Timing Jitter in NbN Superconducting Microstrip Single-Photon Detector

D.Yu. Vodolazov, N.N. Manova, Yu.P. Korneeva, and A.A. Korneev

Phys. Rev. Applied 14, 044041 – Published 21 October 2020

Abstract

We experimentally study timing jitter of single-photon detection by NbN superconducting strips with width $w$ ranging from 190 nm to $3 μ m$ . We find that timing jitter of both narrow (190 nm) and micron-wide strips is about 40 ps at currents where internal detection efficiency $η$ saturates and it is close to our instrumental jitter. We also calculate intrinsic timing jitter in wide strips using the modified time-dependent Ginzburg-Landau equation coupled with a two-temperature model. We find that with increasing width the intrinsic timing jitter increases and the effect is most considerable at currents where a rapid growth of $η$ changes to saturation. We relate it with complicated vortex and antivortex dynamics, which depends on a photon’s absorption site across the strip and its width. The model also predicts that at current close to depairing current the intrinsic timing jitter of a wide strip could be about $ℏ / k_{B} T_{c}$ ( $T_{c}$ is a critical temperature of superconductor), i.e., the same as for a narrow strip.

Received 10 June 2020
Revised 13 September 2020
Accepted 22 September 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.044041

Physics Subject Headings (PhySH)

Optoelectronics Vortices in superconductors

Low-temperature superconductors Optical sources & detectors Thin films

Photon counting

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D.Yu. Vodolazov ^1,2,†, N.N. Manova ¹, Yu.P. Korneeva ^1,*, and A.A. Korneev ^1,3

¹Physics Department, Moscow Pedagogical State University, Moscow 119991, Russia
²Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod GSP-105, Russia
³National Research University Higher School of Economics, Moscow 101000, Russia

^*korneeva@rplab.ru
^†vodolazov@impras.ru

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Vol. 14, Iss. 4 — October 2020

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Images

Figure 1
Probability density function for NbN strips with different widths found at different currents corresponding to $η = 0.2$ , 0.5, 0.95, and $I \approx I_{c}$ [see Fig. 2].
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Figure 2
(a) Dependence of the timing jitter and (b) dependence of internal detection efficiency $η$ on normalized bias current $I / I_{dep}$ . Black line in (a) is the instrumental jitter for the narrowest sample, colored lines are the instrumental jitter for all other samples. The higher level of the instrumental jitter of the narrowest sample is caused by the small current of the sample resulting in small magnitude of voltage pulse. Dashed lines in (b) denote IDE levels of 0.2, 0.5, and 0.95. The IDE curves are not placed monotonously from left to right according to strip width. This is the consequence of not having sufficient accuracy in sample current measurement. Although it does not affect our results concerning jitter. The inset shows depairing current $I_{dep}$ , measured critical current $I_{c}$ , and current corresponding to IDE = 0.5 ( $I_{IDE = 0.5}$ for samples of different width. Good linear dependencies confirm that the samples do not have any noticeable defects.
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Figure 3
(a) Position-dependent delay time in the strip with width $w = 120 ξ_{c}$ calculated at different currents (bath temperature $T = 0.5 T_{c}$ and photon energy $E = 1$ eV). (b) Dependence of $τ_{d}$ on deposited energy for three photon-absorption sites $y = 10, 36, 60 ξ_{c}$ and two values of the current ( $τ_{c} = ℏ / k_{B} T_{c}$ ).
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Figure 4
Time dependence of the voltage drop along the superconducting strip (time is normalized in units of $τ_{c} = ℏ / k_{B} T_{c}$ ) after absorption of the photon at different sites $y = 10 ξ_{c}$ (red curve) and $y = 36 ξ_{c}$ (black curve) across the strip with width $120 ξ_{c}$ . In the insets we show the snapshots of the superconducting order parameter at different times. Current $I = 0.7 I_{dep}$ , $T = 0.5 T_{c}$ , $E = 1$ eV. The yellow region corresponds to the channel with a suppressed order parameter. Red color corresponds to the largest $Δ$ . Two red regions appear because current deviates from the hot region and locally $Δ$ becomes larger (current density locally goes down). At $50 τ_{c}$ (in the case of $y = 36 ξ_{c}$ , black curve), $Δ$ partially recovers in the hotspot and locally current density is increased and $Δ$ goes down. At the moment of time $t = 120 τ_{c}$ , the channel with suppressed $Δ$ appears at the left edge, superconducting current deviates, and $Δ$ increases until two red regions appear again.
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Figure 5
Probability density function calculated for different currents and widths. In calculations we choose $\bar{E} = 1$ eV and $σ = 0.1 \bar{E}$ , which roughly corresponds to photons with energy 1.1–1.2 eV. The best jitter values that we measure at currents near $I_{c}$ , are in the range from 19.6 ps (for $0.19 μ m$ strip) to 28 ps (for 3- $μ m$ -wide strip), which correspond to $23 τ_{c} - 36 τ_{c}$ .
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