Performance and uniformity of a kilo-pixel array of Ti/Au transition-edge sensor microcalorimeters
E. Taralli, M. D'Andrea, L. Gottardi, K. Nagayoshi, M. L. Ridder, M. de Wit, D. Vaccaro, H. Akamatsu, M. P. Bruijn, J.R. Gao
aa r X i v : . [ a s t r o - ph . I M ] F e b Performance and uniformity of a kilo-pixel array of Ti/Au transition-edgesensor microcalorimeters
E. Taralli, a) M. D’Andrea, L. Gottardi, K. Nagayoshi, M. L. Ridder, M. de Wit, D. Vaccaro, H.Akamatsu, M. P. Bruijn, and J. R. Gao
1, 2 SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht,The Netherlands. Faculty of Applied Science, Delft University of Technology, 2600 AA Delft, The Netherlands. (Dated: 19 February 2021)
Uniform large transition-edge sensor (TES) arrays are fundamental for the next generation of X-ray space observatories.These arrays are required to achieve an energy resolution ∆ E < 3 eV full-width-half-maximum (FWHM) in the softX-ray energy range. We are currently developing X-ray microcalorimeter arrays for use in future laboratory and space-based X-ray astrophysics experiments and ground-based spectrometers.In this contribution we report on the development and the characterization of a uniform 32 ×
32 pixel array with 140 × µ m Ti/Au TESs with Au X-ray absorber. We report upon extensive measurements on 60 pixels in order to show theuniformity of our large TES array. The averaged critical temperature is T c = 89.5 ± ∼ ∆ E FWHM = 2.50 ± α and β respectively) and their correlation with the detector’s noise parameter M , showing an homogeneous behaviourfor all the measured pixels in the array. I. INTRODUCTION
Large and uniform array of detectors, with high spectralresolution (SR = ∆ E / E ), are highly demanded for a numberof scientific objectives in space observation and are gettingcrucial for the next generation of space observatories withlarge telescopes. Superconducting microcalorimeter deviceslike transition-edge sensors (TESs) are capable to deliver anSR > 2000 becoming the leading choice in most of the instru-ments.TES sensors are very sensitive thermometers which are able todetect radiation in a wide energy range, e.g. from γ -ray downto submillimeter . TES consists of a single layer of super-conducting material or of a multilayer of materials where ametallic intermedium is included to tune the critical tempera-ture of the entire detector. A TES is weakly thermal coupledto the thermal bath ( T bath < T c ). This weak thermal link is of-ten created via suspension of the TES on a SiN x membrane.Depending on the energy of the photons involved, an absorber,optical cavity or antireflection coating is used to achieve therequired quantum efficiency, allowing the measurement ofthe energy or power of the incoming photons. The TES isself-heated to within its very steep superconducting-to-normalphase-transition by Joule power supplied by a voltage-bias cir-cuit. An electro-thermal feedback insures a self-regulation ina selected working point . When a photon or a particle is ab-sorbed, it generates an increase of the temperature causing asubsequent change in the resistance and therefore in the cur-rent flowing through the TES. This signal is read out using in- a) Author to whom correspondence should be addressed: [email protected]. ductively coupled superconducting quantum interference de-vices (SQUIDs).In the last decades, large arrays of TES microcalorimetershave been used for spectral imaging acquisition and are underdevelopment in a number of space telescopes . Specifi-cally, SRON TES array has been selected as the backup optionfor the X-ray Integral Field Unit (X-IFU) which is one of thetwo instruments on board of the Athena space mission andconsists of an array of over 3000 TESs. It follows that theuniformity of such large arrays plays a crucial role in mostof the applications. Any non-uniformities across the arraycould lead to different detectors having different energy reso-lution and/or response time, which would be inconvenient foran imaging-spectroscopy camera.Fabrication of large arrays passes through a number of stepsand is done in multiple layers as well as involves a wide depo-sition area. Because of this, each pixel may not be impactedequally, leading potentially to degrade the achievable unifor-mity of performance across an array. The capability to bias allthe pixels approximately at the same working point, aimingto get the same performances over the full array, is of coursevery important for the quality and the reproducibility of anexperiment. For these reasons, all the parameters that tend toaffect the performance of the single detector and thus the ho-mogeneity of the whole array have to be investigated. Thoseinclude for instance critical temperature, linearity of the tran-sition curve, thermal conductance to the bath and quality ofthe interface between leads and bilayer.The readout technology used in this work is frequency do-main multiplexing (FDM) . It applies a set of sinusoidalAC carriers, which bias the TES detectors at their workingpoints and are amplitude modulated when the TES detectorsare hit by photons. The detectors are separated in frequencyby placing them in series with LC resonators, each having aspecific resonant frequency. The frequency bands assigned tothe detectors are separated to prevent the detectors from in-teracting with each other. This allows the readout of multipleTES pixels by one amplifier channel, which uses only one setof SQUID current amplifiers. We are currently using an 18-channel FDM readout system with bias frequencies between1-5 MHz, which is a prototype version of the anticipated 40-channel FDM readout.The paper is organized as follows: Sec. II gives a quickoverview of the modifications implemented in the last yearsin the pixel design, inside the TES community in general andin particular at SRON, to further improve TES performances;Sec. III describes the characteristics of the pixel introducedin the kilo-pixel array (Sec. III A) and the experimental setupused during this work (Sec. III B); Sec. IV presents the mea-surements performed on the various pixels on the TES array,in particular the uniformity tests such as critical temperatureand thermal conductance from one side of the chip to the other(Sec. IV A), the partial logarithmic derivatives of TES resis-tance R ( T , I ) with respect to temperature and current, α and β ,respectively and the noise factor M (Sec. IV B), noise equiv-alent power (Sec. IV C) and single pixel energy resolution(Sec. IV D); In Sec. V, we draw the main conclusion aboutthe uniformity of such kilo-pixel array. II. PIXEL EVOLUTION UNDER AC-BIAS
In the last decade, TES pixel design has passed througha number of changes. The matching between the readouttechniques and the detector mainly drives the pixels de-sign in order to get the best performance from the whole ar-ray. For instance, the connection of the bilayer to the higher T c superconducting Nb leads and the presence of normalmetal structures in the bilayer, cause proximity effects thatstrongly affect the TES behaviour both under DC and ACbias . The TES behaves typically as an SS’S or SNS junctioncomposed by two superconductors S and S’ (where T c ′ < T c )or one superconductor S and one normal conductor N, respec-tively. The Josephson effects are regularly observed both inthe response to the perpendicular magnetic field and, underAC bias, in the changes of the TES reactance across the su-perconducting transition. It leads to a considerable variation(Fraunhofer-like oscillations) of the device’s critical current asa function of the magnetic field B . At the same time, the tran-sition curve is characterised by kinks, the location of whichdepends, among other things, on the alignment of the normalmetal structures on the bilayer . Uniform and predictabletuning of TESs across a large array is simplified by the mini-mization of these kinks and oscillations in the TES transitions.Added to this, biasing TES microcalorimeters in AC intro-duces another issue that has to be taken into account dur-ing the pixel design iterations. In AC-biased low-ohmic TESmicrocalorimeters, the Josephson effects are masked by an-other frequency-dependent dissipation mechanism, on whichwe have already reported before and which is related tothe generation of eddy currents in the normal metal structures surrounding the TES.The measurement of the quadrature component of the IV curves in AC-biased TESs and the dependency of the detec-tor’s current as a function of the magnetic field, are usefulmethods to quantify most of these effects. The quadraturecomponent of IV curves shows an oscillatory behaviour de-pendent on the driving bias frequency and generally, the pe-riod and the amplitude of the oscillations decreases with thebias frequency. Moreover, the amplitude is larger at low biasvoltages due to the fact that the Josephson current is reducedwhen √ PR n / F b increases, where P is the detector power, R n is TES normal resistance and F b is the bias frequency .High saturation power, high normal resistance and low biasfrequency readout is one way to minimise the weak-links inthe TES. The saturation power is related to the G of the de-tector, which is typically constrained by the scientific appli-cation while the bias frequency by the engineering require-ments. The only parameter left free for the optimisation is theTES normal resistance. At the same time, the thermal fluc-tuation noise internal to the microcalorimeter increases asthe thickness of the superconducting bilayer decreases. Thisaffects how large the R n can be designed for optimal perfor-mance for a given application.Recently a new generation of TES designs made with athicker bilayer but with high aspect-ratio (to keep a largerTES’s normal resistance) have shown a smaller Joseph-son current under AC bias giving high energy resolutionperformance . We report some specific data in this sec-tion in order to show the effect of these changes on the TESpixel design with an aspect-ratio (length × wide) 140 × µ m placed in the large array subject of this work. Josephson ef-fects can be quantified by measuring the IV curves for 12 pix-els connected at different bias frequencies and in particularby looking at the ratio I Q / I I between the detector quadratureand in-phase current, as shown in Fig. 1a and Fig. 1b. Be-sides the uniformity of the detectors current as a function ofthe bias voltage, it is worth noting how I Q / I I ratio remainsless than 2% low in transition even at high bias frequency.This is an improvement if compared with the previous SRONdevices : I Q / I I <25% in low-ohmic and low-power detectorand I Q / I I <5% in high-power and high normal resistance de-tectors. Fig. 1c shows the variation of the device current as afunction of the magnetic field at T bath = 55 mK where all theTESs measured have been biased at the same working pointsuch that R / R n ∼ ∼ µ T. From Fig. 1c we don’t see any mod-ulation of the TES current versus the applied magnetic fieldup to ∼ µ T. It means that this TES is very weakly affectedby the proximity effect. Other details about the uniformityand the impact of the weak-links on this large array are beingreported in the following of this paper. Iterations to further im-prove the pixel design will be continuing and are still needed.Increasing the thickness of the bilayer to improve the devicethermalisation, enhance more the aspect ratio of the detectorto keep an high normal resistance and finding new materialsfor the leads are only fews of the advances that will be facedin the coming future.FIG. 1: TES current in-phase (a) and the ratio between the quadrature and in-phase current I Q / I I (b), as a function of R / R n for12 pixels. (c) Detector’s current (dashed lines) as a function of the perpendicular magnetic field applied on the same 12 pixelswhen biased in the same bias point R / R n ∼ III. ARRAY DESCRIPTION AND EXPERIMENTALDETAILSA. Kilo-pixel array
The kilo pixel array under test has been fabricated on an 4inch wafer together with a number of 5 × ×
32 uniform kilo pixel arrays withvarious aspect-ratio (length × width) devices. Fig. 2a showsthe 32 ×
32 Ti/Au TES array and in particular the 60 pixelsthat have been measured during four different measurementcycles (from now on called Runs). All the TESs use a 0.5 µ m thick low-stress, silicon-rich silicon nitride SiN x mem-brane and have the same bilayer thickness of Ti (35 nm) andAu (200 nm) resulting in a normal resistance per square R =26.2 m Ω / (cid:3) and critical temperature T c ∼
90 mK. All the ab-sorbers consist of Au (2.3 µ m thick) and have the same size(240 × µ m ) with a heat capacity C = 0.85 pJ/K at T c . Eachabsorber has four supporting stems directly connected to themembrane and two stems directly connected to the bilayer asshown in Fig. 2b. The design of the device with dimension(length × width) 140 × µ m that has been explored in thiswork is shown in Fig. 2c with a normal resistance R n = 121m Ω and an expected thermal conductance G ∼
95 pW/Kat T c . More details on fabrication of such SRON TES arrayshave been published in a previous work . B. Experimental set-up
The characterization of the kilo-pixel arrays was performedin an experimental measurement set-up named XFDMLargeand it is shown in Fig. 3. It was installed in a dilution refriger-ator that can provide a bath temperature of ∼
40 mK. TESswere characterised under AC bias using an existing FDMreadout system (1-5 MHz) in single-pixel mode configura- FIG. 2: (a) Top view of 32 ×
32 kilo-pixels array with thepixels measured during the 4 Runs: purple (Run1), green(Run2), blue (Run3) and red (Run4). (b) Picture of the X-rayabsorbers located in the 32 ×
32 array. The absorber size is240 × µ m with a gap of 10 µ m between the neighborsand six supporting stems. (c) Picture of a 140 × µ m Ti/Au TES (taken before absorber deposition) connected to amicrostrip line via interconnecting leads. Dotted circlesidentify the area where the supporting stems will eventuallybe grown. The area indicated by the arrow is the membranearea (roughly, it is where the SiO layer is removed).tion, where only one device is biased at a time, and all othersare left in the superconducting state. Each TES is connected inseries with an LC resonator on an LC filter chip with a coil in-FIG. 3: Picture of the setup used to characterise thekilo-pixels array, hanged at the mixing chamber of a dilutionrefrigerator and held at a base temperature of 50 mK. Mainparts are highlighted by arrows.ductance L = 2 µ H and a 1:1 transformer chip. The kilo-pixelTES array chip and the cryogenic components of FDM read-out were mounted in a low magnetic impurity copper bracketfitted into an Al superconducting shield. The bracket also ac-commodates a heater, a thermometer and a Helmholtz coil.The heater and thermometer are used to stabilise the temper-ature locally on the chip. The coil is for applying a uniformmagnetic field perpendicular to the TES array to compensateany remnant magnetic field trapped in the experiment set-up.
IV. UNIFORMITY CHARACTERIZATIONA. Critical temperature and thermal conductance
Any variation in the transition temperature of pixels acrossthe array affects the uniformity of the energy resolution, thebias point and the speed of the detectors over the whole array.Achieving a sufficiently homogeneity both in the thickness ofthe bilayer and in the subsequent processing stages over thefull array, guarantees to bias all devices approximately in thesame sensitive part of the transition aiming to the same detec-tor’s performances.By measuring all the IV curves for the selected set of pix-els at different bath temperatures T bath , we are able to calcu-late the TES dissipated power P TES , for example at the min-imum of the IV curve, as a function of T bath . We fit thesedata using the balancing between the dissipated TES electri-cal power and the dissipated TES thermal power to the bath P TES = I × R TES = K × ( T n c − T n b ) , where n is a numberwhose value depends on the dominant thermal impedance be-tween the substrate and the electrons in the superconductingfilm and K is a material and geometry dependent parameter.In this way we determine the critical temperature T c and thethermal conductance G = d P TES / d T for each pixel.In Fig. 4 we highlight the uniformity of the array in terms of critical temperature by means of a heat map. We can eas-ily notice how all the pixels belonging to the same quadrant,show a difference in the transition temperature less than 0.6mK, while the total variation between the lower and upperquadrant over the whole array ( ∼ . We would like to underline that betweentwo runs inside the same quadrant, only the wire-bondingschanged, whereas between two runs in different quadrants thechip array rotated by 180 degrees as well. The position ofthe thermometer and of the other components of the setup hasnot been changed among the runs. Moreover, the same TEShas been measured during Run3 and Run4 and we have ob-tained T c = 89.6 mK and T c = 89.4 mK, respectively. Thistemperature variance of 0.2 mK is smaller than 0.6 mK and1.5 mK that we obtained inside one quadrant and between thetwo quadrants, respectively. For this reason we rule out thepossibility that our characterization is mainly guided by cal-ibration instability or non-repeatability of the measurement.Averaging all the critical temperatures for the 44 pixels we geta T c = 89.5 with a standard deviation of 0.5 mK. The natureof this dispersion around the mean value is still under discus-sion. However, it might be explained considering some of thecritical aspects in the whole fabrication process, e.g. the TESpatterning by means of wet etching process, the stress on themembrane due to the absorber and the uniformity of the ab-sorber itself.The averaged thermal conductance that we have measuredacross the array is G = 117 ±
17 pW/K (diamond point in Fig.5). The thermal transport in the nitride membranes is quasi-ballistic because of extremely long phonon mean-free paths,as we have already shown in the past , resulting in a ther-mal conductance that depends on the perimeter of the TESand the thickness of the membrane. Comparing the value ofour measured thermal conductance with earlier tests of similardevices fabricated by NASA Goddard, we get that our currentvalue is about 20 pW/K above the expected value . Wefound that the combined TES film plus supporting stems areadetermines the thermal conductance. In Fig. 5 we report onthe thermal conductance measured on TES with different ge-ometry (80 ×
20, 100 ×
20, 80 ×
40, 120 ×
20 and 140 × µ m )placed in two arrays with different area of the supporting stem(10 and 5 µ m of diameter). These results scale consistentlywith the detector perimeter (2 W + L ), but also show a clearshifting between them. The dashed line in Fig. 5 is the linearfit of the open dots and the diamond point where a ( W + L ) is the TES thermal conductance scaling with the perimeter and b is the thermal conductance due to the stems. Using the equa-tion G = n ΣΩ T n − where n is the exponent of power flow tothe heat bath, Ω is the material volume and Σ is a material-dependent constant , we can estimate the relative impact ofthe stems to the measured thermal conductance. Assumingthat the perimeter of the stems is the only difference betweenthe two arrays (material, n and height of the stems are thesame), the thermal conductance of the 5 µ m stems is noth-ing but the thermal conductance b of the 10 µ m stems, scaledFIG. 4: Heat map of the critical temperature measured allover the kilo-pixel array. The inset shows the location of thearray in the whole wafer indicated in the black box. Run1 hasbeen neglected due to a different warm electronics used inthis measurement.down by the ratio between the stem’s area, as shown by thedot-dashed line in Fig. 5. A further reducing of the stems di-ameter as well as the number of the stems directly connectedto the membrane will reduce this additional thermal conduc-tance. B. α , β and M factor Frequency dependent complex impedance measurement Z ( f ) is a method extensively used to derive the most impor-tant thermal and electrical TES parameters . All the de-tails about this measurement performed in AC bias has beenpublished in a recent work .Data derived from measurements of the frequency depen-dent complex impedance Z ( f ) give information about the par-tial logarithmic derivatives of TES resistance R ( T , I ) with re-spect to temperature and current α = δ ln R / δ ln T and β = δ ln R / δ ln I , respectively. In Fig. 6a and Fig. 6b we show α and β respectively as a function of R / R n for four pixels at differentbias frequency. It is worth to notice that, as for the quadraturecomponent of the IV curves (Fig. 1b), α and β show oscilla-tions as a function of the voltage bias amplitude with a periodthat depends on the bias frequency as highlighted from theinsets (zoom in between 15-40% of R / R n ) in Fig. 6. The os-cillations are large especially for low values of R / R n and havetheir origin in the earlier mentioned weak-links effect. How-ever, α and β are small-signal parameters, and when an X-rayis absorbed by a TES, typically a large part of the transition issampled, smoothing these peaks. It means that the mean valueof α and β at high frequency bias remains close to the one atlow bias frequency and the effect on the detector performanceis of a secondary importance. The relation between α and β FIG. 5: Thermal conductance of TESs with differentaspect-ratio (perimeters) and 10 µ m stem’s diameter tosupport the absorber: 140 ×
30 (340 µ m) placed in this arrayand averaged over 44 pixels (diamond point), 80 ×
20 (200 µ m), 80 ×
40 and 100 ×
20 (200 µ m) and 120 ×
20 (280 µ m)measured in another setup (open dots). Fit (dashed line)follows the dependency of the thermal conductance fromperimeter (2 W + L ). Same aspect-ratios have beenmeasured on another mixed array with 5 µ m stem’s diameterto support absorbers (open squares). Fit shifted down of ratiobetween the areas of the two different stems (dash-dot line).is independent of the bias frequency, this is something whichbecomes clear when α is plotted versus β . In Fig. 7 we wouldlike to stress the uniformity of the values of α and β amongall the pixels in each bias points that have been measured. Forinstance, the pair α ∼
200 and β ∼ R n ). The darkerpattern highlights the most frequent values among the pixels,while the lighter squares show the values reached by the highfrequency pixel during the oscillations. Solid line in Fig. 7shows an empiric relationship between α and β that could de-pend on the geometry of the device .We usually acquire also the detector noise in the same workingpoints through the transition where TES complex impedancemeasurement has been performed. This turns out to be veryimportant in order to compare the experimental noise with thetheoretical one using all the parameters obtained from the fitof the complex impedance. Ideally the detector noise shouldbe explained by means of the phonon noise at low frequen-cies S P TFN = k B T GF L , the Johnson noise at middle fre-quencies S V = k B T R ( + β ) and the SQUID or readoutnoise at high frequencies, where the T an R are the temper-ature and the resistance of the TES, respectively, G is thethermal conductance to the bath and F L is a unitless func-tion that depends on the thermal conductance exponent andon whether phonon transport to the TES is specular or diffuse.The term 1 + β is the first-order correction to the standardJohnson-noise expression for a non-linear resistor with cur-rent dependence . In reality the experimental noise spectrumshows an excess in comparison with the ideal detector cal-culation in the frequency range where the Johnson noise isdominant. This excess noise is quantified with an additionalfactor of ( + M ) that multiply the expected Johnson noise S V = k B T R ( + β )( + M ) . A number of explanationsfor this excess Johnson noise have been proposed, howevernone of the mechanisms gives quantitative predictions consis-tent with the measured dependencies of the excess electricalnoise. At SRON we are currently working to find a full cor-relation between theoretical and experimental noise in orderto understand the magnitude of the unexplained noise specifi-cally on our new high aspect ratio TESs.In Fig. 8 we show the value of the fitted M factor for thepixels measured in Run 4 as a function of the bias points(upper plot). At the same time, in the lower plot we canconsider together α , β and M to estimate the effective influ-ence of these parameters on the energy resolution ∆ E FWHM ≈ . q k B T C √ ( + β )( + M ) α . This plot shows low bias fre-quency pixels having almost no oscillations down to 15% of R n , whereas shows more oscillating high bias frequency pixelswhich become more stable around 35%-40% of R n . This ex-plains why the higher bias frequency pixels need to be biasedat 30%-40% of R n to get the same good energy resolution asthe lower bias frequency pixels biased around at 20%-30% ofthe R n . Of course understanding the physical origins of α , β and M is essential for further energy resolution optimisation. C. Noise equivalent power An Fe X-ray source is placed closely above the array inthe set-up and illuminates the entire TES array at a count rateof ∼ α Fe X-raypulse and dividing the noise spectra by the detector’s respon-sivity, we get the NEP spectra. Integrating the NEP spectrawe obtain the baseline resolution that is reported in Fig. 9 forRun 2 as a representative example for all the measured pix-els. We observe that at both ends of the transition the averageintegrated NEP is larger. There is an oscillation as a functionof bias resistance which is more prominent for the pixels withhigher bias frequency. This behaviour has been already dis-cussed for the quadrature component of IV curves (Fig. 1b)and for α and β (Fig. 6) being related to the weak-link effect.In Fig. 10 we plotted all the fobtained integrated NEP val-ues as a function of normalised bias resistance with the aimof predicting the distribution of obtainable energy resolutionfor the entire array. We can conclude that there is a consis-tent and populated area from 20% to 40% of the normal-stateresistance where the integrated NEP is between 2.5 and 3 eV. FIG. 6: Logarithmic resistance resistivity with respect totemperature α (a) and current β (b) as a function of TESworking point for some of the pixels in Run 2. D. Energy resolution
Integrating the measured NEP over a wide bias range iden-tifies the promising working points where good energy resolu-tion can be expected. In Fig. 11 we summarise the best energyresolution for each pixel that have been measured from oneside of the array to the other. We usually collect around 5000X-Ray photons to get a statistical error of about ± ± . This confirms the effectivenessof the new pixels design and the relative efforts to reduce theundesired effects depending on the bias frequency, achievingFIG. 7: α versus β for all the 60 pixels that have beenmeasured with empiric relationship between them (solidline).FIG. 8: M factor (top plot) and influence of α , β and M onthe energy resolution (lower plot) as a function of the biaspoint R / R n for pixels measured in Run4.in this way global and uniform good performances as high-lighted by a summed X-ray energy resolution of 2.50 ± Fe X-Ray spectra over the60 pixels measured at the best bias points during the four Runsthat is representative of the quality of the whole array.
V. CONCLUSION
We have extensively characterised our 32 ×
32 pixel arrayby measuring 60 pixels concentrated in two different quad-rants of the chip. The goal of this study was to evaluate theuniformity of such large array in terms of thermal and electri-cal parameters, noise equivalent power and energy resolution.We found a mean critical temperature T c = 89.5 with a stan-dard deviation of 0.5 mK. The temperature variation within FIG. 9: 3D-plot of the integrated NEP for each pixel as afunction of the working point measured during Run 2.FIG. 10: Integrated NEP measured for all the 60 pixelsduring the four Runs as a function of the working point.Most of the pixels show an integrated NEP well below 3 eVbetween 20 and 40 % of the normal-state resistance, asclearly highlighted by the red populated area.the same quadrant is less than 0.6 mK and less than 1.5 mKacross the array ( ∼ G hasbeen found to be 117 ±
17 pW/K, which is larger than ex-pected. It turned out that the stems used to sustain and connectthe absorber to the TES play a role in its final value. A fur-ther reducing of the stems diameter as well as the number ofthe stems directly connected to the membrane will reduce thisadditional thermal conductance.We obtained uniform values of α , β and M factor all over themeasured pixels. Values of α ∼
200 and β ∼ ∆ E <2.28 eV), green (2.28 eV< ∆ E <2.58 eV) and yellow(2.58 eV< ∆ E <2.88 eV). These ranges reflect the statisticalerror of ± M factor, showsconsistency over a wide range of working points and all overthe measured pixels .A summed energy resolution of 2.50 ± ACKNOWLEDGMENTS
This work is partly funded by European Space Agency(ESA) and coordinated with other European efforts underESA CTP contract ITT AO/1-7947/14/NL/BW. It has also re-ceived funding from the European Union’s Horizon 2020 Pro-gramme under the AHEAD (Activities for the High-EnergyAstrophysics Domain) project with grant agreement number654215. FIG. 12: (a) Typical energy resolution measured at the bestbias points as a function of the pixel’s bias frequency for thefour Runs (dots) and corresponding linear fit to evaluatedegradation between low and high bias frequency (dashedline). (b) Summed X-ray spectra at 5.9 keV over the 60pixels measured at the best bias points during the four Runs.The solid line is the best fit to the data, the points are themeasured Mn-K α emission lines and the dashed line is theintrinsic emission of the source. The lower plot shows theresiduals of the fit normalized by the error bars. DATA AVAILABILITY
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