are currently being analyzed following this theoretical framework including the intrinsic jitter behavior and Fano fluctuations. While this model fits very well data with NbN devices, our study adds experimental inputs and could lead to a better understanding of intrinsic jitter mechanisms and to an unified detection mechanism model.

In conclusion, we reported the intrinsically-limited timing jitter with MoSi SNSPDs. We developed an experimental setup that minimize every component of the system jitter of our SNSPDs and allows us to probe and quantify the intrinsic jitter. To reach this intrinsic level with amorphous materials, numerous crucial issues had to be overcome. We showed that the kinetic inductance has to be minimized, taking into account the latching current of the detector. The energy dependence of the intrinsic jitter is shown and points to a material limitation of MoSi-based devices for wavelengths longer than 1064 nm. Finally, we observed that the intrinsic jitter is higher for thicker devices and longer wavelengths. System timing jitter of 6.0 ps at 532 nm and 10.6 ps at 1550 nm photon wavelength has been obtained.

The authors would like to acknowledge the Swiss National Center of Competence in Research—Quantum Science and Technology and the Swiss National Science Foundation (Grant No. 200021E-176284) for financial support. Part of this work was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Support for this work was provided in part by the Defense Advanced Research Projects Agency (DARPA) Defense Sciences Office, through the DETECT program.

1.
G. N.
Gol’tsman
,
O.
Okunev
,
G.
Chulkova
,
A.
Lipatov
,
A.
Semenov
,
K.
Smirnov
,
B.
Voronov
,
A.
Dzardanov
,
C.
Williams
, and
R.
Sobolewski
,
Appl. Phys. Lett.
79
,
705
(
2001
).
2.
R. H.
Hadfield
,
Nat. Photonics
3
,
696
(
2009
).
3.
A.
Boaron
,
G.
Boso
,
D.
Rusca
,
C.
Vulliez
,
C.
Autebert
,
M.
Caloz
,
M.
Perrenoud
,
G.
Gras
,
F.
Bussières
,
M.-J.
Li
,
D.
Nolan
,
A.
Martin
, and
H.
Zbinden
,
Phys. Rev. Lett.
121
,
190502
(
2018
).
4.
F.
Bussières
,
C.
Clausen
,
A.
Tiranov
,
B.
Korzh
,
V. B.
Verma
,
S. W.
Nam
,
F.
Marsili
,
A.
Ferrier
,
P.
Goldner
,
H.
Herrmann
,
C.
Silberhorn
,
W.
Sohler
,
M.
Afzelius
, and
N.
Gisin
,
Nat. Photonics
8
,
775
(
2014
).
5.
L. K.
Shalm
,
E.
Meyer-Scott
,
B. G.
Christensen
,
P.
Bierhorst
,
M. A.
Wayne
,
M. J.
Stevens
,
T.
Gerrits
,
S.
Glancy
,
D. R.
Hamel
,
M. S.
Allman
,
K. J.
Coakley
,
S. D.
Dyer
,
C.
Hodge
,
A. E.
Lita
,
V. B.
Verma
,
C.
Lambrocco
,
E.
Tortorici
,
A. L.
Migdall
,
Y.
Zhang
,
D. R.
Kumor
,
W. H.
Farr
,
F.
Marsili
,
M. D.
Shaw
,
J. A.
Stern
,
C.
Abellán
,
W.
Amaya
,
V.
Pruneri
,
T.
Jennewein
,
M. W.
Mitchell
,
P. G.
Kwiat
,
J. C.
Bienfang
,
R. P.
Mirin
,
E.
Knill
, and
S. W.
Nam
,
Phys. Rev. Lett.
115
,
250402
(
2015
).
6.
M.
Shaw
,
K.
Birnbaum
,
M.
Cheng
,
M.
Srinivasan
,
K.
Quirk
,
J.
Kovalik
,
A.
Biswas
,
A. D.
Beyer
,
F.
Marsili
,
V.
Verma
,
R. P.
Mirin
,
S. W.
Nam
,
J. A.
Stern
, and
W. H.
Farr
, CLEO: 2014 (Optical Society of America, 2014), p. SM4J.2.
7.
M. S.
Allman
,
V. B.
Verma
,
M.
Stevens
,
T.
Gerrits
,
R. D.
Horansky
,
A. E.
Lita
,
F.
Marsili
,
A.
Beyer
,
M. D.
Shaw
,
D.
Kumor
,
R.
Mirin
, and
S. W.
Nam
,
Appl. Phys. Lett.
106
,
192601
(
2015
).
8.
Q.-Y.
Zhao
,
D.
Zhu
,
N.
Calandri
,
A. E.
Dane
,
A. N.
McCaughan
,
F.
Bellei
,
H.-Z.
Wang
,
D. F.
Santavicca
, and
K. K.
Berggren
,
Nat. Photonics
11
,
247
(
2017
).
9.
J. P.
Sprengers
,
A.
Gaggero
,
D.
Sahin
,
S.
Jahanmirinejad
,
G.
Frucci
,
F.
Mattioli
,
R.
Leoni
,
J.
Beetz
,
M.
Lermer
,
M.
Kamp
,
S.
Höfling
,
R.
Sanjines
, and
A.
Fiore
,
Appl. Phys. Lett.
99
,
181110
(
2011
).
10.
P.
Rath
,
O.
Kahl
,
S.
Ferrari
,
F.
Sproll
,
G.
Lewes-Malandrakis
,
D.
Brink
,
K.
Ilin
,
M.
Siegel
,
C.
Nebel
, and
W.
Pernice
,
Light Sci. Appl.
4
,
e338
(
2015
).
11.
S. C.
Ferrari
and
S.
W. Pernice
,
Nanophotonics
7
,
1725
(
2018
).
12.
F.
Marsili
,
V. B.
Verma
,
J. A.
Stern
,
S.
Harrington
,
A. E.
Lita
,
T.
Gerrits
,
I.
Vayshenker
,
B.
Baek
,
M. D.
Shaw
,
R. P.
Mirin
, and
S. W.
Nam
,
Nat. Photonics
7
,
210
(
2013
).
13.
Y. P.
Korneeva
,
M. Y.
Mikhailov
,
Y. P.
Pershin
,
N. N.
Manova
,
A. V.
Divochiy
,
Y. B.
Vakhtomin
,
A. A.
Korneev
,
K. V.
Smirnov
,
A. G.
Sivakov
,
A. Y.
Devizenko
, and
G. N.
Goltsman
,
Supercond. Sci. Technol.
27
,
095012
(
2014
).
14.
V. B.
Verma
,
B.
Korzh
,
F.
Bussières
,
R. D.
Horansky
,
S. D.
Dyer
,
A. E.
Lita
,
I.
Vayshenker
,
F.
Marsili
,
M. D.
Shaw
,
H.
Zbinden
,
R. P.
Mirin
, and
S. W.
Nam
,
Opt. Express
23
,
33792
(
2015
).
15.
M.
Caloz
,
B.
Korzh
,
N.
Timoney
,
M.
Weiss
,
S.
Gariglio
,
R. J.
Warburton
,
C.
Schönenberger
,
J.
Renema
,
H.
Zbinden
, and
F.
Bussières
,
Appl. Phys. Lett.
110
,
083106
(
2017
).
16.
M.
Caloz
,
M.
Perrenoud
,
C.
Autebert
,
B.
Korzh
,
M.
Weiss
,
C.
Schönenberger
,
R. J.
Warburton
,
H.
Zbinden
, and
F.
Bussières
,
Appl. Phys. Lett.
112
,
061103
(
2018
).
17.
J. P.
Allmaras
,
A. D.
Beyer
,
R. M.
Briggs
,
F.
Marsili
,
M. D.
Shaw
,
G. V.
Resta
,
J. A.
Stern
,
V. B.
Verma
,
R. P.
Mirin
,
S. W.
Nam
, and
W. H.
Farr
, Conference on Lasers and Electro-Optics (Optical Society of America, 2017).
18.
L.
You
,
X.
Yang
,
Y.
He
,
W.
Zhang
,
D.
Liu
,
W.
Zhang
,
L.
Zhang
,
L.
Zhang
,
X.
Liu
,
S.
Chen
,
Z.
Wang
, and
X.
Xie
,
AIP Adv.
3
,
072135
(
2013
).
19.
N.
Calandri
,
Q.-Y.
Zhao
,
D.
Zhu
,
A.
Dane
, and
K. K.
Berggren
,
Appl. Phys. Lett.
109
,
152601
(
2016
).
20.
J.
Wu
,
L.
You
,
S.
Chen
,
H.
Li
,
Y.
He
,
C.
Lv
,
Z.
Wang
, and
X.
Xie
,
Appl. Opt.
56
,
2195
(
2017
).
21.
V.
Shcheslavskiy
,
P.
Morozov
,
A.
Divochiy
,
Y.
Vakhtomin
,
K.
Smirnov
, and
W.
Becker
,
Rev. Sci. Instrum.
87
,
053117
(
2016
).
22.
B. A.
Korzh
,
Q.-Y.
Zhao
,
S.
Frasca
,
J. P.
Allmaras
,
T. M.
Autry
,
E. A.
Bersin
,
M.
Colangelo
,
G. M.
Crouch
,
A. E.
Dane
,
T.
Gerrits
,
F.
Marsili
,
G.
Moody
,
E.
Ramirez
,
J. D.
Rezac
,
M. J.
Stevens
,
E. E.
Wollman
,
D.
Zhu
,
P. D.
Hale
,
K. L.
Silverman
,
R. P.
Mirin
,
S. W.
Nam
,
M. D.
Shaw
, and
K. K.
Berggren
(2018); e-print arXiv:1804.06839.
23.
M.
Sidorova
,
A.
Semenov
,
H.-W.
Hübers
,
I.
Charaev
,
A.
Kuzmin
,
S.
Doerner
, and
M.
Siegel
,
Phys. Rev. B
96
,
184504
(
2017
).
24.
D. Y.
Vodolazov
,
Phys. Rev. Appl.
11
,
014016
(
2019
).
25.
C.
Cahall
,
D. J.
Gauthier
, and
J.
Kim
,
Rev. Sci. Instrum.
89
,
063117
(
2018
).
26.
A. J.
Kerman
,
J. K. W.
Yang
,
R. J.
Molnar
,
E. A.
Dauler
, and
K. K.
Berggren
,
Phys. Rev. B
79
,
100509
(
2009
).
27.
J. P.
Allmaras
,
A. G.
Kozorezov
,
B. A.
Korzh
,
K. K.
Berggren
, and
M. D.
Shaw
,
Phys. Rev. Appl.
11
,
034062
(
2019
).