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Journal of Applied Physics

Comparison between hot spot modeling and measurement of a superconducting hot electron bolometer mixer at submillimeter wavelengths

Wei Miao, Y. Delorme, A. Féret, Rolland Lefevre, B. Lecomte, F. Dauplay, Jean-Michel Krieg, G. Beaudin, Wen Zhang, Yuan Ren, Sheng‐Cai Shi

Published Nov 15, 2009• 13 citations
Publisher

Abstract

This paper presents the modeling and measurement of a quasioptical niobium nitride superconducting hot electron bolometer mixer at submillimeter wavelengths. The modeling is performed with a distributed hot spot model which is based on solving a heat balance equation for electron temperature along the superconducting microbridge. Particular care has been taken during the modeling concerning the temperature-dependent resistance and the bias current dependence of the critical temperature of the device. The dc and mixing characteristics of this mixer have been computed and we have observed a quite good match between the predicted and the measured results for both dc characteristics and mixing performances at submillimeter wavelengths.

DOI
10.1063/1.3259381

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Applied Physics Letters•Feb 3, 2014•25 citations
This paper presents the modeling and measurement of a quasioptical niobium nitride superconducting hot electron bolometer mixer at submillimeter wavelengths. The modeling is performed with a distributed hot spot model which is based on solving a heat balance equation for electron temperature along the superconducting microbridge. Particular care has been taken during the modeling concerning the temperature-dependent resistance and the bias current dependence of the critical temperature of the device. The dc and mixing characteristics of this mixer have been computed and we have observed a quite good match between the predicted and the measured results for both dc characteristics and mixing performances at submillimeter wavelengths.
In this paper, we present the modeling and measurement results of niobium titanium nitride hot electron bolometer mixers with different sizes at terahertz frequencies. A distributed hot spot model which is based on solving a heat balance equation is employed to characterize current-voltage curve, electron and phonon temperature distribution along superconducting microbridge, intermediate frequency gain bandwidth and intrinsic noise temperature of the mixers. The simulated intermediate frequency gain bandwidth decreases with the increase of microbridge length, which is in good agreement with measured results. A difference of factor of several tens exists between the calculated and measured mixer noise temperature, which is probably due to the disfigurement of waveguide structure and unknown noise from the mixer.
In this paper, the performance of a quasi-optical phonon-cooled NbN superconducting hot electron bolometer (HEB) mixer is thoroughly investigated. The variation of the receiver noise temperature and the conversion gain around 600 GHz with respect to DC bias voltage and LO pumping level has been measured. The lowest receiver noise temperature is 750 K and reduced to about 250 K after correcting the quasi-optical losses before the HEB mixer. We compared the measured results with the predictions according to one dimensional distributed hot spot model. A reasonable match between theoretical model and experiment is observed. In addition, the direct response of the HEB mixer (integrated with a log-periodic spiral antenna) is measured by using Fourier Transform Spectrometer (FTS). The stability of the receiver is also investigated by means of Allan variance time measurements performed with an intermediate frequency (IF) bandwidth of 40 MHz.
In this paper, we present the intrinsic mixing behavior of superconducting niobium titanium nitride hot electron bolometer mixer based on in-situ technique. We make detailed comparison between simulated and measured performance of the HEB mixers at 0.8 and 1.5 THz. A distributed hot spot model which is based on solving a heat balance equation is employed to characterize current-voltage curve, electron and phonon temperature distribution along superconducting microbridge, intermediate frequency gain bandwidth and intrinsic noise temperature of the mixers. The simulated intermediate frequency gain bandwidth decreases with the increase of microbridge length, which is in good agreement with measured results. For the microbridge with 0.15 µm in length, the IF gain bandwidth is simulated to be 2.6 GHz at 0.8 and 1.5 THz. When the microbridge length is increased to 0.3 µm, the calculated IF gain bandwidth is 1.8 GHz. The simulated results demonstrate the IF gain bandwidth is only related with microbridge length, independent of RF frequency. It's very useful to find the critical parameters which mainly affects the mixer noise temperature and IF gain bandwidth. In this paper we will give the critical factors as the reference for fabrication and measurement of HEB mixers. We have found that when the ratio of length to width of the microbridge is set to be around 0.15, the simulated and measured mixer noise temperature show the lowest value. More details will be presented in the paper.
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
In this paper, we investigate the critical temperature dependence of the performance of niobium nitride superconducting hot electron bolometer (HEB) mixers. The input noise temperature and intermediate frequency (IF) noise bandwidth of superconducting HEB mixers of different critical temperatures Tc(between 6 and 12 K) are simulated with a hot spot model. Simulation results show that the mixer input noise temperature is the lowest at Tcapproximately equal to 7-9.5 K and the IF noise bandwidth increases with Tc. We also measure three superconducting HEB mixers of different critical temperatures (i.e., 7.5, 8.8, and 10.3 K) at 0.85 and 1.3 THz. An agreement between measurement and prediction is observed.
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.