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| Author |
Kawamura, J.; Blundell, R.; Tong, C.-Y. E.; Golts'man, G.; Gershenzon, E.; Voronov B. |
| Title |
Superconductive NbN hot-electron bolometric mixer performance at 250 GHz |
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Conference Article |
| Year |
1996 |
Publication |
Proc. 7th Int. Symp. Space Terahertz Technol. |
Abbreviated Journal |
Proc. 7th Int. Symp. Space Terahertz Technol. |
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331-336 |
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NbN HEB mixers |
| Abstract |
Thin film NbN (<40 A) strips are used as waveguide mixer elements. The electron cooling mechanism for the geometry is the electron-phonon interaction. We report a receiver noise temperature of 750 K at 244 GHz, with / IF = 1.5 GHz, Af= 500 MHz, and Tphysical = 4 K. The instantaneous bandwidth for this mixer is 1.6 GHz. The local oscillator (LO) power is 0.5 1.tW with 3 dB-uncertainty. The mixer is linear to 1 dB up to an input power level 6 dB below the LO power. We report the first detection of a molecular line emission using this class of mixer, and that the receiver noise temperature determined from Y-factor measurements reflects the true heterodyne sensitivity. |
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945 |
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Palma, F.; Teppe, F.; Fatimy, A. E.; Green, R.; Xu, J.; Vachontin, Y.; Tredicucci, A.; Goltsman, G.; Knap, W. |
| Title |
THz communication system based on a THz quantum cascade laser and a hot electron bolometer |
Type |
Conference Article |
| Year |
2010 |
Publication |
35th Int. Conf. Infrared, Millimeter, and Terahertz Waves |
Abbreviated Journal |
35th Int. Conf. Infrared, Millimeter, and Terahertz Waves |
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11623798 (1 to 2) |
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QCL, HEB detector |
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We present the experimental study of the direct emission – detection system based on the THz Quantum Cascade Laser as a source and Hot Electron Bolometer (HEB) detector – in view of its application as an optical communication system. We show that the system can efficiently transmit the QCL Terahertz pulses. We estimate the maximal modulation speed of the system to be about several GHz and show that it is limited only by the QCL pulse power supply, detector amplifier and connection line/wires parameters. |
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1391 |
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Titova, N; Kardakova, A.; Tovpeko, N; Ryabchun, S.; Mandal, S.; Morozov, D.; Klemencic, G. M.; Giblin, S.R.; Williams, O. A.; Goltsman, G. N. |
| Title |
Superconducting diamond films as perspective material for direct THz detectors |
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Abstract |
| Year |
2017 |
Publication |
Proc. 28th Int. Symp. Space Terahertz Technol. |
Abbreviated Journal |
Proc. 28th Int. Symp. Space Terahertz Technol. |
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82 |
| Keywords |
KID, HEB, superconducting diamond films, boron-doped diamond films, Al, TiN, Si substrates, NEP |
| Abstract |
Superconducting films with a high resistivity in the normal state have established themselves as the best materials for direct THz radiation sensors, such as kinetic inductance detectors (KIDs) [1] and hot electron bolometers (nano-HEBs) [2]. The primary characteristics of the future instrument such as the sensitivity and the response time are determined by the material parameters such as the electron-phonon (e-ph) interaction time, the electron density and the resistivity of the material. For direct detectors, such as KIDs and nano-HEBs, to provide a high sensitivity and low noise one prefer materials with long e-ph relaxation times and low values of the electron density. As a potential material for THz radiation detection we have studied superconducting diamond films. A significant interest to diamond for the development of electronic devices is due to the evolution of its properties with the boron dopant concentration. At a high boron doping concentration, n B ~5·10 20 cm -3 , diamond has been reported to become a superconducting with T c depending on the doping level. Our previous study of energy relaxation in single-crystalline boron-doped diamond films epitaxially grown on a diamond shows a remarkably slow energy-relaxation at low temperatures. The electron-phonon cooling time varies from 400 ns to 700 ns over the temperature range 2.2 K to 1.7 K [3]. In superconducting materials such as Al and TiN, traditionally used in KIDs, the e-ph cooling times at 1.7 K correspond to ~20 ns [4] and ~100 ns [5], correspondingly. Such a noticeable slow e-ph relaxation in boron-doped diamond, in combination with a low value of carrier density (~10 21 cm -3 ) in comparison with typical metals (~10 23 cm -3 ) and a high normal state resistivity (~1500 μΩ·cm) confirms a potential of superconducting diamond for superconducting bolometers and resonator detectors. However, the price and the small substrate growth are of single crystal diamond limit practical applications of homoepitaxial diamond films. As an alternative way with more convenient technology, one can employ heteroepitaxial diamond films grown on large-size Si substrates. Here we report about measurements of e-ph cooling times in superconducting diamond grown on silicon substrate and discuss our expectations about the applicability of boron-doped diamond films to superconducting detectors. Our estimation of limit value of noise-equivalent power (NEP) and the energy resolution of bolometer made from superconducting diamond is order 10 -17 W/Hz 1/2 at 2 K and the energy resolution is of 0.1 eV that corresponds to counting single-photon up to 15 um. The estimation was obtained by using the film thickness of 70 nm and ρ ~ 1500 μΩ·cm, and the planar dimensions that are chosen to couple bolometer with 75 Ω log-spiral antenna. Although the value of NEP is far yet from what might like to have for certain astronomical applications, we believe that it can be improved by a suitable fabrication process. Also the direct detectors, based on superconducting diamond, will offer low noise performance at about 2 K, a temperature provided by inexpensive close-cycle refrigerators, which provides another practical advantage of development and application of these devices. [1] P.K. Day, et. al, Nature, 425, 817, 2003. [2] J. Wei, et al, Nature Nanotech., 3, 496, 2008. [3] A. Kardakova, et al, Phys. Rev. B, 93, 064506, 2016. [4] P. Santhanam and D. Prober, Phys. Rev. B, 29, 3733, 1984 [5] A. Kardakova, et al, Appl. Phys. Lett, vol. 103, p. 252602, 2013. |
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1173 |
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Ozhegov, R. V.; Smirnov, A. V.; Vakhtomin, Yu. B.; Smirnov, K. V.; Divochiy, A. V.; Goltsman, G. N. |
| Title |
Ultrafast superconducting bolometer receivers for terahertz applications |
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Abstract |
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2009 |
Publication |
Proc. PIERS |
Abbreviated Journal |
Proc. PIERS |
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867 |
| Keywords |
HEB |
| Abstract |
The research by the group of Moscow State Pedagogical University into the hot-electron phenomena in thin superconducting films has led to the development of new types of detectors and their use both in fundamental and applied studies. In this paper, we present the results of testing the terahertz HEB receiver systems based on ultrathin (∼ 4 nm) NbN and MoRe detectors with a response time of 50 ps and 1 ns, respectively. We have developed three types of devices which differ in the way a terahertz signal is coupled to the detector and cover the following ranges: 0.3–3 THz, 0.1–30 THz and 25–70 THz. In the case of the receiving system optimized for 0.3–3 THz, the sensitive element (a strip of asuperconductor with planar dimensions of 0.2μm (length) by 1.7μm (width)) was integrated witha planar broadband log-spiral antenna. For additional focusing ofthe incident radiation a silicon hyperhemispherical lens was used. For the 0.1–30 THz receivingsystem, the sensitive element was patterned as parallel strips(2μm wide each) filling an area of 500×500μm2with a filling factor of 0.5. In the receivingsystem of this type we used direct coupling of the incident radiation to the sensitive element. Inthe 25–70 THz range (detector type 2/2a in Table 1) we used a square-shaped superconductingdetector with planar dimensions of 10×10μm2. Incident radiation was coupled to the detectorwith the use of a germanium hyperhemispherical lens.The response time of the above receiving systems is determined by the cooling rate of the hotelectrons in the film. That depends on the electron-phonon interaction time, which is less forultrathin NbN than in MoRe. |
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Moscow, Russia |
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The Electromagnetics Academy |
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777 Concord Avenue, Suite 207 Cambridge, MA 02138 |
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1559-9450 |
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978-1-934142-09-7 |
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RPLAB @ sasha @ ozhegovultrafast |
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1022 |
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Smirnov, K. V.; Vakhtomin, Yu. B.; Divochiy, A. V.; Ozhegov, R. V.; Pentin, I. V.; Gol'tsman, G. N. |
| Title |
Infrared and terahertz detectors on basis of superconducting nanostructures |
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Conference Article |
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2010 |
Publication |
Microwave and Telecom. Technol. (CriMiCo), 20th Int. Crimean Conf. |
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823-824 |
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SSPD, SNSPD, HEB |
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Results of development of single-photon receiving systems of visible, infrared and terahertz range based on thin-film superconducting nanostructures are presented. The receiving systems are produced on the basis of superconducting nanostructures, which function by means of hot-electron phenomena. |
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IEEE |
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RPLAB @ sasha @ smirnov2010infrared |
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1025 |
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Goltsman, G. N.; Korneev, A. A.; Finkel, M. I.; Divochiy, A. V.; Florya, I. N.; Korneeva, Y. P.; Tarkhov, M. A.; Ryabchun, S. A.; Tretyakov, I. V.; Maslennikov, S. N.; Kaurova, N. S.; Chulkova, G. M.; Voronov, B. M. |
| Title |
Superconducting hot-electron bolometer as THz mixer, direct detector and IR single-photon counter |
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Abstract |
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2010 |
Publication |
35th Int. Conf. Infrared, Millimeter, and Terahertz Waves |
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1-1 |
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SSPD, SNSPD, HEB |
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We present a new generation of superconducting single-photon detectors (SSPDs) and hot-electron superconducting sensors with record characteristic for many terahertz and optical applications. |
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2162-2027 |
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RPLAB @ sasha @ goltsman2010superconducting |
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1028 |
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Zhang, W.; Miao, W.; Zhong, J. Q.; Shi, S. C.; Hayton, D. J.; Vercruyssen, N.; Gao, J. R.; Goltsman, G. N. |
| Title |
Temperature dependence of superconducting hot electron bolometers |
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Conference Article |
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2013 |
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Not published results: 24th international symposium on space terahertz technology |
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HEB |
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Groningen,The Netherlands |
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1067 |
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Semenov, A.; Richter, H.; Hübers, H.-W.; Petrenko, D.; Tretyakov, I.; Ryabchun, S.; Finkel, M.; Kaurova, N.; Gol’tsman, G.; Risacher, C.; Ricken, O.; Güsten, R. |
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Optimization of the intermediate frequency bandwidth in the THz HEB mixers |
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Abstract |
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2014 |
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Proc. 25th Int. Symp. Space Terahertz Technol. |
Abbreviated Journal |
Proc. 25th Int. Symp. Space Terahertz Technol. |
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54 |
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NbN HEB mixer |
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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. |
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1359 |
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Shcherbatenko, Michael; Lobanov, Yury; Benderov, Oleg; Shurakov, Alexander; Ignatov, Anton; Titova, Nadezhda; Finkel, Matvey; Maslennikov, Sergey; Kaurova, Natalya; Voronov, Boris M.; Rodin, Alexander; Klapwijk, Teunis M.; Gol'tsman, Gregory N. |
| Title |
Antenna-coupled 30 THz hot electron bolometer mixers |
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Conference Article |
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2015 |
Publication |
Proc. 26th Int. Symp. Space Terahertz Technol. |
Abbreviated Journal |
Proc. 26th Int. Symp. Space Terahertz Technol. |
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27 |
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HEB mixer, IR, mid-IR, 30 THz, antenna-coupled |
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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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no |
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1157 |
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Shurakov, Alexander; Maslennikov, Sergey; Tong, Cheuk-yu E.; Gol’tsman, Gregory |
| Title |
Performance of an HEB direct detector utilizing a microwave reflection readout scheme |
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Conference Article |
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2015 |
Publication |
Proc. 26th Int. Symp. Space Terahertz Technol. |
Abbreviated Journal |
Proc. 26th Int. Symp. Space Terahertz Technol. |
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36 |
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HEB detector |
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We report the results of our study on the performance of a hot electron bolometric (HEB) direct detector, operated by a microwave pump. The HEB devices used in this work were made from NbN thin film deposited on high resistivity silicon with an in-situ fabrication process. The experimental setup employed is similar to the one described in [1]. The detector chips were glued to a silicon lens clamped to a copper holder mounted on the cold plate of a liquid helium cryostat. Thermal link between the lens and the holder was maintained by a thin indium shim. The HEBs were operated at a bath temperature of about 4.4 K. Conventional phonon pump, commonly realized by raising the bath temperature of the detector, was substituted by a microwave one. In this case, a CW microwave signal is injected to the device through a directional coupler connected directly to the detector holder. The power incident on the HEB device was typically 1-2 μW, and the pump frequency was in the range of 0.5-1.5 GHz. The signal sources were 2 black bodies held at temperatures of 295 K and 77 K. A chopper wheel placed in front of the cryostat window switched the input to the detector between the 2 sources. A modulation frequency of several kilohertz was chosen in order to reduce the effects of the HEB’s flicker noise. A cold mesh filter was used to define the input bandwidth of the detector. The reflected microwave signal from the HEB device was fed into a low noise amplifier, the output of which is connected to a room temperature Schottky microwave power detector. This Schottky detector, in conjunction with a lock-in amplifier, demodulated the input signal modulation from the copper wheel. As the input load was switched, the impedance of the HEB device at the microwave pump frequency also changed in response to the incident signal power variation. Therefore the reflected microwave power follows the incident signal modulation. The derived responsivity from this detection system nicely correlates with the HEB impedance. In order to provide a quantitative description of the impedance variation of the HEB device and the impact of a microwave pump, we have numerically solved the heat balance equations written for the NbN bridge and its surrounding thermal heat sink [2]. Our model also accounts for the impact of the operating frequency of the detector because of non-uniform absorption of low-frequency photons across the NbN bridge [3]. In our measurements we varied the signal source wavelength from 2 mm down to near infrared range, and hence we indirectly performed the impedance measurements at frequencies below, around and far beyond the superconducting gap. Preliminary results show good agreement between the experiment and theoretical prediction. Further measurements are still in progress. [1] A. Shurakov et al., “A Microwave Reflection Readout Scheme for Hot Electron Bolometric Direct Detector”, to appear in IEEE Trans. THz Sci. Tech., 2015. [2] S. Maslennikov, “RF heating efficiency of the terahertz superconducting hot-electron bolometer”, http://arxiv.org/pdf/1404.5276v5.pdf, 2014. [3] W. Miao et al., “Non-uniform absorption of terahertz radiation on superconducting hot electron bolometer microbridges”, Appl. Phys. Let., 104, 052605, 2014. |
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1158 |
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Tretyakov, I.; Maslennikov, S.; Semenov, A.; Safir, O.; Finkel, M.; Ryabchun, S.; Kaurova, N.; Voronov, B.; Goltsman, G.; Klapwijk, T. M. |
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Impact of operating conditions on noise and gain bandwidth of NbN HEB mixers |
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Conference Article |
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2015 |
Publication |
Proc. 26th Int. Symp. Space Terahertz Technol. |
Abbreviated Journal |
Proc. 26th Int. Symp. Space Terahertz Technol. |
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39 |
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NbN HEB mixers |
| 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). |
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1159 |
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Trifonov, Andrey; Tong, C. Edward; Lobanov, Yury; Kaurova, Natalia; Blundell, Raymond; Gol’tsman, Gregory |
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An investigation of the DC and IF performance of silicon-membrane HEB mixer elements |
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2015 |
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Proc. 26th Int. Symp. Space Terahertz Technol. |
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Proc. 26th Int. Symp. Space Terahertz Technol. |
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40 |
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silicon-membrane HEB waveguide mixer |
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We report on our initial development towards a 2x2 multi-pixel HEB waveguide mixer for operation at 1.4 THz. We have successfully fabricated devices comprising an NbN bridge integrated with antenna test structure using a silicon membrane as the supporting substrate. DC measurements of the test chips demonstrate critical current from 0.1 – 1mA depending on the size of device, with T c of around 10 K and ΔTc ~ 0.8 K. |
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Seliverstov, Sergey V.; Rusova, Anastasia A.; Kaurova, Natalya S.; Voronov, Boris M.; Goltsman, Gregory N. |
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AC-biased superconducting NbN hot-electron bolometer for frequency-domain multiplexing |
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2017 |
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Proc. 28th Int. Symp. Space Terahertz Technol. |
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Proc. 28th Int. Symp. Space Terahertz Technol. |
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120-122 |
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NbN HEB mixer |
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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. |
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Antipov, S.; Trifonov, A.; Krause, S.; Meledin, D.; Desmaris, V.; Belitsky, V.; Gol’tsman, G. |
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Gain bandwidth of NbN HEB mixers on GaN buffer layer operating at 2 THz local oscillator frequency |
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Conference Article |
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2017 |
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Proc. 28th Int. Symp. Space Terahertz Technol. |
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Proc. 28th Int. Symp. Space Terahertz Technol. |
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147-148 |
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NbN HEB mixers, GaN buffer-layer, IF bandwidth |
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In this paper, we present IF bandwidth measurement results of NbN HEB mixers, which are employing NbN thin films grown on a GaN buffer-layer. The HEB mixers were operated in the heterodyne regime at a bath temperature of approximately 4.5 K and with a local oscillator operating at a frequency of 2 THz. A quantum cascade laser served as the local oscillator and a reference synthesizer based on a BWO generator (130-160 GHz) and a semiconductor superlattice (SSL) frequency multiplier was used as a signal source. By changing the LO frequency it was possible to record the IF response or gain bandwidth of the HEB with a spectrum analyzer at the operation point, which yielded lowest noise temperature. The gain bandwidth that was recorded in the heterodyne regime at 2 THz amounts to approximately 5 GHz and coincides well with a measurement that has been performed at elevated bath temperatures and lower LO frequency of 140 GHz. These findings strongly support that by using a GaN buffer-layer the phonon escape time of NbN HEBs can be significantly lower as compared to e.g. Si substrate, thus, providing higher gain bandwidth. |
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Krause, S.; Mityashkin, V.; Antipov, S.; Gol'tsman, G.; Meledin, D.; Desmaris, V.; Belitsky, V.; Rudzinski, M. |
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Study of IF bandwidth of NbN hot electron bolometers on GaN buffer layer using a direct measurement method |
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2016 |
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Proc. 27th Int. Symp. Space Terahertz Technol. |
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30-32 |
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NbN HEB, GaN buffer layer |
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In this paper, we present a reliable measurement method to study the influence of the GaN buffer layer on phonon-escape time in comparison with commonly used Si substrates and, in consequence, on the IF bandwidth of HEBs. One of the key aspects is to operate the HEB mixer at elevated bath temperatures close to the critical temperature of the NbN ultra-thin film, where contributions from electron-phonon processes and self-heating effects are relatively small, therefore IF roll-off will be governed by the phonon-escape.Two independent experiments were performed at GARD and MSPU on a similar experimental setup at frequencies of approximately 180 and 140 GHz, respectively, and have shown reproducible and consistent results. The entire IF chain was characterized by S-parameter measurements. We compared the measurement results of epitaxial NbN grown onto GaN buffer-layer with Tc of 12.5 K (4.5nm) with high quality polycrystalline NbN films on Si substrate with Tc of 10.5K (5nm) and observed a strong indication of an enhancement of phonon escape to the substrate by a factor of two for the NbN/GaN material combination. |
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