IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 2, JUNE 2005 545 Origin of Dark Counts in Nanostructured NbN Single-Photon Detectors J. Kitaygorsky, J. Zhang, A. Verevkin, A. Sergeev, A. Korneev, V. Matvienko, P. Kouminov, K. Smirnov, B. Voronov, G. Gol’tsman, and Roman Sobolewski Abstract—We present our study of dark counts in ultrathin (3.5 to 10 nm thick), narrow (120 to 170 nm wide) NbN superconducting stripes of different lengths. In experiments, where the stripe was completely isolated from the outside world and kept at tempera- ture below the critical temperature , we detected subnanosecond electrical pulses associated with the spontaneous appearance of the temporal resistive state. The resistive state manifested itself as gen- eration of phase-slip centers (PSCs) in our two-dimensional su- perconducting stripes. Our analysis shows that not far from , PSCs have a thermally activated nature. At lowest temperatures, far below , they are created by quantum fluctuations. Index Terms—Dark counts, phase-slip centers, quantum fluctu- ations, single-photon detectors, two-dimensional superconducting stripes. I. INTRODUCTION D ARK counts in NbN superconducting single-photon detectors (SSPDs) strongly correlate with the device quantum efficiency (QE) and determine the ultimate sensitivity of the detector and its noise-equivalent power (NEP) [1]. The nature of dark counts needs to be clarified to further improve our SSPDs. It will also shed a new light on the dynamical behavior of two-dimensional (2-D) and quasi one-dimensional (1-D) superconducting nanostructures. No comprehensive model is capable of explaining the ex- istence of a temporal resistive state in ultrathin (thickness ), relatively narrow (width ) supercon- ducting stripes forming practical SSPDs, kept at temperature far below the critical temperature . Such stripes are essen- tially 2-D superconducting structures, since both the coherence length and the thermal length are larger than at, e.g., . Clearly, vortices cannot propagate through such narrow channels, and, simultaneously, Andreev reflections seem to be too strong for normal-state regions to appear at such temperatures. On the other hand, our stripes are too wide Manuscript received October 4, 2004. This work was supported in part by the US AFOSR under Grant FA9550-04-1-0123 (Rochester), in part by the CRDF under Grant RE2-2529-MO-03 (Moscow and Rochester), in part by the RFBR under Grant 03-02-17697 (Moscow), and in part by an MIT Lincoln Laboratory grant. J. Kitaygorsky, A. Verevkin, and R. Sobolewski are with the University of Rochester, Rochester, NY 14623 USA (e-mail: kitaygor@ece.rochester.edu). J. Zhang was with the University of Rochester, Rochester, NY 14627 USA. He is now with Stanford University, Stanford, CA 94305 USA. A. Sergeev is with the University at Buffalo, State University of New York, Buffalo, NY 14260 USA. A. Korneev, V. Matvienko, P. Kouminov, K. Smirnov, B. Voronov, and G. Gol’tsman are with the Moscow State Pedagogical University, Moscow 119345, Russia. Digital Object Identifier 10.1109/TASC.2005.849914 to directly apply the well-known Langer-Ambegaokar-Mc- Cumber-Halperin (LAMH) theory [2], [3] for phase-slip centers (PSCs) in 1-D superconducting wires. In the SSPD’s photoresponse model, the diameter of an ini- tial hotspot induced by the incident photon is always taken to be significantly smaller than [1], [4], and the appearance of the resistive state across the stripe is due to the supercurrent redistri- bution and formation of PSCs on the sides of the hotspot. In this description, it is difficult to explain the SSPD response to pho- tons, when the device is biased at currents far below the stripe critical current . In fact, the simple model predicts a step-func- tion-like behavior of the dependence of the counting rate versus [5], [6], i.e., for a given hotspot size, the photoresponse can be observed only when is higher than a certain threshold value. This simple prediction disagrees with our experimental data [1], [4], [5], showing near-to-exponential dependence of the photon counting rate versus . We also routinely observe exponential behavior of the dark counts rate versus [1], [4]. In this paper, we report on our measurements of dark counts in nanostructured SSPDs and in simple 2-D superconducting stripes. Our experiments are performed on dc-biased NbN de- vices, maintained at and completely isolated from the outside sources of radiation. We observe transient resistive states in our stripes, measured as a train of voltage pulses that can be explained by PSC formation in our 2-D superconducting nanostructures [7]. Spontaneous PSC generation in SSPDs sets the performance limitation similar to the PSC role in the super- conducting quantum computing devices [8], [9]. II. DEVICES AND EXPERIMENTAL SETUP NbN superconducting films used to fabricate our test struc- tures had thicknesses ranging from 3.5 to 10 nm and were de- posited on -plane sapphire substrates by dc reactive magnetron sputtering. The thinnest, 3.5-nm-thick films were characterized by the surface resistivity of about 160 at , , , and critical current density to at 4.2 K. The deposition process of NbN films was described in detail in [10] and [11]. The samples used in our experiments were made of two ge- ometries: (i) single stripes with the length of 10 , and (ii) meander-type structures that covered a area and had different meander widths, resulting in different total lengths. The test structures were patterned using direct electron-beam lithography and reactive ion etching [11]. The nominal widths of our superconducting stripes were 120 to 170 nm. Table I presents the parameters of the devices used in this study. 1051-8223/$20.00 © 2005 IEEE