Calibration of diamond detectors for dosimetry in beam-loss monitoring
G. Bassi, L. Bosisio, P. Cristaudo, M. Dorigo, A. Gabrielli, Y. Jin, C. La Licata, L. Lanceri, L. Vitale
CCalibration of diamond detectors for dosimetry in beam-loss monitoring
G. Bassi a,d , L. Bosisio b , P. Cristaudo b , M. Dorigo b , A. Gabrielli a,b , Y. Jin b , C. La Licata a,b,c , L. Lanceri b , L. Vitale a,b a Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy b INFN, Sezione di Trieste, I-34127 Trieste, Italy c now at: Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan d now at: Scuola Normale Superiore, I-56126 Pisa, Italy Abstract
Artificially-grown diamond crystals have unique properties that make them suitable as solid-state particle detectorsand dosimeters in high-radiation environments. Sensors based on single-crystal diamond grown by chemical vapourdeposition have been chosen for dosimetry and beam-loss monitoring at the SuperKEKB collider. We describe thecriteria for the selection of the diamond sensors, their purpose-designed mechanical packaging, and the suite of testand calibration procedures adopted to characterise them. The results obtained on 28 detectors are reported, allowingto evaluate the stability and uniformity of the response of these devices.
Keywords: diamond sensor, radiation monitoring, calibration, dosimetry
1. Introduction
Natural diamonds, selected for high purity, have beenknown as good particle detectors with very interest-ing properties since a rather long time [1, 2]. Practi-cal applications became feasible with the advent of newtechniques for the artificial growth of diamond crystalsand their steady improvement. Since the initial pro-posals for applications in high-energy physics experi-ments [3], the growth process by chemical vapour de-position (CVD) [4] has been progressing towards theproduction of single-crystals (sCVD) and poly-crystals(pCVD) of larger size, higher purity and reduced vari-ability, at decreasing cost. At present, artificial-diamondapplications range from medical micro-dosimetry [5, 6]to beam-condition and beam-loss monitors for high-energy accelerators and experiments: examples includethe BaBar experiment at PEP-II (SLAC), CDF at Teva-tron (Fermilab), ATLAS and CMS at LHC (CERN) [7,8, 9, 10].Diamond is an insulating material due to the large en-ergy gap of about 5 . µ rad / s to several hundred krad / s, andperformance stability in locations where an integrateddose in excess of 10 Mrad can be expected through thelifetime of the experiment. Performance of this moni-toring system during the first two years of SuperKEKBoperations is presented in Ref. [13].In this paper, we report on selection criteria, mechan-ical assembly, test and calibration procedures of 28 di-amond detectors employed in such a system, aiming ata comparative assessment of their performance for ourradiation-monitoring purposes.
2. Diamond sensors
An initial study has been aimed at comparing pCVDand sCVD diamond sensors, in order to select the crystaltype that better suits our operating conditions.We used two sources of minimum-ionising particlesto study the charge-collection e ffi ciency and responsestability of di ff erent sensors: high-energy electrons ofabout 3 GeV in a test beam at DESY, and β electronsfrom a source of Sr decays, momentum-selected by a
Preprint submitted to Nuclear Instruments and Methods A February 8, 2021 a r X i v : . [ phy s i c s . i n s - d e t ] F e b mall magnet and collimators, with energies up to about2 MeV.Biased diamond sensors were connected by short ca-bles to a spectroscopy readout chain, including a chargepre-amplifier and a digital shaper and data acquisitionsystem. We observed clean Landau peaks from mini-mum ionisation and derived the charge-collection e ffi -ciency as a function of the bias voltage applied. Wecompared sCVD and pCVD sensors using electrodes ofdi ff erent materials (Al, Ti + Pt + Au). We observed sev-eral advantages of sCVD sensors over those based onpCVD, as sCDV sensors reach full charge-collection ef-ficiency at lower voltage, and are less prone to erraticcurrents; their response is more reproducible, with lesshysteresis e ff ects.Our final choice is to adopt sCVD diamonds from El-ement Six [14] with Ti + Pt + Au electrodes processed byCIVIDEC [15]. The specifications of the supplied sen-sors are: sCVD diamond with (4 . × .
5) mm faces and0 .
50 mm thickness, with a tolerance of + . / − ± .
05 mm for the lateral dimensions and the thickness,respectively; (4 . × .
0) mm electrodes on both faces,made of Ti + Pt + Au layers with (100 + + ±
500 pA in the bias-voltage range ±
500 V,and within ±
20 pA in the range ±
200 V; (ii) averageionisation-energy less than 25 eV and regular pulseshape from a measurement with α particles from Amdecays; (iii) stable current through one-hour irradiationwith β electrons from Sr decays, with bias voltages of ±
100 V and ±
200 V; (iv) visual inspection and rejectionin case of deep scratches.
3. Detector assembly and dark currents
We mounted each diamond sensor in a ceramic-likeRogers printed-circuit board (PCB) [16], as shown inFigure 1. The diamond sensor has been glued with con-ductive glue to a square pad that connects the back-sideelectrode to a soldering pad. After cleaning the PCB-diamond ensemble by isopropyl alcohol, the front-sideelectrode has been connected to the second solderingpad by two ball-bonded gold wires.The inner conductors of two miniature coaxial cables,each 2 . (a)(b) Figure 1: A diamond sensor packaged into a detector unit: (a) the sen-sor is glued on a Rogers printed-circuit board, with electrical contactestablished between the two electrodes (front / back) and the inner con-ductors of two miniature coaxial cables. (b) A zoom of the diamondsensor, with the front-side electrode connected to a soldering pad bytwo ball-bonded gold wires. bending) with respect to soldering the outer conduc-tors of the coaxial cables to the package. The cablelength was determined by constraints imposed by theiruse in the Belle II setup. After the checks presentedin Sect. 4.1, the mechanical and electrical shielding hasbeen completed by gluing a thin (180 µ m) aluminiumcover on the front side of the package.Preliminary measurements of dark current as a func-tion of bias voltage have been performed on all detectorsas a quality check of the assembly process. While keep-ing the diamond detectors in the dark, they have beenconnected to the measuring instrument via the minia-ture coaxial cables. The bias voltage has been scannedup to ±
800 V. Although we observed fairly large vari-ations among di ff erent detectors, in all cases the mea-sured dark current was less than a few pA at ±
500 Vand not larger than about 1 pA at ±
100 V.2 . Detector calibration
The response of diamond sensors as dosimeters is notexpected to be uniform. Crystal imperfections from theCVD-growing process can trap charge carriers gener-ated by irradiation. Such imperfections di ff er from crys-tal to crystal, yielding non-uniform charge-collectione ffi ciency at a given bias voltage. Properties of thediamond-electrode interface are also sensor-dependent.Some detectors might feature non-blocking electrodes,which inject charge into the diamond bulk, and, inconditions that support the so-called photo-conductivegain, the charge-collection e ffi ciency might even exceedunity [17, 18].For these reasons, an individual calibration of eachdetector is needed in order to relate the measured cur-rent to a dose rate. Before the calibration, detailed inSect. 4.3, we carried out two sets of measurements oneach detector. The first set aimed at checking the trans-port properties of the charge carriers and the averageionisation energy to create and electron-hole pair. Withthis study, reported in Sect. 4.1, we got an understandingof the homogeneity of the sensor properties within oursample. The second set of measurements has been car-ried out to determine the best bias voltage for operatingthe sensors and the stability of the output current gener-ated by irradiation. This study is presented in Sect. 4.2. To study the transport properties of electronsand holes, we used the transient-current technique(TCT) [19], which is based on the use of monochro-matic α particles to generate electron-hole pairs lo-calised at a small depth in the diamond bulk, very closeto one electrode. Depending on the bias polarity, chargecarriers of one type are readily collected at the nearbyelectrode, while the others drift to the opposite electrodealong the electric-field lines, inducing a current pulse.Information on the transport properties of the driftingcarriers is determined by the features of this pulse: itsshape is related to the carriers lifetime and to the unifor-mity of the electric field in the diamond bulk; its dura-tion is related to the drift time of the selected carriers;its integral to the collected charge.To carry out the TCT measurements, the diamonddetectors have been assembled on their PCB packagebut without the aluminium cover, so that the α particlescould reach the detector surface. The sensor has beeninserted in an aluminium support and a 5-kBq source of α particles from Am decays has been placed at about3 . α particles, emitted with 5 .
485 MeV energy on average, have been collimated by a Plexiglas screen,2 mm thick, with a circular hole of 1 mm diameter.From a detailed simulation of this setup based on theFLUKA software [20], we estimate that an α particle re-leases in the diamond crystal 89 .
5% of its energy, corre-sponding to 4 .
91 MeV on average; only 3 .
9% is releasedin the metallic electrode, while the rest is distributed be-tween air and the collimating structure. The penetrationdepth in the diamond crystal is limited to about 12 µ m.A high-voltage supply, delivering up to ±
800 V, hasbeen connected to the back-side electrode of the dia-mond detector via a Bias-T circuit [21] that, althoughnot needed to decouple the signal from the DC bias,has proven e ff ective in suppressing the noise. Thefront electrode has been directly connected to the inputof a voltage amplifier with 53 dB gain and 50 Ω inputimpedance (AM-02A from Particulars [21]). The out-put of the amplifier was analyzed by a digital storageoscilloscope.This experimental setup has been optimized after afirst set of measurements on a sub-sample of detectors,made with a less e ff ective collimator, allowing the α particles to hit the whole detector area (including theedges) with a wide range of incidence angles. The read-out scheme was also di ff erent, yielding larger signal at-tenuation from cables and the Bias-T. Those di ff erenceshave a negligible impact in the analysis of the charge-carrier transport, but significantly a ff ect the estimatedionisation energy. We report the results obtained withthe optimised setup and note the distinction from theold configuration only when it is relevant.We investigated the signal generated by the α par-ticles for twelve choices of the bias voltage be-tween ±
800 V. Measurements with bias voltage between ±
150 V have not been considered, because the triggerlevel of the oscilloscope, kept above noise, biased themeasurement for lower pulses. Figure 2 reports the timedevelopment of the average of 1000 signal pulses from adiamond detector. Each measurement provides the aver-age pulse-integral A and the average pulse-width at halfheight w . We assume a uniform electric field in the di-amond bulk (as suggested by the approximately flat topof the signal shapes) and a drift distance of the carriersequals to the sensor thickness h = .
50 mm. For eachvalue of the electric-field intensity E , we estimate thedrift velocity v drift = h / w and the mobility µ = v drift / E for both drifting carriers.The drift velocity can be empirically described by thefollowing expression as a function of E [19]: v drift ( E ) = µ E + µ E v sat , (1)3 ns - - V
150 V –
200 V –
300 V –
400 V –
500 V –
800 V – Figure 2: A summary of the time development of the signals (averagesof 1000 signal pulses) induced by (grey markers) electrons and (blackmarkers) holes, for the di ff erent bias voltages listed in the legend. where µ is the mobility extrapolated to low field-intensity, and v sat is the saturation velocity at high field.Figure 3 shows an example of v drift as a function of E with a fit of the data using Eq. (1). The values of µ and v sat obtained by fitting Eq. (1), averaged over our sampleof diamond detectors, are: µ = . × cm / Vs and v sat = . × cm / s for holes, µ = . × cm / Vsand v sat = . × cm / s for electrons. The standard de-viation of these results is about 20%, confirming that thetransport properties of charge carriers are su ffi cientlyhomogeneous. We did not observe significant di ff er-ences between the results obtained with the optimisedand non-optimised setup.For each pulse integral A measured by the oscil-loscope, the collected charge Q can be estimated as Q = A / Z in − G amp20 , where Z in and G amp are the inputimpedance and the gain of the amplifier, respectively.Independently of the setup used, we observed that theestimated collected charge versus applied voltage satu-rates to an approximately constant value. The fractionaldi ff erence between the collected charge evaluated fromdrifting electrons or holes does not exceed 2%.The collected charge Q can be used to determine theaverage ionisation energy E eh for electron-hole pairs as E eh = q e EQ , (2)where E is the average energy released in diamond bythe α particles and q e is the charge of the electron.The energy E is computed from the detailed simula-tion of the source, the collimator, and the sensor with m] m [V/ e m / s ] m [ d r i f t v electronsholes Figure 3: Example of the measured drift velocity v drift as a function ofthe electric-field intensity E , for (solid markers) electrons and (openmarkers) holes. The lines represent a fit with Eq. (1). its support. We do not simulate the charge-carrier trans-port and we assume a full charge-collection e ffi ciency.We obtain an average value E eh = . E eh = . α particles.Taking into account those biases, all values are consis-tent within 5% with an average value of 13 eV, whichis usually quoted in literature for high-quality diamondsensors [22]. A stable and reproducible response to radiation iscrucial for dosimetry and monitoring. The detector re-sponse might depend on the applied bias voltage, andthe optimal operation value has to be determined. Thishas been obtained by measuring the current-voltage ( I - V ) profile under irradiation for each detector after thefull assembly ( i.e. after gluing the aluminium cover onthe PCB package).We measured the current over a ±
500 V bias-voltagerange. The detectors have been irradiated for 2–5 min-utes for each value of the bias voltage. The radiationwas provided by a steady flux of β electrons from thesource described in Sect. 4.3, using the same setup de-tailed therein. The source was placed at a fixed dis-4 - - [V] V - - [ n A ] I (a) [V] V [ n A ] I (b) − − [V] V − − [ n A ] I (c) − − [V] V − − − − [ n A ] I (d) Figure 4: Examples of I - V measurements from three diamond sen-sors. (a) The I - V profile is symmetric around 0 V for bias volt-ages of opposite polarity, and the current reaches a stable plateau for | V | ≈
60 V; this is a typical situation for half of our sensors. (b) Azoom in the range 0–100 V shows the sharp rise of the current in acouple of volt. (c-d) Two sensors with an asymmetric I - V profile, ex-hibiting also hysteresis e ff ects for negative voltages (the red arrowsindicate the time order of the measurements). (d) A small hystere-sis e ff ect is also present for the best polarisation, but variations of thecurrent are much smaller than those on the opposite side, and are sig-nificant only at high voltages. tance, ranging from about 2 mm to 4 mm from the de-tector, providing currents typically between 1–2 nA at ±
100 V bias.Figure 4 shows some examples of the I - V profiles ob-tained from three sensors exhibiting di ff erent behaviour.Plot (a) represents the situation typical for about a halfof our sensors, which display a symmetric I - V charac-teristic. In these cases, the current reaches a plateau for | V | between 60–80 V, remaining approximately flat upto | V | =
500 V. Plots 4 (c) and (d) are examples of I - V profiles characterising the remaining sensors, where anasymmetric response is observed. For one polarity thecurrent reaches a constant value for | V | typically greaterthan 80 V, while for the opposite polarity no current sat-uration is observed.For those detectors with an asymmetric I - V profile,the response can also present an hysteresis: the currentvalue measured at a given voltage depends on the di-rection of the voltage scan, indicating that the current isnot a function of V alone, but depends also on the previ-ous “hystory”. The variation of the current due to suchhysteresis e ff ects is not significant at | V | =
100 V forthe bias polarity showing the plateau, although it can be much larger in the opposite polarity.We cannot provide a clear explanation for the asym-metric I - V profiles and the hysteresis e ff ects; possiblehypotheses range from a crystal asymmetry from thegrowth process to features of the diamond-electrode in-terface. For these sensors we decided to adopt the volt-age polarity leading to a current saturation.For a couple of sensors, we also sampled the region0–100 V in finer steps, to study in more detail the onsetof charge-collection e ffi ciency. An example is shownin Figure 4 (b). With a bias voltage as small as 2 V, themeasured current is about 50% of the plateau value. Thecharge-collection e ffi ciency rises very steeply within acouple of volt, and slowly saturates increasing the bias.We chose ±
100 V as the optimal operation voltage(with the sign set for each sensor, according to the I - V profiles). With this choice, our detectors have a (steady-state) charge-collection e ffi ciency close to 100% on av-erage.We checked the stability in time of the radiation-induced current at the chosen operation voltage, overa time span ranging from several hours to a few days.Figure 5 reports a few typical examples. On the sensorsexhibiting symmetric I - V profiles, we observe a verystable response over time with values constant within1%. For those with asymmetric I - V profiles, constantcurrent values are observed for the best polarity, withfluctuations no larger than 5%. We noticed larger insta-bilities, also with random spikes, for the opposite polar-ity. These stability tests confirm our choice of the bestpolarity for the sensor with asymmetric I - V profile.We also observed a di ff erent time response betweenthe sensors. Although all detectors react within 1 s(time-resolution of the current sampling in these mea-surements) from the start of the irradiation, some ofthem presents a two-step response: about 90% of thevalue of the current is reached within 1 s, followed bya slower transient to 100% with time duration rangingfrom tens of seconds to many minutes. We attributethis behaviour to di ff erent amounts of crystal defects,corresponding to trapping and de-trapping e ff ects of thecharge carriers following irradiation transients [23]. To employ the diamond detector as a dosimeter, weneed to relate the current measured under irradiation toa dose rate. We define a calibration factor k , such that dDdt ≡ m dEdt = k I , (3)where dD / dt is the dose rate, i.e. the energy per unittime dE / dt released by the radiation in the detector5 s [ n A ] I (a) s [ n A ] I (b) s [ n A ] I (c) s [ n A ] I (d) Figure 5: Examples of current-stability measurements for a couple ofsensors, with a | V | =
100 V bias applied (choosing the best polarity forthe sensors with asymmetric I - V profiles). (a) In the first 25 minutes,a shutter is placed in front of the detector to stop completely the ra-diation; the dark current is constant at a very low value ( < . < I - V profile, on the worst bias polarity the currentcan show large and sudden variations: in this example we observe ran-dom spikes with variations of the order of 10% for a current of about1 nA. mass m , and I is the measured current.To account for non-uniform response of our detec-tors, we split k into two terms, as k ≡ FG , (4)where F is a constant factor that takes the value F ≡ E eh m q e = . / s) / nA , (5)considering the mass of our detectors m =
37 mg and anaverage ionisation energy to create electron-hole pairs E eh =
13 eV. The factor G is a dimensionless constantcharacteristic of each detector. A value G = ffi cient detector, (ii) with block-ing electrodes, and (iii) ionisation energy of 13 eV. Anydeviation from unity is a measurement of the departurefrom the assumptions (i)–(iii). We notice that assump-tion (ii) implies no amplification factor from the “pho-toconductive gain” process [17, 18]. To determine the value of G , we used a silicon diodeas a reference. We exposed the diamond detectors andthe diode to a source of β radiation, and we determinedthe ratio of the signal current from the diamond detectorto the reference current from the diode. The character-istic constant G is obtained by comparing the measured signal / reference current ratio and that expected from adetailed simulation of the experimental setup, where weadopt the hypotheses (i)–(iii) for the diamond detectorsand we assume a good knowledge of the diode response.The use of a reference greatly reduces uncertainties as-sociated to the source activity and to the simulation ofthe setup, that would otherwise limit the accuracy of thecalibration procedure. The diamond detectors have been exposed to a steadyflux of β electrons emitted by a Sr radioactive source.The source could be moved along a straight line orthog-onal to the detector surface and traversing its center.Source-detector distance could be changed from almostzero to more than 20 cm by a stepper motor driven byan Arduino micro-controller [24]. The origin is knownwith an accuracy of 0 . β source was mounted on top of a steel needleembedded in a Plexiglas container. It consists of anion-exchange organic spherical bead, 1 mm in diame-ter, with radioactive nuclei uniformly distributed in thevolume. Electrons are emitted isotropically from the β decays Sr → Y e − ν e and Y → Zr e − ν e , with aknown energy spectrum up to about 2 MeV. The activityof the source from the Sr decays was approximately3 MBq. Being the Y half-life much shorter than thatof Sr, the Y decay rate is in equilibrium with its pro-duction rate. Thus, the rate of β electrons emitted fromthe source is twice the Sr activity.The detector has been connected to a bias-voltagesupply [25] and to a pico-ammeter [26] which measuredthe signal current. Stepper motor, voltage source, andpico-ammeter were interfaced to a computer to automat-ically perform complete sequences of measurements.We explored a range of source-detector distance d from2 mm to 35 mm and for each distance we recorded thesignal current I ( d ), averaging 2 . I r ( d ) from the silicondiode. The diode features an n bulk, a p + layer ob-tained by Boron ion implantation, and a n + layer for theohmic contact. The square-shaped diode, fabricated ona substrate 25 . ± . wide and 0 . ± .
010 mm6
10 20 30 [mm] d [ n A ] I Diamond detectorSilicon diode (a) [mm] d R a ti o R exp R (b) Figure 6: Current versus source-detector distance. (a) Example of(square markers) the signal current I measured from a diamond de-tector, and (triangular markers) reference current I r measured fromthe silicon diode. (b) The signal-to-reference ratio of currents R com-pared to the expected ratio R exp from Eq. (8). thick, is hosted in a package similar to that of the dia-mond detectors. The diode is closely surrounded by a p + guard ring which delimits the charge collection vol-ume of the central diode, given by an e ff ective area of12 . ± . and the depletion thickness. A 100 Vbias was applied to the n + contact, with the p + layer andthe guard ring connected to ground. In this condition,the diode was overdepleted with an active volume givenby the diode e ff ective area and the substrate thickness.The reference current measured as a function of d isshown in Figure 6. While for diamond detectors thedark current was negligible, it contributed significantlyin the measurements with the diode, especially at farsource-detector distance. Thus, each time the distancewas changed, we monitored the dark current, that hasbeen subtracted from the current measured under irradi-ation. The dark current was constant at about 0 .
01 nA.Both signal and reference currents are roughly pro-portional to 1 / d , as expected from the variation of the β -electron flux on the detector surface as a func-tion of d , for an almost-pointlike source. The signal-to-reference ratio of currents, R ≡ I ( d ) I r ( d ) , (6)is constant versus d , as shown in the Figure 6 (b). Theflatness of R denotes that the measured values of thesource-detector distance are compatible in the two setsof data. We compute the expected signal (reference) current I exp ( I rexp ) from the energy released per β electron in thedetector volume, E ( E r ). The FLUKA software [20] isused to obtain the released energy. In the simulation, arealistic and detailed model of the full setup is imple-mented, from the spherical source to the detectors, withall supports and packaging, to account for the full ge-ometry and all materials traversed by the radiation.We do not attempt to model the charge-carrier genera-tion and transport. We use a simplified model where allenergy released in the active volume generates chargecarriers. For the diamond detector, we use assumptions(i)–(iii) presented in Sect. 4.3; for the diode, we assumean average ionisation energy E r eh = . ± .
03 eV [27]and a full charge-carrier collection e ffi ciency. In thismodel, the expected current is expressed as I (r)exp ( d ) = A E (r) ( d ) E (r) eh q e , (7)where the presence of the index “r” identifies thereference-diode quantities; q e is the charge of the elec-tron; and A is the Sr activity, with the factor 2 to ac-count for the β electrons emitted from Sr and Y de-cays.The dependence on the source activity cancels out inthe ratio of expected currents, R exp ≡ I exp ( d ) I rexp ( d ) = E ( d ) E r ( d ) E r eh E eh , (8)which is constant as a function of d . This ratio is shownin Figure 6 (b), where it is compared with the ratio mea-sured from a diamond detector. The expected and mea-sured values are very close to each other. We determine the characteristic constant G for eachdetector from the ratio RR exp = (cid:32) II exp (cid:33) (cid:32) I r exp I r (cid:33) = II exp = G , (9)7 G F r e qu e n c y – > = 0.99 G < (a) D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C D C Diamond detectors [( m r a d / s ) / n A ] k (b) Figure 7: (a) Distribution the of calibration factors G measured fromall detectors. (b) The values of the calibration factor k for each detec-tor. where we assume a precise modelling of the silicondiode ( i.e. I r (cid:39) I rexp ).The distribution of G is shown in Figure 7 (a). Themean value is (cid:104) G (cid:105) = . ± .
04, which corresponds onaverage to fully-e ffi cient detectors, with uniform good-quality crystal ( E eh ≈
13 eV) and blocking electrodes(unitary photoconductive gain). Maximum deviationsfrom this ideal behaviour are limited to about 50%.From the measured G we obtain the calibration fac-tors reported in Figure 7 (b). On average, the dose rateis about 35 mrad / s for a measured current of 1 nA. Thestatistical uncertainty on each value of k is negligiblewith respect to the systematic uncertainty, which is de-tailed in the next section. The relative uncertainty on each calibration factor to-tals δ k / k =
8% from the contributions summarised inTable 1 and described as follows.The largest source of uncertainty is due to possible
Systematic-uncertainty source δ k / k [%]Current transients and fluctuations 5Measurement of source-detector distance 3Silicon ionisation energy < < < < Table 1: Relative systematic uncertainties in % on the calibration fac-tor k . variations of the signal current measured under constantirradiation. As discussed in Sect. 4.2 most detectorsreach a stable output value within a second from thestart of irradiation, with small fluctuations below 1%.Some other detectors present a longer transient timewhere the current varies by 5-10% before reaching aconstant value. To prevent a bias from these variations,for each detector the measurement of the signal currentto compute R from Eq. (6) have been taken after abouttwo hours of irradiation. However, to account for a va-riety of conditions in which the detectors might operate,we assign a systematic uncertainty of 5% to the mea-sured currents, which is propagated to the calibrationfactor.The measured values of R are expected to be con-stant as a function of d , and any trend versus d canbe ascribed to a discrepancy of the source-detector dis-tance between the measurement with the diamond de-tector and the diode. We observe constant values of R within a few percent for all detectors, after correctingthe distance with a detector-dependent o ff set, that aver-ages 0 . ff set correction, the value of R changes on average by 3%. We assign this change asa systematic uncertainty.A major source of uncertainty is related to the refer-ence diode, as we assumed a perfect modelling of itsresponse to obtain G . The estimated current from thediode depends on the ionisation energy, on the charge-collection e ffi ciency, and on the energy released in theactive volume.We propagate to k the uncertainty of 0 .
03 eV on theionisation energy; this contributes a relative systematicuncertainty of 0 . ffi cient diode in collecting allgenerated charge at 100 V bias. This assumption is sup-8orted by I - V measurements under irradiation on thediode, and the uncertainty on this assumption is con-sidered negligible.The released energy is proportional to the active vol-ume of the diode. In the simulation, we changed theactive surface and the depletion thickness by ± . and ± µ m, respectively, to obtain two variations, cor-responding to a minimum and a maximum active vol-ume. For both cases, we computed the released ener-gies as a function of the source-detector distance, andthe resulting expected ratio R exp from Eq. (8). We takethe di ff erence between each new value of R exp and itsnominal value, and we consider the largest di ff erence δ R exp to assign a relative uncertainty δ R exp / R exp . This ispropagated to δ k / k and contributes 4% to the systematicuncertainty.In a similar manner, we compute the contributionassociated to the uncertainty on the thickness of thealuminium packaging that impacts the released energy.We varied in simulation the thickness of the aluminiumcover by ± µ m, which is the uncertainty associated tothe cover used in the diode packaging. Other sourcesthat a ff ect the released energy, such as a 0.1 µ m layer ofsilicon oxide on the surface (the diode area is metallizedonly around the edge), are considered negligible.The value of R exp depends also on the ionisation en-ergy of the diamond detector, on the released energy in-side its active volume, and on its charge-collection e ffi -ciency. Departures of all these factors from the valuesassumed in the calculation of the estimated current areaccounted for by the characteristic constant G . We no-tice that any variation on G due to an uncertainty onthe value of the ionisation energy, or that on the detec-tor volume, are counterbalanced by a variation of F inthe definition of k in Eq. (4). Therefore, no systematicuncertainties are computed for these two sources.The aluminium packaging a ff ects the estimation ofthe released energy in the diamond detectors in a sim-ilar fashion as for the diode, and the impact from theuncertainty on its thickness is computed with the sameprocedure. An uncertainty of 20 µ m on the thickness isconsidered in this case, to account for the di ff erent in-dividual covers of the diamond detectors. The resultingsystematic uncertainty is δ k / k = ff ect the released energy, e.g. the uncertainty on thevolume of the electrodes of the diamond detectors, areconsidered negligible.As for what concerns the charge-collection e ffi ciency,a departure from the assumed value of 100% is includedin the characteristic constant G measured for each de-tector. A possible source of uncertainty is due to smallfluctuations of the voltage provided by the power sup- ply, which presented variations of δ V / V ≈ . I - V results presented in Sect. 4.2, only sub-percentchanges of the e ffi ciency are expected for 0 . k is considered negligible.The statistical uncertainty from the size of the sim-ulated samples contributes a negligible uncertainty too.Uncertainties related to other assumptions entering thesimulation, such as the transport model used in FLUKAfor the β electrons, are found to be smaller than 1%,as these contributions are greatly reduced in the ratio ofEq. (8). For the same reason, an imprecise modellingof the β source (material, density, fraction of radioac-tive nuclei) contributes only a sub-1% systematic un-certainty. By using the silicon diode as a reference, we get ridof the knowledge of the source activity to determine G .Alternatively, the source activity can be measured withthe silicon diode through Eq. (7). In this case, we find anactivity of about 4 . . G would becomputed by the ratio of the current measured from thediamond detector and that computed from Eq. (7). Inthis case, the mean values of G would be about 1 . . I - V measurements reported in Sect. 4.2. Thiswould suggest either a large uncertainty on the nominalactivity, or a bias on the simulation of the experimentalsetup, which is greatly reduced in our method by usingthe diode as a reference through Eq. (8).For two detectors, we also carried out two checks ofthe value of k using photons as a source of radiation.In the first check, we exploited soft photons, with aknown energy spectrum averaging about 15 keV, pro-vided by a small X-ray tube [28]. We measured thesignal-to-reference ratio of currents at a fixed source-detector distance, using the same silicon diode em-ployed in the measurement with the β source. The X-ray flux yielded currents between 0 .
02 nA and 0 .
25 nA.We compared the measured ratio with that estimated bymeans of a full simulation through FLUKA, to obtain G from Eq. 9. The measured values of G are in agreementwith those obtained with the β radiation.9he second check has been aimed at exploring doserates much higher than those provided by the β source.We used a source of γ rays from Co decays, with ener-gies of 1 .
17 MeV and 1 .
33 MeV, available at ISOF-CNRin Bologna. The source (Gammacell 220) has a cer-tified dosimetry performed with alanine dosimeters in2007 by Risø National Laboratory. The dose rate mea-sured by two diamonds is in agreement with the certi-fied dose rate, scaled by the Co reduced activity at thetime of the test due to radiative decay. A very good lin-ear dependence between the measured currents and thedose rates has been observed, spanning a range between6 nA and 130 nA corresponding to dose rates between0 . / s and 4 . / s. The proportionality constantsbetween the current and the dose rates are found to bein very good agreement with the calibration factors k .This builds confidence on the validity of the measuredcalibration factors over a range spanning from tens ofnrad / s to some rad / s.
5. Conclusions
We chose sensors based on single-crystal diamond asdosimeters for a beam-loss monitor at the SuperKEKBelectron-positron collider. The diamond crystals, grownby the chemical vapour deposition, are equipped withTi + Pt + Au electrodes and assembled in dedicated pack-ages. We presented the test and characterisation of asample of 28 sensors.Charge-carrier properties and average ionisation en-ergies, as measured by the transient-current technique,are found to be su ffi ciently homogeneous across the setof sensors for our purpose. For about a half of our detec-tors, hysteresis e ff ects and unstable currents under con-stant irradiation have been observed for bias voltagesof a specific polarity; stable and reproducible values ofthe current for the opposite polarity. The other half ofthe sensors exhibit a symmetric response with respectto bias voltage polarity. We determined the best polarityfor each detector, and we found the optimal bias voltageto be | V | =
100 V, for which a charge-collection e ffi -ciency close to 100% has been observed.We determined the current-to-dose-rate calibrationfactors by irradiating the sensors with β electrons from Sr decays, and by comparing the measured currentwith that expected from a simulation, used to estimatethe dose rate due to the β irradiation. We employed asilicon diode, irradiated under same conditions, as a ref-erence in order to greatly reduce uncertainties related tothe β -source activity and to the simulation, that wouldotherwise spoil the accuracy of the calibration. We ob-tained detector-dependent calibration factors with a rel- ative uncertainty of 8%. The calibration has been val-idated with X and γ radiation for dose-rate spanning arange from tens of nrad / s to some rad / s.The monitor system based on these detectors hasbeen proving crucial for running the Belle II experi-ment in safe conditions during the last two years [13],while beam-background radiation has been continu-ously evolving with the progress of the SuperKEKB col-lider towards unprecedented values of luminosity. Thetest and calibration procedures reported here representvaluable resources for the preparation of eight new dia-mond detectors that will be installed with an upgrade ofthe Belle II silicon vertex detector in 2022. Acknowledgements
This research was supported by Istituto Nazionale diFisica Nucleare (INFN) in the framework of the Belle IIexperiment. Motivation for improving our calibrationprocedures was enhanced by useful discussions withSuperKEKB and Belle II colleagues. We gratefullyacknowledge the contribution of Francesco Di Capua(University Federico II and INFN Naples, Italy) in set-ting up measurements with the Co source.
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