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Semenov, A. D., & Gol’tsman, G. N. (2000). Nonthermal mixing mechanism in a diffusion-cooled hot-electron detector. J. Appl. Phys., 87(1), 502–510.
Abstract: We present an analysis of a diffusion-cooled hot-electron detector fabricated from clean superconducting material with low transition temperature. The distinctive feature of a clean material, i.e., material with large electron mean free path, is a relatively weak inelastic electron scattering that is not sufficient for the establishment of an elevated thermodynamic electron temperature when the detector is subjected to irradiation. We propose an athermal model of a diffusion-cooled detector that relies on suppression of the superconducting energy gap by the actual dynamic distribution of excess quasiparticles. The resistive state of the device is caused by the electric field penetrating into the superconducting bridge from metal contacts. The dependence of the penetration length on the energy gap delivers the detection mechanism. The sources of the electric noise are equilibrium fluctuations of the number of thermal quasiparticles and frequency dependent shot noise. Using material parameters typical for A1, we evaluate performance of the device in the heterodyne regime at terahertz frequencies. Estimates show that the mixer may have a noise temperature of a few quantum limits and a bandwidth of a few tens of GHz, while the required local oscillator power is in the μW range due to ineffective suppression of the energy gap by quasiparticles with high energies.
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Nebosis, R. S., Steinke, R., Lang, P. T., Schatz, W., Heusinger, M. A., Renk, K. F., et al. (1992). Picosecond YBa2Cu3O7−δdetector for far‐infrared radiation. J. Appl. Phys., 72(11), 5496–5499.
Abstract: We report on a picosecond YBa2Cu3O7−δ detector for far‐infrared radiation. The detector, consisting of a current carrying structure cooled to liquid‐nitrogen temperature, was studied by use of ultrashort laser pulses from an optically pumped far‐infrared laser in the frequency range from 25 to 215 cm−1. We found that the sensitivity (1 mV/W) was almost constant in this frequency range. We estimated a noise equivalent power of less than 5×10−7 W Hz−1/2. Taking into account the results of a mixing experiment (in the frequency range from 4 to 30 cm−1) we suggest that the response time of the detector was few picoseconds.
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Gousev, Y. P., Gol'tsman, G. N., Karasik, B. S., Gershenzon, E. M., Semenov, A. D., Barowski, H. S., et al. (1996). Quasioptical superconducting hot electron bolometer for submillmeter waves. Int. J. of Infrared and Millimeter Waves, 17(2), 317–331.
Abstract: We report on a superconducting hot electron bolometer coupled to radiation via a broadband antenna. The bolometer, a structured NbN film, was patterned on a thin dielectric membrane between terminals of a gold slotline antenna. We investigated the response to submillimeter radiation (wave-lengths ∼ 0.1 mm to 0.7 mm) in the fundamental Gaussian mode. We found that the directivity of the antenna was constant within a factor of 2.5 through the whole experimental range. The noise equivalent power of the bolometer at 119 µm was ∼ 3 · 10−13 W/Hz1/2; a time constant of ∼ 160 ps was estimated.
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Lang, P. T., Knott, W. J., Leipold, I., Renk, K. F., Semenov, A. D., & Gol'tsman, G. N. (1992). Generation and detection of tunable ultrashort infrared and far-infrared radiation pulses of high intensity. Int. J. of Infrared and Millimeter Waves, 13(3), 373–380.
Abstract: We report on generation and detection of intense pulsed radiation with frequency tunability in the infrared and far-infrared spectral regions. Infrared radiation is generated with a transversally electrically excited high pressure CO2 laser. A laser pulse of a total duration of about 300 ns consisted, due to self mode locking, of a series of single pulses, some with pulse durations of less than 450 ps and peak powers larger than 20 MW. Using these pulses for optical with durations less than 400 ps were obtained. For detection a new ultrafast superconducting detector was used.
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Schubert, J., Semenov, A., Hübers, H. - W., Gol'tsman, G., Schwaab, G., Voronov, B., et al. (1999). Broad-band terahertz NbN hot-electron bolometric mixer. In Inst. Phys. Conf. (Vol. 167, pp. 663–666).
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Hübers, H. - W., Schubert, J., Krabbe, A., Birk, M., Wagner, G., Semenov, A., et al. (2001). Parylene anti-reflection coating of a quasi-optical hot-electron-bolometric mixer at terahertz frequencies. Infrared Physics & Technology, 42(1), 41–47.
Abstract: Parylene C was investigated as anti-reflection coating for silicon at terahertz frequencies. Measurements with a Fourier-transform spectrometer show that the transmittance of pure silicon can be improved by about 30% when applying a layer of Parylene C with a quarter wavelength optical thickness. The 10% bandwidth of this coating extends from 1.5 to 3 THz for a center frequency of 2.3–2.5 THz, where the transmittance is constant. Heterodyne measurements demonstrate that the noise temperature of a hot-electron-bolometric mixer can be reduced significantly by coating the silicon lens of the hybrid antenna with a quarter wavelength Parylene C layer. Compared to the same mixer with an uncoated lens the improvement is about 30% at a frequency of 2.5 THz.
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Klapwijk, T. M., & Semenov, A. V. (2017). Engineering physics of superconducting hot-electron bolometer mixers. IEEE Trans. THz Sci. Technol., 7(6), 627–648.
Abstract: Superconducting hot-electron bolometers are presently the best performing mixing devices for the frequency range beyond 1.2 THz, where good-quality superconductor-insulator-superconductor devices do not exist. Their physical appearance is very simple: an antenna consisting of a normal metal, sometimes a normal-metal-superconductor bilayer, connected to a thin film of a narrow short superconductor with a high resistivity in the normal state. The device is brought into an optimal operating regime by applying a dc current and a certain amount of local-oscillator power. Despite this technological simplicity, its operation has found to be controlled by many different aspects of superconductivity, all occurring simultaneously. A core ingredient is the understanding that there are two sources of resistance in a superconductor: a charge-conversion resistance occurring at a normal-metal-superconductor interface and a resistance due to time-dependent changes of the superconducting phase. The latter is responsible for the actual mixing process in a nonuniform superconducting environment set up by the bias conditions and the geometry. The present understanding indicates that further improvement needs to be found in the use of other materials with a faster energy relaxation rate. Meanwhile, several empirical parameters have become physically meaningful indicators of the devices, which will facilitate the technological developments.
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Gershenzon, E. M., Gershenzon, M. E., Goltsman, G. N., Semenov, A. D., & Sergeev, A. V. (1991). Wide-band highspeed Nb and YBaCuO detectors. IEEE Trans. Magn., 27(2), 2836–2839.
Abstract: The physical limitations on the response time and the nature of nonequilibrium detection of radiation were investigated for Nb and YBCO film in a wide spectral range from millimeter to near-infrared wavelengths. In the case of ideal heat removal from the film, the detection mechanism is connected with an electron heating effect which is not selective over a wide spectral interval. For Nb, the dependence of the response time on the electron mean free path l and temperature T is tau varies as T/sup -2/l/sup -1/. The values of detectivity D* and tau are 3*10/sup 11/ W/sup -1/ Hz/sup 1/2/ cm and 5*10/sup -9/ s at T=1.6 K, respectively. For YBCO film the tau value of 1-2 ps at T=77 K was obtained; the NEP value of 3*10/sup -11/ W-Hz/sup -1/2/ can be obtained at T=77 K in the case of the optimal film matching to the radiation.
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Gershenzon, E. M., Gol’tsman, G. N., Gousev, Y. P., Elant’ev, A. I., & Semenov, A. D. (1991). Electromagnetic radiation mixer based on electron heating in resistive state of superconductive Nb and YBaCuO films. IEEE Trans. Magn., 27(2), 1317–1320.
Abstract: A theory of an electron-heating mixer which makes it possible to calculate all the characteristics of the device is developed. It is shown that positive conversion gain is possible for such a mixer in the millimeter to near-infrared wavelength range. The dynamic range and the optimum heterodyne power can be selected from a very wide interval by varying the mixing element volume. Measurements made for Nb within the frequency range of 120-750 GHz confirm the theory. The conversion loss obtained at T=1.6 K and normalized to the element reaches 0.3 dB in the intermediate frequency band of 40 MHz; the possible noise temperature is 50 K. The estimation of noise temperature and output band for YBaCuO at T=77 yields 200 K and more than 10 GHz, respectively.
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Gershenzon, E. M., Gol’tsman, G. N., Semenov, A. D., & Sergeev, A. V. (1991). Mechanism of picosecond response of granular YBaCuO films to electromagnetic radiation. IEEE Trans. Magn., 27(2), 1321–1324.
Abstract: Ultrafast mechanisms of radiation detection in granular YBaCuO films are studied in the wide wavelength range from millimeter waves to near infrared. With an increase in radiation frequency, the Josephson detection at the grain-boundary weak links is replaced by electron heating into the grains. This change occurs in the submillimeter wavelength range. The electron-phonon relaxation time tau /sub eph/ is determined from direct measurements, quasi-stationary electron heating measurements, and the frequency dependence of the current at which maximum voltage shift is observed. The temperature dependence of tau /sub eph/ at T<or=40 K was found to be tau /sub eph/ approximately T/sup -1/. The results show that detectors with a response time of a few picoseconds at nitrogen temperature are attainable.
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Semenov, A. D., Hübers, H. - W., Richter, H., Birk, M., Krocka, M., Mair, U., et al. (2003). Superconducting hot-electron bolometer mixer for terahertz heterodyne receivers. IEEE Trans. Appl. Supercond., 13(2), 168–171.
Abstract: We present recent results showing the development of superconducting NbN hot-electron bolometer mixer for German receiver for astronomy at terahertz frequencies and terahertz limb sounder. The mixer is incorporated into a planar feed antenna, which has either logarithmic spiral or double-slot configuration, and backed on a silicon lens. The hybrid antenna had almost frequency independent and symmetric radiation pattern slightly broader than expected for a diffraction limited antenna. At 2.5 THz the best 2200 K double side-band receiver noise temperature was achieved across a 1 GHz intermediate frequency bandwidth centred at 1.5 GHz. For this operation regime, a receiver conversion efficiency of -17 dB was directly measured and the loss budget was evaluated. The mixer response was linear at load temperatures smaller than 400 K. Implementation of the MgO buffer layer on Si resulted in an increased 5.2 GHz gain bandwidth. The receiver was tested in the laboratory environment by measuring a methanol emission line at 2.5 THz.
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Korneeva, Y., Florya, I., Semenov, A., Korneev, A., & Goltsman, G. (2011). New generation of nanowire NbN superconducting single-photon detector for mid-infrared. IEEE Trans. Appl. Supercond., 21(3), 323–326.
Abstract: We present a break-through approach to mid-infrared single-photon detection based on nanowire NbN superconducting single-photon detectors (SSPD). Although SSPD became a mature technology for telecom wavelengths (1.3-1.55 μm) its further expansion to mid-infrared wavelength was hampered by low sensitivity above 2 μm. We managed to overcome this limit by reducing the nanowire width to 50 nm, while retaining high superconducting properties and connecting the wires in parallel to produce a voltage response of sufficient magnitude. The new device exhibits 10 times better quantum efficiency at 3.5 μm wavelength than the “standard” SSPD.
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Lobanov, Y., Shcherbatenko, M., Finkel, M., Maslennikov, S., Semenov, A., Voronov, B. M., et al. (2015). NbN hot-electron-bolometer mixer for operation in the near-IR frequency range. IEEE Trans. Appl. Supercond., 25(3), 2300704 (1 to 4).
Abstract: Traditionally, hot-electron-bolometer (HEB) mixers are employed for THz and “super-THz” heterodyne detection. To explore the near-IR spectral range, we propose a fiber-coupled NbN film based HEB mixer. To enhance the incident-light absorption, a quasi-antenna consisting of a set of parallel stripes of gold is used. To study the antenna effect on the mixer performance, we have experimentally studied a set of devices with different size of the Au stripe and spacing between the neighboring stripes. With use of the well-known isotherm technique we have estimated the absorption efficiency of the mixer, and the maximum efficiency has been observed for devices with the smallest pitch of the alternating NbN and NbN-Au stripes. Also, a proper alignment of the incident Eâƒ<2014>-field with respect to the stripes allows us to improve the coupling further. Studying IV-characteristics of the mixer under differently-aligned Eâƒ<2014>-field of the incident radiation, we have noticed a difference in their shape. This observation suggests that a difference exists in the way the two waves with orthogonal polarizations parallel and perpendicular Eâƒ<2014>-field to the stripes heat the electrons in the HEB mixer. The latter results in a variation in the electron temperature distribution over the HEB device irradiated by the two waves.
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Gol’tsman, G., Okunev, O., Chulkova, G., Lipatov, A., Dzardanov, A., Smirnov, K., et al. (2001). Fabrication and properties of an ultrafast NbN hot-electron single-photon detector. IEEE Trans. Appl. Supercond., 11(1), 574–577.
Abstract: A new type of ultra-high-speed single-photon counter for visible and near-infrared wavebands based on an ultrathin NbN hot-electron photodetector (HEP) has been developed. The detector consists of a very narrow superconducting stripe, biased close to its critical current. An incoming photon absorbed by the stripe produces a resistive hotspot and causes an increase in the film’s supercurrent density above the critical value, leading to temporary formation of a resistive barrier across the device and an easily measurable voltage pulse. Our NbN HEP is an ultrafast (estimated response time is 30 ps; registered time, due to apparatus limitations, is 150 ps), frequency unselective device with very large intrinsic gain and negligible dark counts. We have observed sequences of output pulses, interpreted as single-photon events for very weak laser beams with wavelengths ranging from 0.5 /spl mu/m to 2.1 /spl mu/m and the signal-to-noise ratio of about 30 dB.
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Korneev, A. A., Korneeva, Y. P., Mikhailov, M. Y., Pershin, Y. P., Semenov, A. V., Vodolazov, D. Y., et al. (2015). Characterization of MoSi superconducting single-photon detectors in the magnetic field. IEEE Trans. Appl. Supercond., 25(3), 2200504 (1 to 4).
Abstract: We investigate the response mechanism of nanowire superconducting single-photon detectors (SSPDs) made of amorphous MoxSi1-x. We study the dependence of photon count and dark count rates on bias current in magnetic fields up to 113 mT at 1.7 K temperature. The observed behavior of photon counts is similar to the one recently observed in NbN SSPDs. Our results show that the detecting mechanism of relatively high-energy photons does not involve the vortex penetration from the edges of the film, and on the contrary, the detecting mechanism of low-energy photons probably involves the vortex penetration from the film edges.
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Korneev, A., Korneeva, Y., Manova, N., Larionov, P., Divochiy, A., Semenov, A., et al. (2013). Recent nanowire superconducting single-photon detector optimization for practical applications. IEEE Trans. Appl. Supercond., 23(3), 2201204 (1 to 4).
Abstract: In this paper, we present our approaches to the development of fiber-coupled superconducting single photon detectors with enhanced photon absorption. For such devices we have measured detection efficiency in wavelength range from 500 to 2000 nm. The best fiber coupled devices exhibit detection efficiency of 44.5% at 1310 nm wavelength and 35.5% at 1550 nm at 10 dark counts per second.
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Lobanov, Y., Shcherbatenko, M., Semenov, A., Kovalyuk, V., Kahl, O., Ferrari, S., et al. (2017). Superconducting nanowire single photon detector for coherent detection of weak signals. IEEE Trans. Appl. Supercond., 27(4), 1–5.
Abstract: Traditional photon detectors are operated in the direct detection mode, counting incident photons with a known quantum efficiency. Here, we have investigated a superconducting nanowire single photon detector (SNSPD) operated as a photon counting mixer at telecommunication wavelength around 1.5 μm. This regime of operation combines excellent sensitivity of a photon counting detector with excellent spectral resolution given by the heterodyne technique. Advantageously, we have found that low local oscillator (LO) power of the order of hundreds of femtowatts to a few picowatts is sufficient for clear observation of the incident test signal with the sensitivity approaching the quantum limit. With further optimization, the required LO power could be significantly reduced, which is promising for many practical applications, such as the development of receiver matrices or recording ultralow signals at a level of less-than-one-photon per second. In addition to a traditional NbN-based SNSPD operated with normal incidence coupling, we also use detectors with a travelling wave geometry, where a NbN nanowire is placed on the top of a Si 3 N 4 nanophotonic waveguide. This approach is fully scalable and a large number of devices could be integrated on a single chip.
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Polyakova, M., Semenov, A. V., Kovalyuk, V., Ferrari, S., Pernice, W. H. P., & Gol'tsman, G. N. (2019). Protocol of measuring hot-spot correlation length for SNSPDs with near-unity detection efficiency. IEEE Trans. Appl. Supercond., 29(5), 1–5.
Abstract: We present a simple quantum detector tomography protocol, which allows, without ambiguities, to measure the two-spot detection efficiency and extract the hot-spot interaction length of superconducting nanowire single photon detectors (SNSPDs) with unity intrinsic detection efficiency. We identify a significant parasitic contribution to the measured two-spot efficiency, related to an effect of the bias circuit, and find a way to rule out this contribution during data post-processing and directly in the experiment. From the data analysis for waveguide-integrated SNSPD, we find signatures of the saturation of the two-spot efficiency and hot-spot interaction length of order of 100 nm.
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Zolotov, P. I., Semenov, A. V., Divochiy, A. V., Goltsman, G. N., Romanov, N. R., & Klapwijk, T. M. (2021). Dependence of photon detection efficiency on normal-state sheet resistance in marginally superconducting films of NbN. IEEE Trans. Appl. Supercond., 31(5), 1–5.
Abstract: We present an extensive set of data on nanowire-type superconducting single-photon detectors based on niobium-nitride (NbN) to establish the empirical correlation between performance and the normal-state resistance per square. We focus, in particular, on the bias current, compared to the expected depairing current, needed to achieve a near-unity detection efficiency for photon detection. The data are discussed within the context of a model in which the photon energy triggers the movement of vortices i.e. superconducting dissipation, followed by thermal runaway. Since the model is based on the non-equilibrium theory for conventional superconductors deviations may occur, because the efficient regime is found when NbN acts as a marginal superconductor in which long-range phase coherence is frustrated.
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Zolotov, P., Semenov, A., Divochiy, A., & Goltsman, G. (2021). A comparison of VN and NbN thin films towards optimal SNSPD efficiency. IEEE Trans. Appl. Supercond., 31(5), 1–4.
Abstract: Based on early phenomenological ideas about the operation of superconducting single-photon detectors (SSPD or SNSPD), it was expected that materials with a lower superconducting gap should perform better in the IR range. The plausibility of this concept could be checked using two popular SSPD materials – NbN and WSi films. However, these materials differ strongly in crystallographic structure (polycrystalline B1 versus amorphous), which makes their dependence on disorder different. In our work we present a study of the single-photon response of SSPDs made from two disordered B1 structure superconductors – vanadium nitride and niobium nitride thin films. We compare the intrinsic efficiency of devices made from films with different sheet resistance values. While both materials have a polycrystalline structure and comparable diffusion coefficient values, VN films show metallic behavior over a wide range of sheet resistance, in contrast to NbN films with an insulator-like temperature dependence of resistivity, which may be partially due to enhanced Coulomb interaction, leading to different starting points for the normal electron density of states. The results show that even though VN devices are more promising in terms of theoretical predictions, their optimal performance was not reached due to lower values of sheet resistance.
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Korneev, A., Korneeva, Y., Florya, I., Semenov, A., & Goltsman, G. (2018). Photon switching statistics in multistrip superconducting single-photon detectors. IEEE Trans. Appl. Supercond., 28(7), 1–4.
Abstract: We study photon count statistics in superconducting single-photon detectors consisting of up to 70 narrow superconducting strips connected in parallel. Using interarrival time analysis, we demonstrate that our samples are operated in the “arm-trigger” regime and require up to seven subsequently absorbed photons to form a resistive state in the whole sample. We also performed numerical simulation of the light and dark count rates versus detector bias current, which are in good agreement with the experimental results.
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Korneeva, Y., Sidorova, M., Semenov, A., Krasnosvobodtsev, S., Mitsen, K., Korneev, A., et al. (2016). Comparison of hot-spot formation in NbC and NbN single-photon detectors. IEEE Trans. Appl. Supercond., 26(3), 1–4.
Abstract: We report an experimental investigation of the hot-spot evolution in superconducting single-photon detectors made of disordered superconducting materials with different diffusivity and energy downconversion time values, i.e., 33-nm-thick NbN and 23-nm-thick NbC films. We have demonstrated that, in NbC film, only 405-nm photons produce sufficiently large hot spot to trigger a single-photon response. The dependence of detection efficiency on bias current for 405-nm photons in NbC is similar to that for 3400-nm photons in NbN. In NbC, large diffusivity and downconversion time result in 1-D critical current suppression profile compared with the usual 2-D profile in NbN.
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Lusche, R., Semenov, A., Il'in, K., Korneeva, Y., Trifonov, A., Korneev, A., et al. (2013). Effect of the wire width and magnetic field on the intrinsic detection efficiency of superconducting nanowire single-photon detectors. IEEE Trans. Appl. Supercond., 23(3), 2200205.
Abstract: We present thorough measurements of the intrinsic detection efficiency in the wavelength range from 350 to 2500 nm for meander-type TaN and NbN superconducting nanowire single-photon detectors with different widths of the nanowire. The width varied from 70 nm to 130 nm. The open-beam configuration allowed us to accurately normalize measured spectra and to extract the intrinsic detection efficiency. For detectors from both materials the intrinsic detection efficiency at short wavelengths amounts at 100% and gradually decreases at wavelengths larger than the specific cut-off wavelengths, which decreases with the width of the nanowire. Furthermore, we show that applying weak magnetic fields perpendicular to the meander plane decreases the smallest detectable photon flux.
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Semenov, A. D., & Gol'tsman, G. N. (1999). Non-thermal response of a diffusion-cooled hot-electron bolometer. IEEE Trans. Appl. Supercond., 9(2), 4491–4494.
Abstract: We present an analysis of a diffusion-cooled hot-electron bolometer in the limiting case of a weak thermalization of non-equilibrium quasiparticles. We propose a new model relying on the non-thermal suppression of the superconducting energy gap by excess quasiparticles. Using material parameters typical for Al, we evaluate performance of the bolometer in the heterodyne regime at terahertz frequencies. Estimates show that the mixer may have quantum limited noise temperature and a few tens of GHz bandwidth, while the required local oscillator power is in the /spl mu/W range due to in-effective suppression of the energy gap by quasiparticles with high energies.
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Gousev, Y. P., Semenov, A. D., Goghidze, I. G., Pechen, E. V., Varlashkin, A. V., Gol'tsman, G. N., et al. (1997). Current dependent noise in a YBa2Cu3O7-δ hot-electron bolometer. IEEE Trans. Appl. Supercond., 7(2), 3556–3559.
Abstract: We investigated the output noise of a YBa2Cu3O7-δ (YBCO) superconducting hot-electron bolometer (HEB) in a large frequency range (10 kHz to 8 GHz); the bolometer either consisted of a structured 50 nm thick YBCO film on LaAlO/sub 3/ or a 30 nm thick film on a MgO substrate. We found that flicker noise dominated at low frequencies (below 1 MHz), while at higher frequencies Johnson noise and a current dependent noise were the main noise sources.
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Semenov, A. D., Gousev, Y. P., Renk, K. F., Voronov, B. M., Gol'tsman, G. N., Gershenzon, E. M., et al. (1997). Noise characteristics of a NbN hot-electron mixer at 2.5 THz. IEEE Trans. Appl. Supercond., 7(2), 3572–3575.
Abstract: The noise temperature of a NbN phonon cooled hot-electron mixer has been measured at a frequency of 2.5 THz for various operating conditions. We obtained for optimal operation a double sideband mixer noise temperature of /spl ap/14000 K and a system conversion loss of /spl ap/23 dB at intermediate frequencies up to 1 GHz. The dependences of the mixer noise temperature on the bias voltage, local oscillator power, and intermediate frequency were consistent with the phenomenological description based on the effective temperature approximation.
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Svechnikov, S., Gol'tsman, G., Voronov, B., Yagoubov, P., Cherednichenko, S., Gershenzon, E., et al. (1997). Spiral antenna NbN hot-electron bolometer mixer at submm frequencies. IEEE Trans. Appl. Supercond., 7(2), 3395–3398.
Abstract: We have studied the phonon-cooled hot-electron bolometer (HEB) as a quasioptical mixer based on a spiral antenna designed for the 0.3-1 THz frequency band and fabricated on sapphire and high resistivity silicon substrates. HEB devices were produced from superconducting 3.5-5 nm thick NbN films with a critical temperature 10-12 K and a critical current density of approximately 10/sup 7/ A/cm/sup 2/ at 4.2 K. For these devices we reached a DSB receiver noise temperature below 1500 K, a total conversion loss of L/sub t/=16 dB in the 500-700 GHz frequency range, an IF bandwidth of 3-4 GHz and an optimal LO absorbed power of /spl sime/4 /spl mu/W. We experimentally analyzed various contributions to the conversion loss and obtained an RF coupling factor of about 5 dB, internal mixer loss of 10 dB and IF mismatch of 1 dB.
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Semenov, A. D., Heusinger, M. A., Renk, K. F., Menschikov, E., Sergeev, A. V., Elant'ev, A. I., et al. (1997). Influence of phonon trapping on the performance of NbN kinetic inductance detectors. IEEE Trans. Appl. Supercond., 7(2), 3083–3086.
Abstract: Voltage and microwave photoresponse of NbN thin films to modulated and pulsed optical radiation reveals, far below the superconducting transition, a response time consistent with the lifetime of nonequilibrium quasiparticles. We show that even in 5 nm thick films at 4.2 K the phonon trapping is significant resulting in a quasiparticle lifetime of a few nanoseconds that is an order of magnitude larger than the recombination time. Values and temperature dependence of the quasiparticle lifetime obey the Bardeen-Cooper-Schrieffer theory and are in quantitative agreement with the electron-phonon relaxation rate determined from the resistive response near the superconducting transition. We discuss a positive effect of the phonon trapping on the performance of kinetic inductance detectors.
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Nebosis, R. S., Heusinger, M. A., Schatz, W., Renk, K. F., Gol’tsman, G. N., Karasik, B. S., et al. (1993). Ultrafast photoresponse of a structured YBa2Cu3O7-δ thin film to ultrashort FIR laser pulses. IEEE Trans. Appl. Supercond., 3(1), 2160–2162.
Abstract: The authors have investigated the photoinduced voltage response of a current-carrying structured YBa2Cu3O7-δ thin film to ultrashort far-infrared (FIR) laser pulses in the frequency range from 0.7 THz to 7 THz. The detector has shown an almost constant sensitivity of 1 mV/W and a noise equivalent power of less than 5*10/sup -7/ W/ square root Hz. The temperature dependence of the decay time of the detector signal was studied for temperatures around the transition temperature of the film ( approximately 80 K). For a detector temperature where dR/dT had its maximum, the authors observed bolometric signals with decay times of about 2 ns, and for lower temperatures they observed nonbolometric signals with decay times of approximately 120 ps; the duration of the nonbolometric signals was limited by the time resolution of the electronic registration equipment.
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Semenov, A. D., Goghidze, I. G., Gol’tsman, G. N., Sergeev, A. V., Aksaev, E. E., & Gershenzon, E. M. (1993). Non-equilibrium quasiparticle response to radiation and bolometric effect in YBaCuO films. IEEE Trans. Appl. Supercond., 3(1), 2132–2135.
Abstract: The voltage photoresponse of structured current biased YBCO films on different substrates to 20-ps laser pulses of 0.63- mu m and 1.54- mu m wavelengths and to continuously modulated radiation of 2-mm wavelength is measured to temperatures around Tc. Fast picosecond decay of the response to pulsed radiation is followed by slow exponential relaxation with a nanosecond characteristic time depending on the substrate material and film dimensions. The slow component does not depend on wavelength and is attributed to the bolometric effect, while the magnitude of the fast component associated with nonequilibrium response rises with wavelength. More than an order-of-magnitude increase of the nonequilibrium response is seen from near-infrared to millimeter-wave range. This dependence plausibly reflects the low efficiency of multiplication of photoexcited electrons in YBaCuO compared to conventional superconductors.
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Hübers, H. - W., Semenov, A., Richter, H., Birk, M., Krocka, M., Mair, U., et al. (2002). Terahertz Heterodyn Receiver with a hot-electron bolometer mixer. In U. Wolf, J. Farhoomand, & C. R. McCreight (Eds.), Far-IR, Sub-mm & MM Detector Technology Workshop (pp. 3–24). NASA CP. NASA.
Abstract: During the past decade major advances have been made regarding low noise mixers for terahertz (THz) heterodyne receivers. State of the art hot-electron-bolometer (HEB) mixers have noise temperatures close to the quantum limit and require less than a µW power from the local oscillator (LO). The technology is now at a point where the performance of a practical receiver employing such mixer, rather than the figures of merit of the mixer itself, are of major concern. We have incorporated a phonon-cooled NbN HEB mixer in a 2.5 THz heterodyne receiver and investigated the performance of the receiver. This yields important information for the development of heterodyne receivers such as GREAT (German receiver for astronomy at THz frequencies aboard SOFIA) [1] and TELIS (Terahertz limb sounder), a balloon borne heterodyne receiver for atmospheric research [2]. Both are currently under development at DLR.
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Semenov, A., Hübers, H. - W., Engel, A., & Gol’tsman, G. (2002). Superconducting quantum detector for far infrared astronomy. In J. Wolf, J. Farhoomand, & C. R. McCreight (Eds.), Far-IR, Sub-mm & MM Detector Technology Workshop (pp. 3–49). NASA CP. NASA.
Abstract: We present the concept of the superconducting quantum detector for astronomy. Response to a single absorbed photon appears due to successive formation of a normal spot and phase-slip-centres in a narrow strip carrying sub-critical supercurrent. The detector simultaneously has a moderate energy resolution and a variable cut-off wavelength depending on both the material used and operation conditions. We simulated performance of the background-limited direct detector having the 100-micrometer cut-off wavelength. Low dark count rate will allow to realise 10-21 W Hz-1/2 noise equivalent power at 4 K background radiation. The detection mechanism provides a moderate 1/20 energy resolution at 50-micrometer wavelength.
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Semenov, A., Engel, A., Il'in, K., Gol'tsman, G., Siegel, M., & Hübers, H. - W. (2003). Ultimate performance of a superconducting quantum detector. Eur. Phys. J. Appl. Phys., 21(3), 171–178.
Abstract: We analyze the ultimate performance of a superconducting quantum detector in order to meet requirements for applications in near-infrared astronomy and X-ray spectroscopy. The detector exploits a combined detection mechanism, in which avalanche quasiparticle multiplication and the supercurrent jointly produce a voltage response to a single absorbed photon via successive formation of a photon-induced and a current-induced normal hotspot in a narrow superconducting strip. The response time of the detector should increase with the photon energy providing energy resolution. Depending on the superconducting material and operation conditions, the cut-off wavelength for the single-photon detection regime varies from infrared waves to visible light. We simulated the performance of the background-limited infrared direct detector and X-ray photon counter utilizing the above mechanism. Low dark count rate and intrinsic low-frequency cut-off allow for realizing a background limited noise equivalent power of 10−20 W Hz−1/2 for a far-infrared direct detector exposed to 4-K background radiation. At low temperatures, the intrinsic response time of the counter is rather determined by diffusion of nonequilibrium electrons than by the rate of energy transfer to phonons. Therefore, thermal fluctuations do not hamper energy resolution of the X-ray photon counter that should be better than 10−3 for 6-keV photons. Comparison of new data obtained with a Nb based detector and previously reported results on NbN quantum detectors support our estimates of ultimate detector performance.
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Lobanov, Y. V., Shcherbatenko, M. L., Semenov, A. V., Kovalyuk, V. V., Korneev, A. A., Goltsman, G. N., et al. (2017). Heterodyne spectroscopy with superconducting single-photon detector. In EPJ Web Conf. (Vol. 132, 01005).
Abstract: We demonstrate successful operation of a Superconducting Single Photon Detector (SSPD) as the core element in a heterodyne receiver. Irradiating the SSPD by both a local oscillator power and signal power simultaneously, we observed beat signal at the intermediate frequency of a few MHz. Gain bandwidth was found to coincide with the detector single pulse width, where the latter depends on the detector kinetic inductance, determined by the superconducting nanowire length.
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Baeva, E. M., Titova, N. A., Veyrat, L., Sacépé, B., Semenov, A. V., Goltsman, G. N., et al. (2021). Thermal relaxation in metal films bottlenecked by diffuson lattice excitations of amorphous substrates. arXiv:2101.07071v1 [cond-mat.mtrl-sci]. Retrieved July 4, 2024, from https://arxiv.org/abs/2101.07071v1
Abstract: Here we examine the role of the amorphous insulating substrate in the thermal relaxation in thin NbN, InOx, and Au/Ni films at temperatures above 5 K. The studied samples are made up of metal bridges on an amorphous insulating layer lying on or suspended above a crystalline substrate. Noise thermometry was used to measure the electron temperature Te of the films as a function of Joule power per unit of area P2D. In all samples, we observe the dependence P2D∝Tne with the exponent n≃2, which is inconsistent with both electron-phonon coupling and Kapitza thermal resistance. In suspended samples, the functional dependence of P2D(Te) on the length of the amorphous insulating layer is consistent with the linear T-dependence of the thermal conductivity, which is related to lattice excitations (diffusons) for the phonon mean free path smaller than the dominant phonon wavelength. Our findings are important for understanding the operation of devices embedded in amorphous dielectrics.
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Saveskul, N. A., Titova, N. A., Baeva, E. M., Semenov, A. V., Lubenchenko, A. V., Saha, S., et al. (2019). Superconductivity behavior in epitaxial TiN films points at surface magnetic disorder. arXiv:1903.05009v3 [cond-mat.mtrl-sci]. Retrieved July 4, 2024, from https://arxiv.org/abs/1903.05009v3
Abstract: We analyze the evolution of the normal and superconducting electronic properties in epitaxial TiN films, characterized by high Ioffe-Regel parameter values, as a function of the film thickness. As the film thickness decreases, we observe an increase of in the residual resistivity, which becomes dominated by diffusive surface scattering for d≤20nm. At the same time, a substantial thickness-dependent reduction of the superconducting critical temperature is observed compared to the bulk TiN value. In such a high quality material films, this effect can be explained by a weak magnetic disorder residing in the surface layer with a characteristic magnetic defect density of ∼1012cm−2. Our results suggest that surface magnetic disorder is generally present in oxidized TiN films.
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Korneeva, Y. P., Vodolazov, D. Y., Semenov, A. V., Florya, I. N., Simonov, N., Baeva, E., et al. (2018). Optical single photon detection in micron-scaled NbN bridges. arXiv:1802.02881v1 [cond-mat.supr-con]. Retrieved July 4, 2024, from https://arxiv.org/abs/1802.02881v1
Abstract: We demonstrate experimentally that single photon detection can be achieved in micron-wide NbN bridges, with widths ranging from 0.53 μm to 5.15 μm and for photon-wavelengths from 408 nm to 1550 nm. The microbridges are biased with a dc current close to the experimental critical current, which is estimated to be about 50 % of the theoretically expected depairing current. These results offer an alternative to the standard superconducting single-photon detectors (SSPDs), based on nanometer scale nanowires implemented in a long meandering structure. The results are consistent with improved theoretical modelling based on the theory of non-equilibrium superconductivity including the vortex-assisted mechanism of initial dissipation.
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Arutyunov, K. Y., Ramos-Álvarez, A., Semenov, A. V., Korneeva, Y. P., An, P. P., Korneev, A. A., et al. (2016). Quasi-1-dimensional superconductivity in highly disordered NbN nanowires. arXiv:1602.07932v1 [cond-mat.supr-con]. Retrieved July 4, 2024, from https://arxiv.org/abs/1602.07932v1
Abstract: The topic of superconductivity in strongly disordered materials has attracted a significant attention. In particular vivid debates are related to the subject of intrinsic spatial inhomogeneity responsible for non-BCS relation between the superconducting gap and the pairing potential. Here we report experimental study of electron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. We find that conventional models based on phase slip concept provide reasonable fits for the shape of the R(T) transition curve. Temperature dependence of the critical current follows the text-book Ginzburg-Landau prediction for quasi-one-dimensional superconducting channel Ic~(1-T/Tc)^3/2. Hence, one may conclude that the intrinsic electronic inhomogeneity either does not exist in our structures, or, if exist, does not affect their resistive state properties.
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Sidorova, M., Semenov, A., Korneev, A., Chulkova, G., Korneeva, Y., Mikhailov, M., et al. (2018). Electron-phonon relaxation time in ultrathin tungsten silicon film. arXiv:1607.07321v1 [physics.ins-det]. Retrieved July 4, 2024, from https://arxiv.org/abs/1607.07321v1
Abstract: Using amplitude-modulated absorption of sub-THz radiation (AMAR) method, we studied electron-phonon relaxation in thin disordered films of tungsten silicide. We found a response time ~ 800 ps at critical temperature Tc = 3.4 K, which scales as minus 3 in the temperature range from 1.8 to 3.4 K. We discuss mechanisms, which can result in a strong phonon bottle-neck effect in a few nanometers thick film and yield a substantial difference between the measured time, characterizing response at modulation frequency, and the inelastic electron-phonon relaxation time. We estimate the electron-phonon relaxation time to be in the range ~ 100-200 ps at 3.4 K.
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Sidorova, M. V., Kozorezov, A. G., Semenov, A. V., Korneev, A. A., Chulkova, G. M., Korneeva, Y. P., et al. (2018). Non-bolometric bottleneck in electron-phonon relaxation in ultra-thin WSi film. arXiv:1607.07321v4 [physics.ins-det]. Retrieved July 4, 2024, from https://arxiv.org/abs/1607.07321v4
Abstract: We developed the model of the internal phonon bottleneck to describe the energy exchange between the acoustically soft ultrathin metal film and acoustically rigid substrate. Discriminating phonons in the film into two groups, escaping and nonescaping, we show that electrons and nonescaping phonons may form a unified subsystem, which is cooled down only due to interactions with escaping phonons, either due to direct phonon conversion or indirect sequential interaction with an electronic system. Using an amplitude-modulated absorption of the sub-THz radiation technique, we studied electron-phonon relaxation in ultrathin disordered films of tungsten silicide. We found an experimental proof of the internal phonon bottleneck. The experiment and simulation based on the proposed model agree well, resulting in tau{e-ph} = 140-190 ps at TC = 3.4 K, supporting the results of earlier measurements by independent techniques.
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Murphy, A., Semenov, A., Korneev, A., Korneeva, Y., Gol’tsman, G., & Bezryadin, A. (2014). Dark counts initiated by macroscopic quantum tunneling in NbN superconducting photon detectors. arXiv:1410.7689v2 [cond-mat.supr-con]. Retrieved July 4, 2024, from https://arxiv.org/abs/1410.7689v2
Abstract: We perform measurements of the switching current distributions of three w = 120 nm wide, 4 nm thick NbN superconducting strips which are used for single-photon detectors. These strips are much wider than the diameter the vortex cores, so they are classified as quasi-two-dimensional (quasi-2D). We discover evidence of macroscopic quantum tunneling by observing the saturation of the standard deviation of the switching distributions at temperatures around 2 K. We analyze our results using the Kurkijarvi-Garg model and find that the escape temperature also saturates at low temperatures, confirming that at sufficiently low temperatures, macroscopic quantum tunneling is possible in quasi-2D strips and can contribute to dark counts observed in single photon detectors.
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Tarkhov, M., Claudon, J., Poizat, J. P., Korneev, A., Divochiy, A., Minaeva, O., et al. (2008). Ultrafast reset time of superconducting single photon detectors. Appl. Phys. Lett., 92(24), 241112 (1 to 3).
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Verevkin, A., Zhang, J., Sobolewski, R., Lipatov, A., Okunev, O., Chulkova, G., et al. (2002). Detection efficiency of large-active-area NbN single-photon superconducting detectors in the ultraviolet to near-infrared range. Appl. Phys. Lett., 80(25), 4687–4689.
Abstract: We report our studies on spectral sensitivity of meander-type, superconducting NbN thin-film single-photon detectors (SPDs), characterized by GHz counting rates of visible and near-infrared photons and negligible dark counts. Our SPDs exhibit experimentally determined quantum efficiencies ranging from ∼0.2% at the 1.55 μm wavelength to ∼70% at 0.4 μm. Spectral dependences of the detection efficiency (DE) at the 0.4 to 3.0-μm-wavelength range are presented. The exponential character of the DE dependence on wavelength, as well as its dependence versus bias current, is qualitatively explained in terms of superconducting fluctuations in our ultrathin, submicron-width superconducting stripes. The DE values of large-active-area NbN SPDs in the visible range are high enough for modern quantum communications.
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Ferrari, S., Kovalyuk, V., Vetter, A., Lee, C., Rockstuhl, C., Semenov, A., et al. (2019). Analysis of the detection response of waveguide-integrated superconducting nanowire single-photon detectors at high count rate. Appl. Phys. Lett., 115(10), 101104.
Abstract: Nanophotonic circuitry and superconducting nanowires have been successfully combined for detecting single photons, propagating in an integrated photonic circuit, with high efficiency and low noise and timing uncertainty. Waveguide-integrated superconducting nanowire single-photon detectors (SNSPDs) can nowadays be engineered to achieve subnanosecond recovery times and can potentially be adopted for applications requiring Gcps count rates. However, particular attention shall be paid to such an extreme count rate regime since artifacts in the detector functionality emerge. In particular, a count-rate dependent detection efficiency has been encountered that can compromise the accuracy of quantum detector tomography experiments. Here, we investigate the response of waveguide-integrated SNSPDs at high photon flux and identify the presence of parasitic currents due to the accumulation of charge in the readout electronics to cause the above-mentioned artifact in the detection efficiency. Our approach allows us to determine the maximum photon count rate at which the detector can be operated without adverse effects. Our findings are particularly important to avoid artifacts when applying SNSPDs for quantum tomography.
We acknowledge support through ERC Consolidator Grant No. 724707 and from the Deutsche Forschungsgemeinschaft through Project No. PE 1832/5-1,2, as well as funding by the Volkswagen Foundation. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 675745. V.K. and G.G. acknowledge support from the Russian Science Foundation Project No. 16-12-00045 (NbN film deposition and testing). A.V. acknowledges support from the Karlsruhe School of Optics and Photonics (KSOP).
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Hübers, H. - W., Semenov, A., Holldack, K., Schade, U., Wüstefeld, G., & Gol’tsman, G. (2005). Time domain analysis of coherent terahertz synchrotron radiation. Appl. Phys. Lett., 87(18), 184103 (1 to 3).
Abstract: The time structure of coherent terahertz synchrotron radiation at the electron storage ring of the Berliner Elektronensynchrotron und Speicherring Gesellschaft has been analyzed with a fast superconducting hot-electron bolometer. The emission from a single bunch of electrons was found to last ∼1500ps at frequencies around 0.4THz, which is much longer than the length of an electron bunch in the time domain (∼5ps). It is suggested that this is caused by multiple reflections at the walls of the beam line. The quadratic increase of the power with the number of electrons in the bunch as predicted for coherent synchrotron radiation and the transition from stable to bursting radiation were determined from a single storage ring fill pattern of bunches with different populations.
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Gol’tsman, G. N., Okunev, O., Chulkova, G., Lipatov, A., Semenov, A., Smirnov, K., et al. (2001). Picosecond superconducting single-photon optical detector. Appl. Phys. Lett., 79(6), 705–707.
Abstract: We experimentally demonstrate a supercurrent-assisted, hotspot-formation mechanism for ultrafast detection and counting of visible and infrared photons. A photon-induced hotspot leads to a temporary formation of a resistive barrier across the superconducting sensor strip and results in an easily measurable voltage pulse. Subsequent hotspot healing in ∼30 ps time frame, restores the superconductivity (zero-voltage state), and the detector is ready to register another photon. Our device consists of an ultrathin, very narrow NbN strip, maintained at 4.2 K and current-biased close to the critical current. It exhibits an experimentally measured quantum efficiency of ∼20% for 0.81 μm wavelength photons and negligible dark counts.
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Semenov, A. D., Gousev, Y. P., Nebosis, R. S., Renk, K. F., Yagoubov, P., Voronov, B. M., et al. (1996). Heterodyne detection of THz radiation with a superconducting hot‐electron bolometer mixer. Appl. Phys. Lett., 69(2), 260–262.
Abstract: We report on the use of a superconducting hot‐electron bolometer mixer for heterodyne detection of terahertz radiation. Radiation with a wavelength of 119 μm was coupled to the mixer, a NbN microbridge, by a hybrid quasioptical antenna consisting of an extended hyperhemispherical lens and a planar logarithmic spiral antenna. We found, at an intermediate frequency of 1.5 GHz, a system double side band noise temperature of ≊40 000 K and conversion losses of 25 dB. We also discuss the possibilities of further improvement of the mixer performance.
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Semenov, A. D., Goghidze, I. G., Gol’tsman, G. N., Sergeev, A. V., & Gershenzon, E. M. (1993). Evidence for the spectral dependence of nonequilibrium picosecond photoresponse of YBaCuO thin films. Appl. Phys. Lett., 63(5), 681–683.
Abstract: The transient voltage photoresponse of current biased YBaCuO thin films to 20 ps laser pulses of 0.63 and 1.54 μm wavelengths is measured for temperatures around the superconducting transition region. The fast picosecond decay of the response is followed by a slow nanosecond relaxation which is associated with the bolometric effect. The magnitude of the fast component of the response varies in proportion to the square root of wavelength that plausibly reflects multiplication processes of photoexcited electrons via electron–electron scattering and interaction with high energy phonons.
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Semenov, A. D., Gol’tsman, G. N., Gogidze, I. G., Sergeev, A. V., Gershenzon, E. M., Lang, P. T., et al. (1992). Subnanosecond photoresponse of a YBaCuO thin film to infrared and visible radiation by quasiparticle induced suppression of superconductivity. Appl. Phys. Lett., 60(7), 903–905.
Abstract: We observed subnanosecond photoresponse of a structured superconducting YBa2Cu3O7−δ thin film to infrared and visible radiation. We measured the voltage response of a current biased film (thickness 700 Å) in a resistive state to radiation pulses. From our results we conclude a response time of about 90 ps and a responsivity of about 4×1010 Ω/J. We attribute the response to Cooper pair breaking and suppression of the superconducting energy gap induced by nonequilibrium quasiparticles.
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Lang, P. T., Leipold, I., Knott, W. J., Semenov, A. D., Gol'tsman, G. N., & Renk, K. F. (1991). New far-infrared laser lines from CH3Cl and CH3Br optically pumped with a continuously tunable high pressure CO2 laser. Appl. Phys. B, 53(4), 207–212.
Abstract: In this paper we report on the detection of new far-infrared laser lines from CH3Cl and CH3Br optically pumped with a continuously tunable high pressure CO2 laser. We found 80 new lines for CH3Cl and 9 new lines for CH3Br in the frequency region between 16 cm−1 and 41 cm−1, all due to stimulated Raman scattering. For the Raman gain regions bandwidths up to about 700 MHz were found. We also observed high intensity short far-infrared laser pulses of durations in the nanosecond regime.
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Il'in, K., Siegel, M., Semenov, A., Engel, A., Hübers, H. - W., Hollmann, E., et al. (2004). Thickness dependence of superconducting properties of ultrathin Nb and NbN films. In AKF-Frühjahrstagung.
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Henrich, D., Dorner, S., Hofherr, M., Il'in, K., Semenov, A., Heintze, E., et al. (2012). Broadening of hot-spot response spectrum of superconducting NbN nanowire single-photon detector with reduced nitrogen content. J. Appl. Phys., 112.
Abstract: The spectral detection efficiency and the dark count rate of superconducting nanowire
single-photon detectors (SNSPD) have been studied systematically on detectors made from thin
NbN films with different chemical compositions. Reduction of the nitrogen content in the 4 nm
thick NbN films results in a decrease of the dark count rates more than two orders of magnitude
and in a red shift of the cut-off wavelength of the hot-spot SNSPD response. The observed
phenomena are explained by an improvement of uniformity of NbN films that has been confirmed
by a decrease of resistivity and an increase of the ratio of the measured critical current to the
depairing current. The latter factor is considered as the most crucial for both the cut-off
wavelength and the dark count rates of SNSPD. Based on our results we propose a set of criteria
for material properties to optimize SNSPD in the infrared spectral region. VC 2012 American
Institute of Physics. [http://dx.doi.org/10.1063/1.4757625]
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Gousev, Y. P., Semenov, A. D., Pechen, E. V., Varlashkin, A. V., Nebosis, R. S., & Renk K. F. (1996). Coupling of terahertz radiation to a high-Т(с) superconducting hot electron bolometer mixer. Appl. Phys. Lett.,, 69, 691–693.
Abstract: We report on efficient coupling of THz radiation to a high-T(c) superconducting hot electron bolometer that is suitable for heterodyne detection. Our quasioptical system consisted of a planar self-complementary spiral antenna on a dielectric substrate clamped to an extended hyperhemispherical lens. The antenna was integrated into a co-planar line for broadband intermediate frequency matching. Measurements in the homodyne regime at a frequency of 2.5 THz showed a radiation pattern with a beam width of 1° and a coupling efficiency of 0.1. We measured, at an intermediate frequency of 1.5 GHz, an output noise temperature of'160 K and estimated for the device, operated in the heterodyne regime, a system noise temperature of 30 000 K. We also discuss possibilities of significant improvement of the sensitivity.
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