Study of induced thermoluminescence in CVD diamond film by low-energy X-rays

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Applied Radiation and Isotopes 59 (2003) 79–85

Study of induced thermoluminescence in CVD diamond film by low-energy X-rays Chi-Chang Liua, Jao-Perng Linb, Tieh-Chi Chua,* a

Department of Nuclear Science, National Tsing Hua University, 101, Section 2 Kuang Fu Road, Hsinchu 300, Taiwan b Department of Radiation Oncology, Changhua Christian Hospital, Changhua 500, Taiwan Received 20 January 2003; received in revised form 27 March 2003; accepted 13 May 2003

Abstract For diamond film the one-hit model that is used to interpret low-energy X-ray thermoluminescence (TL) will require some modifications. After the films were irradiated with a superficial X-ray machine with different peak voltages, a twocompartment model with three parameters, the target size, the microscopic saturation factor and the high-LET saturation factor, was used to more precisely describe the TL response to X-ray with energies down to 10 kV. The microdosimetric distribution was calculated using single-event Monte Carlo code developed by authors together with EEDL cross-section data library. Some mechanistic insight into the physical aspect of radiation interaction with solid detectors can be obtained. The sensitive size in diamond was found to be about 15 nm. The saturation of one group of sublevels combined with the activation of another group of sublevels caused the relative efficiency to have a local minimum near 20 keV. The relative efficiency becomes higher below 10 keV, which is similar to the increasing relative biological effectiveness when the linear energy transfer passing through a biological system increases. The similarity made this material to be a molecular-scale dosimeter in the future. r 2003 Elsevier Ltd. All rights reserved. Keywords: CVD diamond; Thermoluminescence; Low-energy X-ray

1. Introduction The energy response of a detector is often defined as the ratio of the response (R) to ionization radiation with specific energy (E) to the response with the same dose for radiation source 60Co (or 137Cs) gamma rays. The radiation dose is generally derived from air kerma (Kair ) that can be measured with an ion chamber and was calibrated so as to be traceable to the national standards. Theoretically, energy response SðEÞ can also be described on the basis of the ratio of mass energy absorption coefficient (men =r). It is implicitly assumed that the detector signal is proportional to the absorbed dose in material. However, for thermoluminescence (TL) dosimeters, the TL efficiency is not always *Corresponding author. Fax: +886-3-5727310. E-mail address: [email protected] (T.-C. Chu).

consistent. A correction factor denoted as relative efficiency ZðEÞ should be considered. The definition of energy response is described as ðR=Kair ÞE ðR=Kair ÞCo-60 ½ðmen =rÞTLD =ðmen =rÞair E ¼ ZðEÞ : ½ðmen =rÞTLD =ðmen =rÞair Co-60

SðEÞ ¼

ð1Þ

The relative efficiency was found to be decreased in the case of high linear-energy-transfer (LET) heavycharged particles. Results were explained on the basis of track-structure theory (Horowitz, 1984, 2001a, b). This efficiency reduction phenomenon was due to the saturation locally induced by high doses from the radial distribution of dose close to the ion’s path. For low-energy photons, the relative TL efficiencies of LiF:Mg, Cu, P and CaF2:Tm were also found to be decreased (Olko et al.,1993; Olko,1998). A model called

0969-8043/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0969-8043(03)00147-7

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one-hit model with different patterns of electron track structure produced by the photon was used to describe the phenomenon by assuming that the saturation of the TL response is near the electron tracks in a small volume with roughly micrometer to nanometer dimensions based on this model. For energy deposited in such a small volume, microdosimetric properties should be considered. In this work, the TL response of chemical vapor deposition (CVD) of diamond film for different doses of photon was analyzed. Diamond film was thought to be a useful dosimeter in radiotherapy applications (Liu et al., 2003). The advantage of tissue equivalent, chemical stability, non-toxicity and easy handling makes it become an attractive material for dosimetry. The radiation quality dependency (equivalent to the definition of energy response) of diamond film was simulated by condensed history Monte Carlo method and found to be consistent with experimental data with an energy down to 10 keV (Mobit et al., 1997). The condensed history Monte Carlo method simulates macroscopic phenomena based on multiple scattering theories where stopping power and energy-straggling empirical model were used to estimate energy loss within a condensed history step. The statistic calculation to obtain meaningful simulation value is history by history. When one studies microscopic properties, an event-by-event trackstructure Monte Carlo simulation for low-energy electron transport should be applied.

geometry. The one-hit model assumes that the detector contains a number of radiation sensitive sites (small volume targets). As radiation energy is deposited within the site, there are certain probabilities that the TL will be produced. The term ‘‘one-hit’’ means that the TL effect saturates near the radiation track with local over-dosing and will not produce any enhancement. The density of occupied states in a tiny sensitive volume after an energy deposition z could be analogous to Eq. (2) and can be expressed as n=NðzÞ ¼ 1  expðazÞ;

where the parameter a is defined as the microscopic saturation factor. The relation between macroscopic and microscopic saturation factors is RN ð1  expðazÞÞf1 ðzÞ dz b¼ 0 ; ð4Þ z%F where z%F is the average dose deposited in the volume by a single event such as excitation or ionization. The parameter b now defines the characteristic dose at which 67% of targets are hit by radiation energy deposition events. In the case of dose induced by low LET radiation, the parameter b is close to a constant. However, in the case of high LET radiations, b is a function of LET. A detailed derivation of Eq. (4) can be found elsewhere (Olko, 2002). For low dose, i.e., D51=b; the detector TL response can be expressed as RðDÞ ¼ 1  expðbDÞEbD;

2. Materials and methods 2.1. Theory of one-hit detector model The occupation probabilities of luminescence centers as a function of dose can be approximated by a linear exponentially saturating function n=N ¼ 1  expðbDÞ;

ð2Þ 3

where n is the density of occupied centers (cm ), N the total number density of the luminescent centers, b the macroscopic dose saturation constant that can be determined experimentally by dose response, and D the dose. In general the probability of occupied density is proportional to the thermoluminescent light intensity and the parameter b is independent of photon energy. For microscopic consideration, the energy imparted, e; within micrometer and nanometer dimensions, fluctuates depending on radiation type, dose level and target topology. The frequency of specific energy deposited, z ¼ e=m; in a hypothetical volume of mass m is stochastic in nature and can be described as a distribution function f1 ðzÞ: The dose as a function of f1 ðzÞ does not depend on the dose level but dose depend on the spatial distribution of ionization events and target

ð3Þ

ð5Þ

where D ¼ Kair ½ðmen =rÞTLD =ðmen =rÞair : The relative TL efficiency defined in Eq. (1) becomes RN ð1=z%EF Þ 0 ð1  eaz Þf1E ðzÞ dz bE RN : ð6Þ ZðEÞ ¼ Co-60 ¼ Þ 0 ð1  eaz Þf1Co-60 ðzÞ dz ð1=z%Co-60 b F The dimension of sensitive volume does not appear in the above equation, yet the f1 ðzÞ strongly depends on the target size. Both the target diameter, d; and microscopic saturation factor, a; are unknown in this model but could be obtained by fitting calculated ZðEÞ value to experimental data.

3. Calculation method To calculate relative efficiency, one must utilize track structure Monte Carlo calculations to obtain the singleevent distribution f1 ðzÞ: Secondary electron spectra of Xand gamma-ray can be calculated by a Monte Carlo code developed by the authors. The relative contribution of Compton electrons and photoelectrons is based on the database of carbon from an evaluated data library EPDL (Cullen and Hubbell, 1997). A set of calculated monoenergetic secondary electrons was used to calculate the energy deposition distribution by another Monte

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Carlo code that was also developed by the authors. The code development was based on the algorithm of ESLOW3 (Evans, 1997) to calculate the low-energy electron transport in carbon. The total cross-sections for electron interactions, such as ionization, excitation and elastic scattering, with carbon nuclei, were compiled from a data library EEDL (Cullen et al., 1991). The cutoff energy is down to 10 eV. Angular distribution of elastic scattering and ejected electron energy spectra after ionization was extrapolated from the database in EEDL. The weighted superposition of results that were calculated using secondary electron spectrum is the microdosimetric distribution function for photon. The same procedures were carried out for the spherical target diameters from 10 to 100 nm. The preliminary studies show that the average dose deposited in the volume, z%F ; is related to the target diameter d: If the integral in Eq. (4) is assumed to be unity, the macroscopic saturation factor will be equal to 1=z%F : The relationship between diameter of a spherical sensitive volume d and z%F calculated by Monte Carlo method was found to fit a polynomial, as shown in Fig. 1 and listed below: z%F ðGyÞ ¼ 867294d 2:445 ðnmÞ:

4. Experiment The diamond film used was a commercial product of DeBeer CVDITE CDM L603502PL CVD. Diamonds cut out to be 3 mm  3 mm  0.2 mm square chips were used for this experiment. A Harshaw 5500 TLD reader in Changhua Christian Hospital with time–temperature profile (TTP) setting at a heating rate 7 K s1 from 333 to 673 K was used to read the glow curve. Irradiations were performed using a superficial X-ray machine (Model RT-100, Philips Co., Holland) at Changhua Christian Hospital. Ten diamond chips were placed on a 10 cm thick polyfoam block to reduce backscattered radiation and were irradiated simultaneously by X-rays with high voltage set at 10, 20, 30, 37, 45, 55, 70 and 100 kVp, respectively. In general, the quality of X-ray used is described as the internal filter added. The corresponding internal filters used were 1 mm Be, 0.15, 0.3, 0.4, 0.55, 0.78, 1.25 and 1.7 mm Al, respectively. However, the effective energies should be determined. The corresponding effective photon energies were derived from the data of half-value layers (HVL) of copper and the database of mass-energy absorption attenuation coefficients (Hubbell and Seltzer, 1997). A log–log interpolation together with the iteration procedure was used to obtain the effective energies. The dose in diamond film when irradiated with Co-60 is corrected by Monte Carlo calculations for high-energy secondary electrons. Glow curve analysis of the TL readout was assumed to follow the first-order kinetics and was simplified by fitting to a two-parameter Weibull distribution function, W ðTÞ; with a shape factor equal to 16 (Pagonis et al., 2001):

ð7Þ

A similar relationship was also found when the target material is water (Olko, 2002). The target size could be derived experimentally from b: However, the integral is known to be always less than one. If z%F is assumed to be 1=b; the derived diameter would be the size limit of sensitive volume. The parameter a and effective diameter were obtained by minimizing relative least-squares values (M) of calculated and measured relative efficiencies, i.e., i 2 N ðZi X exp  Zcal Þ i¼1

Zi2 exp

 15 T  Tm W ðTÞ ¼ 2:713Im þ 0:996 b "  16 # T  Tm þ 0:996 :  exp  b

ð8Þ

:

10000

z F (Gy) = 867294 d(nm) -2.445 2

Average specific energy (Gy)

M¼

81

R =0.9993 1000

100

10

1 10

100

1000

Target diameter (nm)

Fig. 1. Relation between spherical target diameters and average specific energies by Co-60 irradiation.

ð9Þ

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82

Here Im represents the maximum TL intensity and Tm the corresponding temperature, T the temperature, and b the scale factor of the Weibull distribution function. The approximate Tm and Im values can be obtained experimentally. These values were used as the initial parameters and also as input into a best fitting procedure according to the Levenberg–Marquardt algorithm.

5. Results and discussion The dose response of 10 kVp X-ray and Co-60 gamma rays is shown in Fig. 2. The corresponding macroscopic saturation factors for the preceding X- and gamma-ray are 0.0338 and 0.0267 Gy1 respectively. Based on Eq. (7), the sensitive target diameter was derived to be 60.98 nm in diamond, corresponding to z%F ¼ 1=bCo-60 : The sensitivities of different X-ray energies are shown in Fig. 3. Results of this work can be extended to the data of Mobit et al. (1997) to lower photon energy range. The energy response of TL signal of diamond film seems to be quite consistent with the ratio of absorption coefficient for almost the full energy range. However, in the case of effective photon energy lower than 10 keV, the response is higher than that of others. The dose distribution for such low-energy photons is near the surface of diamond film. The ‘‘dose’’ here is assumed to be the average dose within the depth equal to mean free path. The self-absorption of TL light correction is based on the data of TL readout with the irradiated side up and down, as suggested by Majborn et al. (1977). This overestimated phenomenon is more significant, as shown in Fig. 4, when it is expressed in the form of

relative efficiency. This could be predicted both by Eq. (6) and the larger macroscopic saturation factor of 10 kVp X-ray shown in Fig. 2, and is expected to be well described by one-hit model. To obtain diameter and microscopic saturation factor, we performed the least-squares fitting of M as defined in Eq. (8). The best-fit parameters are a ¼ 1:94 106 Gy1 and d ¼ 1572 nm. The relevant diameter in water could be obtained by scaling with the density, r: The relationship is found to be rdiamond ddiamond ¼ rwater dwater : The corresponding diameter in water is 54 nm. This is about the size of some macromolecules such as protein. The sensitive target size of diamond is comparable to those of LiF:Mg, Cu, P and CaF2:Tm, that were found to be 24 and 16 nm respectively (Olko, 2002). The physical interpretation of this model parameter is not straightforward. The hypothetical target size could be related to more complex energetic states near the defects in diamonds that formed recombination centers and electron traps. The fitted target diameter is much smaller than that derived from Eq. (7), implying that there are various mechanisms between macro- and microscopic radiation response. The efficiency calculated by one-hit model, shown in Fig. 4, is not totally consistent with the experimental data. Larger discrepancies are observed for those cases when effective photon energies are close to 20 keV and less than 10 keV. Modifications should be made under these conditions. The response of biological molecules to ionization radiation has been studied for many years and the accumulated experiences might be useful. A well-known two-compartment theory describes two classes of significant DNA damage after irradiation within

800

Termoluminscence intensity (nC)

700

Co-60 10kVp

600

Co-60 Y=944.7 exp(-0.0267x) 2 R =0.9977

500 400 10 kVp Y=653.5 exp(-0.0338x) 2 R =0.9956

300 200 100 0 0

10

20

30

40

50

60

Dose (Gy)

Fig. 2. The TL response of diamond irradiated with Co-60 and 10 kVp X-ray. The dose indicated in the abscissa refers to air kerma.

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1.1 Absorption Coeff. Ratio Mobit, P.N. (1997) Experimental results

0.9

10 kVp Co-60

1.0 Normalized intensity

1.0

0.8 S(E)

83

0.7 0.6 0.5

0.8

Tmax=604 K for Co-60

Tmax=602 K for 10kVp

0.6 0.4 0.2

0.4 0.3 100

101

102

0.0 500

103

Fig. 3. Comparison of sensitivity of TL energy response with the mass-energy–absorption-coefficient ratio ½ðmen =rÞTLD = ðmen =rÞair X-ray =½ðmen =rÞTLD =ðmen =rÞair Co-60 :

1.3 Relative efficiency One-hit model Modified model

Relative efficiency

1.1 1.0 0.9 0.8 0

5

10

15

20

25

600

650

700

Temperature (K)

Effective photon energy (keV)

1.2

550

30

35

Effective photon energy (keV)

Fig. 4. Comparison between the experimental relative efficiency of diamond and the calculated ones with one-hit model and modified two-compartment model.

nanometer scale (Schulte et al., 2001). Fewer than five ionization events within sensitive sites are thought to cause reparable damage, whereas irreparable damage is caused by more than six ionization events. The dose dependence of the induction of lethal damage from reparable process can be described by a second-order polynomial as a simplified multi-hit-model. The production of lethal damage from the irreparable process is assumed to be linearly proportional to increasing dose. Furthermore, by assuming a Poisson distribution of lethal damages, the survival fraction of cells may be expressed as expðaD2 Þ and expðbDÞ; respectively, where D is the dose, and both a and b are scaling constants. The microscopic TL responses of diamond are quite similar to those of DNA damage. A model assuming

Fig. 5. The glow curve of 1 Gy irradiation by Co-60 and 10 kVp X-ray.

continuous distribution of traps is proposed to explain the TL saturation in diamond induced by high dose (Furetta et al., 2000). According to the model the traps are filled during irradiation in a way that depends on the depth of the sub-levels. Presumably, there are two groups of sub-levels that could trap electrons produced by irradiation near the defect location in diamond crystal. Before one group (L) of sub-levels is fully filled, the other group (H) of sub-levels could not trap any electrons. The activation energies of these two groups are about the same. During readout, the TL emission comes from these sub-levels which are emptied all together at the same time. However, the differences still could be observed from the glow curves. In Fig. 5, the glow curves of TL irradiated with the same dose (1 Gy) of different sources are shown. The position of the temperature at the maximum depends on the activation energy that is related to trap depth. The peak temperature of 10 kVp X-rays is 602 K, while that of Co-60 is 604 K. Although the difference is quite small, there should exist some sub-levels that could only be filled under high-energy transfer condition. The one-hit model could then be modified to become a twocompartment model. For low specific energy deposition, zozcutoff ; the survival fraction is the same as that described by the one-hit model, expðaL zÞ: By contrast, for high-energy deposition condition, the survival curve fraction is expressed as a quadratic form in an exponential function, expðaH z2 Þ: Eq. (5) can now be modified as shown below: ZðEÞ ¼ ð1=z%EF;L Þ

R zcutoff 0

RN 2 ð1  eaL z Þf1E ðzÞ dzþð1=z%EF;H Þ z ð1eaH z Þf1E ðzÞ dz cutoff R ; N ð1=z%Co-60 Þ 0 ð1  eaz Þf1Co-60 ðzÞ dz F

ð10Þ

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where zcutoff is the trigger level to induce high-LET trapping procedure. The aL is assumed to be the same as a that was defined in one-hit model. The aH is the highLET saturation factor. The fitted results of this modified model are also shown in Fig. 4. Obviously the results are more reasonable. The effective photon energy less than 20 keV will increase the efficiency by supporting more traps. For high-energy photons, the response still follows the one-hit hypothesis. That is why the local minimum efficiency appears close to 20 keV. The parameters were fitted to obtain zcutoff C30000 Gy and aH ¼ 4  1011 Gy2. On average about 50 ionization events would occur in a target within a short time to reach the zcutoff : Part of the energy should be absorbed by the crystal lattice to an excited state. Such excited states will vanish and atoms will return to ground state in a short time by energy losses due to phonon interaction. If an ionization event occurred near the exciting defect site, almost simultaneously the ionized electron would be trapped in those sub-levels belonging to H group. The connection between TL response and relative biological effectiveness (RBE) is an interesting issue. However, the lack of experimental data about energy-dependent RBE of low-energy photons has made it difficult to discuss in detail. Since both the RBE and one-hit model are based on target theory, the trend of LET dependency should be similar. The presence of impurities in the lattice has been identified to be a factor which strongly affects the linearity and sensitivity of TL response (Mazzocchi et al., 2002). If the CVD diamond fabrication could be controlled by adding a appropriate amount of impurities, the TL response may be related to the dose response for DNA molecules. Diamond film can then become a potential material for a dosimeter in molecular scale.

6. Conclusion The modified microscopic one-hit detector model, a phenomenological model for the calculation of the response of some biological system after irradiation with ionizing radiation, has been successfully applied to analyze the TL response of diamond film after different radiation modalities. Three parameters are involved in the model: the diameter of spherical sensitive volume, the microscopic saturation factor and the high LET saturation factor; these parameters determine the probability of effect after energy is imparted to the target. The saturation of TL response is caused by saturation of the numbers of traps in the vicinity of particles track while another state in the traps becomes active. Regarding the LET effect and related micro-

scopic parameters of diamond film, we draw following conclusions: 1. The sensitive diameter in diamond is found to be 15 nm, which is related to 54 nm in water. The interpretation of the target size is the average charge carrier migration distance over which recombination takes place. 2. The saturation factors are a ¼ 1:94  106 Gy1 and aH ¼ 4  1011 Gy2 respectively. When the specific energy deposition is less than 30,000 Gy, the highenergy state could not trap any electrons. 3. Combination of saturation of one group and activation of another group makes relative efficiency locally minimized at an effective photon energy of about 20 keV. 4. Solid-state detector model shows similarities of the response of radiation to the responses of some biological systems. For some proper controlled fabrication processes, the material could be used as a molecular-scale dosimeter.

Acknowledgements The authors are grateful to Professor Pao-Shan Weng for useful suggestions.

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