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Physics Procedia

Non-Uniform Absorption of Terahertz Radiation in Superconducting Hot Electron Bolometer Mixers

W. Miao, Wen Zhang, Y. Delorme, R. Lefèvre, A. Féret, S. C. Shi

Published Jan 1, 2012• 5 citations
Publisher

Abstract

We present an improved hot spot model that includes the non-uniform absorption of terahertz radiation on a superconducting HEB microbridge. We propose that the terahertz radiation is indeed absorbed mainly in the region of the superconducting microbridge with its energy gap (2Δ), in connection with the local electron temperature, less than the photon energy of the incoming radiation. With this improved hot spot model, we can precisely model LO (Local Oscillator)-pumped current-voltage and LO-pumped resistance-temperature characteristics of superconducting HEB mixers.

DOI
10.1016/j.phpro.2012.06.168

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IEEE Transactions on Applied Superconductivity•Jan 1, 2014•7 citations
We present an improved hot spot model that includes the non-uniform absorption of terahertz radiation on a superconducting HEB microbridge. We propose that the terahertz radiation is indeed absorbed mainly in the region of the superconducting microbridge with its energy gap (2Δ), in connection with the local electron temperature, less than the photon energy of the incoming radiation. With this improved hot spot model, we can precisely model LO (Local Oscillator)-pumped current-voltage and LO-pumped resistance-temperature characteristics of superconducting HEB mixers.
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.
High-TCsuperconductor (YBaCuO) hot electron bolometers (HEB) are promising THz mixers due to the large predicted bandwidth and the low local oscillator (LO) power requirement. Recently, we introduced the hot-spot model, initially dedicated to low-TCNbN devices, to predict YBaCuO mixer performance. Major improvements to the model have been introduced: local description of the power absorption along the HEB constriction, THz dependence of the resistive transition, impedance matching between the THz antenna and the constriction. Mixer noise temperature TNand conversion gain G were predicted up to 2.5 THz. For instance, TN= 2700 K (DSB) and G = -13 dB are obtained with 9 μW of LO power at 1 THz.
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 gain is 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.
Abstract — A hot spot mixer model for phonon cooled hot electron bolometers is set up to accurately determine the dependence of the bolometer resistance on bias and absorbed LO power. An one-dimensional power balance for the nonequilibrium electrons containing an electron heat conduction term along the film and a loss term due to phonon escape to the substrate is solved. In the device's operating region of interest the absorbed heating power is usually large enough to heat a part of the bolometer bridge above the critical temperature forming a normal conducting hot spot. In this model heating due to the LO is assumed to be uniform whereas bias heating takes place in the hot spot region only. Solving the nonlinear power balance for the hot spot length allows to predict current-voltage characteristics, required heating powers and regions of optimal operation. Applying a small signal model in a given operating point yields an estimate for the intrinsic conversion gain. I. LARGE SIGNAL MODEL Existing device models for hot electron bolometers [1,2] treat the bolometer as a lumped element. It is assigned an effective temperature for the phonons and another for the electrons at a given bath temperature. In terms of heating bias power and RF power are equivalent and exchangeable. From this a method [3,4] to calculate the absorbed RF power is derived. This method is referred to as "isotherm " method: Operating points with identical device resistance must have identical temperatures since R(To„,,(,,, ) is a single valued monotonous function. Identical temperature implies identical power losses and identical 592
We report our studies of the effect of microwave radiation, with a frequency much lower than that corresponding to the energy gap of the superconductor, on the performance of the NbN hot-electron bolometer (HEB) mixer incorporated into a THz heterodyne receiver. It is shown that exposing the HEB mixer to microwave radiation does not result in a significant rise of the receiver noise temperature and degradation of the mixer conversion gain so long as the level of microwave power is small compared to the local oscillator drive. Hence the injection of a small, but controlled amount of microwave radiation enables active compensation of local oscillator power and coupling fluctuations which can significantly degrade the stability of HEB mixer receivers.
To investigate the THz mixing performance of YBCO hot electron bolometers (HEB), the influence of the local oscillator (LO) radiofrequency (RF) radiation has been considered in detail. As opposed to the usual hot spot modeling approach, where the LO power is assumed to be uniformly distributed over the HEB constriction length, a uniform RF current has been assumed. The local electron temperature-as obtained by solving the coupled electron and phonon thermal reservoir equations-could then be used to determine the local YBCO complex resistivity, hence the locally dissipated LO power. Besides, the use of a modified two-fluid description allowed to determine the RF-dependent temperature shift (~-1% THz-1) and broadening (~+20% THz-1) of the resistive transition. Finally, the impedance matching to the THz antenna was considered. For a typical constriction, the conversion loss and noise temperature TDSBwere computed, with TDSB× exp(0.32f) behavior up to 2.5 THz.