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Nuclear Instruments and Methods in Physics Research A 587 (2008) 125–129

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Numerical simulations for diamond sensors as real-timeX-ray skin dosemeters; comparison to silicon

M. Junga, J. Morela,�, P. Siffertb

aLaboratoire INESS (UMR 7163 du CNRS), 23 rue du Loess, BP 20 CR, 67037 Strasbourg Cedex 2, FrancebEURORAD, 23 rue du Loess, BP 20 CR, 67037 Strasbourg Cedex 2, France

Received 23 October 2006; received in revised form 21 December 2007; accepted 21 December 2007

Available online 31 December 2007

Abstract

Simulation results from Monte Carlo codes developed in our laboratory are used to analyze and improve detector responses against

unknown high flux X-ray spectra exposures, as encountered in medicine. The algorithms are applied to diamond and silicon based

dosemeters studies. The simulations are focused on real-time skin dosimetry for X-ray energies between 10 and 200 keV. The detector

response is simulated as an induced collected charge under high fluence irradiation, to control patient injury.

The dose equivalent response at 0.07mm skin depth is calculated for a large set of diamond sensors. Their sensitivity, accuracy and

angular response dispersion are presented. The quasi-tissue equivalent property of the diamond material allows maximum response

uncertainties lower than 10% at least up to 75� opening incidences. For such monitors the amount of collected charges shows an

asymptotic maximum limit near 80 nCSv�1 per mm3 sensor interaction volume. These performances are discussed, and compared to

those of silicon diodes.

r 2008 Elsevier B.V. All rights reserved.

PACS: 29.40.Wk; 81.05.Cy; 87.52.�g; 87.53.Bn; 87.53.Wz

Keywords: X-ray; Diamond; Silicon; Skin dosimetry; Monte Carlo numerical simulation

1. Introduction

Sensors based on diamond are investigated to measurehigh level X-ray doses at the body surface for real-timemedical exposure controls. In this framework the detectorresponse is analyzed as a current measurement attached tothe radiation. Indeed large fluence controls are necessarysince many patient diagnostics or treatments need radio-graphic investigations or radiotherapic X-ray irradiation.Above certain dose intensities, skin injuries appearpresenting dangerous secondary effects for the exposedpatient [1]. In addition, the acceptable accumulated annualdose has been restricted by new regulations [2,3] requiringfor real-time measurements and encouraging their imple-mentation in high risk environments.

e front matter r 2008 Elsevier B.V. All rights reserved.

ma.2007.12.028

ing author.

ess: jacques.morel@iness.c-strasbourg.fr (J. Morel).

Our previous simulations performed for silicon anddiamond sensor responses to large absorbed air kerma andambient dose equivalent irradiations achieved good experi-mental comparisons [4,5]. In this paper they are extendedto skin dose monitoring of normal and open angle X-rayirradiations between 10 and 200 keV energy.

2. General procedure

The investigation consists in numerical simulations of so-called detection channel responses associating filters anddetectors. The output signal of these channels is a chargecollected per unit dose, noted QðF Þ, associated with thefilter F. Without filter, QðF Þ becomes Q0. The aim of themethod is to achieve a flat, i.e. constant, dose responseQðF Þ over the whole X-ray energy range of interest: theQðF Þ fluctuations being kept within the recommendedICRP agreement of less than 30% uncertainty [6]. If this

ARTICLE IN PRESSM. Jung et al. / Nuclear Instruments and Methods in Physics Research A 587 (2008) 125–129126

requirement cannot be achieved, it becomes necessary tostudy a response QðMÞ of a more complex monitor M,associating optimized weighted signals from two sensorfiltrations:

QðMÞ ¼ aQðF1Þ þ ð1� aÞQðF2Þ.

Most aspects of the calculation method can be found in ourprevious papers referring to photon dose controls bysilicon or diamond [4,5,7,8]. Our codes (MCGET series),are of the Monte Carlo type, processing each individualincident photon interaction with the crossed matter in athree-dimensional geometric system. The detection channelis a planar stack of metallic filters covering the sensor. Thephoton incidence is chosen randomly over the wholeparallepipedic shaped detector front surface (equal to1 cm2 in all the simulations carried out here).

The induced charge is calculated for each individualinteraction, during 1ms integration time. The chargesinduced by a fixed number of incident photons are summedand renormalized per unit fluence. Absorbed air kermadose [9] and dose equivalent conversion coefficients at0.07mm skin depth [10] are attached to each incidentphoton energy. They convert the number of charges(coulombs) per unit fluence into coulombs per sievertðnCSv�1Þ.

Table 1

Characteristics of the studied sensors

Index Sensor

material

W ðmm) Bias

voltage (V)

t ðmsÞ CCDe=W

D03 Diamond 10 1.5 0.001 2.7

D33 Diamond 10 1.5 1 2.7�103

D04 Diamond 30 30 0.001 6

D44 Diamond 30 30 1 6� 103

D05 Diamond 30 3.6 0.001 0.72

D05.2 Diamond 30 3.6 0.1 72

D55 Diamond 30 3.6 1 720

D02 Diamond 300 3.6 0.001 7.2 �10�3

D02.1 Diamond 300 30 0.001 6 �10�2

D02.2 Diamond 300 60 0.001 0.12

D02.3 Diamond 300 100 0.001 0.20

D02.4 Diamond 300 150 0.001 0.30

D02.42 Diamond 300 150 0.1 30

D02.5 Diamond 300 500 0.001 1

D02.51 Diamond 300 500 0.01 10

D02.52 Diamond 300 500 0.1 100

D22 Diamond 300 3.6 1 7.2

D01 Diamond 300 300 0.001 0.6

D11 Diamond 300 300 1 600

D09 Silicon 300 0 Holes lifetime: 100msD99 Silicon 300 3.6 Holes lifetime: 100msD9 Silicon 300 3.6 Damaged diode

All detectors are assumed to have a 1 cm2 active area. CCDe, local free

electron charge collection distance; W , sensor thickness; t, carriers

lifetime.

The calculations are essentially devoted to diamondsensors but comparisons are also performed with themore conventional N-type silicon detectors. The set ofsensors used for the present calculations are shown inTable 1.

3. Charge collection and detection accuracy

Many stacks of material have been investigated. Thecollected amount of charges QðF Þ is calculated for severalthicknesses of Al, Fe, Sn filters covering either the diamondor silicon sensors. The configuration which is selected is theso-called best one, showing the minimal QðF Þ responsefluctuations over the 10–200 keV X-ray energy range, i.e. aflat response vs energy.

3.1. Diamond sensor detection efficiency and response

accuracy

As opposed to the kerma dose control [5], which needslight filtering, the best detection channels for diamond areall calculated for sensors without any filter, QðF Þ ¼ Q0

which points out the tissue equivalent behavior of this lightZ material. An example of Q0 variations against X-rayenergy is shown in Fig. 1. All curves correspond to the lesssensitive sensor within each category. Table 2 summarizesboth mean response hQ0i limits inside each sensor indextype. A slight accuracy improvement with increasingangular dispersion can be noted.Furthermore, to avoid the thickness parameter W, all

Table 1 sensor responses Q0 are renormalized per unitsensitive volume and called q0.

200

400

600

800

1000

1200

0

X-ray energy in keV

Q0

: nC

.Sv-1

D03D05D04D02D01

25 50 75 100 125 150 175 200 225 250

Fig. 1. Diamond based sensor response curves, Q0, vs X-ray energy drawn

for the less sensitive Table 1 detector of each index category.

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Table 2

Diamond mean response hQ0i calculated for several open angle irradiations Y

Detector Y� 0� Y� 30� Y� 60� Y� 75�

CB Er (%) hQ0i (nCSv�1) CB Er (%) hQ0i (nCSv�1) CB Er (%) hQ0i (nCSv�1) CB Er (%) hQ0i (nCSv�1)

D03 28 34 24 37 20 46 16 59

13.9 12.4 10.9 8.3

D33 26 42 23 45 19 56 16 71

13.2 12.5 9.6 8.2

D04 7 138 6 146 4 182 4 228

3.8 3.7 2.7 2.6

D44 7 150 5 162 4 198 5 249

4.3 3.1 2.8 3.0

D05 9 69 8 75 5 94 4 118

6.1 5.1 3.2 2.7

D55 6 154 5 165 5 198 6 249

3.2 2.8 3.3 3.5

D02 16 106 11 122 10 148 9 182

10.0 8.1 7.6 7.0

D22 16 1586 16 1652 17 1944 19 2324

9.4 9.8 11.1 13.0

D01 14 885 14 927 15 1099 17 1324

8.6 9.0 10.0 11.7

D11 16 1674 17 1747 18 2059 20 2461

9.9 10.3 11.4 13.5

CB, percentage of maximum Q0, response fluctuation around the mean value; Er, relative least mean square error for X-ray energies between 10 and

200 keV.

0

10

20

30

40

50

60

70

10-3 10-2 10-1 1 10 102 103 104

CCD / W

<q0>

: nC

.Sv-1

.mm

-3

10 µm

30 µm

300 µm

Fig. 2. Mean sensor responses hq0i per unit interaction volume calculated

for normal X-ray irradiation incidence (Y ¼ 0�) on all Table 1 diamond

detectors.

0

20

40

60

80

100

10-3 10-2 10-1 1 10 102 103 104

CCD / W

<q0>

: nC

.Sv-1

.mm

-3

10 µm

30 µm

300 µm

Fig. 3. Mean sensor responses hq0i per unit interaction volume calculated

for Y ¼ �75� X-ray irradiation incidence on all Table 1 diamond

detectors.

M. Jung et al. / Nuclear Instruments and Methods in Physics Research A 587 (2008) 125–129 127

The values are given as a function of the undimen-sioned parameter: CCD=W , where CCD ¼ m � t � E withE ¼ V=W .

CCD can be understood as being the mean carrier driftlength and is roughly related to a local charge collectiondistance. It depends on the carrier mobilities m set equal to1800 and 1200 cm2 s�1 V�1 for electrons and holes,respectively [11]. As mentioned previously [5], other values

are available in the literature which also propose lifetimes tthat are mostly within Table 1 boundary values. Theselarge variations of t result from the different kinds ofdiamond used, natural, CVD and with defect structure.One can observe a monotonous increase of the responsewith asymptotic values near 56 nCSv�1 mm�3 for normalirradiations (Fig. 2), with a light increase up to83 nCSv�1 mm�3 for �75� open angle irradiations (Fig. 3).

ARTICLE IN PRESSM. Jung et al. / Nuclear Instruments and Methods in Physics Research A 587 (2008) 125–129128

3.2. Comparison with the simulated response of silicon

detectors: sensitivity and accuracy

A similar analysis has been performed on three silicondiodes (Table 1). Results of mono channel simulations aresummarized in Table 3. In regard to CB values, theresponse fluctuations are too large inside both reportedX-ray energy intervals. At least two channel responses mustbe associated, as already pointed out in previous papers[4,5]. The numerical procedure minimizes the weightedQðMÞ summations of two channel responses within a fixedX-ray energy range as mentioned above. It calculates thecoefficient a by least-mean-square minimization of QðMÞ

fluctuations around the QðMÞmean value. The calculationsare performed with the CERN library code MINUIT [12].

To improve the response of these detectors we usedseveral channel combinations. The results are given inTable 4. One notices that it is very difficult to get aconfident response down to 20 keV X-rays. Above 50 keV,the best accuracies (lowest CB values) are calculated for thedamaged diode D9 in which the undepleted layer does notcontribute to the charge generation.

Table 3

Monochannel silicon detectors

Diode Filter F (mm) 10–200 keV 50–200 keV

CB

(%)

hQðF Þi

(nCmSv�1)

CB

(%)

hQðF Þi

(nCmSv�1)

D09 0 80 45.5 71 31.2

D09 2.0 Al 72 31.7 69 28.1

D09 1:0 Feþ 1:0 Al 100 8.8 35 12.9

D09 1:5 Feþ 1:0 Al 100 6.5 41 9.2

D99 0 81 47.7 72 32.6

D99 2.0Al 72 33.9 69 29.5

D99 1:0 Feþ 1:0 Al 100 9.2 36 13.5

D99 1:5 Feþ 1:0 Al 100 6.8 41 9.6

D9 0 89 7.8 80 4.4

D9 0.5 Al 78 6.9 70 4.9

D9 1:5 Alþ 0:5 Sn 100 5.9 96 6.1

Table 4

Silicon two weighted channels response association, QðMÞ ¼ aQðF1Þ þ ð1� aÞ

Monitor Silicon F1 (mm) F2 (mm) a

M-1 D09 2.0 Al 1:5 Feþ 1:0 Al 2

M-2 D99 2.0 Al 1:5 Feþ 1:0 Al 2

M-3.1 D9 0 1:5 Alþ 05 Sn 5

M-3.2 D9 0.5 Al 1:5 Alþ 0:5 Sn 6

The mean response hQðMÞi is reported for fixed energy ranges.

These comparisons show that silicon has a largersensitivity than diamond.

4. Dose rate detection thresholds

For this evaluations, the number of accumulated chargesper unit dose is transformed into a current per unit doserate measured in nASv�1 ðnCSv�1 s�1Þ. The monitor doserate detection threshold is related to the intrinsic sensordark current.Due to the very large band gap of diamond, the detectors

can be manufactured with very low leakage currents of theorder of 1 pA. On the contrary, silicon biased diodes showdark currents near to a few nA (RT), the low leakagecurrent could be achieved only for the unbiased one (D09).The detection thresholds per unit sensitive volume as

simulated are shown in Table 5. The values attached todiamond sensors correspond to their maximum responsesplotted in Figs. 2 and 3, whereas for silicon the values referto Table 4 mean responses. The dark current is set at 1 pAfor diamond and unbiased silicon sensors, to 5 nA for thebiased silicon diodes.Absolute dose rate detection thresholds are summarized

in Table 6. They correspond to a 1 cm2 front area and thethree thicknesses of Table 1 sensors. Both limits relative tonormal and open angle irradiations are also given. Forcomparison, in this table, several results are recalled

QðF2Þ

(%) X-ray (keV) CB (%) hQðMÞi (nCmSv�1)

4.6 20–200 69 10.1

50–200 36 12.5

4.2 20–200 69 10.5

50–200 36 13.1

7.9 20–200 41 6.0

50–200 23 4.6

7.1 20–200 34 6.1

50–200 17 4.9

Table 5

Detection thresholds Dt per mm3 sensitive sensor volume

Monitor Dt mm�3 X-ray beam

Diamond 1:07mSvmin�1 10–200 keV: normal incidence

Diamond 0:72mSvmin�1 10–200 keV: �75� incidence

M-1 0:144mSvmin�1 50–200 keV: normal incidence

M-2 687mSvmin�1 50–200 keV: normal incidence

M-3.1 1:96 Svmin�1 50–200 keV: normalincidence

M-3.2 1:84 Svmin�1 50–200 keV: normal incidence

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Table 6

Absolute detection threshold Dt values recalculated from Table 5

Monitor Dt

(mSvh�1)

Thickness

(mm)

Energy range

(keV)

CB interval

(%)

Diamond 64.3 10 10–200 26–28

43.4 16

Diamond 21.4 30 10–200 6–9

14.5 4–6

Diamond 2.14 300 10–200 14–16

1.45 9–20

M-1 0.29 300 50–200 36

2:5Sv year�1

M-2 1:37Svh�1 300 50–200 36

M-3.1 3:9Svh�1 300 50–200 23

M-3.2 3:7Svh�1 300 50–200 17

M. Jung et al. / Nuclear Instruments and Methods in Physics Research A 587 (2008) 125–129 129

showing an improvement in favor of diamond in terms ofaccuracy and energy interval width.

5. Conclusion

Our numerical simulations show their interest as veryhelpful tools to improve the knowledge on the differentmaterials when selecting real-time radiation detectorsfor dosimetric applications. In this work our codeshave been used to evaluate the possibilities offered bydiamond sensors in medical interventions compared tothose of silicon.

For instance, a more confident detection accuracy iscalculated for diamond skin dosemeters since no filtrationis necessary to flatten their response against an unknownX-ray beam energy. This property together with a lownoise level shifts their domain of application down to10 keV X-ray energies, even for large open angle irradia-tions. Regarding silicon monitors, an accurate doseequivalent response is only achieved within a restrictedX-ray energy range. This is due to the needed filtrationwhich masks the low energy component spectral detection.

Also, in contrast to silicon, the very simple diamonddosemeters based on a single sensor, non sensitive to visiblelight [13], without any metallic filter, have the advantageof a non-opacity disturbative effect in radiographicexaminations.Rather large sensor detection thresholds are not very

selective in high fluence irradiation measurements. Dia-mond sensors achieve detection thresholds equivalent tothose of the most sensitive silicon monitor, much lowerthan for biased silicon. These dose rates are able to controldoses accumulated by high risk populations lower than theannual maximum authorized (i.e. 20 or 50mSv as amaximum [2,3] of the 100mSv five year tolerance), duringintervention time scales down to hours.

Acknowledgments

The authors are very grateful to Dr. P. Montgomery forrereading the text.

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