Characteristics of a miniature dosimeter developed for measurement of electrons

NUCLEAR INSTRUMENTS AND METHODS ~41 (1977) 87-92;

~) NORTH-HOLLAND PUBLISHING CO.

CHARACTERISTICS OF A MINIATURE DOSIMETER DEVELOPED FOR MEASUREMENT OF ELECTRONS AKIRA MARUHASHI* Department of Nuclear Engineering, Kyoto University, Kyoto, Japan

Received 8 July 1976 and in revised form 21 October 1976 Characteristics of the miniature dosimeter developed for the measurement of electrons are described in this report. This dosimeter is very easily used without applied bias voltages. This is a silicon diffused n-p + junction device. The silicon detecting element of this dosimeter has the form of a disk, and the front area is 1.72 x 10-2 cm< The energy range of electrons used in this experiment is 0.6-1.8 MeV. The electron-induced currents were proportional to the number of incident electrons over the range of 1.5 x 104-1.5 x 109 electrons/s, and the energy absorbed in the sensitive volume of this dosimeter was about 39 keV per incident electron and had little dependence on the electron energy range of 0.8-1.8 MeV. The depletion layer of this dosimeter and the contribution of backscattered electrons to the total energy absorbed in the sensitive volume were about 90 Itm and about 15%. respectively.

1. Introduction Since more than ten years ago, the miniaturized dosimeter has been developed for the m e a s u r e m e n t of tracer activity a n d for m o n i t o r i n g g a m m a and beta fields in body cavities in c o n j u n c t i o n with radiation therapy1 s). A silicon semiconductor is quite useful for m a k i n g a miniature dosimeter due to its characteristics2). A miniaturized silicon dosimeter was developed for the m e a s u r e m e n t of bremsstrahlung4). The dosimeter was improved for the m e a s u r e m e n t of electrons from a n accelerator. The improved dosimeter is useful to obtain i n f o r m a t i o n on the fluctuations of the intensity, the direction of the electron beam, a n d the spatial spread of the electron beam in air. In this paper, the characteristics of this dosimeter are described, such as linearity, energy dependence a n d the effect of radiation damage. The energy absorbed in the sensitive region per incident electron and the thickness of the depletion layer of this dosimeter were calculated a n d the c o n t r i b u t i o n of backscattered electrons to the energy absorbed in the sensitive region was estimated.

the surface area is 1.72 × 10 - 2 c m 2. The p-region was obtained by b o r o n diffusion into an n-type silicon semiconductor whose resistivity was a b o u t 120 Q-cm. The copper was evaporated over the front and side surface of the device to make the window thickness thin and to suppress electrical noise. A negative electrode was contacted with this copper film and the contact was made away from the silicon crystal. To investigate the characteristics of this dosimeter for electron measurement, an electron Van de Graaff accelerator of the D e p a r t m e n t o f Nuclear Engineering of Kyoto University was used a n d the energy range of the electron beam used in this experiment was 0.61.8 MeV. Fig. 2 shows the schematic diagram of the experimen-

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2. Experimental methods Fig. I shows developed for dosimeter is a n-type silicon element of this

a cross sectional view of the dosimeter the m e a s u r e m e n t of electrons. This diffused j u n c t i o n device utilizing an semiconductor. The silicon detecting dosimeter has the form of a disk, a n d

* Present address: Radiation Control Center, Institute for N uclear Study, University of Tokyo, Tanashi-Machi, Kitatama-Gun, Tokyo, Japan.

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Fig. 1. Cross sectional view of the diffused n-p + junction device. ( 1): Silicon detecting element.

88

A. M A R U H A S H I

tal arrangement. The electron beam from the accelerator was collimated by an aluminum collimator of 2.0 mm in inner diameter and 8.0 mm in length, after penetrating through a titanium foil (50 Hm thick) that contains the vacuum o f the accelarator. The dosimeter was moved on a circle of 3.5 cm in radius from - 9 0 " to 90 ~ to the beam direction as shown in fig. 2. The collimator was connected with the accelerating-tube electrically, and composed a Faraday cup (Fb) as shown in fig. 2, by which the electron current in the accelerating-tube was measured. Electron currents passing through the collimator were measured with a removable Faraday cup (F,). The external circuit to measure the radiationinduced current had very low impedance, and so the current through the external circuit was equal to the radiation-induced current at zero biasS).

3. Experimental results and discussion

by subtracting the bremsstrahlung-induced currents from currents that were measured when the hole of the collimator was not obstructed. The angular distribution function was in good agreement with the Gaussian distribution function. Currents induced by bremsstrahlung, on the other hand, are independent of the angle (0). This may be because bremsstrahlung produced from the aluminum collimator is not large in comparison with that from the accelerating-tube made of stainless steal owing to poor focussing of the electron beam. Currents induced by bremsstrahlung are less than I % in comparison with those induced by electrons at 0 = 0 , and are the same at about 0 = 22". The ratio of the currents induced by bremsstrahlung and by electrons at E < 1.8 MeV is the same as at E = 1.8 MeV. 3.2. ANGULAR DISTRIBUTIONOF ELECTRONS PASSING THROUGH THE COLLIMATOR Fig. 4 shows angular distributions of the electron-

3,1. CONTRIBUTION OF BREMSSTRAHLUNG-INDUCED CURRENT TO ELECTRON-INDUCEDCURRENT Fig. 3 shows angular distributions of currents induced in the detector by electrons and bremsstrahlung at E = 1.8 MeV, where E is the energy o f electrons incident on the titanium foil. Bremsstrahlung-induced currents were measured under the condition that the 2.0 mm hole o f the collimator was obstructed with the aluminum bar. Electron-induced currents were obtained

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Fig. 3. R e l a t i o n b e t w e e n e l e c t r o n - a n d b r e m s s t r a h l u n g - i n d u c e d c u r r e n t s as a f u n c t i o n o f the a n g l e (0), Both c u r r e n t s are norrealized to a v a l u e I at 0 = 0 for the e l e c t r o n - i n d u c e d c u r r e n t s .

MINIATURE

induced currents at several electron energies and at Iv = 10 -~ I~A, where Iv is the current measured by the Faraday cup Fb. This figure shows that the current in the dosimeter decreased with electron energy. The attenuation of the current was caused by the electron scattering by the titanium foil which contains the vacuum of the accelerator. Then with the decrease of electron energy, electrons transmitting through the foil are scattered to larger angles with larger probability, smaller numbers of electrons are able to pass through the aluminum collimator and inject the dosimeter in spite of the same current Iv. The induced current 1(0) can be fitted by a Gaussian distribution at 0 < 20 °. The half width of the distribution function

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DOSIMETER

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increased with decreasing electron energy. As shown in fig. 2, the maximum angle to which electrons reach without any scattering by the collimator after being transmitted through the titanium foil is about 16° . Fig. 4 shows that the electrons passed through the collimator spread to about 25 ° at 1.8 MeV electron energy, and the spread slightly increases with decreasing electron energy. This discrepancy may be attributed to

1) scattering of electrons in the air after passing through the collimator, 2) grazing scattering of electrons by the collimator wall. To estimate the air scattering effect (I), the dosimeter was moved on concentric circles of 0.9, 3.5 and 7.1 cm in radius at E = 1.25 MeV. The experiments showed that the electron-induced currents depend on the geometrical effects and the air-scattered effect was negligible. From this result, it is concluded that the current measured at larger angles than 16" was caused by the grazing scattering of electrons by the collimator wall. The average energy loss resulting from this grazing scattering and from traversal of the titanium foil is a small fraction of incident energy E. From this reason, the energy of all electrons incident on the dosimeter is neary equal to E, and the angular distribution of electrons passing through the collimator is equal to that of electron-induced currents.

1,5

3.3.

DEPENDENCE OF REDIATION SENSITIVITY ON KINETIC ENERGY OF INCIDENT ELECTRONS

The dependence of radiation sensitivity of this dosimeter on kinetic energy of incident electrons was estimated from the energy absorbed in the sensitive volume per incident electron at several accelerating energies E. This absorbed energy E,b was calculated from the relationship between the number of electrons passing through the collimator Ni,, which was measured using the Faraday cup F,, and a value IT, which was obtained from integrating 1(0) over all solid angles. Supposing that the total energy absorbed in the sensitive volume is consumed for producing electron-hole pairs,

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where co is the average energy required per electron hole pair produced in the silicon semiconductor and is about 3.66 eV, and e is elementary charge. The value E,b, calculated from eq. (I), is shown in fig. 5 as a function of E. From this result, the energy absorbed in the sensitive region per incident electron is about

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A. MARUHASH1

39 keV with little dependence on electron energy in the range 0.8-1.8 MeV. This absorbed energy, however, decreased with decreasing electron energy in the region below 0.8 MeV. 3.4. LINEARITY Fig. 6 shows the relationship between the electroninduced current and the number of electrons perpendicularly incident on the dosimeter per unit time at E = 1.8 MeV. The electron number ND(0), was calculated from the following equation under the assumption that the number of electrons incident on the dosimeter, Nt~(0), at angle 0 is proportional to the electron-induced current 1(0). ND(O )

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0 = 0 ° to the total current obtained from integrating 1(0) over all solid angles, IT, at an / v of 0.1 /~A. The current 1(0) was proportional to the electron number ND(0), when ND(0 ) iS less than 1.5× 109 electrons/s. The relationship between l(0) and ND(0) is expressed as /(0) = (1.75_+0.075)× 10 -9 ND(0),

where the units ofl(0) and ND(0) are pA and electrons/s, respectively. This equation was satisfied for the incident electron energy range 0.8-1.8 MeV+ and the linearity of this dosimeter is very good for numbers of electrons perpendicularly incident on the dosimeter over the range 1.5x l04 1.5x 100 electrons/s. The standard deviations are +_0.075 and so small that the dosimeter is usable as electron dosimeter. It can be thought that the main cause of the errors was the instability of the accelerator. Beyond the number of incident electrons 1.5x 10~ electrons/s, the value 1(0) tends to be gradually saturated and reaches the saturated value of about 4 x 10 -5 A, where the number of electron-hole pairs produced in the sensitive volume is about 2.5 x 10t4 per second. This corresponds to the fact that the total charge produced in the sensitive volume is not fully

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Fig. 6. Electron-induced currents as a function of the n u m b e r o f incident electrons at incident energy 1.8 MeV.

MINIATURE DOSIMETER collected because of polarization and recombination6). These undesirable effects increase with increasing electron-hole pairs in the sensitive volume per unit time. 3.5. CALCULATIONOF THICKNESSOF THE DEPLETION LAYER When the number of electrons perpendicularly incident on the dosimeter, ND(E), at the energy of incident electrons E, supposing that every electron backscattered from the insensitive layers traverses normally the depletion layer, the total number of electrons traversing the depletion layer, NTD(E ), is given by

NTD(E ) = ND(E ) T(E) [1 + R(E)-I,

(4)

where T(E) and R(E) are the number transmission coefficient for the thickness of the window and the number reflection coefficient for the thickness of the insensitive layers beyond the sensitive region of the dosimeter, respectively, for electrons with kinetic energy E normally incident on the dosimeter. Provided that the electron energy is continuously slowing down in transmitting through the depletion layer, the energy transferred in the sensitive volume ED(E), is given by

91

From eq. (5), the energy transferred in the sensitive volume per electron incident on the dosimeter, Eab(E ), is given by Eab(E ) • T(E) L a x

x [ ( - d E / d X ) E + R(E)'(-dE/dX)o.3E].

(7)

From eq. (,6), the thickness of the depletion layer of this dosimeter, La, is given by

L d = E.b(E)/T(E ) x x [ ( - d E / d X ) a + a(E) ( - d E / d X ) o . 3 t ] . (8) The cross sectional view of the dosimeter is diagrammatically represented in fig. 7, supposing that the depletion layer of the dosimeter is located on the center of the silicon semiconductor. The quantities L1, Lz, L3 and /.4 represent the thickness of the copper film, of the p+-region of the silicon detecting element before the depletion layer, of the n-region of the silicon detecting element after the depletion layer and of the copper pin, and are about 3, 26, 26 and 900 mg/cm 2, respectively. The transmission coefficient T(E) and the reflection coefficient R(E) are given by

T(E) = 7'(Ll, E) T ( L 2 , E),

(9)

ED(E ) = ND(E ) T(E) Lo

R(E) --- R(L3, E) + T ( L 3 , E) R(L4, E) T ( L 3 , 0 . 3 E ) , (10) where Lo is the thickness of the depletion layer and ( - d E / d X ) E is the linear collision stopping power of the silicon semiconductor at electron energy Ev), and n(E) is the energy spectrum of electrons backscattered from the insensitive layers, then R(E) = S~n(E')dE', The energy spectra of backscattered electrons have been obtained by BergerS), Rester and Rainwater')), Jakshik and Jungst 1°) and Seizer and Berger11). From these data, the average collision stopping power ~E o ( - d E / d X ) E , ' n ( E ' ) d E ' / ~ n(E') dE', was calculated and was equal to about (-dE/dX)o.3 a at E = 0 . 5 and 1.0 MeV. The average energy of backscattered electrons .(~ E'.n(E') dE'/S~ n(E') dE', is nearly equal to ½E independent of E at 0.5 MeV < E < 2.0MeV s-1 z). Assuming that the average collision stopping power is equal to (-dE/dX)o.3F independent of E at 0.6 MeV
(6)

where T(L, E) and R(L, E) indicate the transmission

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A. MARUHASHI

a n d reflection coefficient for electrons with energy E on a material o f thickness L, respectively. The thickness L,~ is thick e n o u g h for the a p p r o a c h to s a t u r a t i o n backscatteringS"~°). The ratio o f the saturation backscattering per electron incident p e r p e n d i c u l a r l y on c o p p e r is a b o u t 0.16, 0.21 and 0.25 for electrons with energies 1.8, 1.0 a n d 0.6 MeV, respectivelyT). D a t a o f the dependence o f electron backscattering and transmission on foil thickness are shown in refs. 8, 10, I1 and 14. The depletion layer thickness La was calculated from eqs. (8)-(10), a n d was a b o u t 91.3, 92.4 and 90.0/~m at E = 1.8, 1.0 and 0.6 MeV, respectively. These values are in g o o d agreement with the value which was o b t a i n e d previously as the thickness o f the depletion layer o f the dosimeter for the m e a s u r e m e n t of bremsstrahlung~), from which this d o s i m e t e r for the m e a s u r e m e n t o f electrons was reconstructed. An average energy EC"ttt~ab t--,, a b s o r b e d in the silicon foil (thickness: 90 tim, density: 2.42 g/cm a) per incident electron was calculated from 90 x 2.42 x 10-4 x ( - d E / d X ) E under the a s s u m p t i o n that a beam of electrons with kinetic energy E is incident perpendicularly on the foil a n d the electron kinetic energy is c o n t i n u o u s l y slowing d o w n in t r a n s m i t t i n g t h r o u g h the foil. Eab~l(E) and E , b ( E ) / E ~ ( E ) are shown in fig. 5 as a function o f electron energy. E , b ( E ) - E ~ , J ( E ) i s the energy transferred in the sensitive volume by electrons backscattered from the materials constituting the insensitive layer o f the dosimeter, a n d the ratio o f this value to the value E,,b(E) was a b o u t 0.15 at E from 1.8 MeV to 0.8 MeV, a n d decreased slightly with E at E < 0 . 8 MeV. This decrease was caused by the a b s o r p t i o n o f backscattered electrons in the n-region o f the silicon detecting element after the depletion layer. 3.6. OTHER CHARACTERISTICS a) The induced current a n d the leakage current d e p e n d on the a p p l i e d bias voltages. The ratio o f the induced current to the leakage current increased with decreasing bias voltage as well as the description in ref. 4, a n d the leakage current increased slightly with exposure due to radiation d a m a g e if reversed bias is applied. Drifting o f the leakage current will give rise to large errors. F o r these reasons the r a d i a t i o n - i n d u c e d current flowing in the external circuit was measured with no externally applied bias voltage.

b) To examine the effect o f radiation damage, the d o s i m e t e r was irradiated up to 108 rad which is the dose a b s o r b e d in the silicon semiconductor. It was found in this experiment that the sensitivity o f the d o s i m e t e r was constant up to this exposure, but the leakage current increased slightly with exposure if reverse bias was applied.

4. Conclusion F r o m the results o f experiment and calculation, it was clearly shown that this dosimeter was applicable for d o s i m e t r y o f electrons. The sensitivity o f the dosimeter is a l m o s t independent o f electron energy in the range 0.8-1.8 MeV, and the linearity o f this dosimeter is very good for the n u m b e r o f incident electrons over the range 1.5 x 104-1.5 x 109 electrons/s. The thickness o f the depletion layer is a b o u t 901~m a n d the energy a b s o r b e d in the sensitive volume per incident electron is a b o u t 39 keV. The a u t h o r wishes to t h a n k Mr. K. N o r i s a w a for his helpful c o n t r i b u t i o n during the experiment using the electron Van de G r a a f f accelerator, a n d he is indebted to Dr. T. H y o d o for his valuable discussions a n d suggestions.

References a) N. A, Baily and A. Norman, Nucleonics 21 (1963) 64. 2) A. Lauber, Nucl. Instr. and Meth. 101 (1972) 545. 3) k. Birstein, F. Li and R. Klawer, Nucl. Instr. and Meth. 133 (1976) 279. 4) A. Maruhashi et al., Nucl. Instr. and Meth. 128 (1975) 441. s) F. H. Attix and W. G. Roesch, Radiation dosimetry, 2nd ed., vol. 2 (Academic Press, New York, 1966) p. 301. 6) W.J. Price, Nuclear radiation detection, 2nd ed. ( McGraw-H ill New York, 1964) p. 212. 7) H. Sugiyama, Circulars of the Electrotechnical Laboratory No. 170 Dec. (1970). ~) B. Alder, S. Fernbach and M. Rotenberg, Methods in computationalphysics, vol. I (Academic Press, New York, 1963) p. 135. ~) D. H. Rester and W.J. Rainwater, Nucl. Instr. and Meth. 41 (1966) 51. ~o) j. Jakschik and K. P. Jungst, Nucl. Instr. and Meth. 79 (1970) 240. ~f) S. M. Seizer and M.J, Berger, Nucl. Instr. and Meth. 119 (1974) 157. ~2) E. J. Sternglass, Phys. Rev. 95 (1954) 345. J3) K. A. Wright and J, G. Trump, J. Appl, Phys. 35 (1962) 687. 14) B. W. Mar, Nucl. Instr. and Meth. 24 (1966) 193.