IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 17, NO. 3, SEPTEMBER 2007 3789 Physical Modeling of Hot-Electron Superconducting Single-Photon Detectors Zhizhong Yan, Student Member, IEEE, A. Hamed Majedi, Member, IEEE, and Safieddin Safavi-Naeini, Member, IEEE Abstract—In this paper, we treat the incident photons as an elec- tromagnetic plane wave and simulate the wave power coupling to the the hot-electron superconducting single-photon detector to in- vestigate its connection with the experimental system quantum ef- ficiency over different wavelengths. Then we propose a lumped equivalent circuit model based on the kinetic inductance variation induced by the incident photon stream when the serpentine super- conducting thin-film nano-wire is dc-biased close to its critical cur- rent. The computed output voltage matches experimental results for both amplitude and frequency. Index Terms—Circuit simulation, electromagnetic (EM) propa- gation, photonics, quantum optics, superconducting devices, super- conducting optoelectronics, superconducting radiation detectors. I. INTRODUCTION T HE research of optical single-photon detectors recently has made remarkable progress. They are of key significance in attaining the highest resolution to discern the number of in- coming photons. Among these detectors, hot-electron supercon- ducting single-photon detectors (HE-SSPDs) proposed in [1] have received considerable attention because of their particular characteristics of high counting rates, low phase jitters, low dark counts [2], [3], and a lower operational temperature constraint compared to transition edge superconducting photon detectors [4], [5]. In contrast, semiconductor avalanche photon detectors based on the Geiger counting mode have longer recovery time, resulting in a counting speed of only a few megahertz [6], [7]. The slower counting speed prevents the quantum communica- tion from getting higher transfer bandwidth [8]. Recently, optical HE-SSPDs have found applications in three main areas: free-space quantum communication [9], VLSI quality control [10], [11], and fiber-optics communication [12], [13]. Other potential applications include astronomy [14], [15], biological living cell chemical reaction monitoring, and linear optics quantum computation. Manuscript received March 29, 2006; revised August 16, 2006 and September 28, 2006. This work was supported by the Canadian Institute for Photonic Inno- vations (CIPI) and by the Institute for Quantum Computing (IQC), University of Waterloo. This paper was recommended by Associate Editor M. Mueck. Z. Yan and A. H. Majedi are with the Department of Electrical and Computer Engineering and the Institute for Quantum Computing (IQC), University of Wa- terloo, Waterloo, ON N2L 3G1, Canada (e-mail: zyan@maxwell.uwaterloo.ca; ahmajedi@maxwell.uwaterloo.ca). S. Safavi-Naeini is with the Department of Electrical and Computer En- gineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: safavi@maxwell.uwaterloo.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2007.906001 HE-SSPDs are fabricated on a low-temperature supercon- ducting thin film, e.g., niobium nitride (NbN) thin film, sput- tered onto sapphire or silicon substrates. The sputtered thin film is then patterned into nano-serpentine strips to construct the photon detection area. The size of the area is usually a few tens of square micrometers [16]–[18]. The photon detection mech- anism of HE-SSPDs has been developed as a particle based model in which the incident photons are treated as indepen- dent particles. When a photon has been absorbed, the localized heating formulates a small hotspot in which the superconduc- tivity is suppressed or even destroyed locally because the photon energy introduces a local disequilibrium perturbation with a large number of excited hot electrons, leading to an in- crease of the average electron temperature close to or above . The bias supercurrent is thus expelled from the hotspot volume to the “sidewalks” between the hotspot and the edges of the film. If the bias current exceeds the critical current in the side- walks, a resistive barrier is formed across the entire width of the nano-wire, resulting in a voltage signal. The conclusion of this view is the so-called “hotspot” model [19]–[21]. The hotspot model matches well experimental observations for high energy particles such as or particles. However, when the wavelength associated with the photon energy becomes longer, this model begins to disagree with quantum efficiency (QE) mea- surements [13], [26], [31]. When the wavelength of photon flux falls in the range of visible light or even longer, the diameter of the hotspot generated by the incident photon flux becomes smaller than the width of serpentine nano-wire. Thus, the HE-SSPD pho- toresponse is expected to abruptly disappear at a given bias cur- rent density ratio to the critical current density in conjunc- tion with a given wavelength. However, this prediction disagrees with the experimental results, in particular when the thickness of HE-SSPD nano-wire strips is close to 10 nm [13], [26], [31]. To justify this contradiction, Semenov [22] et al. proposed a refined hotspot model to account for disordered NbN HE-SSPD whose energy gap and coherence length are both reduced. On the other hand, for epitaxial NbN-based HE-SSPDs, the theory of a phase slip center (PSC) caused by either thermal or quantum fluctuations seems to be a promising approach. However, it has been argued that 1-D quantum phase slip is not an observable, given the width of HE-SSPD nano-structured wires [23], [24]; on the other hand, the thermal PSC can occur only at a temper- ature very close to its critical point. The goal of single-photon detection is to detect or retrieve the number of photons in the photon flux associated with the electromagnetic (EM) waves. However, the known parameters to the experimentalist are the wavelength , average photon 1051-8223/$25.00 © 2007 IEEE