*,1,2, moritz guthoff2, anne dabrowski2, wim de boer · device based on 32 poly-crystalline (pcvd)...

physica status solidi

Description of radiation damage indiamond sensors using an effectivedefect modelFlorian Kassel*,1,2, Moritz Guthoff2, Anne Dabrowski2, Wim de Boer1

1 Institute for Experimental Nuclear Physics (IEKP), KIT, Karlsruhe, Germany2 CERN, Meyrin, Switzerland

Received XXXX, revised XXXX, accepted XXXXPublished online XXXX

Key words: Diamond detector, Radiation damage, Polarization, Trap model, CMS.

∗ Corresponding author: e-mail [email protected], Phone: +41 75 411 7486

The Beam Condition Monitoring Leakage (BCML) sys-tem is a beam monitoring device in the CMS experimentat the LHC consisting of 32 poly-crystalline (pCVD)diamond sensors. The BCML sensors, located in ringsaround the beam, are exposed to high particle ratesoriginating from the colliding beams. These particlescause lattice defects, which act as traps for the ionizedcharge carrier leading to a reduced charge collection ef-ficiency (CCE). The radiation induced CCE degradationwas however much more severe than expected from lowrate laboratory measurements. Measurement and simula-tions presented in this paper show that this discrepancyis related to the rate of incident particles. At high par-ticle rates the trapping rate of the ionization is stronglyincreased compared to the detrapping rate leading to anincreased build-up of space charge. This space chargelocally reduces the internal electric field increasing thetrapping rate and hence reducing the CCE even further.

In order to connect these macroscopic measurementswith the microscopic defects acting as traps for the ioni-zation charge the TCAD simulation program SILVACOwas used. It allows to introduce the defects as effectivedonor and acceptor levels and can calculate the electricfield from Transient Current Technique (TCT) signalsand CCE as function of the effective trap properties, likedensity, energy level and trapping cross section. Aftereach irradiation step these properties were fitted to thedata on the electric field from the TCT signals and CCE.Two effective acceptor and donor levels were needed tofit the data after each step. It turned out that the energylevels and cross sections could be kept constant and thetrap density was proportional to the cumulative fluenceof the irradiation steps. The highly non-linear rate depen-dent diamond polarization and the resulting signal losscan be simulated using this effective defect model and isin agreement with the measurement results.

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1 Introduction The CMS Beam Condition MonitorLeakage (BCML) system at LHC is a beam monitoringdevice based on 32 poly-crystalline (pCVD) diamond sen-sors. The BCML sensors measure the ionization currentcreated by beam losses leaking outside the beam pipe, e.g.by scattering on the residual gas or beam collimators. Incase of very intense beam loss events, which could poten-tially damage the CMS detector, the BCML system triggersthe LHC beam abort leading to a beam dump to protect theCMS detector.Although diamond sensors were expected to be radiationhard, the charge collection efficiency (CCE) dropped much

faster [1,2,3] in this high particle rate environment in com-parison to low particle rate laboratory measurements [4]and simulations [5,6], see Fig. 1. Here the charge collec-tion distance (CCD) of the BCML sensors with an averagethickness of d = 400µm is plotted as funtion of particlefluence. The CCD defines the average drift length of thecharge carriers before beeing trapped. After a total fluenceof Φ = 16 × 1014 p24GeV/cm2 the CCD of the pCVD di-amonds used at the CMS detector dropped about twice asfast compared to the expectations based on laboratory mea-surements. This discrepancy in CCD between the real ap-plication in a particle detector and laboratory experiments


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Figure 1 Comparison between expected (green) and mea-sured (blue) CCD, or equivalently the radiation inducedsignal degradation of pCVD diamond sensors used at theCMS detector in the BCML system. The expected signaldegradation is based on measurements done by the RD42collaboration [10]. The measured curve shows a fit to theexperimental data [11].

can be explained by the rate dependent polarization [7,8,9]of the diamond detector, as was deduced from detailed lab-oratory measurements and simulations. The rate dependentdiamond polarization describes the asymmetrical build-upof space charge in the diamond bulk, which leads to a lo-cally reduced electric field configuration. The charge car-rier recombination is increased in this low field region re-sulting in a reduced CCE of the diamond detector. At highparticle rates the trapping rate of the ionization is evenmore increased compared to the de-trapping rate leadingto an increased build-up of space charge. The increasedamount of space charge causes an even stronger local re-duction in the internal electric field and hence reduces theCCE further. The study presented in the following is anupdate to the work presented in [7].

2 Effective defect model describing the radiationinduced signal degradation of diamond detectorsWithin the scope of this publication an effective defectmodel will be introduced, capable of explaining the radia-tion induced signal degradation of diamond detectors. Thiseffective defect model was found by optimizing simula-tions to experimental Transient-Current-Technique (TCT)[12,13] and CCE measurement results of an irradiationcampaign with high-quality single-crystal CVD (sCVD)diamonds detectors. The basic properties of this effectivedefect model like energy level and charge carrier cross sec-tions for electrons and holes are based on [7].

2.1 Diamond irradiation campaign A dedicated ir-radiation campaign was carried out to gain quantitativeunderstanding of the diamond polarization affecting thecharge collection efficiency of diamond detectors. The di-amond samples were irradiated stepwise up to a maximumfluence of Φ = 30.1×1013 n1MeV,eq./cm2. After each ir-radiation step the electrical properties of the diamond sen-

sors were studied using the TCT method for an indirectelectric field measurement and by measuring the chargecollection efficiency. The diamond polarization, crucial inunderstanding the irradiation damage, is modifying the in-ternal electrical field, which can be measured using TCT.The CCE measurements were used to study the reduced de-tector efficiency due to these electrical field modifications.

In order to measure the build-up of polarization in thediamond for a given radiation damage the following mea-surement procedure is used for the TCT and CCE measure-ments:

1.The diamond is exposed during the entire measurementto a constant ionization rate by a 90Sr source creatingelectron-hole pairs in the entire diamond bulk filling upthe traps. In the steady-state the trapping and detrap-ping rates are in equilibrium. According to the simula-tions discussed below about 55 % of the effective deeptraps are filled.

2.In order to remove any residual field and set the dia-mond into a unpolarized state, the sensor is exposedto the 90Sr source for a duration of 20 minutes with-out bias voltage applied. A homogeneous trap filling inthe diamond bulk, and hence an unpolarized diamondstate, is reached.

3.The bias voltage is ramped up fast (tramp ≤ 10 s) andthe measurement is started immediately (t = 0 s).

4.The diamond starts to polarize as soon as bias voltageis applied. The measurement is performed over an ex-tended period of time (t > 3000 s) until the diamond isfully polarized and the measurement results are stable.

Four new single crystalline diamonds of highest qual-ity ’electronic grade’ corresponding to small nitrogen andboron impurities ([N ] < 5 ppB and [B] < 1 ppB), pro-duced by Element6 [14] were used to investigate the ra-diation induced signal degradation. The diamond sampleswere irradiated stepwise with either 23 MeV protons orwith neutron particles with an energy distribution up to10 MeV [15]. More detailed information to the diamondsamples, the TCT and CCE measurement setup can befound in [7].

TCT measurement results The TCT measurementsof the different irradiated diamond samples are shown inFig. 2 for the hole carrier drift. The expected rectangu-lar TCT pulse shape, indicating a constant electrical field,is measured for the un-irradiated diamond sensor and re-mains stable as function of exposure time to the 90Srsource. This rectangular TCT pulse shape is measured aswell for the irradiated diamond samples immediately af-ter the TCT measurement has been started (t = 25 s) eventhough radiation damage leads to an increased amount ofdefects trapping free charge carriers. In this initial mo-ment the diamond is in a pumped state and the defectsare homogeneously ionized leading to a neutral effectivespace charge. Applying of bias voltage changes howeverthe charge carrier distribution resulting in an inhomoge-neous trapping. Trapped charge carriers, acting as space


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Figure 2 TCT measurements of the hole charge carriers at an electrical field of E = 0.36 V/µm for different irradiationdamages. The increased radiation damage causes an increased build-up of space charge as function of exposure time to the90Sr source.

charge, are modifying the electric field configuration andleading to a modified TCT pulse shape. Increased radi-ation damage leads to an even stronger TCT pulse mo-dification as function of the ionization duration. Further-more, a faster transition to the final stable TCT pulse andhence to the final electrical field configuration is measuredwith respect to increased radiation damage. These TCTmeasurements demonstrate the increased build-up of spacecharge which leads to a strongly modified electric field dis-tribution caused by radiation damage. The TCT measure-ment results for the electron drift are in agreement withthe hole drift measurements and are therefore not explic-itly discussed here. A direct comparison of the electron andhole drift can be found in [7].

CCE measurement results The charge collectionefficiency of the diamond sensors used in the irradiationcampaign was measured regularly at the CCE setup atDESY in Zeuthen [16] using minimum ionizing particles(MIP). The CCE measurement results are discussed in thefollowing as function of measurement time, during whichthe diamond is exposed to an ionization source (90Sr). Theinfluence of the ionization source to the CCE measurementresult is shown in Fig. 3 for different radiation damages.The un-irradiated diamond sample is not influenced by theionization source and remains constant at a CCE of 100%.The radiation damaged diamond sensors are however af-fected by the ionization source. A steep decrease of the ini-tial measured CCE is observed. The time constant of thisreduction matches the time constant of the TCT pulse mod-ification. Hence the modified electric field distribution di-rectly affects the CCE and demonstrates the importance ofthe build-up of space charge in diamond sensors in order to

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understand the effects of radiation damage. This direct cor-relation of the TCT pulse modification and the measuredCCE value is discussed in more detail in [7].

The stabilized CCD measurements are plotted inFig. 4 as function of fluence for an electrical field ofE = 1.0 V/µm. The CCD as function of radiation damagecan be described by the following equation:

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Table 1 Physical parameters of the effective recombinationcenters [7]. Both effective recombination centers eRC1/2are present as acceptor- and donor-like traps.

Trap name eRC1 eRC2

Energy level Et (eV) 1.8 0.83Cross section σe (×10−14 cm2) 0.7 2.0Cross section σh (×10−14 cm2) 0.7 1.0

Irradiation studies done by the RD42 collaboration withpCVD diamond sensors determined a radiation constant ofk = 6.5×10−19 cm2/µm [10] for irradiation with 24 GeVprotons. The conversion of the radiation damage createdby n1MeV to p24GeV is caluclated using NIEL [17], whichis increased by a factor of 3.59.

Based on the measurements done within this paper aradiation constant of k = (8.2 ± 0.5) × 10−19 cm2/µmwas found which is in reasonable agreement with the RD42value.

2.2 TCAD simulation of radiation damage In or-der to create a defect model for diamond sensors and gainquantitative understanding of the radiation induced signaldegradation, the diamond sensor was modeled with thesoftware Silvaco TCAD [18]. Besides the electrical dia-mond properties, like e.g. band gap or mobility parameters,radiation induced lattice defects can be taken into accountby introducing effective deep traps acting as recombinationcenters. The properties of these defects, like energy levels,capture cross section for electrons and holes, were foundby optimizing the simulation of TCT and MIP pulses tomatch the experimental data and are listed in Table 1, fur-ther information can be found in [7]. The simulated MIPpulses were used to calculate the charge collection effi-ciency of the diamond sensor. The TCAD simulation in-cluded furthermore a detailed implementation of the geo-metrical properties of the TCT and CCE measurement se-tups, affecting e.g. the energy deposition of the ionizationsources in the diamond sensors.

Optimization of the effective defect densities tothe TCT and CCE measurements Within the scope ofthe irradiation campaign TCT and CCE measurements for12 different irradiation steps were obtained. The TCT andCCE simulation were fitted to each TCT and CCE mea-surement and a uniquely optimized trap configuration wasfound with respect to the particular fluence. The traps wereoptimized by adjusting the trap density of the effectiverecombination centers (ρeRC1 and ρeRC2), since the trapproperties like energy level or cross section should not beaffected by the fluence. In Fig. 5 the simulated and mea-sured TCT pulses of the hole charge carrier drift are shownfor different fluences. The TCT simulation were optimizedto the measurement results at the lowest measurable biasvoltage, where the polarization is affecting the electric fieldmost. The build-up of the internal polarization field is soquick for higher fluences that a reliable TCT measurementat low bias voltages was not possible. The TCT measure-ments were therefore done at increased bias voltages.

The simulated MIP signal is shown in Fig. 6a,b as func-tion of the ionization time (Texp) for two different fluences.The MIP signal was integrated to calculate the charge col-lection efficiency of the simulation result. The MIP signalfor the sensor with the lowest fluence is simulated for anelectrical field of E = 0.18 V/µm. The build-up of spacecharge leads to a two peak structure in the MIP pulse shape,which results in an overall reduced charge collection ef-ficiency. The MIP particle for the highly irradiated dia-mond sample is simulated at an increased electrical fieldof E = 0.72 V/µm. The build-up of space charge is aswell influencing the signal shape of the MIP particle re-sulting in a reduced charge collection efficiency. Based onthe simulated MIP signals, the calculated charge collectionefficiency is shown in Figs. 6c,d as function of exposuretime to the 90Sr source. The simulated charge collectionefficiency is in agreement with the experimental measuredCCE values.

2.3 Effective defect model as function of radi-ation damage The optimization of the effective defectmodel to the experimental measurement results shown inFig. 5 and 6 are representative for the fitting of the defectmodel for each of the 12 different irradiation steps. Theoptimized trap densities for both effective recombinationcenters eRC1 and eRC2 for each irradiation step are plot-ted as function of the radiation damage caused by the par-ticle fluence of Φ (p24GeV eq./cm2) in Fig. 7. The error tothe absolute radiation damage in the x-dimension is due tothe limited accuracy of the irradiation facilities. The accu-racy of the proton irradiation is ±20% and the accuracy ofthe neutron irradiation is ±30%. The linear regression ofthe trap densities with respect to the total radiation damagegives:

ρeRC1 = Φ · 0.0252 (cm−1) + 9.40 × 1011 (cm−3), (2)

ρeRC2 = Φ · 0.0215 (cm−1) + 6.67 × 1011 (cm−3), (3)



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Figure 5 Comparison between the TCT simulation and measurement for the hole charge carrier drift for different fluencesvarying from Φ = 0.6 × 1013 n1MeV eq.cm−2 to Φ = 30.1 × 1013 n1MeV eq.cm−2 in panel a) to f). The defect densitiesρeRC1 and ρeRC2 were optimized for each fluence to match the measurement results.

with Φ as (p24GeV eq./cm2) particle fluence. A possibil-ity to verify this effective trap model is the simulation ofthe radiation induced signal degradation in terms of chargecollection efficiency as function of radiation damage, seeFig. 8. Based on this degradation the radiation constantcan be calculated using Eq. 1 and be compared to the ra-diation constant found by the experimental measurements.The CCE of the diamond sensor is simulated for a typi-cal particle rate environment created by a 90Sr and at anelectrical field of E = 1 V/µm.

The simulated charge collection distances matchesthe experimental measurement results for the laboratoryrate environment. Based on the simulation a radiationconstant of ksim. = (8.9 ± 1.1) × 10−19 cm2µm−1

is calculated. The simulated radiation constant is inagreement with the experimental measurement result ofkmeas. = 8.2 × 10−19 cm2µm−1. This is however notsurprising since the effective defect model was optimizedto these particular measurements.

The effective defect model is now used to simulateincreased particle rate environments. In laboratory mea-surements the particle rate created by a 90Sr source typ-ically creates a particle rate of f90Sr = 0.15 GHz/cm3

[7]. The particle rates at the CMS detector are signifi-cantly higher and depend on the exact detector location.For the BCML detector location a MIP particle rate offBCML1 ≈ 10 GHz/cm3 is estimated based on FLUKA[19,20] simulations. The simulated charge collection dis-

tance for the increased particle rate is indicated in Fig. 8in blue dashed lines. The increased particle rate environ-ment leads to a strongly reduced charged collection dis-tance. After a radiation damage, corresponding to a particlefluence of Φ = 10 × 1014 p24GeV/cm2, the charge collec-tion distance simulated for the particle rate environmentat the BCML location is reduced by 53% compared tothe 90Sr particle rate environment. Based on these simu-lation results a three times increased radiation constant ofksim. = 27.7 × 10−19 cm2µm−1 is calculated. This ra-diation constant can be directly compared to the radiationconstant measured with the BCML pCVD diamond sen-sors at the CMS detector (indicated in solid blue), since theradiation constant is independent of the diamond material(sCVD or pCVD) used to measure the radiation inducedsignal degradation [10]. The different diamond material isonly reflected in a different initial charge collection dis-tance value, compare sec. 2.1.

The calculated radiation constant based on the BCMLdetector degradation of kmeas. = 56.0 × 10−19 cm2µm−1

is still by a factor of two higher than the simulation result,see Table 2. This discrepancy can be caused e.g. by an un-derestimation of the radiation damage, which is based ona FLUKA simulation. Furthermore, the BCML sensors areexposed to a mixed particle field that could contribute tonon linear degradation effects of the sensors.

A radiation damage of Φ = 1.5 × 1015 p24GeV/cm2

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Figure 7 The optimized trap density of eRC1 (blue) andeRC2 (green) for the different irradiation damages of theproton and neutron irradiated diamond sensors. As ex-pected, the trap densities of both effective recombinationcenters increase linearly with the irradiation damage.

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Figure 10 Simulation of the CCD as function of fluencefor a diamond sensor exposed to a 90Sr source. The radi-ation induced signal degradation was simulated for threedifferent electrical fields at which the diamond detectorsare operated: E = 0.18 V/µm in red, E = 0.36 V/µmin green and E = 1.00 V/µm in blue. Based on the sim-ulated CCD as function of radiation damage, the standardradiation model was fitted to the data, indicated in dashedlines.

Table 2 Overview of the measured and simulated radiationconstants of diamond sensors for different particle rate en-vironments. The diamond sensors were operated at an elec-trical field of E = 1.0 V/µm.

Particle rate kmeas. ksim.

environment (×10−19 cm2/µm) (×10−19 cm2/µm)90Sr 8.2± 0.5 8.9± 1.1

CMS 56.0± 4.1 27.7± 0.2

90Sr and BCML particle rate environment, respectively.The corresponding electrical field configurations of thediamond sensors operated at an electrical field of E =1 V/µm are shown in Fig. 9a. The expected electric fieldmodification due to an almost linear build-up of spacecharge (Fig. 9b) in the 90Sr particle rate environment leadsto a local minimum in the electric field. This results in a

Table 3 Overview of the simulated radiation constants ofthe diamond sensor operated at different electrical fields.The diamond was simulated for a particle rate environmentcreated by a 90Sr source.

Electrical field E Radiation constant k(V/µm) (×10−19 cm2/µm)

1.00 8.9± 1.1

0.36 41.5± 2.6

0.18 101.0± 15.7

slightly increased recombination rate (Fig. 9c) leading tothe reduced CCE. The electrical field is significantly modi-fied at the increased particle rate environment of the BCMLdetector location, see Fig. 9a in red. The highly increasedbuild-up of space charge leads to a suppression of the elec-trical field in about ∼ 230µm, that is about half of thesensor thickness. In this region the charge carrier recombi-nation is strongly increased and explains the poor chargecollection efficiency of ∼ 30%.

3 Simulation of radiation damage for differentelectrical fields In this section the effective defect modelis used to analyze the charge collection distance as func-tion of the electric field at which the sensor is operated. InFig. 10 the radiation induced signal degradation is simu-lated for three different electric fields of E = 1.00 V/µm,E = 0.36 V/µm andE = 0.18 V/µm. Based on the simu-lation results the radiation constant is calculated and listedin Table 3. Comparison the radiation constants demon-strates the importance of preferably high operational elec-tric fields. A three times reduced electric field from 1 to0.36 V/µm leads to an increased radiation constant by afactor of ∼ 4.7. Furthermore, reducing the electric field bya factor of 5 to an electric field of E = 0.18 V/µm leadsto a ∼ 11.3 times increased radiation constant. Hence,the diamond polarization leads to a non-linear increase inthe radiation induced signal degradation as function of theelectric field at which the diamond is operated.



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3 s−

1 ) E = 0.18 V/µmE = 0.36 V/µmE = 1.00 V/µm

c) Normalized recombination

Figure 11 Simulation of damaged diamond sensors with a fluence of Φ = 2 × 1015 p24GeV/cm2 in a 90Sr particle rateenvironment for three different electrical fields: E = 1.00 V/µm (blue), E = 0.36 V/µm (green) and E = 0.18 V/µm(red).

A more detailed understanding of the diamond polar-ization leading to the severe signal degradation is obtainedby analyzing the corresponding electric field and spacecharge inside the diamond sensors for a particular fluence,see Fig. 11. Although the total amount of space charge isreduced for the lower electrical field configurations, the im-pact to the overall electric field inside the diamond sensoris strongly increased. This leads to the suppression of theelectric field in more than half of the detector thicknessleading to a strongly increased charge carrier recombina-tion, see Fig. 11c.

4 Conclusion The radiation induced signal degrada-tion of diamond detectors can be described using the ef-fective defect model presented in this paper. This defectmodel was found by optimizing TCT and CCE simulationsto the experimental measurement results of different irra-diated diamond sensors. The simulation and measurementresults underline the crucial role of the polarization effectto understand the radiation induced signal degradation ofdiamond detectors. The build-up of space charge leads to alocally reduced electric field at which the increased chargecarrier recombination leads to a reduced CCE. Using theeffective defect model to extrapolate the reduction of theelectric field by the polarizing space charge inside the sen-sor to the high rate environment of the CMS detector ex-plains the poor performance of the diamond sensors in thisharsh environment of the LHC.

The effective defect model showed furthermore the im-portance of high bias voltages in order to minimize the ra-diation induced signal degradation. At reduced bias volt-ages the diamond polarization leads to a non-linear in-crease in the radiation induced signal degradation. Henceone should try to increase the high voltage breakthroughvoltage, so one could operate with an electric field fromthe bias voltage well above the electric field from the spacecharge. Alternatively, the switching of the bias voltage witha few Hz, so that space charge would switch direction as

well and could not build-up inhomogeneously could avoidthe diamond polarization.

Acknowledgements This work has been sponsored by theWolfgang Gentner Programme of the Federal Ministry of Edu-cation and Research and been supported by the H2020 projectAIDA-2020, GA no. 654168 (http://aida2020.web.cern.ch/).

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