Full characterization of small volume NbN HEBmixers for Space Applications

J. Baselmans, J. Kooi, A. Baryshev, Z.Q. Yang, M. Hajenius, J.R. Gao, T.M. Klapwijk, B. Voronov, and G.Gol’tsman

Abstract— NbN phonon cooled HEB’s are one of the mostpromising bolometer mixer technologies for (near) future (space)applications. Their performance is usually quantified by mea-suring the receiver noise temperature at a given IF frequency,usually around 1 - 2 GHz. However, for any real applicationsit is vital that one fully knows all the relevant properties ofthe mixer, including LO power, stability, direct detection, gainbandwidth and noise bandwidth, not only the noise temperatureat low IF frequencies. To this aim we have measured all theseparameters at the optimal operating point of one single, smallvolume quasioptical NbN HEB mixer. We find a minimum noisetemperature of 900 K at 1.46 THz. We observe a direct detectioneffect indicated by a change in bias current when changingfrom a 300 K hot load to a 77 K cold load. Due to thiseffect we overestimate the noise temperature by about 22%using a 300 K hot load and a 77 K cold load. The LO powerneeded to reach the optimal operating point is 80 nW at thereceiver lens front, 59 nW inside the NbN bridge. However,using the isothermal technique we find a power absorbed inthe NbN bridge of 25 nW, a difference of about a factor 2. Weobtain a gain bandwidth of 2.3 GHz and a noise bandwidth of4 GHz. The system Allan time is about 1 sec. in a 50 MHzspectral bandwidth and a deviation from white noise integration(governed by the radiometer equation) occurs at 0.2 sec., whichimplies a maximum integration time of a few seconds in a 1 MHzbandwidth spectrometer.

Index Terms— HEB mixers, sensitivity, bandwidth, stability,LO power

I. INTRODUCTION

NBN phonon cooled hot electron bolometer (HEB) mixersare currently the most sensitive heterodyne detectors at

frequencies above 1.2 THz [1], [2]. Their performance isusually specified by means of double sideband receiver noisetemperature and the mixer IF Gain bandwidth. The present daystate-of-the-art mixers combine a good sensitivity (8-15 timesthe quantum limit), an IF bandwidth of the order of 4-6 GHz[3], [4], [5], [6] and a wide RF bandwidth from 0.7-5.2 THz.However, if these mixers are to be used as central elements inreal heterodyne receiver systems, either ground based or spacebased, it is not enough to know the sensitivity and bandwidthalone. A complete evaluation of a HEB mixer needs to includethe following device properties: The noise temperature over

J. Baselmans, A. Baryshev, Z.Q. Yang, M. Hajenius and J.R. Gao are withthe SRON National Institute for Space Research, Sorbonnelaan 2, 3584 CAUtrecht, The Netherlands.

J. Kooi is with the California Institute of Technology, MS 320-47 Pasadena,California 91125, USA.

M. Hajenius, j.R. Gao and T.M. Klapwijk are with the Kavli Instituteof NanoScience Delft, Faculty of Applied Sciences, Delft University ofTechnology, Lorentzweg 1, 2628 CJ Delft, The Netherlands.

B. Voronov, and G. Gol’tsman are with the Moscow State PedagogicalUniversity, Moscow 119435, Russia.

the entire IF band, the Gain bandwidth, the RF bandwidth ofthe antenna, the beam pattern, the direct detection effect, theLO power requirement and the stability of the mixer. In thispaper we discuss a complete set of measurements of all theseparameters performed on one single small volume HEB mixer.The device under consideration is one of many similar devices,which have all comparable DC and RF properties [7].

II. DEVICE LAYOUT AND EXPERIMENTAL SETUP

The device is fabricated on a double side polished highpurity Si wafer with a measured thickness of 0.335 mm thatis covered at MSPU, Moscow with a NbN film with a criticaltemperature Tc = 9.3 K and a thickness of about 4 nm. The

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bolometer length is 0.15 µm, the width 1 µm, the criticalcurrent Ic = 51 µA at 4.2 K, The transition temperature ofthe bridge is 8.9 K, the normal state resistance is 175 Ω at11 K. The contact pads between the NbN bridge and theantenna are made by cleaning the NbN layer in-situ priorto the deposition of 10 nm NbTiN and 40 nm of Au, fordetails we refer to Refs. [3], [7]. To couple the RF radiationto the HEB we use a twin slot antenna [8] designed to givean optimum response at 1.6 THz. A SEM picture of theantenna including all relevant dimensions is given in Fig 1a.The calculated direct response of the antenna as well as themeasured response using a Fourier Transform Spectrometer(FTS) is shown in Fig. 1b. Model calculation and experimentoverlap nicely. The direct response peaks at 1.6 THz asexpected and has an effective bandwidth of 0.9 THz, obtainedby integrating the normalized measured curve.

In the experiment we use a quasi-optical coupling schemein which the HEB mixer chip is glued to the center of anelliptical Si lens with a design identical to the HIFI band6 lens design. It has a diameter of 4.995 mm, an ellipticityof 1.0193, a flange diameter of 12 mm and an extensionlength of 0.421 mm, which results in a total extension lengthfrom the ellipse center to the HEB antenna structure of0.756 mm. The beam from the antenna-lens combinationhas been evaluated at 1.1 THz using an uncoated lens. Thebeam is within a few % of the expected f-number at thatfrequency and also shows a good agreemenet with a PILRAPsimulation (for details see Ref. [9]). For the experimentsdiscussed hereafter the lens is coated with a 29 µm thicklayer of Parylene-C as a anti-reflection coating with a centerfrequency of 1.6 THz. The lens is placed in a mixerblockwith internal bias-T, identical to the HIFI band 6 design andthermally anchored to the 4.2 K plate of a liquid Heliumcryostat. We use one layer Zytex G104 at 77 K and 2 layers

HDPE

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IR Filters

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Yig Filter

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Fig. 2. Schematical picture of the experimental setup.

at 4.2 K as infrared filter and 0.9 mm HDPE sheet as vacuumwindow. A focusing mirror is used to convert the fast beamform the lens into a f/D=23.7 beam with a 3 mm waistlocated at the cryostat window.

The setup is designed to measure all relevant mixerparameters as discussed above. A schematic picture is givenin Fig. 2. As LO source we use a JPL 1.45-1.55 THz LOChain, SN 2 [10]. The chain is used at 1462.4 GHz whereit has a peak output power 11 µW. This value has beenevaluated using a calibrated Thomas-Keating power meterand a Neil-Erickson power meter. Directly in front of the LOis a 2 mirror system, consisting of a focusing ellipse and aflat mounted on a XYZ stage on a second optical parallelrail. This element behaves as a single lens, with 3 degreesof freedom less than a mirror, enabling an easier alignment.A two grid system, consisting of a computer controlled wiregrid and a fixed wire grid with a vertical polarization followswhich is used to attenuate the signal from the LO. Becausethe LO is vertically polarized each grid attenuates the powerby a factor of cos(φ)2 (with φ the rotation angle of therotatable grid), giving an expected attenuation of cos(φ)4 forthe full system, which has been verified using a measurementwith a Golay cell (See the inset of Fig. 5). After the grids thesignal is coupled into the Cryostat reflectively by a 3.5 µmMylar beam splitter. The total transmitted power from theLO horn output to the front of the HEB mixer lens is givenby 1.66%. We measure the Y facor using a 300 K hot loadand a 77 K cold load by means of a chopper wheel withabsorber and 2 large holes allowing optical acces to a smalldewar filled with liquid nitrogen. This signal is transmittedthrough the beam splitter. The loss from the callibration loadto the HEB lens front is estimated to be -1.52 dB at theLO frequency, the total loss from the hot/cold load to theHEB itself is -2.82 dB, which includes -1.3 dB loss from thelens surface to the HEB itself, caused by lens absorption andthe theoretical antenna efficiency. The effective temperatureof the hot and cold load at the mixer chip are calculatedin the Callan and Wellton limit to be 204 K and 92 Krespectiveley and the total power difference between the hotand cold load evaluated at the mixer chip is about 1.4 nWat the mixer, calculated from the antenna bandwidth (Fig. 1)and the effective temperatures from the hot and cold loads.The IF output of the mixer unit is connected with a 10 cmsemi-rigid Al SMA cable to the input of Low Noise Amplifier(LNA), a SRON/Kuo-Liang SN 2, with a bandwidth from2.4-2.8 GHz with 25-26 dB of Gain and a noise tempersatureof 5 K. Because of its low gain this amplifier is connectedto a second cryogenic LNA, the Sandy Weinreb 2-14 GHzSN 20B MMIC with 35-36 dB of Gain and 5 K of noise.In between is a 6 dB attenuator to prevent standing waves.The signal is further amplified at room temperature, routed toa Yig filter with a 50 MHz bandwidth and detected using aHP power meter. Note that the entire setup, and in particularthe grid transmission, DC bias Voltage and Hot-Cold chopperposition, is computer controlled

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III. EXPERIMENTS

A. Noise performance and direct detection

In the first experiment we measure the uncorrected doublesideband receiver noise temperature TN at each bias pointat the IF frequency that yields the lowest noise temperature,experimentally found to be FIF = 2.78 GHz. This is doneby measuring the Y factor Y = Phot/Pcold. Phot/cold is theoutput power of the receiver at a hot/cold load evaluated at asingle bias point, i.e. at one single value of V and PLO. Weuse the Callen and Welton definition to calculate TN from themeasured Y factor [11]. Simultaneously we measure Ihot/cold,the mixer bias current at a hot/cold load at each bias point. InFig. 3a we present the measured values of TN . We observe a

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Fig. 3. aTN,DSB uncorrected for any optics losses over the entire IV planeof the mixer, the minimum value is TN = 1400 K. b: The direct detectioncurrent IDD = Ihot − Icold

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Fig. 4. The double sideband receiver noise temperature in the small signallimit, TN,S , around a background corresponding to the 77 K load. Theminimum value is TN,S = 900 K. A background corresponding to the 300 Kload gives an identical result.

relatively broad region of optimal response with a maximumsensitivity of TN = 900 K. Interestingly we observe also thatthe mixer bias current is not stable when we switch from hotload to cold load. This current change is the telltale sign ofthe direct detection effect. In Fig. 3b we show the measureddirect detection current, IDD defined as IDD = Ihot − Icold.We observe that IDD is always negative, in agreement withresults reported in [12], [13], [14], [15]. This indicates thatthe difference in RF power PRF between the 77 K and 300 Kload changes the bias current of the mixer in the same wayas an increase in PLO. The magnitude of the direct detectioncurrent ranges from virtually 0 µA at high bias voltages tomore than −1 µA at very low bias voltages. Imagine nowthat we observe, with the receiver discussed in this paper, anastronomical source which represents itself as a small inputpower change on top of a background with an identical powerinput as our 77 K load. A small input power change is in thiscontext defined as a power change that results in a negligiblevalue of IDD. To obtain the receiver noise temperature in thiscase we need to evaluate the small signal Y factor, defined asthe Y factor obtained at an identical value of the bias currentfor both hot and cold load. This implies that we have to reducePLO at hot load to make sure that the bias current remainsconstant, thus compensating for the bias current shift causedby PRF at hot load. We realized this after the measurementby constructing a 2 dimensional graph of the receiver outputpower at hot load and at cold load as a function of bias voltageand current. From these two maps we evaluate the smallsignal Y factor from which we obtain the noise temperaturein the small signal limit, TN,S as shown in Fig. 4. We find aminimum value of TN,S = 700 K, which is 22% lower thanthe minimum value of TN = 900 K. We also observe that thelocation of the minimum in the noise temperature is shiftedto lower bias voltages. For a more detailed analysis we referto Ref. [15]. Note that this result is strongly dependent onthe transparency of the receiever optics and that it implies acomplication in any instrument calibration. The only way outof this for the present mixer design is to reduce the 1.4 nWpower difference between the hot and cold load within the fullRF bandwidth of the mixer. This can be achieved by eitherusing a narrow band metal mesh filter in the signal path or byreducing the tempersature difference between the calibrationloads.

B. LO power requirement

Since we know the total optics loss from the LO horn outputto the mixer lens front and because the optics is designed togive a perfect beam coupling we can replot the data from Fig. 3as to give the noise temperature as a function of the LO poweravailable at the receiver lens front. This is shown in Fig. 5.It is obvious that 80 nW of LO power is needed in front ofthe mixer unit ens to bring the mixer to its optimal operatingpoint. This corresponds to 56 nW of power inside the NbNbridge itself, calculated from the power at the lens front byadding -1.3 dB losses, consisting of the theoretical antennaefficiency and Si lens loss. However, using the isothermaltechnique [16] on the unpumped an optimally pumped IV

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curve we obtain an LO power absorbed in the NbN bridgeat the optimal operating point of only 25 nW. Hence there isa factor of 2.3 difference between LO power inferred fromthe isothermal technique and the one inferred from the LOsource output power and known optics losses. Using the grid toevaluate the LO power difference between more closely spacedpumping levels gives a similar result. This discrepancy can beinvestigated further by using the direct detection effect aroundthe optimal operating point: Around the optimal pumping levelwe see a clear direct detection current, resulting in a differencebetween the IV curves at hot load and at cold load. Using theisothermal technique we find a difference in absorbed powerin the NbN bridge between hot and cold load IV curves atthe optimal pumping level of 1.45 nW. This value is in goodagreement with the calculated power difference between hotand cold load available at the mixer (1.4 nW). Hence we mustconclude that the isothermal technique correctly addresses thepower absorption in the mixer. The 1 to 1 correspondencebetween isothermal technique and real LO power has also beenreported for waveguide HEB mixers [17] and a calculationbased upon a distributed temperature model also gives a 1 tocorrespondence between the calculated IV curve for a givenLO power and the isothermal technique LO power obtainedfrom the calculated IV curves [18]. The factor two in ourquasioptical experiment can therefore only be attributed toeither imperfect beam matching between the diagonal LO hornand the twin slot antenna beam or a misalignment in the optics,despite the great care that was taken to optimize the latter.

C. Bandwidth

The measured noise bandwidth is shown by the gray line inFig. 6. Obviously we have severe problems in the IF circuitwhich make a correct evaluation of the mixer properties all butimpossible at higher IF frequencies. We therefore re-measurethe noise- and gain bandwidth using an identical HEB mixerin a different mixer block. We use a basic IF board of TMM

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Fig. 5. Uncorrected DSB receiver noise temperature as a function of the LOpower available at the mixer unit lens front.

that only forms the transition between a CPW at the HEB chipand a SMA launcher at the other end. An external Miteq bias-T is used to enable mixer biasing. After the bias T we usea Pamtech 3-10 GHz isolator followed by the Sandy WeinrebLNA described before. The rest of the setup remains identical.In the experiment we measure, at the optimum bias operatingpoint of the mixer, the hot and cold load output power as afunction of the YIG filter center frequency. Since the noise ofthe amplifier is very low this measurement enables a directmeasurement of both the noise temperature from the Y factorusing the Callan and Wellton definition together with the singlesideband mixer gain GCW

mix,SSB using:

GCWmix,SSB =

∆Pout

2 · BWIF · kBGIF (TCWin,hot − TCW

in,cold)(1)

with ∆Pout = Phot−Pcold, TCWin,Hot/Cold

the effective temper-ature of the hot and cold load at the input of the receiver, GIF

Fig. 6. SSB Gain bandwidth obtained form the measured hot and coldload output power using the Sandy Weinreb MMIC LNA, Pamtech isolator at1462.4 THz. Stars: SSB Gain bandwidth using the same setup but obtainedat 670 GHz using two coherent sources. The dotted line represents a singlepole Roll-Off at 2.3 GHz.

Fig. 7. DSB receiver noise temperature as a function of IF frequency at1.4624 THz at the optimal operating point of the mixer. Black line: using theSandy Weinreb MMIC LNA and isolator. Grey line: Using the original setupas shown in Fig. 2. The dotted line represents a single pole roll off at 4 GHz.

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the gain of the IF chain, kB Boltzmann’s constant and BWIF

the Yig filter bandwidth. A correct evaluation of GCWmix,SSB is

thus only possible if all the parameters of the above equationare known, especially the (frequency dependence of) the gainof the IF chain. To obtain this we calibrate the If chain afterthe measurement by using the HEB mixer as a thermal loadwith known temperature and impedance. To be able to do thiswe mount a resistive heater and a thermometer on the mixerblock and reduce the thermal anchoring of the mixer block byplacing a thin Stainless Steel plate in between the copper blockand the 4.2 K plate of the cryostat and by adding a thin copperthermal strap. In addition we use 5 cm of stainless steel SMAbetween the mixer block and the bias-T. We now measurethe IF output power as a function of frequency for differenttemperatures of the mixer. Since the HEB mixer is, in thistemperature range, just a thermal radiator with a resistance of175 Ω we know the exact input (noise) power of the IF chainand can therefore use this measurement to calibrate the IFchain gain and noise. We find an IF chain noise temperatureof about 10 K, which is higher than the amplifier noise dueto the impedance mismatch between the HEB and the isolatorand the isolator noise, and a gain of approximately 90 dB at2 GHz which slowly decreases to 80 dB at 9 GHz. As a controlmeasurement we also measure the total gain of the warmpart of the chain using a Vector Network Analyzer. Addingto this measurement the known gain of the cryogenic LNAgives a IF circuit gain virtually identical to the one obtainedfrom the the calibration measurement using the HEB mixeras a thermal load. The measured gain- and noise bandwidthare shown in Figs. 7 and 6 respectively. In Fig. 7 we showalso, by the stars, a direct measurement of the (relative) SSBconversion Gain at 670 GHz using 2 coherent sources, oneas LO signal and the other as the RF signal. Within theerror bars both datasets overlap nicely. Also shown is a firstorder fit to a single pole, yielding a 3 dB Gain bandwidthof 2.3 GHz. Note that this experimental result agrees verywell with totally independent results obtained in Ref. [20]elsewhere in these proceedings. There it is shown that theexperimental single pole in the gain bandwidth is in realitya synthesized pole consisting of 4 time constant. Note thatthe frequency dependence of the noise temperature (Fig. 6)obtained with the new setup Bblack line) does not show theIf circuit problems of the original measurement (grey line)and that both datasets can be fitted to first order by a 4 GHzsingle pole roll-off. The measured ratio of the noise bandwidthwith the gain bandwidth, fN/fG = 1.7, can be compared to atheoretical estimation based upon the analysis used in Ref. [21]and [22], where it is found that fN/fG =

√

Tout(0)+TIF

TJ (0)+TIF. Here

Tout(0) is the single sideband mixer output noise at low IFfrequencies, 45 K in our case, TJ(0) the mixer Johnson Noise,which is approximately equal to Tc = 9 K [22], [21] andTIF = 10 K the IF chain noise temperature. Thus we findfN/fG = 1.7 in good agreement with the measurements.

D. Stability

In the last experiment we have measured the stability of themixer at the optimal bias point by means of a measurement of

the Allan Variance [19]. In practice the noise from a receiversuch as a HEB mixer appears to be a combination of threeterms: 1/f noise, low frequency drift and uncorrelated (white)noise. To first order, only white noise can be integrated down,with the result that there is an optimum integration time,known as the ”Allan” time (tA), after which the observingefficiency is lost. Experimentally a measurement of the ”AllanVariance”, defined as σ2

A(t) = 1

2σ2(t) is a powerful tool to

discriminate between the various noise terms in a real receiver.Plotting σ2

A(t) on a log-log plot demonstrates the usefulness ofthis approach in analyzing the noise statistics. The minimumin the plot gives the ”Allan” time. For the sake of optimumintegration efficiency, one is advised to keep the integrationtime well below the system’s Allan time at a level wherethe noise still closely follows the white noise behavior. Inthe experiment we have changed the IF chain of the setupas depicted in Fig. 2 slightly. We have added, after the firstroom temperature amplifier, a 3 dB splitter. After the splitterwe use in each channel a Yig filter with a 50 MHz bandwidth,a room temperature amplifier and, in one of the channels,a tunable attenuator. A dual frequency power head is thenused to measure the power output as a function of time P (t′)for two IF channels simultaneously at a rate of 40 times persecond. This has been done for IF frequencies very closeto each other at the low end of the IF band (2.5 GHz and2.7 GHz), and for two frequencies near the IF band edges(2.5 GHz and 4.7 GHz). The attenuator allows us to keepthe powers in each channel about identical which is importantto maintain an equal effective bandwidth in both channels.The reason for this is that the power meter is a widebanddetector with the result that the ratio of in band signal powerto the total power as seen by the detector will change theeffective measurement bandwidth. For the same reason it isvital to use signal powers of the order of 0 dBm within theYIG filter bandwidth to ensure a measurement of the mixerproperties in stead of a measurement of the noise statisticsout of the YIG filter band. We show, In Fig. 8, the single

Fig. 8. Single channel Allan Variance at 1.4624 THz, obtained in a 50 MHzbandwidth around 2.5, 2.7 and 4.7 GHz together with the spectroscopic AllanVariance at 1.4624 THz as defined by Eqn. 2, between closely spaced (2.5-2.7 GHz) and far spaced (2.5-4.7 GHz) IF channels. The theoretical whitenoise behavior is included for comparison.

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channel Allan Variance taken at the optimal bias point at 3different IF frequencies, 2.5 GHz, 2.7 GHz and 4.5 GHz. Inthese measurements the mixer stability curves deviate fromthe white noise integration time at already 0.2 seconds. Wealso show in Fig. 8 the spectroscopic Allan Variance. This isthe Allan variance of the quantity s(t′) given by

s(t′) =x(t′)

< x(t′) >+

y(t′)

< y(t′) >(2)

with x(t′) and y(t′) the original measurements of the powersin each IF channel as a function of time t′. Note that thespectroscopic HEB receiver stability is considerably betterthan the one observed for a single channel observation, thisimplies that observing the spectral response of an astronomicalsource is less limited by the HEB stability than a single chan-nel continuum observation. Note that the spectroscopic databetween 2.6 and 4.5 GHz represents the stability within the fullspectroscopic IF band of HIFI band 6. The spectroscopic Allanvariance between the closer spaced 2.5 and 2.7 GHz is evenbetter. Given that the mechanics of the measurement setupwas very rigid, and the loss in air small ( 0.1 dB), it is likelythat we are observing the effect of a frequency dependent hotelectron bolometer mixer gain.

IV. CONCLUSIONS

The small volume twin slot antenna coupled HEB mixeris the detector of choice for a heterodyne observatory atfrequencies above 1.3 THz. The low LO power need of 80 nWat the lens front makes it easily compatible with present dayTHz LO sources with an output power in the µW range up tofrequencies of 2 THz. The sensitivity is comparable to the oneof large volume devices, we measure 900 K at 1.4 THz andhave obtained 700 K [23] for another device at 1.6 THz usingan optimised optical coupling in the signal path. However, thebandwidth of the devices is limited to 2.3 GHz for the Gainand 4 GHz for the noise, limiting the IF band edge to about4-5 GHz. Increasing the bandwidth with a similar performancewould greatly enhance the practical usability of these mixers.The stability is also limited allowing integration times of theorder of a few seconds, which is enough for a line surveyin chopped mode, however, continues observations are likelyimpossible. As a last point we found that there is a directdetection effect due to the low LO power requirements and thelarge direct bandwidth of these devices. As a result the mixersensitivity is underestimated by about 20%-30%, dependenton the optics transmission when evaluated using a 300 K hotload and 77 K cold load, furthermore, the optimal operatingpoint is shifted to higher bias voltages due to this effect.

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