Analysis of the Broad IF-Band Performance of MgB2 HEB Mixers

We present an experimental study of gain and noise bandwidths in superconducting MgB2 hot-electron bolometer (HEB) terahertz mixers in a 0.1–20 GHz intermediate frequency (IF) range. At an elevated temperature and with a 90-GHz local oscillator (LO), we measure a gain bandwidth of 13–14 GHz, which is the first accurate data for ultrathin MgB2 films. The output noise spectrum has its maximum in the 100–200 K range, depending on the temperature (or the LO power) and the bias point, and its spectrum also confirms the gain bandwidth data obtained with the mixing experiment. Using both the gain and the output noise spectra, we obtain the mixer input noise temperature, which is nearly constant up to 20 GHz. Using the measured data and the HEB mixer theory, we argue that noise bandwidth in the current MgB2 HEB mixers is ∼30 GHz.


I. INTRODUCTION
URING the last two decades, superconducting hot-electron bolometer (HEB) mixers have proven to be a successful technology for extremely low-intensity molecular line observations at frequencies above 1 THz [1], [2], [3]. This is because, unlike SIS mixers, the highest operation frequency of HEBs is not limited by the superconducting gap, and, compared to Schottky diode mixers their noise temperature is much lower. The most extensively studied and used HEB mixers are those based on phonon-cooling mechanism of non-equilibrium electrons created by the incident THz radiation [4], [5]. Among them, NbN HEB mixers are the most sensitive heterodyne detectors, with a minimum noise temperature of  500-1000 K [6], [7], [8], [9]. Despite of being state-of-the-art, the gain bandwidth of NbN based phonon-cooled HEB mixers is limited to 2-4 GHz due to about 12 ps of electron-phonon interaction time (eph) and 30-40ps of phonon escape time into the substrate [10], [11]. Although for many astronomical tasks such instantaneous bandwidth is sufficient, for observations of broad spectral lines towards the Galactic Center, extragalactic observations, and heterodyne lines surveys a bandwidth in excess of at least 8 GHz is required in order to use a single (or reduced in numbers) LO settings [12], [13]. This work was supported by the Swedish Research Council (VR), the Swedish Space Agency and the European Research Council.
There have been some efforts to enhance the gain bandwidth of NbN HEBs by initiating a faster phonon escape through an improved film-substrate interface system in various substrate materials [14], [15]. Despite some improvements in the noise temperature, the enhanced IF bandwidth in NbN HEBs has only been reported up to 5-6 GHz. Alternatively, bolometric mixing in chemically doped graphene was recently presented with a demonstrated gain bandwidth of 8 GHz, determined by electron diffusion [16]. However, high sensitivity in graphene hot-electron bolometer mixers, predicted theoretically, is still to be confirmed experimentally.
Due to the advancement in ultrathin superconducting MgB2 film fabrication technology [17], [18] , in recent years, MgB2 based HEBs have become a center of interest due to their very fast inelastic electron-phonon interaction (eph 1-2 ps at 40 K) and efficient acoustic matching to both sapphire and SiC substrates [19], [20], [21]. A receiver noise temperature of 1000 K and a noise bandwidth (NBW) of 11 GHz have been reported for MgB2 HEBs using the Yfactor technique at both 700 GHz and 1.63 THz LO frequencies, with an optimal Local Oscillator power of about 10 W [22]. With a critical temperature of 30 K, the mixer showed only a minor reduction of sensitivity for operation temperatures up to 20 K.
Earlier gain bandwidth measurements showed that for MgB2 thin films the gain is almost constant up to 10 GHz (no roll-off), which is a huge improvement compared to any existing state-of-the-art HEBs. Such gain bandwidth (GBW) does not match the 11 GHz NBW [22], because for HEBs an NBW/GBW ratio of 2 is to be expected [23], [24]. The obvious reason for this discrepancy is the imperfection of the utilized receiver layout, involving the mixer block, the IF amplifier and the interaction between those. In this paper, we study the intrinsic performance of MgB2 HEB mixers, namely the gain and noise temperature bandwidths, without the influence of the IF chain. In order to be able to do this, we placed the co-planar waveguide (CPW) integrated MgB2 micro bridges into a cryogenic millimeter wave probe station with an optical signal path and a readout bandwidth of 67 GHz. We measured the gain bandwidth and the output noise spectrum up to 20 GHz, and then calculated the spectrum of the input noise temperature. A similar approach was utilized earlier for the MgB2 HEB mixer study vs the bias and temperature variations [25]. In order to benchmark the obtained results, we fabricated and tested NbN HEB mixers in the same setup.

A. HEB Mixer Fabrication
Our device fabrication process starts with the deposition of ultrathin MgB2 films (5-8 nm) on SiC substrates using a custom built hybrid physical chemical vapor deposition (HPCVD) system. Details about our HPCVD system and ultrathin film growth conditions have been described in our previous reports [17], [26] and this process is based on that reported by Zeng et.al. [27]. MgB2 film growth occurred at a substrate temperature of 730 ºC and at a chamber pressure of 20 Torr (maintained by the 400 sccm flow of hydrogen (H2) carrier gas). Magnesium was supplied through the evaporation of Mg slugs placed around the substrate on a resistively heated substrate holder, while boron is provided through the decomposition of diborane gas (5% B2H6 in H2), which is introduced into the vacuum chamber at 2 sccm only during growth. Subsequently, MgB2 films were transferred to a dc-magnetron sputtering system where plasma cleaning of the film surface (from MgOx) was carried out, followed by in situ sputtering of a 20 nm thick Au film. Similarly, NbN films were deposited on 330 µm thick, C-plane (0001), double-side polished, sapphire substrates by DC reactive magnetron sputtering. The films were deposited from the 2inch Nb (99.95%) target in an Ar and N2 environment at 800 °C substrate temperature. For this study, approximately 5 nm thick NbN films were utilized and the thickness was estimated based on the deposition rate.
Both MgB2 and NbN HEB devices were fabricated by electron beam lithography. First, we defined the coplanar waveguide (CPW) contact pads and alignment marks on the films (Fig. 1). Polymethyl methacrylate (PMMA -70 nm) on top of copolymer (MMA-470 nm) was utilized as a positive-tone two-layer resist system for electron beam lithography. The subsequent development in mixture of isopropanol and DI water (10:1), electron beam physical vapor deposition (PVD) of Ti-Au-Ti (10 nm-200 nm-40 nm), and lift-off in acetone, leaves the desired patterns on the substrate. The first 10 nm titanium layer promotes the adhesion of Au whereas the final 40 nm layer serves as a mask for gold contact pads later on during the Ar ion milling. The HEB bridges were defined via another electron beam lithography step, with a negative-tone resist (ma-N 2401-100 nm), and developed in tetramethylammonium hydroxide aqueous solution (ma-D 525) followed by rinse in DI water. In the final step, the remaining MgB2 and NbN were removed by Ar ion milling.

B. Noise and Gain Characterization
In order to characterize the gain and the noise spectra, two wafers (one with MgB2 and another with NbN HEB mixers), were mounted onto the sample holder inside the Lakeshore cryo-probe station (CRX-4K) chamber ( Fig.1), which we operated from 40 K (above the Tc of MgB2) down to 5 K (the base temperature). The measurement set-up diagram, the contact probe, the device layout and the photograph of the Lakeshore probe station are shown in the Fig.1. We have presented data for a 0.5 µm wide  2 µm long MgB2 and a 2 µm wide  0.3 µm long NbN HEBs. In order to be able to contact the samples with the high frequency GSG probe (100m pitch), the samples have to face upwards, without any Si lens or horn antenna, i.e. with an effective detector area of 20-30 m (center contact length of the CPW line ( Fig.1)). The sample-to-quartz window distance is 15 cm, which makes optical coupling quite poor, even for a large focusing lens/mirror above the window. Therefore, in order to make measurements possible, we chose to employ high power WR-10 band sources.
A 90 GHz LO (Omnisys Instruments AB, 20-30 mW output power) and 90-110 GHz Signal (Virginia Diodes Inc., WR10 TxRx modul, mW output power) sources were combined with a 10 dB waveguide directional coupler with a 90 waveguide bend and a smooth conical horn facing down towards the window. Two Teflon lenses with focal lengths of 75 mm and 100 mm (not shown in the photo) refocused the beam onto the sample.
Both the DC bias and the IF readout were arranged via a coplanar waveguide probe with the ground-signal-ground  contact geometry. Low thermal conductivity semirigid coaxial cables lead to a stable sample temperature and microwave readout up to 67 GHz without an appreciable loss. At room temperature, the IF chain consisted of a 40 GHz bias tee (SHF BT45B, SHF AG) and two broadband LNAs (SHF 810, SHF AG and AFS4-0012000 Miteq). The IF chain noise temperature (600-700 K) across the 0.1-20 GHz band (100 MHz step) was measured using Y-factor technique with a microwave noise diode. Both the mixing signal and mixer output noise were recorded using a spectrum analyzer. For the noise measurements, the maximum resolution bandwidth of B=50 MHz was utilized to increase measurements accuracy. The output noise of the HEB mixers was obtained from the following equations: Here, PN is the measured noise (the HEB and the LNA) with the HEB at the desired operation point; GLNA is the IF chain gain; Pref is the measured noise when the HEB was biased at 100 mV, i.e. in the normal state (see Fig.3a,b); Tref =35 K is the HEB temperature in the normal state (a linear I(V)). In a separate set of measurements we observed that the equivalent noise temperature of the HEB bridge at a physical temperature of 35 K (zero bias) is the same as when the HEB is biased at 100 mV being at <Tc. It was essential to keep the device at the same physical temperature for both PN and Pref in order to avoid thermal expansion of the coax cable, which otherwise would lead to standing waves in the Tout -spectrum.
As is known [4], the HEB mixer gain (at a particular bias point and LO power) follows the dependence: where G(0) is the gain at zero IF, f is the intermediate frequency, and f0 is the 3 dB gain roll-off frequency, determined approximately by the electron cooling time  (this being slightly modified by the bias current effect) as f0=1/. Although the absolute mixer gain could not be measured in our experiments, its IF-dependence was obtained by recording the power of the mixing signal from the LO and the Signal source, Pif(f) G(f), when the Signal frequency is tuned from 90 GHz to 110 GHz. Fitting the measured Pif(f) with (2) provides the gain bandwidth (f0) of the mixer.
Samples with CPW contacts did not have antennas, and the coupling of both the LO and the Signal to MgB2 and NbN micro bridges occurred via the CPW contacts (Fig.1). The coupling factor varied significantly across the frequency tuning range of the Signal source. In order to calibrate for the signal coupling variation, Amplitude Modulation (AM) at 10 kHz was applied to the Signal source, and the coupled power was measured as the HEB direct detection response using a lock-in amplifier. The measured Pif(f) data were also corrected for the gain in the IF chain (GLNA).
At 5 K, the photon energy of the 90 GHz LO is much lower than the superconducting energy gaps in both MgB2 and NbN. Therefore, the samples temperature was set close to Tc in order to reduce the energy gap, hence bringing the devices to the conditions in which the I(V) has to correspond to that where the lowest mixer noise temperatures are typically measured with THz LOs. This approach was frequently utilized for HEB mixer studies, and its validity has been confirmed for NbN HEB mixers (see e.g. [14]). For MgB2 HEBs, the I(V)-curves under the optimal power 700 GHz, 1.6 THz, and 2.6 THz LOs have been confirmed to correspond well to the I(V) without an LO, but at a temperature close to Tc [22]. The same being valid also for the output noise [25].
Additionally, a batch of MgB2 devices was fabricated with THz spiral antennas using MgB2 films similar to those for the devices described above. Packaged into a mixer block with a Si lens, the noise temperature was measured with Yfactor technique at a 1.63 THz LO at 5 K, 15 K, 20 K, and 25 K operation temperatures (Fig.2) as a reference (see [22]). The measured minimum noise temperature is about 1000 K, i.e. close to that published previously. The fit to the noise temperature spectrum (9) reveals a noise bandwidth of 13 GHz, which is larger than the previously published 11 GHz. We explain this difference by a higher critical temperature and a slightly smaller film thickness for the current batch (32-33 K), which leads to a shorter electron cooling time [21]. An important note: the NBW is the same

III. RESULTS AND DISCUSSION
A. I(V) characteristics I(V) characteristics of the NbN HEB at both 5 K and 9.5 K, and that for the MgB2 HEB at various temperatures from 5 K to 32 K, are shown in Fig. 3(a) and Fig 3(b), respectively. At 5 K, the critical current (Ic) of this MgB2 HEB sample is 1.25 mA, corresponding to a rather high critical current density of 310 7 A/cm 2 . Similarly, the normal state resistance of the tested device was 90 Ω (>40 mV), which is consistent with the resistance obtained from the Resistance vs Temperature R(T) measurement (>35 K). The critical temperatures Tc of both NbN and MgB2 HEBs were deduced from the R(T) measurement and come in at 10 K (a typical Tc for thin NbN films) and 33-34 K, respectively (Fig  3 (a), (b), insets). In both samples, narrow transition widths were observed, indicating that the high quality of films was preserved through the HEB fabrication.

B. Gain bandwidth of NbN HEB mixers
In order to benchmark MgB2 HEB mixers against the well-established technology of NbN HEB mixers, the gain bandwidth of NbN HEBs, integrated with the same CPW contacts as for MgB2 HEBs, was measured in the same setup.
The critical current of the tested NbN sample (w=2 m  L=0.3 m) was Ic(5 K)=0.39 mA (Fig. 3(a)). At 9.5 K the I(V) curve is very similar to that pumped to the optimal performance, with a high frequency LO (f>2) from 4 K [28]. The best fit for the measured (from 100 MHz to 20 GHz) IF response (Pif(f)) to (2) shows a 3 dB roll-off at 2-3 GHz (Fig.4 (a)), i.e. similar to that previously reported [10], [24].

C. The gain bandwidth and the output noise spectrum of MgB2 HEB mixers
Based on previous experience [22], [25] , as well as on the sample presented in Fig.2 (2)) vs IF, measured at the same bias points as Pif,(f) in Fig.4(b). The solid line represents the output noise Tout= TJ+ TFL , calculated using TJ= Tc and TFL according to equation (2). (b) Normalized mixer noise temperature, Tm of the MgB2 HEB at 30 K and 28 K, obtained as Tmix(f)=[Tout (f)/ Pif,(f) +Normalization Factor]. In this case Pif,(f) was converted to the linear scale. DOI: 10.1109/TTHZ.2019.2945203 , This paper has been published in IEEE Trans.THz,Sci.Technol. v.9, (2019) / Open Access 5 range 28 K-30 K. Consequently, gain bandwidth was measured at these temperatures, with a small LO power at 90 GHz. The measured gain bandwidth is 13-14 GHz (Fig.4b), which is the same as for both 28 K and 30 K, and is independent on the bias point along the I(V).
Measured output noise (Fig.5a) at low IF is in the range 100-200 K, as has been previously reported for both 0.7 THz and 1.63 THz LOs [22]. The noise rolls off as the IF increases, reaching a frequency independent value at IF>10 GHz. Despite the IF chain noise temperature being much higher than the mixer output noise Tout, we managed to conduct quite reproducible measurements of Tout(f). This fact is confirmed by two curves presented for the 28 K-I(V) (Fig.5a).

D. Discussion
The output noise in HEBs (as well as in any other thermal detector) is composed of two constituents: the thermal (Johnson) noise TJ, and the temperature fluctuation noise TFL: Tout= TJ+ TFL. [29] The thermal fluctuation noise is a strong function of the electron temperature Te (in superconducting HEBs at the optimal LO and dc drive Te  Tc) and . Following the lumped element HEB model [30], [31]: where the differential resistance , the dc resistance R0=V0/I0, and the bias voltage and current V0 and I0 can be obtained from the I(V) characteristics, RL is the input impedance of the mixer load (the IF amplifier). Equations (3) and (4) are from the lumped HEB model, which is rather simplified and does consider the microscopic physics in superconducting micro bridges. However, being combined with empirically obtained C0, they have shown to describe well experimental results for low-Tc HEB mixers (Nb, and NbN).
The fluctuation noise spectral dependence is similar to the mixer gain spectrum, i.e.: The Johnson noise is, to the contrary, frequency independent:

TJ= Tc
Following [4], the ratio of output noise and gain provides the spectrum of the mixer (input) noise temperature: is called the noise bandwidth (the IF at which the mixer input noise temperature increases by a factor of 2 from its value at zero IF). It is clear that the higher the Tout(0)/ TJ ratio, the larger the vs 0 becomes. Noise temperature is the main figure of merit of the mixer, and the fact that > 0 is indeed a nice feature in superconducting HEBs where (0) > 2 is fairly common.
In practice, HEB mixers operate with (cryogenic) IF amplifiers (LNA), where the system noise temperature (the receiver noise temperature) can be expressed as: Where is the system (or the receiver) noise bandwidth. In a terahertz astronomical receiver it is * which matters, hence the lower the vs ( , ) the better. Using device parameters (Fig.3), the measured GBW of 13 GHz and equations (3)(4)(5)(6), we calculated the output noise spectrum for the MgB2 HEB ( Fig.5a-solid line). No fitting parameters were utilized in these calculations however, and as can be seen, the calculated curve matches the measured data rather well. Measured Tout(f) data can be considered as an independent verification for the mixer gain bandwidth.
Nearly linear scaling of the gain bandwidth with the film thickness, observed for both MBE-grown MgB2 films on sapphire [21] and HPCVD-grown films on SiC [26], suggests that the process of electron energy relaxation occurs mainly due to inelastic electron-phonon collisions and consequent phonon energy transfer to the substrate [4], [32]: where ( , , ) = (1 + 2 1 )(1 + 2 2 ) (1 + 2 3 ) Here eph, esc are electron-phonon interaction time and phonon escape (from the film into the substrate) time. Electron and phonon specific heats ce and cph in MgB2 as well as electron-phonon interaction time and phonon escape (eph, esc) time have been discussed in previous publications (e.g. [21], [33]). Both mass density and sound velocity in SiC are close to those in sapphire. Therefore, we assume that the phonon escape time from MgB2 into SiC is the same as into sapphire. With the other relevant parameters in hand (Table  I), we simulate the IF spectrum of the conversion gain for the studied MgB2 HEB mixer (Fig.4b, open circles). The resulting 3 dB roll-off frequency is 13.5 GHz, i.e. very close to the experimental value. For the modeling, the electron DOI: 10.1109/TTHZ.2019.2945203 , This paper has been published in IEEE Trans.THz,Sci.Technol. v.9, (2019) / Open Access 6 temperature Te is assumed to be equal to Tc [14], [21]. The phonon temperature (Tph =0.8 Te) was calculated using the system of two heat balance equations: electron-phonon and phonon-substrate [32].
Finally, using the measured gain and the output noise spectra, we can calculate (using (7)) the spectrum of the mixer input noise temperature (Fig.5b). The absolute value of the mixer gain is not known, therefore it is the IF dependence of Tm that we consider. However, we normalized Tm in Fig.5b in order to fit the low IF Tm data obtained with the Y-factor approach (Fig.2). The obtained Tm(20 GHz) is only 20-25 % higher than Tm(1 GHz), which suggests that the noise bandwidth is >20 GHz. On the other hand, using (9), f0=14 GHz ( Fig.4(b)), Tout(0) 150 K (Fig.5(a)), and TJ 33 K (TJ  Tc), we obtain fN30 GHz, which should be achievable with a well-designed IF readout.
MgB2 HEB mixers have much larger (100-200 K) compared to NbN HEBs (20-40´K) [34], and the fact that LNA performance is far less critical to MgB2 HEBs compared to NbN HEBs has been previously emphasized. Indeed, with a noise temperature of 3-6 K for cryogenic broadband microwave amplifiers being quite common, the effect of the IF LNA noise on the MgB2 HEB receiver sensitivity is not expected to be significant.
However, so far we have been neglecting the impedance matching and interference between mixer and LNA, the importance of which has been pointed out in previous publications [35], [36]. Therefore, understanding each and every single component in the THz receiver (the mixer, the LNA and the interaction between these) is crucial to obtaining top receiver performance, as is required for astronomy.

IV. CONCLUSION
In summary, we have characterized MgB2 HEB mixer gain and noise spectra in a broad IF band (from 100 MHz to 20 GHz) utilizing a high quality readout setup at the Lakeshore cryo probe station CRX-4K. We have demonstrated that HEB mixers made from thin (5 nm) MgB2 films have a gain bandwidth of 13-14 GHz, which was also confirmed by the output noise spectrum. This experimental result is in agreement with modeling, which presumes electron cooling via electron-phonon interaction. Mixer noise temperature (excluding the LNA) is nearly constant up to 20 GHz , with noise bandwidth of fN30 GHz, calculated based on GBW and output noise. On the other hand, a Silens integrated MgB2 HEB mixer shows a minimum noise temperature of 1000 K and a NBW of 13 GHz when a standard IF LNA (2-8 GHz) is used. This, confirms that in order to make use of the full potential of MgB2 HEB mixers, all parts of the receiver (mainly, the mixer and the LNA) have to be carefully designed.