Godunova, E. K., & Levin, V. I. (1966). Some general features of heat conduction. USSR Computational Mathematics and Mathematical Physics, 6(6), 212–220.
Abstract: LET the initial temperature distribution in an infinite insulated rod without a heat source be given by a continuously differentiable function y = f(x), having a single maximum at x = 0 and two points of inflexion. The equation f′ = 0 then has a unique solution x = 0, where f′(x) > 0 for x < 0 and f′(x) < 0 for x > 0, We shall describe this as a one-hymped distribution. We shall assume that f/(x) also satisfies: (1) f(x) > 0 for − ∞ < x < ∞; (2) f(x) and x(fx) are integrable throughout the axis. Then the distribution remains one-humped for all t > 0.
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Gol'tsman, G., Maslennikov, S., Finkel, M., Antipov, S., Kaurova, N., Grishina, E., et al. (2006). Nanostructured ultrathin NbN film as a terahertz hot-electron bolometer mixer. In Proc. MRS (Vol. 935, 210 (1 to 6)).
Abstract: Planar spiral antenna coupled and directly lens coupled NbN HEB mixer structures are studied. An additional MgO buffer layer between the superconducting film and Si substrate is introduced. The buffer layer enables us to increase the gain bandwidth of a HEB mixer due to better acoustic transparency. The gain bandwidth is widened as NbN film thickness decreases and amounts to 5.2 GHz. The noise temperature of antenna coupled mixer is 1300 and 3100 K at 2.5 and 3.8 THz respectively. The structure and composition of NbN films is investigated by X-ray diffraction spectroscopy methods. Noise performance degradation at LO frequencies more than 3 THz is due to the use of a planar antenna and signal loss in contacts between the antenna and the sensitive NbN bridge. The mixer is reconfigured for operation at higher frequencies in a manner that receiver’s noise temperature is only 2300 K (3 times of quantum limit) at LO frequency of 30 THz.
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Zhang, W., Jiang, L., Lin, Z. H., Yao, Q. J., Li, J., Shi, S. C., et al. (2005). Development of a quasi-optical NbN superconducting HEB mixer. In Proc. 16th Int. Symp. Space Terahertz Technol. (pp. 209–213).
Abstract: In this paper, we report the performance of a quasi-optical NbN superconducting HEB (hot electron bolometer) mixer measured at 500 and 850GHz. The quasi-optical NbN superconducting HEB mixer is cryogenically cooled by a 4-K close-cycled refrigerator. Measured receiver noise temperature at 850 and 500GHz are 3000K and 2500K respectively with wire grid as beamsplitter, while the lowest receiver noise temperature is found to be approximately 1200K with Mylar film. The theoretical receiver noise temperature (taking into account the elliptical polarization of log-spiral antenna) is consistent with measured one. The receiver noise temperature and conversion gain with 15-μm Mylar film as the beamsplitter at 500GHz are thoroughly investigated for different LO pumping levels and dc biases. The stability of the mixer’s IF output power is also demonstrated.
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Gol'tsman, G., Jacobsson, S., Ekstrom, H., Karasik, B., Kollberg, E., & Gershenzon, E. (1994). Slot-line tapered antenna with NbN hot electron mixer for 300-360 GHz operation. In Proc. 5th Int. Symp. Space Terahertz Technol. (pp. 209–213a).
Abstract: NbN hot-electron mixers combined with slot-line tapered antennas on Si wdnitride membranes had been fabricated. Several strips of 1 gm wide and 5 tan long made from 100 A NbN film are inserted into the slot antenna. IV-curves under local oscillator power in 300-350 GHz frequency range and conversion gain dependencies on intermediate fre- quency in the 0.1-1 GHz range are measured and compared with that for 100 GHz frequency band. Our results show that pumped IV-curves and intermediate frequency bands are different for 100 GHz and 300 GHz frequency ranges. The interpretation exploits the fact that for the lowest radiation frequency the superconducting energy gap is larger than the radiation quantum energy while they are comparable at the higher frequency. Tha results show that such mixers have good perspectives for terahertz receiving technology.
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Gershenzon, E. M., Gershenzon, M. E., Gol'tsman, G. N., Semyonov, A. D., & Sergeev, A. V. (1984). Heating of electrons in superconductor in the resistive state due to electromagnetic radiation. Solid State Communications, 50(3), 207–212.
Abstract: The effect of heating electrons with respect to phonons in a thin superconducting film driven into the resistive state by the current and the external magnetic field has been observed and investigated. This effect caused by the electromagnetic radiation is manifested in the increased resistance of the film and is not selective over the frequency range from 1010 to 1015 Hz. That the effect is frequency independent under the conditions of strong electron scattering caused by static defects is explained by the decisive role of electron -electron collisions in forming the distribution function. The characteristic time of resistance change, obtained experimentally, corresponds to the relaxation time of the order parameter near the superconducting transition and to the relaxation time of the nonelastic electron-phonon interaction at lower temperatures and in lower magnetic fields.
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