Characterization of a Silicon Drift Detector for High-Resolution Electron Spectroscopy
Matteo Gugiatti, Matteo Biassoni, Marco Carminati, Oliviero Cremonesi, Carlo Fiorini, Pietro King, Peter Lechner, Susanne Mertens, Lorenzo Pagnanini, Maura Pavan, Stefano Pozzi
aa r X i v : . [ phy s i c s . i n s - d e t ] J un C HAR ACTERIZATION OF A S ILIC ON D R IFT D ETEC TOR FOR H IGH -R ESOLUTION E LEC TRON S PEC TROSCOPY
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Matteo Gugiatti
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, ItalyINFN, Sezione di Milano, 20133 Milano, Italy [email protected]
Matteo Biassoni
Dipartimento di Fisica, Università di Milano-Bicocca, 20126 Milano, ItalyINFN, Sezione di Milano-Bicocca, 20126 Milano, Italy
Marco Carminati
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, ItalyINFN, Sezione di Milano, 20133 Milano, Italy [email protected]
Oliviero Cremonesi
Dipartimento di Fisica, Università di Milano-Bicocca, 20126 Milano, ItalyINFN, Sezione di Milano-Bicocca, 20126 Milano, Italy
Carlo Fiorini
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, ItalyINFN, Sezione di Milano, 20133 Milano, Italy
Pietro King
Dipartimento di Elettronica, Informazione e BioingegneriaPolitecnico di Milano, 20133 Milano, ItalyINFN, Sezione di Milano, 20133 Milano, Italy
Peter Lechner
Halbleiterlabor of the Max-Planck SocietyMunchen, 81739, Germany
Susanne Mertens
Max Planck Institute for Physics,80805 Munchen, GermanyTechnische Universitat Munchen80333 Munchen, Germany
Lorenzo Pagnanini
Dipartimento di FisicaUniversità di Milano-Bicocca, 20126 Milano, ItalyINFN, Sezione di Milano-Bicocca, 20126 Milano, Italy
Maura Pavan
Dipartimento di FisicaUniversità di Milano-Bicocca, 20126 Milano, ItalyINFN, Sezione di Milano-Bicocca, 20126 Milano, Italy
Stefano Pozzi
Dipartimento di FisicaUniversità di Milano-Bicocca, 20126 Milano, ItalyINFN, Sezione di Milano-Bicocca, 20126 Milano, ItalyJune 30, 2020
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Silicon Drift Detectors, widely employed in high-resolution and high-rate X-ray applications, areconsidered here with interest also for electron detection. The accurate measurement of the tritiumbeta decay is the core of the TRISTAN (TRitium Investigation on STerile to Active Neutrino mix-ing) project. This work presents the characterization of a single-pixel SDD detector with a mono-energetic electron beam obtained from a Scanning Electron Microscope. The suitability of the SDDto detect electrons, in the energy range spanning from few keV to tens of keV, is demonstrated.Experimental measurements reveal a strong effect of the detector’s entrance window structure onthe observed energy response. A detailed detector model is therefore necessary to reconstruct thespectrum of an unknown beta-decay source.
The ability to precisely measure the energy spectra of electrons, originating from radioactive isotopes, would opennew frontiers for the β -decay spectroscopy. The accurate energy reconstruction of β -decay spectra has a remarkableimpact in the field of nuclear physics, in the field of neutrino physics, and in the double β -decay investigation.A detection system for electron spectroscopy, with both high-resolution and high-rate capabilities, has wide applica-tions. Among all, the one leading in the research presented in this paper is the TRISTAN project [1], where the tritium β -decay spectrum is measured, to search for a keV-scale sterile-neutrino signature [2]. For this application, since apost-acceleration is applied to shift at higher energies the Tritium spectrum, the energy range of interest starts fromfew keV up to
30 keV , the targeted energy resolution is <
300 eV
FWHM @
30 keV , and the average count rate is
100 kcps per channel [3, 4]. Other detector requirements, such as radiation hardness for operation in the focal plane ofthe experiment, are still under definition.High-resolution and high-count-rate capabilities are characteristic features of the well consolidated Silicon Drift De-tector (SDD) technology [5], widely employed to precisely resolve X-ray lines [6, 7, 8]. Combining a large areacoverage and small anode capacitance, these fast detectors are widely adopted for high-resolution X-ray spectroscopy,for photons with energy comprised between few hundreds of eV up to 20-
30 keV [9]. This paper aims at provingthe potentialities of the Silicon Drift Detector, extended in the field of electron detection, for precision β -decay spec-troscopy.While studies of SDD detection for low-energy X-rays have been carried out [10, 11], in literature, a limited number ofarticles report the study of the Silicon Drift Detector response, and other Si detectors [12], to electrons. The responseto Internal Conversion Electrons (ICEs) has been measured, using Cs and m Xe radioactive sources [13], withenergies ranging from 129 to
656 keV . A different research reports the response to other ICEs originating from
Cd,
Ba, and
Xe sources [14], exploring an additional energy range down to
45 keV . However, to our knowledge, asystematic study of the SDD aiming at building a model of the detector response to electrons is still missing.This work presents a methodical characterization of a single pixel SDD performed by using an artificial electron source,the measurements have been conducted with discrete energy settings between 5 and
20 keV . In this energy range, theelectronic noise and the incomplete energy absorption, due to dead layer effects, have the most relevant effect on themeasured spectra. Spanning from the optimization of the biasing voltages of the detector, to maximise its detectionefficiency, to high-statistics measurements of mono-energetic electrons with various energies and incidence angles, acomprehensive set of experimental data is built and here reported. This data is the starting point to build and validate,by means of Geant4 Monte Carlo simulations, a precise physics model of the detector. This model will allow tofaithfully reconstruct an unknown β -decay spectrum starting from its experimentally measured data. The ensemble ofdetector, characterization method, and detector model, constitutes the basis for the Tritium β -decay measurement inthe TRISTAN project, and it is of great interest also in other applications such as particle and nuclear physics [15].The paper is organised as follows. In Section 2, the experimental setup employed in this work will be reported, fromthe hardware to the operation point of view. In the following Section 3, multiple sets of experimental measurementsare shown: optimisation of the SDD’s voltages, rise time of the signal, and detector response to various e - incidenceangles. In the last section 4, a preliminary analytical entrance window model of the SDD is described. Finally, someconclusions are drawn. A mono-energetic e - beam is a suitable source to characterize the response of the SDD to electrons. In contrast, β -decay isotopes emit electrons with a broad energy range and are hence less suitable for the study of the detector’s2 PREPRINT - J
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30, 2020response. In alternative, isotopes which emit ICEs can be viable candidates as mono-energetic electron sources, e.g. m Kr does emit electrons at
18 keV and
30 keV which is in our energy range of interest.In this work, we use electrons created in an electron scanning microscope (SEM). The electrons are created via thethermionic effect and are then accelerated to a well defined energy through an electric field. The electron beam is sub-sequently deflected by a system of electromagnetic coils to scan the portion of the sample under analysis. Finally, bythe detection of the electrons backscattered by the sample, the electron image is point-by-point reconstructed. A SEM,by combining a variable electron rate and energy, and a collimated and steerable beam, is the ideal characterizationsource for low-energy electrons.
A dedicated setup has been developed for our SEM, model Tescan VEGA TS 5136XM, and a picture of its installationis shown in Fig. 1. It consists of the electron source, the preamplifier board, and the detection module with a single-pixel SDD. The preamplifier board is hosting the filter capacitors and the Ettore ASIC [16], an integrated chargepreamplifier designed to readout the SDD with integrated JFET for the TRISTAN project.The detection module and the preamplifier board are fixed on a single aluminium frame which is mounted on thesample holder of the microscope. The sample holder allows to move the detector assembly along its x, y, and z axes,including tilt (with respect to the e - beam) and rotation. The connections towards the preamplifier board are made withflex cables to allow the free movement of the stage. The cables end on a custom designed 27-pin vacuum feedthroughon the inner wall of the chamber, responsible to transfer all the signals and bias voltages to the outside electronics.Figure 1: (a) Experimental setup installed in the SEM. The system is composed of: I) electron beam source, II)board hosting the ASIC charge preamplifier and the filter capacitors, III) detection module with the single SDD, IV)moveable sample holder. (b) Close up view of the board hosting the SDD, seen from the entrance window side, andthe aluminium cover to protect the detector and to host an Fe calibration source.The detector board is hosting a wedge-bonded single-pixel SDD with a diameter of . operated in pulsed resetregime. The board is a special-made rigid-flex with three layers of flexible circuit permitting an easy and reliableconnection to the preamplifier board, and offering a good signal integrity against crosstalk. Above the detector board,a machined aluminium cover is fixed in place with nylon screws. The cover has a protection purpose and embeds a slotfor an Fe source, which provides uncollimated photons for calibration purposes. The cover is made of a conductivematerial and it is connected to ground in order to avoid, during the time of the measurement, the accumulation ofelectrons on its surface, a phenomenon which has been observed using a plastic material. Below the SDD board, thereis a second aluminium support which is thermally contacting a Peltier cell for cooling the detector. In this paper,however, the measurements were taken at room temperature, obtaining a sufficiently good energy resolution of
190 eV
FWHM @ . , for X-rays, with µ s filter peaking time. The removal of the heat generated by the thermoelectriccell, on a moving stage and inside the vacuum environment of the SEM, is critical and needs to be addressed with acustom-made liquid cooling strategy. 3 PREPRINT - J
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30, 2020The detector employed in the measurements is fabricated by the Semiconductor laboratory of the Max-Planck Society(MPG-HLL). Its entrance window is a thin implanted diode covered by a
22 nm -thick SiO insulating layer withoutany other additional layer. The integrated JFET is biased by a drain current I D = µ A and has a nominal transcon-ductance g m = µ S . The illustration in Fig. 2 represents the structure of the silicon device describing the name ofits contacts and the doping of its regions: p + corresponds to . × cm − . The wafer is a high resistivity one( · cm ) with standard thickness ( µ m ).Figure 2: Structure of the SDD with integrated JFET, and its contacts, employed in the TRISTAN project. Aluminium markersAccumulated charge region
Figure 3: Image of the SDD’s entrance window acquired by the SEM. The aluminium features, present on the SDD’ssurface, have been used as a position reference in the measurements. Light rectangular shapes, caused by surfacecharge accumulation, are visible.A portion of the SDD’s entrance window, imaged by the SEM, is visible in Fig. 3. Aluminium markers are deposited onthe entrance window, during the manufacturing phase, and are used as an accurate reference for the e - beam position. Inthe same figure an interesting effect can be observed: the presence of lighter rectangular shapes on the uniform SDD’sentrance window. This effect is likely due to the temporary accumulation of charges (electrons) in the passivation layeron the SDD. Trapping of excess charge in SiO under SEM illumination is a well known effect and depends on severalparameters of the layer such as permittivity, density of defects and stress [17]. However, no differences in the spectrahave been observed from measurements inside and outside these slightly charged regions. The effect is reversible and4 PREPRINT - J
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30, 2020fades away, with a time constant in the order of some minutes, if the entrance window is left unexposed. Overall, theeffect is not considered to be an issue for two reasons: first, it is reversible and does not create permanent damage inthe short term, and second, when the SEM is used as an e - source for characterization, the beam current is loweredby several orders of magnitude with respect to its nominal µ A value used for imaging purposes. For comparison, a µ A e - beam would lead to a rate of × cps , much higher than the × cps / pixel rate required by theTRISTAN project. During imaging, an area of µ m x µ m is scanned in 3 minutes by the beam focused on a µ m spot, corresponding to a charge of about
45 nC impinging on each spot for . (comparable to what reportedin [17]). In order to achieve a charge of .
45 nC / µ m (well below a critical threshold for the dielectric), during theoperation as focal plane detector of the TRISTAN experiment, an exposure time in excess of 7000 years would berequired. The setup described so far, in section 2.1, is contained in the microscope’s chamber. Outside, the electronic chainis completed by power supplies, the bias system and the DAQ. The bias system provides all the required voltages tosupply the ASIC preamplifier and the SDD. The manual adjustment of the following detector voltages is allowed: V BC (back contact voltage), V BF (back frame voltage), V R1 ( st ring voltage), V RX (last ring voltage), V IGR (inner guardring voltage), V D (JFET drain voltage), V H (SDD reset diode high level), and V L (SDD reset diode low level). Thebias system also includes an amplifying stage for the signal G = +3 before the DAQ system. The electronics is poweredby two bench-top power supplies: ± V for the low voltages, and +150
V from which are derived all the SDD’s highvoltages. A signal generator is employed to select the reset period of the SDD and the charge preamplifier, to adapt tovarious rate and leakage current conditions. The DAQ is a commercial single-channel DPP (Digital Pulse Processor),DANTE by XGLab, implementing a trapezoidal shaping filter.
During the normal imaging mode of a SEM, the electron beam is scanned across the area to be imaged using an e - current in the order of tens of µ A ( µ A for our specific model). This operation mode is not suitable for our scope,where a very low-current and position-fixed beam is required. In order to obtain an e - beam with those characteristics,the manual adjustment of the microscope’s parameters is needed. First, to reduce the count rate, the e - current isdecreased by reducing the heating power, thus the temperature, of the filament emitting the electrons. Secondly, thebeam position is set to fixed coordinates in the point of interest. At this stage, any imaging capability of the SEM islost, but the beam has acquired the characteristics needed for our use. A collimated beam with a spot size of ∼
100 nm and an e - current in the order of is obtained. This current corresponds to an average rate on the detector of fewkcps. The energy of the beam is selectable, changing the acceleration voltage, between the following fixed values: 5,10, and
20 keV . This section presents the experimental results of the SDD’s characterization with electrons. All the measurements havebeen carried out inside the microscope’s chamber (pressure < − mbar), at room temperature, with the simultaneouspresence of a collimated mono-energetic e - beam and uncollimated X-rays, with µ s filter peaking time.The different nature of photons and electrons determines the characteristic energy response, to these particles, observedby the SDD. For X-ray photons, the photoelectric absorption mechanism is dominant, while electrons are directlyconverted to electron-hole pairs along their trail in the detector. Fig. 4 illustrates the absorption mechanism for thetwo types of particles. The absorption of a photon generates a photoelectron of equal energy which, for 5.9 keVphotons, is statistically well inside in the detector’s active volume (for very-low-energy photons the absorption occursvery close to the entrance windows instead). The spectrum originating from a typical X-ray line, neglecting the chargelosses during the collection of the photoelectrons, can be considered a Gaussian function. Electrons, instead, have tointeract first with the entrance window before releasing their energy into the active volume, where they will, eventually,come at rest. A part of their energy is always released in the superficial layer of the SDD and cannot be measured.Furthermore, there is the possibility to have electrons which release a part of their energy, in the active volume, andthen backscatter still retaining a considerable fraction of their initial kinetic energy. The effect of the dead layer andbackscattering lead to different features in the response. The dead layer determines the shift, to lower energies, and theasymmetry of the electron peak. Whereas, the backscattering creates a low-energy continuum in the spectrum. Theexperimental measurement in Fig. 5 shows the response to X-rays only and to X-rays with a 20-keV e - beam focused µ m away from the centre of the device. The energy resolution obtained with the setup, at room temperature, is5 PREPRINT - J
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30, 2020 e l ec t r on s pho t on s D ead l aye r S e n s iti ve l aye r B acksca tt e ri ngEne r gy l os t i n t he dead l aye r Pho t oe l ec tri ce ff ec t E l ec tr on ' s tr a il s SDD
Figure 4: Qualitative comparison between the absorption of photons and electrons in a Si detector. The photoelectronsgenerated by the photons are mostly absorbed inside the device, whereas the electrons arriving from the outside areabsorbed in proximity of the entrance window and are subject to energy loss and the backscattering effect.
190 eV
FWHM at the Fe K α line ( . ) and
265 eV
FWHM at the 20-keV e - peak (calculated by fitting theright-hand side of the e - semi-Gaussian peak). BackscatteringEscape peak
Low-energytail
Figure 5: Comparison between Fe K α and K β X-ray lines and mono-energetic 20-keV electrons having normalincidence with respect to the entrance window surface.
This section presents a series of measurements aiming at optimizing the detector’s biasing voltages to obtain the bestperformance. The biasing voltages of the SDD shape the electric field inside the detector. The best set of voltagesis the one which maximises both the absorption capabilities and the collection of charge carriers generated by theincoming radiation. Two fundamental bias voltages to be optimised are: the V BC (back contact) and the V RX (lastring) voltages which control the depletion of the detector’s volume. The best method to optimise the bias parameters isthrough a series of measurements where each bias voltage is changed step by step and the peak position, of a reference6 PREPRINT - J
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30, 2020incoming radiation, is monitored: the voltage range that yields to the highest centroid position is the good operatingregion where the electric field optimally collects the generated electron-hole pairs. F(cid:0) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)s 2(cid:6)(cid:7)(cid:8)(cid:9)V (cid:10)(cid:11)(cid:12)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)
Figure 6: Series of experimental spectra with different V BC biasing conditions. The voltage of the SDD back contact(entrance window) is varied from −
90 V to −
140 V by steps. The V RX contact is at −
125 V while the V BF contactis always
10 V more negative than the V BC voltage. The color of each spectrum represents the position (in bins) of the20-keV electron peak, green is the full energy.The three-dimensional plot in Fig. 6 reports a series of spectra taken at different V BC voltages. A green region can bedenoted, where the signals of X-rays and electrons are maximised. This region is the best operating condition for theV BC voltage of our specific SDD.The V BC is necessary to fully deplete the substrate of the SDD and to provide the drifting field towards the anoderegion, whose potential is kept fixed around , with respect to ground, by the feedback loop of the preamplifier. Fig.7 shows the position of the centroids of the Fe K α and the electron’s peak, normalised to their respective maximumvalues, as a function of the V BC voltage. If the V BC voltage is less negative ( > −
100 V ) some charge starts to be lostdue to an insufficient depletion of the device, if V BC is too negative ( < −
125 V ) a part of the charge cloud is lost in theinnermost drift rings. The typical plateau region where the charge collection is optimal can be identified from the plotand the final chosen voltage is V BC = −
110 V .A similar optimisation procedure has been adopted for the SDD’s last ring voltage V RX , keeping V BC = −
110 V fixed.The last ring is one of the two terminals of the integrated voltage divider biasing the drift rings. By controlling theV RX potential, the radial field in the detector, concentrating the photoelectrons to the anode, changes of magnitude.A minimum voltage in needed to properly drift and collect the charge carriers generated in the whole volume. Amaximum voltage limit exists at V RX = − · | V Depletion | ≃ −
180 V , beyond which, a reach-through current arises fromthe back-contact side of the detector [18].In Fig. 8 the centroid position is shown similarly to the previous measurement, with the V RX voltage being a variableparameter. A fraction of uncollimated X-rays is measured, from the central region of the entrance window, at V RX = −
50 V . Collimated radiation ( e - ) µ m from the centre, is successfully measured with V RX = −
70 V . Finally,collimated radiation hitting close to the border ( µ m ), is properly collected with V RX = −
80 V . For V RX < −
80 V the device is in optimal working conditions, the whole volume being sensitive, and minimal differences are observed ifthe bias is further increased. However, an higher radial field is beneficial to decrease the drift time of the charge carries,effect which is confirmed by the measurements presented in section 3.3. A shorter drift time generates a faster signalwhich is advantageous because of lower ballistic deficit due to the enlargement of the electron cloud width. Hence, thefinal value adopted in our setup is V RX = −
140 V .All the remaining SDD’s bias voltages, acting in the readout zone (integrated JFET, inner rings, and guard rings), havebeen optimised in a different laboratory setup to obtain the best Fe energy resolution. In this setup the detector can be7
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Platea u region
Figure 7: Normalised centroid position for calibration X-rays and 20-keV electrons in two positions (middle and outer,respectively µ m and µ m from the centre of the SDD) versus the V BC voltage. V RX = −
125 V . (cid:19)(cid:20)(cid:21)(cid:22)(cid:23)r (cid:24)(cid:25)(cid:26)(cid:27) (cid:28)(cid:29)(cid:30)(cid:31) Figure 8: Normalised centroid position for calibration X-rays (uncollimated) and 20-keV electrons collimated in twopositions ( µ m and µ m from the centre of the SDD) versus the V RX voltage. V BC = −
110 V .cooled down to − ◦ C reducing the leakage current down to ∼
100 fA . The complete set of the voltages adopted forour SDD is summarised in Table 1. These values are consistent with what is typically obtained from device simulations.The best energy resolution which has been obtained for X-rays, in the cooled laboratory setup, is
127 eV
FWHM @ . with µ s filter peaking time.Table 1: Complete list of the optimised SDD bias voltages. Please refer to section 2.2 for the naming of the differentvoltages. V BC V BF V R1 V RX V IGR V D V H V L −
110 V −
125 V −
20 V −
140 V − . .
25 V − . PREPRINT - J
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The availability of a beam with excellent collimation and precise positioning, both in the sub-µ m range, allows tostudy the position-dependence of the detector response. The SDD has been scanned across its 3.2-mm diameter, witha 20-keV e - beam using µ m steps ( µ m steps for the central points), the centroid position has been calculated foreach point and the result is plotted as a function of the position. Given the circular shape of the detector, a scan alonga single diameter was performed assuming perfect radial symmetry of the device. From the measurements, which arereported in Fig. 9, the presence of an insensitive central region of the SDD is clealry visible. The position of the e - peak, in the spectrum, is rapidly decreasing and disappearing getting closer to the centre of the entrance window. Thenumber of counts drops to zero accordingly. -1500 -1000 -500 0 500 1000 1500 e - beam position [ m] e - c en t r o i d po s i t i on [ b i n ] Figure 9: Centroid position of the e - peak versus the position of the beam in different points along the diameter of theSDD. The charge loss in the centre of the detector is visible.This behaviour is expected for the SDD used in this measurements, where the charge carriers generated above the anoderegion are collected by the Drain (the most positive electrode) instead of the anode. From the measurements, the deadspot is a circle with a diameter < µ m which is less than . of the entrance window’s total area. Therefore, theimpact due to the lost events is negligible. However, in a new production of the detectors for TRISTAN, this effectwill be eliminated by an improved design of the integrated read-out structure which prevents the collection of thecharges into the JFET electrodes. Outside of the central region, the measured energy of the events is homogeneousand stable over the measurement time of about 30 minutes (all the points are within their statistical oscillations withoutan observable long-term drift). The rise-time performance of the detector connected to the charge preamplifier has been evaluated with a set of dedi-cated measurements here presented. Instead of using a DPP, the signal is sampled by a very fast digitizer. The detectoris illuminated with 20-keV collimated electrons and its output waveform is acquired at
10 GS / s with 12-bit depth.The waveforms are then processed in order to extract the rise-time information. The events are detected, from the rawwaveform, with a derivative filter, then a selection is made to take only full-energy non-saturating events. Each one isthen fitted with a parametric erf (Gaussian error function) and the associated - rise time is calculated.Fig. 10 reports the rise time in different points of irradiation, along the radius of the SDD’s entrance window, scannedwith the electron beam. The measured rise time is determined by the convolution between the response of the SDDand the transfer function of the electronics. In our case, the electronics is faster (BW ≃
40 MHz ) than the detector andthe difference in signal width, between particles absorbed at different distances from the anode, can be appreciated.The charge cloud, travelling from the e - interaction point to the anode, guided by the drift field, is subject to a spatialbroadening effect which is proportional to the drift time. The charge cloud associated to radiation absorbed far fromthe anode, requires more time to reach its destination and its broadening is translated into a slower electrical signal i.e. slower rise time. The additional information coming from the signal rise time can be, in principle, employed to9 PREPRINT - J
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30, 2020 R i s e t i m e - % [ n s ] Figure 10: Rise time of the signal at the output of the preamplifier for different 20-keV radial beam positions. Theerror bars indicate the ± σ uncertainties for each point.implement an electronic collimation of the detector. A useful scenario would be the rejection of events which producecharge sharing between adjacent pixels in multi-pixel SDD matrices. -140-130-120-110-100-90 V RX Last Ring voltage [V]20222426283032 R i s e t i m e - % [ n s ] Figure 11: Signal rise time versus last ring voltage. The position of the e - beam is fixed µ m from the anode. ± σ error bars are represented for each measurement point.Another rise time measurement is reported in Fig. 11, where the rise time is measured as a function of the SDD biasvoltage. The electrons are focused on a fixed spot distant µ m from the centre of the SDD, which is the region ofthe detector with lower field, so the most sensitive to voltage variations. The last ring voltage is swept from −
90 V to −
140 V keeping V R1 = −
20 V and the rise time is measured. For higher magnitudes of the V RX biasing voltage, afaster signal is observed. The setup, mounted on the microscope’s sample holder, can be tilted with respect to the e - beam. The angle can rangefrom zero, when the beam is perpendicular to the entrance window, up to ◦ without loosing the line of sight. The10 PREPRINT - J
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30, 2020amount of energy lost in the passivation layer of the detector, which does not generate any signal, depends on thethickness of the passivation layer itself. If the detector is not perpendicular to the electron beam and it is assumed thatelectrons travel, in average, in a straight line, the effective insensitive layer that they encounter is increasing with theincidence angle. The backscattering probability of the incoming electrons is also affected by geometrical parameterssuch as the angle. Both these effects have been experimentally observed. C oun t s ° tilt angleTail fitPeak fit C oun t s ° tilt angleTail fitPeak fit C oun t s ° tilt angleTail fitPeak fit Figure 12: Spectra of 10-keV electrons and Fe X-rays for various e - incidence angles. The energy axis is calibratedon the X-ray lines. The Fe calibration source is fixed in the reference system of the detector.In Fig. 12 the spectra obtained at ◦ , ◦ , and ◦ incidence angles, with 10-keV electrons, are plotted in log scale. Byincreasing the angle of incidence, the energy corresponding to the maximum of the e - peak is progressively decreasingdue to the increased energy loss in the superficial layer of the detector. The fraction of counts in the low-energycontinuum is also increasing due to the higher backscattering probability.11 PREPRINT - J
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For each incidence angle, the e - tail and the peak in the spectra are fitted with cubic spline functions constrained bythresholds defining the end of the tail and the beginning of the peak, while the Fe lines are ignored in the fitting. Forenergies below . , where the DAQ threshold cuts off, the fitting of the tails are interpolated using third-orderpolynomial functions. For each spectrum, the integral of the fitted tail and the integral of the fitting of the peak arecalculated, then the ratio between the tail and the total (tail counts plus peak counts) is determined. Angle of incidence [ ° ] T a il t o t o t a l r a t i o Figure 13: Tail to total ratio of the 10-keV electron beam for different incident angles ranging from ◦ to ◦ . Thefitting of the spectra, in the tail (low-energy continuum) and in the peak, is done as per the algorithm used in Fig. 12.Fig. 13 shows the measured tail-to-total ratio for the electrons as a function of their incidence angle. The observedincreasing trend, which is expected, quantitatively shows the higher backscattering probability as the incident angle isincreased. If a simplified Si detector structure is considered, i.e. a thin dead layer with thickness t on top of an ideal sensitivelayer, and the propagation of the electrons in the SDD is approximated to a straight line, it is possible to define ageometrical link between the energy loss in the dead layer and the angle of incidence of the electrons. The effectivedistance d eff , travelled by e - in the silicon, as a function of the incidence angle α is geometrically given by (1), where Γ represents the additional factor relative to the dead layer thickness t . d eff = t (1 + Γ) = t cos α ⇒ Γ = 1cos α − (1)Assuming the energy of the 10-keV electron beam to be accurate within few eV and the potential of the SDD’s entrancewindow being set at V BC = −
110 V , with respect to the microscope’s ground, the energy of the electrons reaching thedetector is E eff = E beam + V BC = 10 keV − .
11 keV = .
89 keV . Defining as E meas ( α ) the energy of the maximumof the e - peak, with respect to the X-ray calibration, the energy lost when the beam is perpendicular to the detectoris E lost (0 ◦ ) = E eff − E meas (0 ◦ ) . Assuming the travel of the electrons being straight, the energy being lost in the deadlayer can be described by (2). E lost ( α ) = (1 + Γ) E lost (0 ◦ ) = 1cos α E lost (0 ◦ ) (2)In conclusion, the actual energy measured on the electron peak E meas ( α ) is described by equation (3). With E lost (0 ◦ ) =190 eV being determined experimentally from the α = 0 ◦ data. E meas ( α ) = E eff − E lost ( α ) = E beam + V BC − α E lost (0 ◦ ) (3)12 PREPRINT - J
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Angle of incidence [ ° ] e - pea k ene r g y [ k e V ] MeasureModel
Figure 14: Energy of the maximum of the electron peak versus the incidence angle of the 10-keV beam measured with ◦ steps, compared to the model of equation (3). The energy axis is calibrated with the Fe X-ray lines.The energy loss changes with the energy of the impinging electrons. Geant4 Monte Carlo simulations allow to accu-rately model this energy dependence. Here we focus on the effect of the incident angle and take as reference the energyof
10 keV . In Fig. 14 the energy of the maximum of the 10-keV e - semi-Gaussian peak and the result of the equation(3) are plotted as a function of the angle of incidence. A very good agreement is found between the experimental dataand the model obtained with the geometrical considerations. The maximum energy residual is . ( . ) andthe root mean square of the residuals is . ( . ). This confirms the strong impact of the detector’s entrancewindow on the measured energy of the beam and the goodness of the geometrical assumptions made in this section. The difficulty in the electron spectroscopy lies in the estimation of the real energy of the detected electrons from theenergy effectively measured by the detector. It is demonstrated that the entrance window has a strong effect in theresponse to electrons, hence a correct modelling of its structure is a critical aspect in this application.In this work, a comprehensive set of high-quality high-statistics data has been collected in different experimentalconditions ( e.g. various beam energies and incidence angles). This data is used by a closely related work [19], whichimplements and reports a method to model the SDD’s entrance window by combining the experimental data withGeant4 [20] simulations. The main result, focusing on the detector’s structure, is here briefly illustrated.An analytical function describing the charge collection efficiency (CCE) versus the depth z in the entrance window isdefined as per equation (4), which reflects the technology used to build the SDD. The model for the entrance windowis known as partial event model, which has been developed for X-ray response [10, 11, 21]. f CCE ( z ; t, p , p , λ ) = p z < t p −
1) exp (cid:18) − z − tλ (cid:19) z > t (4)The entrance window is characterised by an oxide layer (SiO ) with thickness t =
22 nm which is completely insen-sitive ( p = 0). After the oxide layer, the implantation of the entrance window contact occurs. Here it is assumed aCCE starting from a value p which gradually approaches the unitary value following an exponential equation with acharacteristic constant λ . p and λ are free parameters in the model.Geant4 Montecarlo simulations reproduce a series of spectra spanning all the possible combinations of the free param-eters in (4). The values of the free parameters which minimise the discrepancy between the simulated spectra and theexperimental spectra are considered to be the optimal parameters to describe the entrance windows model. The modelhereby defined can be employed to predict the response of the SDD to any source of electrons. The outcome of this13 PREPRINT - J
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30, 2020study is shown in Fig. 15. The optimized parameters, and related uncertainties, are p = 0.09 ± λ = . ± . . t t ! p1 " t = 22 nmp = 0p = 0.09 ± 0.05 = 59.8 ± 3.1 nm Figure 15: Model of the SDD’s entrance window describing the charge collection efficiency as a function of the depthin the device. The values of the parameters and their uncertainties are shown.
Silicon Drift Detectors despite being considered so far mainly for X-ray detection, can represent an excellent sensoralso to measure electrons, with energies ranging from the keV to tens of keV, offering high-count-rate and high-resolution capabilities equivalent to their usual X-ray applications. However, the spectra generated by electrons areconsiderably different from the ones generated by photons of similar energy.The process dominating the electrons energy loss is the ionization along the track. The electron-hole pairs which arecreated in the most superficial part of the detector cannot be collected by the drift field. A fraction of the energy isalways lost in the entrance window and the effect is depending on its structure. Moreover, the non-zero probabilityof electron backscattering adds a characteristic low-energy continuum due to incomplete energy deposition by theincoming particles. The incidence angle between the electrons and the detector is also playing a role in the shape ofthe measured spectrum, since the electrons travel through an increased effective thickness of superficial layer. If the e - beam source is not collimated, it is convenient to place the detector in a space where a combination of electrical andmagnetic fields guarantees a good perpendicularity between the charged particles and the SDD’s entrance window toavoid the mixing of various incidence angles.The optimal biasing of an SDD does not change between the measurement of photons or electrons. Once eitherparticle releases its energy, creating h + - e - pairs, there are no differences in the charge collection mechanism insidethe detector’s volume.Experimental data, acquired during the measurements presented in this work, are the basis to build a model of theSDD detector, which is illustrated, for reconstructing unknown β -decay spectra. Future developments will includenew measurements featuring a multi-pixel SDD matrix to study the effects of charge sharing between adjacent pixels. Acknowledgments
This work has been supported by INFN through TRISTAN and by Max Planck Institute for Physics. The experimentalmeasurements have been carried out in the Electron Microscopy laboratory inside the Department of Material Scienceof the University of Milano-Bicocca. We would like to thank Prof. M. Acciarri and Dr. P. Gentile for their competence,support, and patience. 14
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