Klapwijk, T. M., Barends, R., Gao, J. R., Hajenius, M., & Baselmans, J. J. A. (2004). Improved superconducting hot-electron bolometer devices for the THz range. In Proc. SPIE (Vol. 5498, pp. 129–139).
Abstract: Improved and reproducible heterodyne mixing (noise temperatures of 950 K at 2.5 THz) has been realized with NbN based hot-electron superconducting devices with low contact resistances. A distributed temperature numerical model of the NbN bridge, based on a local electron and a phonon temperature, has been used to understand the physical conditions during the mixing process. We find that the mixing is predominantly due to the exponential rise of the local resistivity as a function of electron temperature.
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Gurevich, A. V., & Mints, R. G. (1987). Self-heating in normal metals and superconductors. Rev. Mod. Phys., 59(4), 941–1000.
Abstract: This review is devoted to the physics of current-carrying superconductors and normal metals having two or more stable states sustained by Joule self-heating. The creation, propagation, and localization of electrothermal domains and switching waves leading to the transition from one stable state to another in uniform and nonuniform samples are treated in detail. The connection between thermal bistability and hysteresis, dropping and stepped current-voltage characteristics, self-induced oscillations of current and voltage, selfreplication of electrothermal domains, and the formation of periodic and stochastic resistive structures are considered.
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Pekker, D., Shah, N., Sahu, M., Bezryadin, A., & Goldbart, P. M. (2009). Stochastic dynamics of phase-slip trains and superconductive-resistive switching in current-biased nanowires. Phys. Rev. B, 80, 214525 (1 to 17).
Abstract: Superconducting nanowires fabricated via carbon-nanotube templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: can a single phase-slip event occurring somewhere along the wire—during which the order-parameter fluctuates to zero—induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as a tool for evaluating and analyzing the mean switching time at a given value of current (smaller than the depairing critical current). The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the rather counterintuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way of unearthing and exploring the physics of nanoscale quantum tunneling of the one-dimensional collective quantum field associated with the superconducting order parameter.
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Phillips, T. G., & Jefferts, K. B. (1973). A low temperature bolometer heterodyne receiver for Millimeter wave astronomy. Rev. Sci. Instrum., 44(8), 1009–1014.
Abstract: Liquid helium cooled InSb hot electronbolometers are used in a balanced mixer configuration as detectors for an imagelessmicrowave receiver. The system is designed for mounting at the prime focus of the National Radio Astronomy Observatory (NRAO) 11 m antenna at Kitt Peak, Arizona, and is suitable for the study of rotational line spectra of interstellar gas molecules. Currently the operating frequency is in the 90–140 GHz band where the double sideband system noise temperature is 250 K.
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Miao, W., Zhang, W., Zhong, J. Q., Shi, S. C., Delorme, Y., Lefevre, R., et al. (2014). Non-uniform absorption of terahertz radiation on superconducting hot electron bolometer microbridges. <ef><bf><bc>Appl. Phys. Lett., 104, 052605(1–4).
Abstract: We interpret the experimental observation of a frequency-dependence of superconducting hot electron bolometer (HEB) mixers by taking into account the non-uniform absorption of the terahertz radiation on the superconducting HEB microbridge. The radiation absorption is assumed to be proportional to the local surface resistance of the HEB microbridge, which is computed using the Mattis-Bardeen theory. With this assumption the dc and mixing characteristics of a superconducting niobium-nitride (NbN) HEB device have been modeled at frequencies below and above the equilibrium gap frequency of the NbN film.
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Huard, B., Pothier, H., Esteve, D., & Nagaev, K. E. (2007). Electron heating in metallic resistors at sub-Kelvin temperature. Phys. Rev. B, 76, 165426(1–9).
Abstract: In the presence of Joule heating, the electronic temperature in a metallic resistor placed at sub-Kelvin temperatures can significantly exceed the phonon temperature. Electron cooling proceeds mainly through two processes: electronic diffusion to and from the connecting wires and electron-phonon coupling. The goal of this paper is to present a general solution of the problem in a form that can easily be used in practical situations. As an application, we compute two quantities that depend on the electronic temperature profile: the second and the third cumulant of the current noise at zero frequency, as a function of the voltage across the resistor. We also consider time-dependent heating, an issue relevant for experiments in which current pulses are used, for instance, in time-resolved calorimetry experiments.
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Bardeen, J., & Mattis, D. C. (1958). Theory of the anomalous skin effect in normal and superconducting metals. Phys. Rev., 111(2), 412–417.
Abstract: Chambers' expression for the current density in a normal metal in which the electric field varies over a mean free path is derived from a quantum approach in which use is made of the density matrix in the presence of scattering centers but in the absence of the field. An approximate expression used for the latter is shown to reduce to one derived by Kohn and Luttinger for the case of weak scattering. A general space-and time-varying electromagnetic interaction is treated by first-order perturbation theory. The method is applied to superconductors, and a general expression derived for the kernel of the Pippard integral for fields of arbitrary frequency. The expressions derived can also be used to discuss absorption of electromagnetic radiation in thin superconducting films.
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Kawamura, J., Blundell, R., Tong, C. - Y. E., Golts'man, G., Gershenzon, E., & Voronov B. (1996). Superconductive NbN hot-electron bolometric mixer performance at 250 GHz. In Proc. 7th Int. Symp. Space Terahertz Technol. (pp. 331–336).
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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Shurakov, A., Tong, C. -yu E., Grimes, P., Blundell, R., & Golt'sman, G. (2015). A microwave reflection readout scheme for hot electron bolometric direct detector. IEEE Trans. THz Sci. Technol., 5, 81–84.
Abstract: In this paper, we propose and present data from a fast THz detector based on the repurpose of hot electron bolometer mixers (HEB) fabricated from superconducting NbN thinfilm. This detector is essentially a traditional NbN bolometer element that operates under the influence of a microwave pump. The in-jected microwave power serves the dual purpose of enhancing the detector sensitivity and reading out the impedance changes of the device in response to incidentTHz radiation. We have measured an optical Noise Equivalent Power of 4 pW/ Hz for our detector at a bath temperature of 4.2 K. The measurement frequency was 0.83 THz and the modulation frequency was 1.48 kHz. The readout
scheme is versatile and facilitates both high-speed operation as well as multi-pixel 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%.
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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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Seliverstov, S., Maslennikov, S., Ryabchun, S., Finkel, M., Klapwijk, T. M., Kaurova, N., et al. (2015). Fast and sensitive terahertz direct detector based on superconducting antenna-coupled hot electron bolometer. IEEE Trans. Appl. Supercond., 25(3), 2300304.
Abstract: We characterize superconducting antenna-coupled hot-electron bolometers for direct detection of terahertz radiation operating at a temperature of 9.0 K. The estimated value of responsivity obtained from lumped-element theory is strongly different from the measured one. A numerical calculation of the detector responsivity is developed, using the Euler method, applied to the system of heat balance equations written in recurrent form. This distributed element model takes into account the effect of nonuniform heating of the detector along its length and provides results that are in better agreement with the experiment. At a signal frequency of 2.5 THz, the measured value of the optical detector noise equivalent power is 2.0 × 10-13 W · Hz-0.5. The value of the bolometer time constant is 35 ps. The corresponding energy resolution is about 3 aJ. This detector has a sensitivity similar to that of the state-of-the-art sub-millimeter detectors operating at accessible cryogenic temperatures, but with a response time several orders of magnitude shorter.
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Maslennikov, S. (2014). RF heating efficiency of the terahertz superconducting hot-electron bolometer. arXiv, 1404.5276, arXiv:1404.5276.
Abstract: We report results of the numerical solution by the Euler method of the system of heat balance equations written in recurrent form for the superconducting hot-electron bolometer (HEB) embedded in an electrical circuit. By taking into account the dependence of the HEB resistance on the transport current we have been able to calculate rigorously the RF heating efficiency, absorbed local oscillator (LO) power and conversion gain of the HEB mixer. We show that the calculated conversion gai nis in excellent agreement with the experimental results, and that the substitution of the calculated RF heating efficiency and absorbed LO power into the expressions for the conversion gain and noise temperature given by the analytical small-signal model of the HEB yields excellent agreement with the corresponding measured values
Keywords: superconducting hot-electron bolometer mixer, HEB, NbN, distributed model, HEB model, HEB mixer model, heat balance equa-tions, conversion gain, RF heating efficiency, noise temperature, simulation, Euler method
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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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Hajenius, M., Barends, R., Gao, J. R., Klapwijk, T. M., Baselmans, J. J. A., Baryshev, A., et al. (2005). Local resistivity and the current-voltage characteristics of hot electron bolometer mixers. IEEE Trans. Appl. Supercond., 15(2), 495–498.
Abstract: Hot-electron bolometer devices, used successfully in low noise heterodyne mixing at frequencies up to 2.5 THz, have been analyzed. A distributed temperature numerical model of the NbN bridge, based on a local electron and a phonon temperature, is used to model pumped IV curves and understand the physical conditions during the mixing process. We argue that the mixing is predominantly due to the strongly temperature dependent local resistivity of the NbN. Experimentally we identify the origins of different transition temperatures in a real HEB device, suggesting the importance of the intrinsic resistive transition of the superconducting bridge in the modeling.
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