PTW NATURAL DIAMOND DETECTOR

In this paper the suitability of a PTW natural diamond detector (DD) for relative and reference dosimetry of photon and electron beams, with dose per pulse between 0.068 mGy and 0.472 mGy, was studied and the results were compared with those obtained by a stereotactic silicon detector (SFD). The results show that, in the range of the examined dose per pulse the DD sensitivity changes up to 1.8% while the SFD sensitivity changes up to 4.5%. The fitting parameter, D, used to correct the dose per pulse dependence of solid state detectors, was D = 0.993±0.002 and D = 1.025±0.002 for the diamond detector and for the silicon diode respectively. The D values resulted independent of particle type of two conventional beams (a 10 MV x-ray beam and a 21 MeV electron beam). So if D is determined for a radiotherapy beam, it can be used to correct relative dosimetry for other conventional radiotherapy beams. Moreover the diamond detector shows a calibration factor independent of beam quality and particle type, so an empirical dosimetric formalism is proposed here to obtain the reference dosimetry. This formalism is based on a dose-to-water calibration factor and on an empirical coefficient, that takes into account the reading-dependence on the dose per pulse. This procedure is applicable also to silicon diode determining its calibration factor for each energy or quality of the beam.

Keywords: diamond detector, dose rate dependence, dosimetry.

1. Introduction

The PTW diamond detector (type 60003) has been widely used for relative dosimetry of photon and electron beams ^1-4. The quasi water-equivalence in terms of atomic number and the small dimensions of the sensitive volume make the diamond detector attractive for dose measurements involving small radiation fields that are affected by the presence of lateral electron disequilibrium ⁴ and steep dose gradients. Moreover the literature reports that the PTW diamond detector sensitivity is independent of the photon beam quality in the range between 4 and 25 MV ⁵, and of the electron beam energy in the range between 5 and 20 MeV ⁶. Although this is to be expected, to be due to the near water equivalence of diamond, an energy dependence of the PTW detector sensitivity might be introduced by the presence of the contact materials ⁷.

The use of the diamond detector in reference dosimetry has some interest because of its high resistance to radiation damage⁷, whereas the silicon detector has some problems caused by radiation damage⁸. Recently Mobit et al ⁶, by using a Monte Carlo simulation of electron beams, have studied the applicability of the Spencer-Attix cavity equation to determine the absorbed dose in the phantom from the absorbed dose in the sensitive volume of the diamond detector. Their results showed that the PTW diamond detector may be calibrated against an ionization chamber, at the maximum dose depth, d_max, for a given electron beam energy. This calibration factor can be used for the dosimetry of electron beams in the energy range between 5 and 20 MeV with uncertainty of 1 %, for depths of irradiation close to d_max,and 3% for all the other depths. However it is known that the diamond detector has an under-response with increasing dose rate ^1,2, due to a very short electron-hole recombination time, which decreases as dose rate increases. Fowler ⁹ has introduced a fitting parameter, D , to correct the dose rate dependence of solid state detector reading. Heydarian et al. ² showed that D is energy-independent for photon beams in the range between 4 and 23 MV with an average dose rate ranging between 0.69 Gy min^-1 and 7.85 Gy min^-1.

In this paper the D values obtained for a PTW diamond detector, by using a 10 MV photon beam and two 21 MeV electron beams, are showed and compared with the D values evaluated for a stereotactic silicon diode (the characteristics of the two solid state detectors are described in materials and methods section). Moreover, the sensitivity dependence on the dose per pulse has been determined for the two solid state detectors, and for the PTW detector an empirical dosimetric formalism for the dose to water determination is proposed here.

2. Materials and methods

The PTW diamond detector (DD) (type 60003, serial number 7-031) has been well documented by Rustigi et al³. The used DD consists of a natural diamond crystal with a sensitive area of 3.8 mm² and 0.26 mm thick. The sensitive volume of the diamond is located 1 mm below the detector front surface of 7.3 mm in diameter. A bias voltage of 100 V was applied and , as suggested by the detector certificate, to stabilize the DD reading a preirradiation dose of 5 Gy was applied each time the detector was used to obtain a set of measurements , while no preirradiation was carried out by the manufacturer.

The stereotactic field detector (SFD) manufactured by Scanditronix is a high-doped p-type silicon diode ¹⁰ (model DEB050 serial number 1029). The SFD sensitive area of 1.1 mm² , 0.06 mm thick, is located 0.7 mm below the detector front surface of 4.5 mm in diameter. The SFD was preirradiated by the manufacturer to 8 kGy and no preirradiation is required before the experimental use.

A PTW parallel plate Markus ionization chamber, model 23343, was used as a reference dosimeter to determine the dose per pulse of the radiation beams. The Markus ionization chamber presents: a nominal sensitive volume equal to 0.055 cm³, a nominal electrode distance equal to 2 mm, a polarity effect less than 0.5 % and a recommended bias polarizing voltage equal to 300 V. The Markus calibration factor, N_D,P= 5.030 10⁸ GyC^-1 (±0.5%, 1s), in terms of absorbed dose to the air cavity, was determined in a water phantom by comparison with a cylindrical reference ionization chamber ENEA, model ESC/87 (calibrated in terms of air kerma), applying the Italian Protocol ¹¹ (that follows the recommendations of the IAEA ¹²). The dose to water was determined by using the Italian Protocol ¹¹, in particular the Markus reading was corrected by using the saturation factor (that ranged between 0.2 % and 0.6 %). The Markus ionization chamber was connected to a Keithey electrometer model 35617.

The measurements were performed with a 10 MV x-ray beam with a monitor unit rate (MUR) equal to 200 MU min^-1 and two electron beams of 21 MeV with MUR equal to 200 MU min^-1 and 400 MU min^-1. All the beams were supplied by a linac Saturne 43 G.E., operating in the Radiotherapy Department of the UCSC. Table I reports the MUR, the pulse repetition frequency (PRF) and the range of the dose per pulse, for the photon and electron beams here used. The pulse duration of the beams was 5 ms and the different dose per pulse values were obtained by changing the source surface-phantom distance (SSD).

The aim of the photon and the electron beam selection was to verify, for the two detectors, the independence of the D values as well as the diamond sensitivity on the particle type. The two frequencies supplied by the Saturne 43, were used to verify the independence of the results on the PRF used by conventional linacs.

The measurements were carried out in a Nucletron automatic water phantom of 60x65x67 cm³ where the three detectors were irradiated simultaneously with a beam entering the surface of the water phantom perpendicularly. The Markus ionization chamber was positioned on the beam central axis, with its reference point (inner surface of the entrance plate) placed at d_max (the depth of maximum dose) for the electron beams and at d_max and 5 cm for the photon beam. The DD and the SFD were positioned laterally to the ionization chamber, on right and on the left side respectively, at the same depth in water. In this way the centers of the DD and SFD sensitive volumes were at a distance of 3 cm from the beam’s central axis; in that region the dose homogeneity was better than 0.2 % at all chosen SSDs .

For the electron beam measurements the used SSDs were 90 cm, 120 cm, 150 cm, 180 cm and 204 cm, for all chosen SSDs the field size was 27x27 cm² at d_max=3.8 cm. The energy at phantom surface, E₀, resulted equal to 19.5±0.2 MeV for all chosen SSDs.

For the photon beam measurements the different dose per pulse values were obtained using the SSDs of 80 cm, 100 cm, 120 cm, 150 cm, 180 cm and 204 cm, and for all chosen SSDs the field size was 30x30 cm² at the detector’s depths of 5 cm and d_max=2.5 cm respectively.

As reported in section 2.2 the measurements obtained by the Markus ionization chamber were converted in dose to water per pulse values, D_w, (table I), taking into account the PRF values and the irradiation time. The detectors were irradiated with a number of monitor units (MU) sufficient to obtain an accuracy of 0.5 % on the interval time measured by the linac clock. D_w was selected instead of the average dose to water to compare the detector sensitivity obtained with different PRF and dose per pulse of the used beams.

In order to determine the relationship between the reading per pulse of the solid state detectors, M, and the dose per pulse, D_w, the empirical expression was used ⁴:

where a is a constant and D is the fitting parameter to correct the dose rate dependence of the detector reading (equal to 1 for a detector with linear reading per pulse). The D values were determined separately for each PRF and type of the particles as the slope of the linear fit of the log normalized M against log normalized D_w. The normalization is obtained at the values of lowest D_w¹. Figure 1 shows a logarithmic plot of normalized reading per pulse for DD and SFD detectors as a function of the log normalized D_w obtained for a 21 MeV electron beam with a PRF of 200 Hz.

The photon beam measurements were performed at d_max and at 5 cm to evaluate the D dependence on the electron contamination from the collimator system. The D values turn out to be the same within the experimental uncertainties in the two experimental conditions for both the detectors.

Table II reports the D values of the two solid state detectors obtained by electron and photon beams. The reading precision or reproducibility equal to 0.5% (1s) was evaluated for the two solid state detectors while for the Markus ionization chamber resulted equal to 0.3% (1s). The D variations reported in table II were obtained with the method of least squares and assumed as experimental uncertainties. Table II shows that the D values, for each detector, are the same within the experimental uncertainties for the two types of the particles and the PRF values examined. The D independence of PRF was expected because, in the described experimental conditions, the charges produced by each pulse are collected independently. Indeed the transit time, t_r, required for an electron to pass through the solid from one electrode to the other is t_r=L²/Vm, where L is the thickness of the sensitive volume, V is the operating bias and m is the electronic mobility ⁹. Since the transit times are t_r = 3.8 ns for the DD and t_r= 55.4 ms for the SFD, and the smallest interval time between two pulses is about 5 ms, the charges produced by a pulse (that are not recombined with holes) are entirely collected before the start of the successive pulse.

Figure 2 reports the DD sensitivity as a function of the dose to water per pulse D_w for the two electron beams with PRF equal to 100 and 200 Hz, and for the photon beam with PRF=100 Hz. In this paper the detector sensitivity is defined as the ratio between the solid state detector reading per pulse, M, and the dose per pulse, D_w, determined by Markus chamber. The bars, 0.6 %, are obtained as the square root combination of diamond and Markus chamber precisions (1s). Figure 2 shows that the DD has an under-response with increasing dose to water per pulse ^1,2,4 and this trend is independent of the particle type and the PRF.

Figure 3 reports the SFD sensitivity values as a function of the D_w values, obtained using the two electron beams with PRF equal to 200 and 100 Hz, and the photon beam with PRF = 100 Hz. Figure 3 shows that the silicon diode has an over-response with increasing dose to water per pulse^1,2 and a sensitivity dependence on the beam quality. This is essentially due to the non water equivalence of the silicon material ¹⁰.

Mobit et al.⁶, for electron beams, and Laub et al.⁵, for photon beams, showed that the DD sensitivity is energy independent, and the results reported in figure 2 show that, within the experimental uncertainties, the DD sensitivity as a function of the dose per pulse is also independent of the particle type. So the DD can be used for dose measurements, only correcting the M reading per pulse for the dose per pulse dependence. As for the non linearity of M versus D_w (equation 1) in the range from 0.068 mGy to 0.472 mGy, an empirical coefficient of linearity-rate, P_lr, was determined as the DD calibration factor (the reciprocal of the sensitivity) N_w,D=D_w /M normalized at N_w,D_ref =D_w,ref/M_ref with a reference reading per pulse M_ref=0.0167 nC obtained for a reference dose per pulse D_w,ref=0.300 mGy:

Figure 4 reports the P_lr values as a function of the M values and the solid line was obtained by the expression (3), with a value of D=0.993 that is the average value of the data reported in table II.

4. Discussion and conclusion

The DD and the SFD detectors present a reading per pulse, M, dependent on the dose per pulse, but they can be suitable to obtain the percentage depth dose, PDD(d), at depth, d, by the expression proposed by Laub et al.

were d_max is the depth of maximum dose. The results reported in table II show that for the examined DD and SFD detectors the D values are, within the experimental uncertainties, independent of the particle type, the beam quality and the PRF. However, it is important to observe that the D value has to be determined for each PTW diamond detector or Scanditronix SFD, because the D value is detector dependent as reported in literature^7-8.

The results reported in figure 2 show that the DD sensitivity, in a range of dose per pulse from 0.068 mGy to 0.472 mGy (that covers the conventional radiotherapy dose rate, measured at reference depths in water phantom for beam calibration), is independent of the particle type and beam quality. So if N_w,Dref and P_lr are determined for a DD detector with a radiotherapy beam, the dose per pulse at depth d, D_w(d), can be obtained, also for other radiotherapy beams using the expression :

The dose to water in terms of Gy/MU may be obtained by expression (5) multiplying D_w(d) by the number of pulses per MU. This number is determined multiplying the PRF by the irradiation time per MU used. So the DD may be used for reference dosimetry in those cases of small field size and steep dose gradients, for which a ionization chamber may be difficult to use.

The results reported in figure 3 show that the dosimetric formalism, above described, is applicable to the silicon diode examined only if the calibration factor, N_w,Dref, is determined for each quality and energy of the beam (in fact its sensitivity depends on the energy and the quality of the beam).

This work has been developed by a grant from MURST 1998 (Ministero dell’Università e della Ricerca Scientifica e Tecnologica). We gratefully acknowledge D. Di Nucci, P. Di Nicola, A. Porcelli for their technical assistance.

¹ P.W. Hoban, M. Heydarian, W.A. Beckham, and A.H. Beddoe, “Dose rate dependence of a PTW diamond detector in the dosimentry of a 6 MV photon beam,” Phys. Med. Biol. 39, 1219-1229 (1994).

² M. Heydarian, M. Zahmatkesh, P.W. Hoban, and A.H. Beddoe, “Dose rate correction factors for diamond detectors for megavoltage photon beams,” Phys. Med. 13, 55-60 (1997).

³ S.N. Rustgi, D.M.D. Frye, “Dosimetric characterisation of radiosurgical beams with a diamond detector,” Med. Phys. 22, 2117-2121 (1995).

⁴ A. Piermattei, L. Azario, A. Fidanzio, G. Arcovito, “Quasi water-equivalent detectors for photon beams that present lateral electron disequilibrium,” Phys. Med. 14, 9-17 (1998).

⁵ W.U. Laub, T.W. Kaulich, and F. Nusslin, “Energy and dose rate dependence of a diamond detector in the dosimetry of 4-25 MV photon beams,” Med. Phys. 24, 535-536 (1997).

⁶ P.N. Mobit, G.A. Sandison, “An EGS4 Monte Carlo examination of the response of a PTW-diamond radiation detector in megavoltage electron beams,” Med. Phys. 26, 839-844 (1999) .

⁷ B. Planskoy, “Evaluation of diamond radiation dosimeter,” Phys. Med. Biol. 25, 519-532 (1980).

⁸ D. Wilkins, X.A. Li, J. Cygler, and L. Gerig. “The effect of dose rate dependence of p-type silicon detectors on linac relative dosimetry”. Med. Phys. 24 , 879-881 (1997) .

⁹ J.F. Fowler, “Solid state electrical conductivity dosimeters” Radiation Dosimetry ed F.H. Attix and W.C. Roesch, (New York : Academic) (1966).

¹⁰ G. Rikner, “Silicon diodes as detectors in relative dosimetry of Photon, electron and proton radiation fields,” (Sweden : Uppsala Universitet) (1983).

¹¹ Associazione Italiana Fisica Biomedica (AIFB), “Protocollo per la dosimetria di base nella radioterapia con fasci di fotoni ed elettroni con E_max fra 1 e 40 MeV,” Notiziario della A.I.F.B. (VI), 2 (1988)

¹² International Atomic Energy Agency (IAEA), “Adsorbed dose determination in photon and electron beams: An international code of practice,” Technical Reports Series No. 277, Vienna, (1987).

Table I . Monitor unit rate (MUR), pulse repetition frequency (PRF) and range of dose per pulse, for photon and electron beams, supplied by a linac Saturne 43 G.E.

Radiation beam	MUR (MU min^-1)	PRF (Hz)	Range of dose per pulse (mGy)
Photon 10 MV	200	100	0.069-0.472
Electron 21 MeV	200	100	0.071-0.400
Electron 21 MeV	400	200	0.068-0.384

oooooTable II . Dose rate correction factor, D, values obtained for the diamond detector (DD) and the stereotactic field detector (SFD) by photon and electron beams.

Detector

Photon

(100 Hz)

Electron

0.994±0.002

0.991±0.002

SFD

1.023±0.002

1.025±0.002

1.026±0.002