Development of highly sensitive nanoscale transition edge sensors for gigahertz astronomy and dark matter search
Federico Paolucci, Vittorio Buccheri, Gaia Germanese, Nadia Ligato, Riccardo Paoletti, Giovanni Signorelli, Massimiliano Bitossi, Paolo Spagnolo, Paolo Falferi, Mauro Rajteri, Claudio Gatti, Francesco Giazotto
HHighly sensitive nano-TESs for gigahertz astronomy and dark matter search
Federico Paolucci,
1, 2, ∗ Vittorio Buccheri,
2, 1
Gaia Germanese,
1, 3
Nadia Ligato, Riccardo Paoletti,
4, 2
Giovanni Signorelli, Massimiliano Bitossi, Paolo Spagnolo, Paolo Falferi,
5, 6
Mauro Rajteri, Claudio Gatti, and Francesco Giazotto † NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy INFN Sezione di Pisa, Largo Bruno Pontecorvo, 3, I-56127 Pisa, Italy Dipartimento di Fisica dell’Universit`a di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy Dipartimento di Scienze Fisiche, della Terra e dell’Ambiente dell’Universit`a di Siena, Strada Laterina, 8 I-53100 Siena, Italy IFN-CNR and Fondazione Bruno Kessler, via alla Cascata 56, I-38123 Povo, Trento, Italy INFN, TIFPA, via Sommarive 14, I-38123 Povo, Trento, Italy Istituto Nazionale di Ricerca Metrologica (INRIM), Str. delle Cacce, 91, I-10135 Torino, Italy INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi, 54, I-00044 Frascati, Italy
Terahertz and sub-terahertz band detection has a key role both in fundamental interactions physicsand technological applications, such as medical imaging, industrial quality control and homelandsecurity. In particular, transition edge sensors (TESs) and kinetic inductance detectors (KIDs) arethe most employed bolometers and calorimeters in the THz and sub-THz band for astrophysics andastroparticles research. Here, we combine the widespread TES detection with the most advancednano-technology to design, fabricate and experimentally demonstrate an innovative nanoscale TES(nano-TES). Thanks to the reduced dimensionality of the active region and the efficient Andreevmirror (AM) heat confinement, our devices reach state-of-the-art TES performance. In particular,as a bolomenter the nano-TES shows a noise equivalent power (NEP) of 5 × − W/ √ Hz and arelaxation time of ∼
10 ns for the sub-THz band, typical of cosmic microwave background studies.When operated as single-photon sensor, the devices show a remarkable frequency resolution of100 GHz, pointing towards the necessary energy sensitivity requested in laboratory axion searchexperiments. Finally, different multiplexing schemes are proposed and sized for imaging applications.
Keywords: transition edge sensor, nanoscale, superconductivity, Andreev mirrors, gigahertz, axion, cosmicmicrowave background
I. INTRODUCTION
In the last decade, astronomy and astrophysics havebroadened their interest towards low energy phenom-ena, such as cosmic microwave background (CMB) [1],atomic vibrations in galaxy clusters [2], and new parti-cles in dark matter [3]. To obtain physical insight of thesephenomena, the detection of faint signals in the micro-(terahertz) and sub-millimeter (gigahertz) spectral rangeplays a fundamental role. To this end, the key ingredi-ent is the development of new ultrasensitive bolometersand single-photon detectors, i.e., calorimeters. On theone hand, the temperature and polarization maps of theCMB fluctuations [4, 5] and the detection of polarized ra-diation due to the hydrogen atom emission in the galaxyclusters [6] are the main astronomy applications for gi-gahertz (GHz) and terahertz (THz) bolometers. On theother hand, low frequency calorimeters could play a fun-damental role in axions search [7], one of the principalcandidates for the dark matter. Axions are very weaklyinteracting particles with small mass ( ∼ ∗ [email protected] † [email protected] the laboratory [8], differently from experiments focusedon space surveys, such as CAST [9] and IAXO [10].Nowadays, the most employed detectors in the THzenergy band are the superconducting sensors, such astransition edge sensors (TESs) [11–13] and kinetic in-ductance detectors (KIDs) [14], for their high sensitivity,robustness and mature technology. The state-of-the-artof these detectors in bolometric operation shows a noiseequivalent power (NEP) of ∼ − W / √ Hz for TESs[15] with large active area ( ∼ µ m ), and ∼ − W / √ Hz for KIDs [16]. More sensitive and efficient su-perconducting detectors have been proposed and realizedby taking advantage of device miniaturization [17] andJosephson effect. For instance, detectors based on su-perconductor/normal metal/superconductor (SNS) junc-tions showed a
NEP of the order of 10 − W / √ Hz [18],devices based on the temperature-to-phase conversion(TPC) are expected to provide
N EP ∼ − W / √ Hz[19], while a fully superconducting tunable Josephson es-cape sensor (JES) showed a record intrinsic
NEP as lowas 10 − W / √ Hz [20].To push the TES technology towards lower values of
NEP with the possibility to detect single photons in theGHz band [21], a strong reduction of the thermal ex-change mechanisms of the active region, i.e., the portionof the device transitioning to the normal-state when ra-diation is absorbed, is necessary [22]. To this end, we en-vision a nanoscale TES (nano-TES) exploiting a simpleand sturdy miniaturized design together with the An- a r X i v : . [ c ond - m a t . m e s - h a ll ] J u l dreev mirrors (AM) effect [23] to thermally isolate thesensor active region. Indeed, operating in the bolometerconfiguration our nano-TESs reach a total noise equiv-alent power ( N EP tot ) of ∼ − W / √ Hz, while ascalorimeters they reach a resolving power ( δν/ν ) of 10in sub-THz band. Their thermal and electrical perfor-mance are several orders of magnitude better than de-vices with identical dimensions but without the Andreevmirrors heat constrictions. Finally, we propose and sizetwo possible multiplexing circuits in frequency domain(FDM) and microwave resonators (MR) as readout fora nano-TES array enabling the realization of multi-pixelcameras. In addition to gigahertz astronomy and par-ticle physics, the nano-TES could find applications formedical imaging [24], industrial quality controls [25] andsecurity [26].This paper is organized as follows. Section II reportsthe simple fabrication of the nano-TES and of a sec-ondary device used to extract all the parameters of theactive region. Section III describes the electrical prop-erties of the nano-TES. The spectral and thermal char-acterization of the active region are resumed in Sec. IVand V, respectively. The nano-TES performance as abolometer and a calorimeter are reported in Sec. VI to-gether with the comparison of a TES of identical materi-als and dimensions but not equipped with AM. Finally,Sec. VII covers possible multiplexing readout circuits todesign multi-pixel cameras.
II. DEVICES FABRICATION
The experiments discussed in this paper are performedthanks to two different device architectures: the nano-TES and a secondary device (SD). Measurements on thenano-TES provided the detector resistance versus tem-perature characterization, R A ( T ), the active region criti-cal I c and retrapping I r current, and the critical temper-ature T c . Instead, the active region spectral and thermalproperties have been obtained by the experiments per-formed on the SD.The false-color scanning electron microscope (SEM)pictures of a typical nano-TES and SD are shown inFig. 1-a and -b, respectively. The nano-TES, highlightedby the dashed white box in Fig. 1-a, consists in a 1.5 µ m-long, 100 nm-wide and 25 nm-thick Al/Cu bilayernanowire-like active region (red), which is sandwichedbetween the Al electrodes (blue). Since the supercon-ducting gap of the Al layer is higher than that of theAl/Cu bilayer (due to inverse proximity effect [27]), theelectrodes act as AM for the active region, leading tothe advantages discussed in Sec. V. The same nano-TESstructure is visible in the SD (see Fig. 1-b) with theaddition of two oxidized Al probes (yellow) lying underthe active region forming two tunnel Josephson junctions(JJs) [28]. These two Al probes allow to characterize boththe energy gap and the thermal properties of the activeregion. bacd S SA S AIP S -600 -300 0 300 600-60-3003060 V ( V ) I (nA) I c I r I V S SA μ m 1 μ m
50 70 90 110 130 150 17004080 R A ( ) T bath (mK) n-T1 n-T2 Lock-in - + V ∼ R l V ac T c S SA
FIG. 1. False-color SEM pictures of the nano-TES (a) andSD (b). The three different layers are the active region Al/Cubilayer A (red), the Al electrodes S (blue) and the Al-oxidizedtunnel probes IP (yellow). The detector structure is pointedout by the dashed white box in the nano-TES SEM. (c) Four-terminal V I measurement of sample n-T1 for a positive (greyline) and a negative (yellow line) current slope at T bath = 20mK. The black dotted lines highlighted the critical current I c ∼
600 nA and the retrapping I r ∼
27 nA of A , where the S → N and the
N → S transitions occur, respectively.
Inset :Experimental setup for the
V I measurement. (d) Temper-ature dependence of the nano-TES active region resistance, R A , for n-T1 (green line) and n-T2 (purple line). By follow-ing a positive T bath slope, R A goes from zero to the normalstate resistance value. The critical temperature T c (grey pointfor n-T2) is the temperature corresponding to the half of thenormal resistance of the samples. Inset : Experimental setupfor the R A versus T bath measurements. Both the nano-TES and the SD were realised duringthe same fabrication process, ensuring the homogeneityof their properties. They were fabricated by electron-beam lithography (EBL) and 3-angles shadow mask evap-oration of metals onto a silicon wafer covered with 300nm of thermally grown SiO . The evaporation was per-formed in an ultra-high vacuum electron-beam evapora-tor with base pressure of about 10 − Torr. By referringto the color code of Fig 1-a and -b, the fist Al layer (yel-low) with thickness 13 nm was evaporated at an angleof -40 ◦ and then oxidized by exposition to 200 mTorr ofO for 5 minutes to obtain the tunnel probes in the SD.In a second step, the Al/Cu bilayer (red) was evaporatedat an angle of 0 ◦ to form the active region with partialthicknesses h Al = 10 . h Cu = 15 nm for the alu-minum and copper layer, respectively. Finally, a secondAl layer (blue) of thickness 40 nm was evaporated at anangle of +40 ◦ to obtain the AM electrodes.The notation A , S , P and I will be used to indicate theAl/Cu active region, the Al electrodes, the Al probes andthe probes insulating barrier, respectively. The nano-TES measurements have been performed on two differentdevices, n-T1 and n-T2. All the following experimentshave been performed in a He- He dilution refrigeratorwith bath temperature T bath ranging from 20 mK to 250mK. III. NANO-TES ELECTRICAL PROPERTIES
The four-terminal voltage-current
V I characteristics ofn-T1 are shown in Fig. 1-c at T bath = 20 mK for a posi-tive (grey line) and a negative (yellow line) current slope.The electrical measurement setup is schematized in theinset. Here, the normal N and the superconducting S state are recognizable by the linearly growing and the flatbehaviour of the V I traces, respectively. The
S → N transition occurs at the critical current I c ∼
600 nA,whereas the
N → S occurs at the retrapping current I r ∼
27 nA [29]. The normal-state resistance R A is obtainedby the slope of the V I and gets value R A,n − T = 70 Ω,while it is obviously zero in the S . This change of R A hasa key role in the operation mechanism of a TES detector[12] (see Sec. VII for further details).The temperature dependence of R A is shown in Fig.1-d for n-T1 (green line) and n-T2 (purple line). The in-set shows the experimental setup. The AC current biasis produced by applying a voltage V ac at 13.33 Hz to aload resistance R l = 100 kΩ ( R l >> R A ) in order toobtain I ac = 15 nA independent from R A . The voltagedrop V across the nano-TES is measured as a function of T bath via a voltage pre-amplifier connected to a lock-inamplifier. By rising T bath , the resistance changes fromzero to its normal-state value, by following an edge tran-sition behaviour. The nano-TES critical temperature T c is defined as the temperature corresponding to half of thenormal-state resistance (grey point for n-T2 in Fig. 1-d).Thus, we have T c = 128 mK and T c = 139 for n-T1 and n-T2, respectively.
150 180 210 2400204060 I SA I P ( n A ) V SAIP ( V)
20 mK 250 mK ( e V ) T (K) Δ S (T) Δ A (T) μ V abc -0.5 0.0 0.5-3000300 I SA I P ( n A ) V SAIP (mV)
20 mK 250 mK
S SA
IPV
SAIP I SAIP A FIG. 2. (a) The IV characteristic of the SAIP junction at T bath = 20 mK (grey line) and T bath = 250 mK (green line).The slope of the linear region (dotted line) represents the N -state tunnel resistance of the JJ, R I (cid:39)
12 kΩ.
Inset :Schematic representation of SD with the experimental setupused for the spectral characterization. (b) The IV character-istics of the SAIP junction zoomed on the positive switch-ing point for two bath temperatures: the high temperatureswitching point corresponds to ∆ ,P (cid:39) µ eV, while thedifference between the two onset points is ∆ ,A (cid:39) µ eV. (c)Calculated superconducting gaps as a function of the temper-ature for S (blue line and right scale) and A (red line andleft scale). The critical temperatures are T c,A = 150 mK and T c,S = 1 . A closes when ∆ P can be stillconsidered constant. IV. SPECTRAL CHARACTERIZATION OFTHE ACTIVE REGION
In the framework of the Bardeen-Cooper-Schrieffer(BCS) theory, the temperature-dependent superconduct-ing energy gap ∆( T ) can be obtained self-consistently bysolving [27]1 λ = (cid:90) (cid:126) ω D d(cid:15) tanh ( √ (cid:15) + ∆ / k B T ) √ (cid:15) + ∆ , (1)where (cid:126) is the reduced Plank constant, ω D is the De-bye frequency, (cid:15) is the energy and k B is the Boltzmannconstant. ∆( T ) decreases monotonically from its zero-temperature value ∆ to zero at the critical temperature T c . In addition, the superconducting gap is almost con-stant at ∆ for T ≤ . T c . Typically, aluminum thinfilms show a T c higher than the bulk Al value ( ∼ . S and P ,∆ S ( T ) and ∆ P ( T ), are temperature independent up toat least 500 mK, thus preserving their zero-temperaturevalues (∆ ,S and ∆ ,P ). By contrast, due to inverse prox-imity effect [27], superconductivity in A is strongly sup-pressed. In fact, our resistance versus temperature ex-periments showed a value T c,A (cid:39) (cid:28)
500 mK (seeFig. 1-d), thus enabling the possibility to independentlydetermine both ∆ ,A and ∆ ,P .To this end, the IV characteristics of a SAIP
JJ weremeasured at base temperature and just above T c,A , asreported in Fig. 2-a with the grey and the green line, re-spectively. The experimental setup of the measurementsis schematically shown in the inset of the panel. At basetemperature, the JJ switches to the N -state when thevoltage bias reaches V SAIP = ± (∆ ,A + ∆ ,P ) /e [28],where e is the elementary charge. Instead, at T bath = 250mK the transition occurs at V SAIP = ± ∆ ,P /e , since A is in the N -state. The tunnel resistance of the JJ is givenby the slope of the IV characteristic in the linear region,as highlighted by the black dotted line, and gets value R I (cid:39)
12 kΩ.In order to provide a precise evaluation of the en-ergy gaps, the IV characteristics are zoomed around theswitching points acquired for positive voltage bias, asshown in Fig. 2-c. The measurement at T bath = 250mK (green line) indicates a value of the zero-temperaturesuperconducting gap of the aluminum probes ∆ ,P (cid:39) µ eV, corresponding to a critical temperature T c,P =∆ ,P / (1 . k B ) (cid:39) . ,A (cid:39) µ eV corresponding to a critical temperature T c,A (cid:39)
150 mK, in good agreement with the data re-ported in Fig. 1-d.Importantly, the superconducting gap of A is con-stant along the out-of-plane axis (i.e., the sample thick-ness), because the bilayer is within the Cooper limit[31, 32]. In fact, the aluminum thin film follows h Al =10 . (cid:28) ξ ,Al = (cid:112) (cid:126) D Al / ∆ ,Al (cid:39)
80 nm (where D Al = 2 . × − m s − is the diffusion constant of Aland ∆ ,Al (cid:39) µ eV is the superconducting energy gap),while the copper layer respects h Cu = 15 nm (cid:28) ξ Cu = (cid:112) (cid:126) D Cu / (2 πk B T ) (cid:39)
255 nm (where D Cu = 8 × − m s − is the copper diffusion constant and the tem-perature is chosen T = 150 mK thus higher than the nano-TES operation value). Furthermore, the active re-gion is much thinner than its superconducting coherencelength, that is h A = h Al + h Cu = 25 . (cid:28) ξ A = (cid:112) l (cid:126) / [( h Al N Al + h Cu N Cu ) R A e ∆ ,A ] (cid:39)
220 nm, where e is the electron charge, while N Al = 2 . × J − m − and N Cu = 1 . × J − m − are the density of states( DOS s) at the Fermi level of aluminum and copper, re-spectively.Finally, we note that the S -electrodes have a supercon-ducting gap similar to the probes (∆ S ∼ ∆ P ), since theirthickness are similar [33]. Thus, by knowing ∆ ,A and∆ ,S , Eq. 1 has been solved to obtain the temperaturedependence of the superconducting gaps of A [∆ A ( T )]and S [∆ S ( T )] reported in Fig. 2-d with the red and theblue line, respectively. Note that ∆ A drops to zero when∆ S can be still considered constant, as expected. V. THERMAL CHARACTERIZATION OF THEACTIVE REGION
Energy exchange has a key role in determining thenano-TES performance, such as sensitivity and responsetime, since the increase of the A electronic temperature T A due to the incident radiation strongly depends on thecapability of maximizing the thermal confinement. Thescope of this section is to study the most prominent heatexchange mechanisms in the active region of the nano-TES for typical operating conditions.Metallic elements in mesoscopic devices at sub-kelvintemperatures show weak coupling between the electronand the phonon thermal subsystems [28], which can leadto T e (cid:54) = T ph , where T e and T ph are the electron andphonon temperature, respectively. Due to the thicknessof the films lower than the phonon wavelength and van-ishing Kapitza resistance, the device phonons are ther-mally anchored to the substrate ( T ph = T sub ) [34], so thatthe temperature of both systems can be considered as aparameter set via the refrigerator temperature T bath . Thegeometry of our device also guarantees electronic tem-perature of the superconducting electrodes T S and thetunnel probes T P equal to the phonon temperature, thatis T S = T P = T bath . By contrast, the A electronic tem-perature T A is the fundamental thermal variable in thenano-TES operation mechanism. In general, the value of T A results from the balance between the main thermalexchange channels of A . In our case: P in = P e − ph + P AIP + P loss , (2)where P in is the power injected, P e − ph is the electron-phonon relaxation, P loss represents the heat lossesthrough S and P AIP is the energy diffusion by an IP probe.The use of S with energy gap much larger than A canensure negligible heat out-diffusion from A to S . Indeed,the normalised DOS of a superconductor reads [28]:
DOS ( E, T ) = | E | (cid:112) E − ∆ ( T ) Θ( E − ∆ ( T )) . (3) M1 M2 M3 PMM T A ( m K ) P in (fW) b c
150 250 35004080120 V T m e t e r ( V ) T bath (mK) T A =T bath -2000200 Δ Δ E ( μ e V ) DOS T bath = 20 mK a d e I bias S SA IP V Tmeter V V heater P e-ph T bath T A T bath P in P AIP
PMM
FIG. 3. (a) BCS
DOS s of S (blue) and A (red) at T bath = 20 mK with the gaps obtained experimentally, ∆ A = 23 µ eV and∆ S = 200 µ eV. (b) Schematic representation of the experimental setup used for the thermal characterization: the left andthe right SAIP
JJ are used as electron thermometer and heater, respectively. (c) Thermometer calibration curve which linksthe voltage output V Tmeter to the A electronic temperature T A . (d) Electronic temperature of A as a function of the inputpower for three different data sets Mi , with i = 1 , ,
3, (colored symbols) at T bath = 150 mK. The fitting curve (black line) isobtained by solving Eq. (4) of the PMM. (e) PMM thermal model of A : the input power from the heater P in relaxes throughthe outward components: P e − ph , due to the electron-phonon interaction, and P AIP , due to the losses through the thermometertunnel junction.
Thus, the zero-temperature energy-dependent
DOS of S and A are calculated by inserting the measured values of∆ ,S and ∆ ,A . The resulting functions are shown in Fig.3-a with the blue and the red line, respectively. The ther-mally excited quasi-particles in A do not find availablestates towards S , thus the resistance for heat diffusion ex-ponentially rises by decreasing the bath temperature [23].In particular, at k B T A (cid:28) ∆ S the superconducting leadsact as AM, namely as perfect barriers for energy diffu-sion ( P loss = 0). In addition, the big difference betweenthe two superconducting gap ensures that the nano-TESsuperconducting to dissipative transition affects only A ,leading to a better control in the resistance change anda small overheating of the detector.The experimental setup employed to perform the ther-mal study of A is schematically shown in Fig. 3-b: theleft SAIP junction was current-biased (at I bias ) to op-erate as thermometer, whereas the right JJ was voltage-biased (at V heater ) to work as heater [28]. The thermome-ter has been calibrated by varying T bath and measuring V T meter at I bias = 10 pA and V heater = 0 V, as reportedin Fig. 3-c. The bath temperature ranges from ∼ ∼
350 mK, so ∆ A = 0, i.e. A is in the normalstate, whereas ∆ S (cid:39) µeV . In this normal metal( A )/insulator/superconductor ( P ) JJ, the IV character-istics depends only on the electronic temperature of thenormal metal [28]. Therefore, the values of V T meter di-rectly reflect T A .
1. Perfect Andreev mirrors
Figure 3-d shows T A as a function of the input poweracquired at T bath = 150 mK in three different sets ofmeasurements. The electronic temperature monotoni-cally increases from 150 mK to ∼
270 mK by rising P in to ∼ k B T A (cid:28) ∆ ,S is always satisfied. Therefore,the perfect mirror model (PMM) can describe the data:the heat exchange between A and S s is fully suppressed( P loss = 0), i.e. A is thermally isolated from S . Thus, theinjected power P in relaxes only via electron-phonon in-teraction P e − ph and out-diffuses through the thermome-ter IP P
AIP . The resulting quasi-equilibrium equationdescribing the PMM reads P in = P e − ph + P AIP , (4)as schematically represented in Fig. 3-e.Since A is in the N -state, the power exchanged viaelectron-phonon interaction can be written as [28]: P e − ph = Σ A V A (cid:0) T A − T bath (cid:1) , (5)where Σ A is the electron-phonon thermal relaxation con-stant and V A is the volume of A . The power which flowsthrough the thermometer JJ takes the form [28] P AIP = 1 e R T meter (cid:90) + ∞−∞ d EE DOS P ( E, T bath ) × [ f ( E A , T A ) − f ( E, T bath )] , (6)where DOS P ( E, T bath ) is the
DOS of the superconduct-ing probe, E A = E − eV T meter is the energy of the active
150 mK PMM T A ( m K ) P in (fW) T A ( m K ) P in (fW) with mirror mirrorless
150 200 250 300012345 T bath (mK)150160170180200 P l o ss ( a . u . ) T A (mK)
150 175 200270280290 T x ( m K ) T bath (mK) a cb FIG. 4. (a) Electronic temperature of the active region versus input power measured (grey points) and calculated with thePMM (black line) at T bath = 150 mK. The red shaded area highlights the values of T A where the PMM fails to describethe experimental data. (b) Power diffusion towards the superconducting leads P loss calculated as the difference between theexperimental data and PMM theoretical curve at each T A for different values of T bath . The curves have been vertically shiftedfor clarity. Inset : Threshold temperature T x as a function of T bath . P loss (cid:54) = 0 for T A ≥
280 mK independently from T bath . (c)Calculated T A versus P in characteristics calculated in the presence (solid lines) and absence (dashed lines) of Andreev mirrorsfor different values of T bath . The color code for T bath follows panel (c). The presence of Andreev mirrors is expected to stronglyimprove the power sensitivity of the nano-TES. region, and f ( E, T
A,bath ) = [1 + exp (
E/k B T A,bath )] − is the Fermi-Dirac distribution of A and P , respectively.By solving Eq. (4), we fit the experimental electronictemperature of the A as a function of P in , as shown bythe black line in Fig. 3-d. Since all the other deviceparameters are known ( V A = 38 × − m , R T meter =11 . T bath = 150 mK), we extracted the valueof the electron-phonon coupling constant of the Al/Cubilayer Σ A (cid:39) . × W/m K . We notice that thePMM provides a remarkable fit of the experimental datathus describing correctly the system. Furthermore, theresulting electron-phonon relaxation constant is in goodagreement with the average of Σ Cu = 2 . × W/m K and Σ Al = 0 . × W/m K [28], weighted with thevolumes of the copper and the aluminium layer formingthe active region: Σ A,theo = (Σ Cu V Cu + Σ Al V Al ) / V A =1 . × W/m K , with V Al (cid:39) . × − m − and V Cu (cid:39) . × − m − .
2. Low-efficiency Andreev mirrors
In order to test the AM efficiency and the limits of thePMM, we investigated the dependence of T A on largervalues of P in . The PMM fails for P in ≥ S -electrodes is no longer negligible ( P loss (cid:54) = 0) andthe resulting increase of T A is reduced.The energy losses through the superconducting elec-trodes can be evaluated by calculating the difference be-tween the measured P in necessary to produce a specific T A and its value estimated from the PMM. The depen-dence of P loss on T A is shown in Fig. 4-b for differ- ent values of T bath . For all the curves, the energy lossthrough the Andreev mirrors is negligible until reachinga threshold temperature T x . Notably, for all measure-ments we obtain T x (cid:39)
280 mK (see the inset of Fig.4-b), independently from the value of T bath and thus T S .Furthermore, the energy filtering of the superconduct-ing electrodes starts to fail for T x /T c,S ∼ .
22, that isin good agreement with the theoretical prediction of An-dreev ∼ . T c [23].The T A versus P in characteristics change dramaticallyin a mirror-less device. Indeed, in a TES based on thesame structure and dimensions but without AMs, theactive region extends to the entire device, i.e. it is com-posed by a single superconductor. Fig. 4-c shows thedifference between our nano-TES (solid lines) and a TESwithout Andreev mirrors (dashed lines) calculated for thesame values of bath temperature of our experiments. Asexpected, at a given value of P in the temperature of theactive region rises more in the presence of energy filter-ing than in a composite device, since the main channelfor thermalization, the electron-phonon coupling, linearlydepends on the volume (see Eq. 5). As a consequence,the presence of Andreev mirrors promises enhanced sen-sitivity of the nano-TES. VI. NANO-TES PERFORMANCE
This section is devoted to the evaluation of the per-formance of our nano-TES and the comparison with anidentical device without AM. Our study will focus onboth the bolometric operation, i.e. measuring the powerof continuous incident radiation, and the calorimetric op- R sh TESL Read-outSQUID
Unit Cell I bias I T ES I s h FIG. 5. Schematic of the read-out circuit of a single nano-TES. The dashed line highlight the circuit providing the neg-ative electro-thermal feedback NETF, where the nano-TESis biased by the current I TES and operates in parallel to theshunt resistor R sh . The I TES variations are measured with aSQUID amplifier coupled to the circuit by an inductance L . eration, i.e. measuring the overheating due to a singlephoton.The typical read-out circuit for a TES is schematized inFig. 5. On the one hand, the decrease of the current I T ES flowing through the inductance L due to photon absorp-tion can be measured by means of an inductively coupledsuperconducting quantum interference device (SQUID)amplifier. On the other hand, the shunt resistor R sh implements the negative electro-thermal feedback mech-anism (NETF), which guarantees constant voltage biasof the nano-TES and faster heat removal after radiationabsorption [35]. To this end, the shunt resistor needsto satisfy the relation R sh (cid:28) R A [36]. In the follow-ing, we will use a value R sh = 10 mΩ typical for SQUIDamplifier-based read-out. A. Bolometer
Starting from the structure and the measured param-eters, we evaluate the performance of our nano-TESs interms of response time τ and N EP . The parameters thatwe will deduced in this section are reported in Tab. I.The thermal response time τ defines the dissipationrate of the overheating arising from radiation absorptionin A . The value of τ is related to the quasi-particle ther-malization with the phonons residing at T bath . Namely,it depends on the electron heat capacity C e,A and thethermal conductance G th,A of A through [12] τ = C e,A G th,A . (7)The A electron heat capacitance reads C e,A = Υ A V A T c,A , (8)with Υ A the Sommerfeld coefficient of A . Since A is formed by an Al/Cu bilayer, we have to substitute Υ A V A = Υ Cu V Cu +Υ Al V Al (with Υ Cu = 70 . − m − ,Υ Cu = 91 JK − m − ) in Eq. 8 .The A total thermal conductance G th,A is the deriva-tive of the heat losses of A with respect to its electronictemperature [12, 28]. Considering the nano-TES oper-ation at T c,A (cid:28) T c,S we can consider P loss = 0, thuselectron-phonon relaxation is the only relevant thermalexchange mechanism. Therefore, the total thermal con-ductance reads G th,A = dP e − ph dT A = 5Σ A V A T A . (9)In our nano-TESs, the electron heat capacitance is C e,A = 4 × − J/K for n-T1 ( C e,A = 4 . × − J/K for n-T2), while the thermal conductance is as low as G th,A = 6 . × − W/K ( G th,A = 9 . × − W/K).As a consequence, the active region relaxation time islimited by G th,A to a few microseconds for both devices( τ (cid:39) µ s and τ (cid:39) µ s).The negative electro-thermal feedback (see Fig. 5) af-fects the thermal response of the nano-TES. In partic-ular, the sharpness of the superconducting to normal-state phase transition defines the effective recovery timethrough τ eff = τ α/n , where typically n = 5 for a cleanmetal and α = d log( R ) d log( T ) is the electro-thermal parameterthat takes into account the sharpness of the transitionfrom the superconducting to the normal-state. As re-ported in Tab. I, τ eff is one or two orders of magnitudesmaller than the thermal response time ( τ eff << τ ).Namely, the effective response time is τ eff, = 0 . µ sand τ eff, = 0 . µ s for n-T1 and n-T2, respectively.The N EP is the most important figure of merit for abolometer, since it determines the minimum power thatcan be detected above the noise level. Taking into ac-count the equivalent circuit, highlighted by the dashedline in Fig. 5, the total
N EP of the nano-TES is givenby three uncorrelated sources [37, 38]
N EP tot (cid:39) (cid:113)
N EP T F N + N EP Jo + N EP sh , (10)where N EP
T F N is associated to the thermal fluctuations,
N EP Jo is due to the Johnson noise in the nano-TES and N EP sh is related to the shunt resistor. Other externalnoise contributions, such as the noise of the read-out elec-tronics and the photon background noise, are not takeninto account, because they can not be directly attributedto the device.The thermal fluctuation noise given by [22] N EP
T F N = (cid:113) k B Λ G th,A T c,A , (11)where Λ = n/ (2 n + 1) describes the effect of the tem-perature gradient across the thermal link. Our nano-TESs show an extremely low thermal fluctuation noise, N EP
T F N, = 5 . × − W/ √ Hz and
N EP
T F N, =6 . × − W/ √ Hz, since G th is limited by the smallvolume of the active region. n-T T c τ τ eff NEP
TFN
NEP tot δν ν/δν (mK) ( µs ) ( µs ) (W/ √ Hz) (W/ √ Hz) (GHz) 100 GHz 300 GHz 1 THz1 128 6 0.01 5.2 x 10 − −
100 1 3 101* 6 0 .
01 1.1 x 10 − − − − − − −
540 0.18 0.55 1.82* 5 0 . − − − − − TABLE I.
Principal figures of merit.
The time constant τ , the pulse recovery time τ eff , the Noise Equivalent Power dueto the thermal fluctuation noise NEP
TFN and the total noise
NEP tot , the Frequency Resolution δν , and the Resolving Power ν/δν (at 100 − − T c . The n-T1* and n-T2* values are referred to the superconducting elements without the Andreev mirrors. The Johnson noise is originated by the charge trans-port, when the nano-TES is in the normal-state. Therelated
NEP is written [22]
N EP Jo = (cid:113) k B R A ( T c ) T c,A G th,A T c,A V α (cid:113) π f τ eff ,(12)where R A ( T c ) (cid:39)
40 Ω is the value of R A at T c , V is thevoltage drop and f is the signal bandwidth. In orderto detect the temperature variations in A , we chose asignal bandwidth f = 100 MHz ≥ /τ eff, and f =5 MHz ≥ /τ eff, for n-T1 and n-T2, respectively. For I T ES = 15 nA, our devices show similar normal stateresistances ( R A, (cid:39)
70 Ω and R A, (cid:39)
72 Ω), but differentvalues of the electro-thermal parameter ( α = 2742 and α = 122). Therefore, the Johnson contributions to thenoise equivalent power are N EP
Jo, = 6 × − W/ √ Hzand
N EP
Jo, = 2 × − W/ √ Hz for n-T1 and n-T2,respectively.Finally, the shunt noise is related to charge fluctuationsthrough R sh . Its contribution to the N EP reads [22]
N EP sh = (cid:112) k B R sh T bath G th,A T c,A V α × (cid:113) (1 − L ) + 4 π f τ eff , (13)where L = α/n is the loop gain. Since the shuntingresistor needs to satisfy R sh (cid:28) R A , the contribution of N EP sh is usually negligible compared to Johnson noise.Indeed, in our nano-TESs we have N EP sh, = 3 × − W/ √ Hz and
N EP sh, = 1 × − W/ √ Hz for n-T1 andn-T2, respectively.The total noise equivalent power of our nano-TESs isdominated by the thermal fluctuation contribution, thatis Johnson and shunt resistor noise are negligible, andit shows state-of-the-art values
N EP tot, = 5 . × − W/ √ Hz and
N EP tot, = 6 . × − W/ √ Hz for TEStechnology [39].We now consider devices characterized by the samestructure of our nano-TESs, but fabricated without thelateral aluminum banks, namely they are completelymade of the Al/Cu bilayer. The result of this structureis the absence of heat confinement in the small nanowire and the increase of the net device volume to about1 . × − m . On the one hand, this change of struc-ture does not affect the thermal response time, since boththe heat capacity and the thermal conductance dependlinearly on the volume (see Eqs. 8 and 9, respectively).On the other hand, the total noise equivalent power isstrongly influenced by the volume increase ( N EP tot, ∗ =5 × − W/ √ Hz and
N EP tot, ∗ = 8 × − W/ √ Hz).In particular,
N EP Jo and N EP sh depend linearly on G th thus showing the larger worsening ( N EP
Jo, ∗ =4 × − W/ √ Hz,
N EP
Jo, ∗ = 5 × − W/ √ Hz and
N EP sh, ∗ = 4 × − W/ √ Hz,
N EP sh, ∗ = 6 × − W/ √ Hz) and becoming sizeable with respect to ther-mal fluctuations (
N EP
T F N, ∗ = 1 × − W/ √ Hz and
N EP
T F N, ∗ = 1 . × − W/ √ Hz). Therefore, the re-moval of AM has a heavy negative impact on the detec-tion performance of the TES bolometer.
B. Calorimeter
In single-photon detection, the value of τ eff determinesthe minimum speed of the read-out electronics necessaryto detect a single photon. Moreover, it defines the deadtime, that is the minimum time interval between two in-coming photons in order to be recorded as two differentevents. The NETF ensures that the energy injected intothe sensor by the single photon absorption is efficientlyremoved by decreasing its Joule overheating instead ofbeing dissipated through the substrate thus compensat-ing for the initial temperature increase.The fundamental figure of merit for a single-photondetector is the frequency resolution δν , that is the min-imum photon frequency detected by the sensor. For thenano-TES, it is defined [12] δν = 2 . (cid:126) (cid:115) (cid:114) n k B T c C e,A α . (14)Since the minimum detectable single-photon energydepends on α , our nano-TESs show different values of δν . In particular, we have δν (cid:39)
100 GHz ( δE (cid:39) δν (cid:39)
540 GHz ( δE (cid:39) FIG. 6. Resolving power as a function of single-photon fre-quency for n-T1 (green) and n-T2 (purple). The dashed linesrepresent similar devices not equipped with Andreev mir-rors. The presence of Andreev mirrors improved the resolvingpower of more than 3 orders of magnitude. and n-T2, respectively. Accordingly, the resolving power( ν/δν ), which indicates the sensitivity in detecting ra-diation of a specific energy, achieves values larger than1 for ν ≥
100 GHz for n-T1, as shown in Fig. 6. Wenote that the sensitivity of the devices could be furtherimproved by increasing the sharpness of the supercon-ducting to normal-state transition of the active region,i.e. rising the value of α .In the absence of AM, the electron heat capacitanceincreases of about 7 orders of magnitude due the volumeincrease. Therefore, the frequency resolution downgradesof more than 3 orders of magnitude (see Tab. I), and thedevices could operate only above 300 THz. VII. MULTIPLEXING CIRCUITS FORDETECTOR ARRAYS
Astronomy and astrophysical experiments require tele-scopes equipped with arrays of hundreds or thousandsdetectors. Therefore, efficient multiplexing schemes arefundamental to decrease the wiring, lower the relatednoise, and reduce the mechanical and thermal loads.Several multiplexing architectures differing for the out-put signals are used: time division multiplexing TDM,code division multiplexing CDM, frequency division mul-tiplexing FDM and microwave resonator MR based read-out [40].For the frequency operation range and the target ap-plications of our nano-TESs, FDM and MR represent theoptimal strategies to create multipixel detectors. Thus,we will estimate the circuit parameters to build arrays ofour nano-TESs.
Resonant CircuitCPW Line V out R HEMTC C n R sh TES I bias L L L ab C L n SQUID
TES L C L C L n C n SQUIDR sh V out I bias LR l FIG. 7.
Multiplexing read-out circuits. a) Scheme of fre-quency division multiplexing (FDM) read-out. FDM is com-posed by N independent unit cells, which resonate at differentfrequencies set by the RLC circuit ( L n = 10 µ H, a capacitancerange C between 10 pF and 25 pF, R A ( T c ) = 40 Ω). Theirfrequencies are summed and coupled with a SQUID linked toan amplifier. b) Scheme of microwave resonator (MR) basedmultiplexing read-out. The schematic circuit is formed by Nindependent unit cells coupled with an RC resonant circuit,composed by an inductance L , a coaxial cable and a capac-itance C , through a SQUID determining a unique frequencyfor each resonator. All resonators are read out by a frequencycomb applied by an AC generator through a Coplanar Waveg-uide (CPW) Line. The signal can be amplified by an HighElectron Mobility Transistor (HEMT) ( R = 50 Ω, C n be-tween 60 pF and 2 nF. A. Frequency Division Multiplexing
The FDM circuit is schematically shown in Fig 7-a[41, 42]. Each unit cell operates at its own frequency[ f n = 1 / (2 π √ L n C n )] defined by the RCL circuit and ad-equately separated from the others to avoid cross talk.The signal bandwidth of each pixel is larger than the re-laxation effective time-scale of the nano-TES after thephoton absorption ( BW > /τ eff ) suppressing all noise0signals outside the band. In order to have a signal band-width [ BW = R A ( T c ) / (2 πL n )] constant for each pixel ofthe array, the same inductance is usually set for everychannel. For example, considering the values of n-T2 wepropose a bandwidth BW of 60 kHz, an inductance of10 µ H and a capacitance range between 10 pF and 25 pFto have ∼
31 pixels for an array. Therefore, each pixelhas a resonance frequency between 10 MHz and 16 MHz,and it is spaced of 200 kHz to suppress cross-talk. Thetotal signal is measured with a single SQUID amplifierof time constant shorter than the effective pulse recov-ery time to follow the current variation in the nano-TES( τ s (cid:28) τ eff ). Its bandwidth BW of 20 MHz is consistentwith state-of-the-art SQUID amplifiers [44, 45]. CustomLC lithographed boards with multiplexing factors > B. Microwave resonator multiplexing
The MR multiplexing exploits a SQUID amplifier con-necting the sensing elements of each pixel to a differentRLC resonant circuit (see Fig. 7-b). This configurationmaximizes the dynamic range per pixel and removes thelimit on the pixel number, but the system is more bulky.Photon absorption shifts the resonance of the related cir-cuit which is connected in parallel and excited simultane-ously to all the others. Then, the transmitted signals aresummed into a low noise amplifier, such as the high elec-tron mobility transistor (HEMT) placed at a higher tem-perature. The bandwidth of n-T2 is BW = 5 MHz. Con-sidering a SQUID amplifier with bandwidth BW s = 10MHz, we can choose resonant circuits with bandwidth BW r = 50 MHz separated by 50 MHz in frequency rangegoing from 300 MHz to 2 GHz. To this end, each linecould implement systems with resistance of 50 Ω, fixedinductance of 0.2 µ F and capacitance values between 0 . . VIII. SUMMARY AND CONCLUSIONS
We have presented a new class of extra-sensitive minia-turized transition edge sensors: the nano-TES. The ultra-low volume of the active region and the exploitation ofheat barriers, the so-called Andreev mirrors, ensure theoptimal thermal efficiency of the devices. In addition, theengineering of the working temperature thanks to the su-perconducting inverse proximity effect allows full controlof the nano-TES performance. To extract all the de-vice parameters and determine the performance both in the bolometer and calorimeter operation, we performeda complete series of experiments. On the one hand, bycharacterizing electrically the nano-TES we measured thecritical current and the critical temperature of the activeregion. On the other hand, we fabricated and character-ized a secondary device equipped with superconductingtunnel probes extracting the spectral and thermal prop-erties of A .The nano-TES reaches a total noise equivalent powerof ∼ × − W/ √ Hz, limited exclusively by the ther-mal fluctuations, when operated as bolometer. In single-photon detection, our device shows a best frequency reso-lution of ∼
100 GHz, thus having the potential to operatein THz and sub-THz regime with a relaxation time of ∼
10 ns.With its simple design, the nano-TES could be imple-mented in widespread multiplexing circuits (FDM andMW Resonators) for detector arrays in multipixel giga-hertz cameras [40]. As a consequence, the nano-TEScould become an asset as bolometer and calorimeter forastronomy and astrophysics research, detecting cosmicmicrowave background [1] and atomic vibration in galaxycluster [2], and be the key for searching axions [3, 7, 8],one of the principal candidates of dark matter. More-over, it could find application for medical imaging [24],industrial quality controls [25] and security [26] in THzband.
ACKNOWLEDGEMENTS
We acknowledge A. Tartari, and G. Lamanna for fruit-ful discussions. The authors acknowledge the Euro-pean Union’s Horizon 2020 research and innovation pro-gramme under the grant No. 777222 ATTRACT (ProjectT-CONVERSE) and under grant agreement No. 800923-SUPERTED. The authors acknowledge CSN V of INFNunder the technology innovation grant SIMP. The work ofF.P. was partially supported by the Tuscany Government(Grant No. POR FSE 2014-2020) through the INFN-RT2 172800 project. The work of V.B. is partially fundedby the European Union (Grant No. 777222 ATTRACT)through the T-CONVERSE project. G.S. acknowledgesthe ASI grant 2016-24-H.0.
CONFLICT OF INTEREST
The authors declare that they have no conflict of in-terest.
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