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Semenov, A., Richter, H., Hübers, H. - W., Petrenko, D., Tretyakov, I., Ryabchun, S., et al. (2014). Optimization of the intermediate frequency bandwidth in the THz HEB mixers. In Proc. 25th Int. Symp. Space Terahertz Technol. (54).
Abstract: We report on the studies of the intermediate frequency (IF) bandwidth of quasi-optically coupled NbN hot-electron bolometer (HEB) mixers which are aimed at the optimization of the mixer performance at terahertz frequencies. Extension of the IF bandwidth due to the contribution of electron diffusion to the heat removal from NbN microbolometers has been already demonstrated for NbN HEBs at subterahertz frequencies. However, reducing the size of the microbolometer causes degradation of the noise temperature. Using in-situ multilayer manufacturing process we succeeded to improve the transparency of the contacts for electrons which go away from microbolometer to the metallic antenna. The improved transparency and hence coupling efficiency counterbalances the noise temperature degradation. HEB mixers were tested in a laboratory heterodyne receiver with a narrow-band cold filter which allowed us to eliminate direct detection. We used a local oscillator with a quantum cascade laser (QCL) at a frequency of 4.745 THz [1] which was developed for the H-Channel of the German Receiver for Astronomy at Terahertz frequencies (GREAT). Both the noise and gain bandwidth were measured in the IF range from 0.5 to 8 GHz using the hot-cold technique and preliminary calibrated IF analyzer with a tunable microwave filter. For optimized HEB geometry we found the noise bandwidth as large as 7 GHz. We compare our results with the conventional and the hot-spot mixer models and show that further extension of the IF bandwidth should be possible via improving the sharpness of the superconducting transition. The cross characterization of the HEB mixer was performed in the test bed of GREAT at the Max-Planck-Institut für Radioastronomie with the same QCL LO and delivered results which were consistent with the laboratory studies.
Keywords: NbN HEB mixer
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Tretyakov, I. V., Finkel, M. I., Ryabchun, S. A., Kardakova, A. I., Seliverstov, S. V., Petrenko, D. V., et al. (2014). Hot-electron bolometer mixers with in situ contacts. Radiophys. Quant. Electron., 56(8-9), 591–598.
Abstract: We report on the latest achievements in the development of superconducting hot-electron bolometer (HEB) mixers for terahertz superheterodyne receivers. We consider application ranges of such receivers and requirements for the basic characteristics of the mixers. Main features of the mixers, such as noise temperature, gain bandwidth, noise bandwidth, and required local-oscillator power, have been improved significantly over the past few years due to intense research work, both in terms of the element fabrication quality and in terms of understanding of the physics of the processes occurring in the HEB mixers. Contacts between the superconducting bridge and the planar antenna play a key role in the mixer operation. Improvement of the quality of the contacts leads simultaneously to a decrease in the noise temperature and an increase in the gain bandwidth of a mixer.
Keywords: HEB mixers
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Tretyakov, I., Seliverstov, S., Zolotov, P., Kaurova, N., Voronov, B., Finkel, M., et al. (2014). Noise temperature and noise bandwidth of hot-electron bolometer mixer at 3.8 THz. In Proc. 25th Int. Symp. Space Terahertz Technol. (77).
Abstract: We report on our recent results of double sideband (DSB) noise temperature and bandwidth measurements of quasi-optical hot electron bolometer (HEB) mixers at local oscillator frequency of 3.8 THz. The HEB mixers used in this work were made of a NbN thin film and had a superconducting transition temperature of about 10.3 K. To couple terahertz radiation, the NbN microbridge (0.2 μm long and 2 μm wide) was integrated with a planar logarithmic-spiral antenna. The mixer chip was glued to an elliptical Si lens clamped tightly to a mixer block mounted on the 4.2 K plate of a liquid helium cryostat. The terahertz radiation was fed into the HEB device through the cryostat window made of a 0.5 mm thick HDPE. A band-pass mesh filter was mounted on the 4.2 K plate to minimize the direct detection effect [1]. We used a gas discharge laser irradiating at 3.8 THz H 2 0 line as a local oscillator (LO). The LO power was combined with a black body broadband radiation via Mylar beam splitter. Our receiver allows heterodyne detection with an intermediate frequency (IF) of a several gigahertz which dictates usage of a wideband SiGe low noise amplifier [2]. The receiver IF output signal was further amplified at room temperature and fed into a square-law power detector through a band-pass filter. The DSB receiver noise temperature was measured using a conventional Y-factor technique at IF of 1.25 GHz and band of 40 MHz. Using wideband amplifiers at both cryogenic and room temperature stages we have estimated IF bandwidth of the HEB mixers used. The obtained results strengthen the position of the HEB mixer as one of the most important tools for submillimeter astronomy. This device operates well above the energy gap (at frequencies above 1 THz) where performance of state-of-the-art SIS mixers starts to degrade. So, HEB mixers are expected to be a device of choice in astrophysical observations (ground-, aircraft- and space-based) at THz frequencies due to its excellent noise performance and low LO power requirements. The HEB mixers will be in operation on Millimetron Space Observatory. References 1. J. J. A. Baselmans, A. Baryshev, S. F. Reker, M. Hajenius, J. R. Gao, T. M. Klapwijk, Yu. Vachtomin, S. Maslennikov, S. Antipov, B. Voronov, and G. Gol'tsman, Appl. Phys. Lett., 86, 163503 (2005). 2. Sander Weinreb, Life Fellow, IEEE, Joseph C. Bardin, Student Member, IEEE, and Hamdi Mani, “Design of Cryogenic SiGe Low-Noise Amplifiers”, IEEE Transactions on Microwave Theory and Techniques, 55, 11, 2007.
Keywords: NbN HEB mixer
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Kinev, N. V., Filippenko, L. V., Ozhegov, R. V., Gorshkov, K. N., Gol’tsman, G. N., & Koshelets, V. P. (2014). Superconducting integrated receiver with HEB-mixer. In Proc. 25th Int. Symp. Space Terahertz Technol. (78).
Abstract: Detectors in THz range with high sensitivity are very essential nowadays in different fields: space technology, atmospheric research, medicine and security. The most sensitive heterodyne detectors below 1 THz are the SIS- mixers due to its extremely high non-linearity and low noise level. Nevertheless, their effective range is strongly limited by superconducting gap Δ (about 1 THz for NbN circuits). Above 1 THz the detectors based on HEB (hot electron bolometers) are more effective [1]; their operation frequency is not limited from above and can be up to 70 THz [2]. HEBs can perform as both direct and heterodyne detectors (mixers). All HEB-mixers are used with external heterodyne, most useful are synthesizer with multipliers, quantum cascade lasers or far infrared lasers and backward-wave oscillators. Superconducting integrated receiver (SIR) is based on implementation of both SIS-miser and flux flow oscillator (FFO) acting as heterodyne at single chip [3]. Such receiver has been successfully applied at TELIS balloon-borne instrument for study of atmospheric constituents [4] and looks as very promising device for other THz missions including space research. Thus, there is a task to expand its operating range to higher frequencies. The frequency range of the SIR the operation is limited by both the SIS-mixer and the FFO maximum frequencies. The idea of present work is implementation of the HEB as a mixer in the SIR instead of the SIS traditionally used. We introduce the first results of integrating the HEB-mixer coupled to planar slot antenna with the FFO on one chip. For properly FFO operation the SIS harmonic mixer is used to phase lock the oscillator. The scheme of the SIR based on the HEB- mixer is presented in fig. 1. We have demonstrated the principal possibility of integration of both the HEB-mixer and the flux-flow oscillator on a single chip and succeed with sufficient power coupling for properly receiver operation. We measured the direct response of the HEB coupled to the antenna at THz frequencies by the FTS setup and noise temperature of the receiver with standard Y- factor measuring technique. The SIR operating range 450-620 GHz was achieved with the best uncorrected noise temperature of about 1000 К. One should note that it is still quite low frequencies for effective operation of the HEB-mixer; therefore we expect to obtain the better results for frequencies above 700 GHz (up to 1.2 THz). Another additional task is to increase the FFO frequencies by using NbTiN electrodes instead of NbN; currently we are working on this issue. This work was supported by the RFBR grant, the Ministry of Education and Science of Russia and Russian Academy of Sciences. References 1. D. Semenov, H.-W. Hubers, J. Schubert, G. N. Gol’tsman, A. I. Elantiev, B. M. Voronov, E. M. Gershenzon, Design and performance of the lattice-cooled hot-electron terahertz mixer, J. Appl. Phys. 88, 6758, 2000. 2. Maslennikov S. N., Finkel M. I., Antipov S. V. et al. Spiral antenna coupled and directly coupled NbN HEB mixers in the frequency range from 1 to 70THz. Proc. 17 th international symposium on space terahertz technology. Paris, France: 2006.—may. Pp. 177 – 179. 3. V.P. Koshelets, S.V. Shitov. Integrated Superconducting Receivers. Supercond. Sci. Technol. Vol. 13. P. R53-R59. 2000. 4. Gert de Lange, Dick Boersma, Johannes Dercksen et.al. Development and Characterization of the Superconducting Integrated Receiver Channel of the TELIS Atmospheric Sounder. Supercond. Sci. Technol. vol. 23, No 4, 045016 (8pp). 2010.
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Shcherbatenko, M., Lobanov, Y., Finkel, M., Maslennikov, S., Pentin, I., Semenov, A., et al. (2014). Development of a 30 THz heterodyne receiver based on a hot-electron-bolometer mixer. In Proc. 25th Int. Symp. Space Terahertz Technol. (122).
Abstract: We present new Hot-Electron-Bolometer (HEB) mixers designed for mid-IR spectroscopy targeting astrophysical and geophysical observations where high sensitivity and spectral resolution are required. The mixers are made of an ultrathin NbN film deposited on GaAs substrates. Two entirely different types of the devices have been fabricated. The first type is based on a direct radiation coupling concept and the mixing devices are shaped as squares of 5×5 μm 2 (which corresponds to the diffraction limit at the chosen wavelength) and 10×10 μm 2 (which was used to establish a possible influence of the contact pads on the radiation absorption). The second type utilizes a spiral antenna designed with HFSS. The fabrication and layout of the devices as well as the performance comparison will be presented. During the experiments, the HEB mixer was installed on the cold plate of a LHe cryostat. A germanium window and an extended semi-spherical germanium lens are used to couple the radiation. The cryostat is equipped with a germanium optical filter of thickness 0.5 mm and with a center wavelength of 10.6 mμ. The incident power absorption is measured by using the isothermal method. As a Local Oscillator, a 10.6 micrometers line of a CO2 gas laser is used. We further characterize the frequency response of the spiral antenna with a FIR-spectrometer. The noise characteristics of the mixers are determined from a room temperature cold load and a heated black body at ~600 K as a hot load.
Keywords: mid-IR NbN HEB mixers, GaAs substrates
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Tong, C. E., Trifonov, A., Blundell, R., Shurakov, A., & Gol’tsman, G. (2014). A digital terahertz power meter based on an NbN thin film. In Proc. 25th Int. Symp. Space Terahertz Technol. (170).
Abstract: We have further studied the effect of subjecting a superconducting Hot Electron Bolometer (HEB) element made from an NbN thin film to microwave radiation. Since the photon energy is weak, the microwave radiation does not simply heat the film, but generates a bi-static state, switching between the superconducting and normal states, upon the application of a small voltage bias. Indeed, a relaxation oscillation of a few MHz has previously been reported in this regime [1]. Switching between the superconducting and normal states modulates the reflected microwave pump power from the device. A simple homodyne setup readily recovers the spontaneous switching waveform in the time domain. The switching frequency is a function of both the bias voltage (DC heating) and the applied microwave power. In this work, we use a 0.8 THz HEB waveguide mixer for the purpose of demonstration. The applied microwave pump, coupled through a directional coupler, is at 1 GHz. Since the pump power is of the order of a few μW, a room temperature amplifier is sufficient to amplify the reflected pump power from the HEB mixer, which beats with the microwave source in a homodyne set-up. After further amplification, the switching waveform is passed onto a frequency counter. The typical frequency of the switching pulses is 3-5 MHz. It is found that the digital frequency count increases with higher microwave pump power. When the HEB mixer is subjected to additional optical power at 0.8 THz, the frequency count also increases. When we vary the incident optical power by using a wire grid attenuator, a linear relationship is observed between the frequency count and the applied optical power, over at least an order of magnitude of power. This phenomenon can be exploited to develop a digital power meter, using a very simple electronics setup. Further experiments are under way to determine the range of linearity and the accuracy of calibration transfer from the microwave to the THz regime. References 1. Y. Zhuang, and S. Yngvesson, “Detection and interpretation of bistatic effects in NbN HEB devices,” Proc. 13 th Int. Symp. Space THz Tech., 2002, pp. 463–472.
Keywords: waveguide NbN HEB mixers
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Maezawa, H. (2015). Application of superconducting hot-electron bolometer mixers for terahertz-band astronomy. IEICE Trans. Electronics, 98(3), 196–206.
Abstract: Recently, a next-generation heterodyne mixer detector – a hot electron bolometer (HEB) mixer employing a superconducting microbridge – has gradually opened up terahertz-band astronomy. The surrounding state-of-the-art technologies including fabrication processes, 4 K cryostats, cryogenic low-noise amplifiers, local oscillator sources, micromachining techniques, and spectrometers, as well as the HEB mixers, have played a valuable role in the development of super-low-noise heterodyne spectroscopy systems for the terahertz band. The current developmental status of terahertz-band HEB mixer receivers and their applications for spectroscopy and astronomy with ground-based, airborne, and satellite telescopes are presented.
Keywords: HEB mixer applications, HEB applications
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Trifonov, A., Tong, C. - Y. E., Blundell, R., Ryabchun, S., & Gol'tsman, G. (2015). Probing the stability of HEB mixers with microwave injection. IEEE Trans. Appl. Supercond., 25(3), 2300404 (1 to 4).
Abstract: Using a microwave probe as a tool, we have performed experiments aimed at understanding the origin of the output-power fluctuations in hot-electron-bolometer (HEB) mixers. We use a probe frequency of 1.5 GHz. The microwave probe picks up impedance changes of the HEB, which are examined upon demodulation of the reflected wave outside the cryostat. This study shows that the HEB mixer operates in two different regimes under a terahertz pump. At a low pumping level, strong pulse modulation is observed, as the device switches between the superconducting state and the normal state at a rate of a few megahertz. When pumped much harder, to approximate the low-noise mixer operating point, residual modulation can still be observed, showing that the HEB mixer is intrinsically unstable even in the resistive state. Based on these observations, we introduced a low-frequency termination to the HEB mixer. By terminating the device in a 50-Ω resistor in the megahertz frequency range, we have been able to improve the output-power Allan time of our HEB receiver by a factor of four to about 10 s for a detection bandwidth of 15 MHz, with a corresponding gain fluctuation of about 0.035%.
Keywords: NbN HEB mixer, stability, Allan-variance
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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.
Keywords: HEB mixer, IR, optical antenna
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Shcherbatenko, M., Lobanov, Y., Benderov, O., Shurakov, A., Ignatov, A., Titova, N., et al. (2015). Antenna-coupled 30 THz hot electron bolometer mixers. In Proc. 26th Int. Symp. Space Terahertz Technol. (27).
Abstract: We report on design and characterization of a superconducting Hot Electron Bolometer Mixer integrated with a logarithmic spiral antenna for mid-IR range observations. The antenna parameters have been adjusted to achieve the ultimate performance at 10 µm (30 THz) range where O3, NH3, CO2, CH4, N2O,…. lines in the Earth’s atmosphere, in planetary atmospheres and in the interstellar space can be observed. The HEB mixer is made of a thin NbN film deposited onto a GaAs substrate. To couple the radiation we rely on the quasioptical approach: the device is glued to a semi-spherical germanium lens with diameter~ 3 mm. A wet cryostat equipped with a germanium window and narrow band-pass filter is used to characterize the antenna and estimate the mixer performance.
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Tretyakov, I., Maslennikov, S., Semenov, A., Safir, O., Finkel, M., Ryabchun, S., et al. (2015). Impact of operating conditions on noise and gain bandwidth of NbN HEB mixers. In Proc. 26th Int. Symp. Space Terahertz Technol. (39).
Abstract: Hot-electron bolometer mixers (HEB’s) are the most promising devices as mixing element for terahertz spectroscopy and astronomy at frequencies beyond 1.4 THz. They have a low noise temperature and low demands on local oscillator (LO) power. 1,2 An important limitation is the IF bandwidth, of the order of a few GHz, and which in principle depends on energy relaxation due to electron- phonon processes and on diffusion-cooling. It has been proposed by Prober that a reduction in length of the HEB would lead to an increased bandwidth. 3 This appeared to be achieved by Tretyakov et al by measuring the gain bandwidth close to the critical temperature of the NbN. 2 Unfortunately, the noise bandwidth of similar devices operated at temperatures around 4.2 K appear not depend on the length. The fundamental problem to be addressed is the position-dependent superconducting state of the HEB- devices under operating conditions, which determines the conditions for the cooling of the hot quasiparticles. Some progress has been made by Barends et al in a semi-empirical model to describe the I,V curves under operating conditions at a bath temperature around 4.2 K. 4 In more recent work Vercruyssen et al have analyzed the I,V curve, without any LO-equivalent bias, of a model NSN system. 5 This work suggests that the most appropriate model for an HEB under operating conditions is that of a potential-well in the superconducting gap in the center of the NbN, analogous the bimodal superconducting state described by Vercruyssen et al. Hot quasiparticles in the well can not diffuse out and can only cool by electron-phonon processes, those with higher energies than the heights of the walls of the well can diffuse out. Using this working hypothesis we have carried out experiments on a sub-micrometer NbN bridge connected to a gold (Au) planar spiral antenna. An in situ process is used to deposit Au on NbN. The Au is removed in the center to define the uncovered NbN, which will act as the superconducting mixer itself. The antenna is deposited on the remaining Au layer on the NbN. The Au contacts suppress the energy gap of the NbN film located underneath the gold layer 7,8 . The measured resistive transition is shown in Fig.1. It clearly shows a T c of the bilayer at 6.2 K and the resistive transition of the NbN itself around 9 K. In addition we show the measured noise bandwidth (red squares) for different bath temperatures. Clearly the noise bandwidth increases strongly by increasing the bath temperature from 5 K to 8 K, up to 13 GHz. We interpret this pattern as evidence for improved out-diffusion of hot electrons due to normal banks and a shallow superconducting potential well compared to k B T. As expected the noise temperature in this regime is much bigger than when biased at 4.2 K. R EFERENCES 1 W. Zhang, P. Khosropanah, J. R. Gao, E. L. Kollberg, K. S. Yngvesson, T. Bansal, R. Barends, and T. M. Klapwijk Appl. Phys. Lett. 96, 111113, (2010). 2 Ivan Tretyakov, Sergey Ryabchun, Matvey Finkel, Anna Maslennikova, Natalia Kaurova, Anastasia Lobastova, Boris Voronov, and Gregory Gol’tsman Appl. Phys. Lett. 98, 033507 (2011). 3 D. E. Prober, Appl. Phys. Lett. 62, 2119 (1992). 4 R. Barends, M. Hajenius, J. R. Gao, and T. M. Klapwijk, Appl. Phys. Lett. 87, 263506 (2005). 5 N. Vercruyssen, T. G. A. Verhagen, M. G. Flokstra, J. P. Pekola, and T. M. Klapwijk Physical Review B 85, 224503 (2012).
Keywords: NbN HEB mixers
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Tong, C. - Y. E., Trifonov, A., Shurakov, A., Blundell, R., & Gol’tsman, G. (2015). A microwave-operated hot-electron-bolometric power detector for terahertz radiation. IEEE Trans. Appl. Supercond., 25(3), 2300604 (1 to 4).
Abstract: A new class of microwave-operated THz power detectors based on the NbN hot-electron-bolometer (HEB) mixer is proposed. The injected microwave signal ( 1 GHz) serves the dual purpose of pumping the HEB element and enabling the read-out of the internal state of the device. A cryogenic amplifier amplifies the reflected microwave signal from the device and a homodyne scheme recovers the effects of the incident THz radiation. Two modes of operation have been identified, depending on the level of incident radiation. For weak signals, we use a chopper to chop the incident radiation against a black body reference and a lock-in amplifier to perform synchronous detection of the homodyne readout. The voltage measured is proportional to the incident power, and we estimate an optical noise equivalent power of 5pW/ √Hz at 0.83 THz. At higher signal levels, the homodyne circuit recovers the stream of steady relaxation oscillation pulses from the HEB device. The frequency of these pulses is in the MHz frequency range and bears a linear relationship with the incident THz radiation over an input power range of 15 dB. A digital frequency counter is used to measure THz power. The applicable power range is between 1 nW and 1 μW.
Keywords: NbN HEB mixer
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Shcherbatenko, M., Tretyakov, I., Lobanov, Y., Maslennikov, S. N., Kaurova, N., Finkel, M., et al. (2016). Nonequilibrium interpretation of DC properties of NbN superconducting hot electron bolometers. Appl. Phys. Lett., 109(13), 132602.
Abstract: We present a physically consistent interpretation of the dc electrical properties of niobiumnitride (NbN)-based superconducting hot-electron bolometer mixers, using concepts of nonequilibrium superconductivity. Through this, we clarify what physical information can be extracted from the resistive transition and the dc current-voltage characteristics, measured at suitably chosen temperatures, and relevant for device characterization and optimization. We point out that the intrinsic spatial variation of the electronic properties of disordered superconductors, such as NbN, leads to a variation from device to device.
Keywords: HEB mixer, contacts
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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.
Keywords: HEB mixers
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Seliverstov, S. V., Rusova, A. A., Kaurova, N. S., Voronov, B. M., & Goltsman, G. N. (2017). AC-biased superconducting NbN hot-electron bolometer for frequency-domain multiplexing. In Proc. 28th Int. Symp. Space Terahertz Technol. (pp. 120–122).
Abstract: We present the results of characterization of fast and sensitive superconducting antenna-coupled THz direct detector based on NbN hot-electron bolometer (HEB) with AC-bias. We discuss the possibility of implementation of the AC-bias for design the readout system from the multi-element arrays of HEBs using standard technique of frequency-domain multiplexing. We demonstrate experimentally that this approach does not lead to significant deterioration of the HEB sensitivity compared with the value obtained for the same detector with DC- bias. Results of a numerical calculations of the HEB responsivity at AC-bias are in a good agreement with the experiment.
Keywords: NbN HEB mixer
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