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Bardeen J, Mattis DC. Theory of the anomalous skin effect in normal and superconducting metals. Phys Rev. 1958;111(2):412–7.
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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Shcherbatenko M, Tretyakov I, Lobanov Y, Maslennikov SN, Kaurova N, Finkel M, et al. Nonequilibrium interpretation of DC properties of NbN superconducting hot electron bolometers. Appl. Phys. Lett.. 2016;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.
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Miao W, Zhang W, Zhong JQ, Shi SC, Delorme Y, Lefevre R, et al. Non-uniform absorption of terahertz radiation on superconducting hot electron bolometer microbridges. <ef><bf><bc>Appl Phys Lett. 2014;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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Sidorova M, Semenov AD, Hübers H-W, Ilin K, Siegel M, Charaev I, et al. Electron energy relaxation in disordered superconducting NbN films. Phys Rev B. 2020;102(5):054501 (1 to 15).
Abstract: We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product qTl (qT is the wave vector of thermal phonons and l is the elastic mean free path of electrons). In the temperature range 14–30 K, the electron-phonon scattering rates obey temperature dependencies close to the power law 1/τe−ph∼Tn with the exponents n≈3.2–3.8. We found that in this temperature range τe−ph and n of studied films vary weakly with the thickness and square resistance. At 10 K electron-phonon scattering times are in the range 11.9–17.5 ps. The data extracted from magnetoconductance measurements were used to describe the experimental photoresponse with the two-temperature model. For thick films, the photoresponse is reasonably well described without fitting parameters, however, for thinner films, the fit requires a smaller heat capacity of phonons. We attribute this finding to the reduced density of phonon states in thin films at low temperatures. We also show that the estimated Debye temperature in the studied NbN films is noticeably smaller than in bulk material.
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Cherednichenko S, Drakinskiy V, Baubert J, Krieg J-M, Voronov B, Gol'tsman G, et al. Gain bandwidth of NbN hot-electron bolometer terahertz mixers on 1.5 μm Si3N4 / SiO2 membranes. J Appl Phys. 2007;101(12):124508 (1 to 6).
Abstract: The gain bandwidth of NbN hot-electron bolometer terahertz mixers on electrically thin Si3N4/SiO2 membranes was experimentally investigated and compared with that of HEB mixers on bulk substrates. A gain bandwidth of 3.5 GHz is achieved on bulk silicon, whereas the gain bandwidth is reduced down to 0.6–0.9 GHz for mixers on 1.5 μm Si3N4/SiO2 membranes. We show that application of a MgO buffer layer on the membrane extends the gain bandwidth to 3 GHz. The experimental data were analyzed using the film-substrate acoustic mismatch approach.
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