The electron-photon cascade Monte Carlo code EGS4 has been used to study the energy response of the detector-grade low-cost PIN Si photodiode, which is used as the detector for personal dosimetry application. The energy deposition distribution in the active volume of the photodiode was calculated. The effect of the discrimination level and the dimension of the active volume on the sensitivity of the photodiode was studied. The sensitivities of the photodiode with Cu, Sn, Cu+Sn, and Pb compensation filter, respectively were investigated in detail. The energy response of the Si photodiode was also measured in the X-ray calibration field with effective energies from 46 to 202 keV and by using Cs-137 and Co-60 |Gamma~-ray sources. Good agreement has been obtained between results of the measurement and the Monte Carlo calculation. I. INTRODUCTION A pocket digital dosimeter is the long term goal as well as the dream in the development of the personal dosimeter. Tracing the history of the personal dosimetry development, the main evolution stages developed in the following sequence: film badge and pocket electrostatic ion chamber, TLD badge, pocket radiation chirper with GM-tube, with CdTe detector|1~, and with silicon diode|2~, pocket digital dosimeter with GM-tube, and with silicon diode. In addition to the widely-used conventional TLD badge and pocket ion chamber, pocket digital dosimeters with GM-tube|3,4~ and with silicon diode|5,6~ are already commercially available. Silicon diodes, due to their relatively high noise level, for long time have been applied almost exclusively as a radiation detector for the detection of charged particles. From the rapid development of the semiconductor technology, high-purity detector-grade silicon can be in mass production|7~ and with the improved fabrication process, silicon diode detectors with low leakage currents and therefore reduced noise levels can be achieved|8~, which are suitable for the detection of X- and |Gamma~-rays. A low-cost, detector-grade PIN silicon photodiode with low leakage current is now easily available from the commercial market. In addition, PIN silicon photodiodes have the following inherent advantages compared with GM-tube: much more rugged and compact, more stable, no high voltage bias required, and much less power consumption. Therefore, the PIN silicon photodiode is the choice as the detector for our development of pocket digital dosimeters|9~. As a personal dosimeter, the energy response of the photodiode detector requires intensive investigation and some kinds of compensation filters must be designed in order to achieve a constant sensitivity independent of the incident X- or |Gamma~-ray energy. In this paper the electron-photon cascade Monte Carlo code EGS4 was used for the study of the energy response and filter compensation of the PIN silicon photodiode. Measurements in calibrated radiation fields were performed for a verification of the simulation results. II. MONTE CARLO SIMULATION Energy deposition in the active region of the silicon photodiode for the incident photon energies from 10 keV to 10 MeV was calculated by using EGS4|10~, which is a code system for the Monte Carlo simulation of electron-photon cascade showers. Figure 1 depicts the geometrical modeling of the silicon photodiode which consists of package and window layer(region 2), Si|O.sub.2~ passivation layer(region 3), Si dead region(regions 4, 6, and 7), and Si active region(region 5) and is surrounded by vacuum(regions 1 and 8). For the study of filter compensation, filter layer or layers are added before package and window layer. A photon beam incident perpendicular to and uniformly distributed over the photodiode surface was simulated. For each case study, |10.sup.5~ photons were sampled and for each particle history, photon was traced downed to 10 keV and electron down to 1 keV. For each history tracing, energy deposition, if any, in the active region was calculated; this will induce a detector signal and cause a detector count if it is over a preset discrimination level. Here the energy-deposition distribution in the active region was treated as the pulse-height distribution of the photodiode detector under the assumption that the signal pulse comes exclusively from the collection of the charge carriers produced in the active region and that the charge collection is perfect. The sensitivity of the photodiode detector was calculated in terms of the detector counts divided by incident photon exposure. III. PARAMETRIC INVESTIGATION A. Discrimination Level In a real counting system, setting a discrimination level is indispensable to prevent the dominant noise counts. However, signals with lower pulse amplitude will also be lost. The effect of the discrimination level to the detector sensitivity has been investigated. Figure 2 shows the sensitivity curves of the photodiode detector with no setting of discrimination level and with setting of discrimination levels from 0.02 to 0.08 MeV, respectively. It can be seen from Fig. 2 that the discrimination-level setting has strong influence on the detector sensitivity for photon energies up to several hundreds keV. For higher energies the decrease in sensitivity is smooth and mild as the discrimination level is raised. This tendency of sensitivity change can be implied from the energy-deposition distributions in the active region of the photodiode detector as shown in Fig. 3. For incident photons with lower energies the interaction comes essentially from the photoelectric effect or from the competition of the photoelectric effect and the Compton scattering and, therefore, the energy-deposition distribution is much more complicated. For incident photons with higher energies the energy deposition is caused dominantly by Compton recoil electrons and, therefore, the distribution is flat. B. Dimension of Active Region The sensitivity of the photodiode detector depends obviously on the dimension of the active region. The variation of the sensitivity was studied by changing the effective surface and the thickness of the depletion layer, separately. It is found that sensitivity changes essentially proportional to the effective surface for incident photons of any energies. Although sensitivity also changes proportionally to the thickness of the depletion layer, the variation is not uniform. For lower energies the variation of the sensitivity with the thickness of the depletion layer is more of less uniformly proportional, however, the variation diminishes at the region of higher energies as shown in Fig.4. C. Filter Compensation The sensitivity of the photodiode detector is strongly energy dependent and decreases monotonically from about 40 keV to 10 MeV with a difference of two to three orders of magnitude as can be seen from Figs. 2 to 4. For the application of personal dosimetry, energy compensation, therefore, must be done to the photodiode detector in a way to achieve an energy-independent sensitivity. The investigation of the filter compensation was performed for copper(Cu), tin(Sn), combined copper and tin(Cu+Sn), and lead(Pb) filters. Figures 5 to 7 show the sensitivity curves of photodiode detector with Cu, Sn, and Cu+Sn filters of different thicknesses, respectively. It can be seen that the sensitivity is suppressed at the low-energy region and raised at the high-energy region and remains essentially unchanged at the intermediate-energy region between about 200 keV and 2 MeV. The compensation effect is enhanced as the filter thickness increases. At the low-energy region the sensitivity suppression should obviously be due to the attenuation through the large photoelectric cross section. At the high-energy region the sensitivity raise might be mainly due to the buildup of electrons in the filter which then enter the active region of the photodiode. The competition between photon attenuation and electron buildup causes the more or less unchanged sensitivity at intermediate-energy region. From Figs 5 and 7 it can be seen that at the low-energy region the sensitivity curves for filters with 0.9-mm Cu and with 0.15-mm Cu + 0.21-mm Sn show a more or less flat value within |+ or -~20% in a broad range from about 50 keV to 200 keV, which covers the energy range of most popular X-ray machines. It is advised, therefore, that a photodiode with filter of 0.9-mm Cu or 0.15-mm Cu + 0.21-mm Sn should be suitable for personal dosimetry applications in the radiation environment of X-ray facilities. Since at intermediate energy the sensitivity curve of the photodiode can be compensated by neither copper nor tin filter, a lead filter was investigated. Figure 8 shows sensitivity curves for lead filters of 4 mm and 10 mm thick, respectively, on which for comparison sensitivity curves with no filter and with filters of 0.9-mm Cu and of 0.15-mm Cu + 0.21-mm Sn are also plotted. It can be seen from Fig. 8 that a lead filter of about 6 mm thick can compensate the sensitivity to within |+ or -~25% between about 300 keV to 10 MeV and a lead filter of 10 mm thick can obtain a constant sensitivity to within |+ or -~20% up about 500 keV to 10 MeV. Silicon photodiodes with filter thicker than about 6 mm, therefore, may find good application in the radiation environment of nuclear power plants, where high-energy gamma rays with energies larger than several hundreds of keV dominate the radiation dose. When calibrated at Cs-137(0.662 MeV) or Co-60(1.25 MeV) calibration field, it will be able to measure the N-16(6.3 MeV) radiation dose around steam generators of PWR and in the turbine building of BWR nuclear power plants accurately to within 20%. The arrangement order of the combined filters of 0.15-mm Cu and 0.21-mm Sn has also been studied. It was found that for energies higher than about 100 keV there is essentially no perceivable difference between sensitivity curves. At lower energies, however, sensitivity curve for filters of Sn followed by Cu shows remarkably higher value. This phenomenon has also been verified from the comparison between the energy-deposition distributions for both combined filters. The reasons for this phenomenon may be inferred to be due to the larger gamma-ray buildup factor for the combined filters of heavier material(Sn) followed by lighter material(Cu), which is more remarkable for incident gamma rays of lower energies. D. Other Parameters Some parameters in the Monte Carlo simulation were studied. The sampling numbers were increased from |10.sup.5~ to |10.sup.6~ and different seeds for random number were tested. Essentially no perceivable difference was found. The parameter ESTEP in EGS4 calculation, which accounts for energy loss in each step of electron scattering, was changed from the default value of 0.2 to 0.01. It was found that only at a small energy range just above the discrimination levels it shows a significantly lower sensitivity value and that there is essentially no influence to the sensitivity curve if no discrimination level is set. IV. MEASUREMENTS Two types of Hamamatsu PIN silicon photodiodes, namely, S2506 and S1723-06 were measured in the national accredited calibration field of X rays as well as Cs-137(0.662 MeV) and Co-60(1.25 MeV) gamma rays. The photodiodes were encapsulated in an aluminum box to protect from environmental interference. The signals were processed through preamplifier, shaping amplifier, and connected to a counter as well as a multichannel analyzer. The bias to S2506 was 3 V and to S1723-06 30 V. Bare S2506 photodiode as well as with 0.15-mm Cu filter and with 0.15-mm Cu + 0.21-mm Sn filter was measured in the X-ray field with effective energies from 46 keV to 202 keV(peak high voltage 60 kV to 250 kV) and exposure rate ranging from several hundreds mR/hr to several thousands mR/hr. The measured sensitivity curves are shown in Fig. 9. For the S1723-06 photodiode only a bare one was measured in both X-ray and gamma-ray calibration fields with exposure rate ranging from several mR/hr to several hundreds mR/hr and with different settings of discrimination level. Figure 10 shows the measured sensitivity curves for a bare S1723-06 photodiode. V. COMPARISON BETWEEN CALCULATION AND MEASUREMENT In order to make a comparison between Monte Carlo simulation and measurement, sensitivity curves for S2506 and S1723-06 photodiodes were calculated by using EGS4 code. For the calculation of the S2506 photodiode, the epoxy mold package was modeled with 1-mm polyethylene, the depletion layer was 35 ||micro~meter~, and the effective area was 7.7(2.77 X 2.77) |mm.sup.2~ |11~. The calculated sensitivity curves with and without filters cut off at 0.02 MeV are shown in Fig.9 for comparison with measured ones. It can be seen from Fig.9 that all the measured sensitivities sand steeply at 46 keV and were much lower than the calculated ones. This might be mainly due to the fact that the discrimination level setting was too high so that part of the signal from 46-keV X rays was eliminated. In general, the agreement between measurement and calculation was fairly good. The measured discrepancy between bare sensitivity and filtered ones was larger than calculated. The most probable reason for this is that there was air-induced electron contamination in the calibration field which was, however, not taken into account in the EGS4 modeling and this electron contamination might make a remarkable contribution to the bare photodiode, nevertheless, would be blocked by the filters. For the calculation of the bare S1723-06 photodiode, the resin coating window and plastic tape package was modeled with 0.1-mm polyethylene, the depletion layer was taken as 200 ||micro~meter~, and the effective area was 100(10 X 10) |mm.sup.2~|11~. The calculated sensitivity curve with discrimination cut off at 0.02 MeV is shown in Fig. 10 for comparison with measured ones with different discrimination levels. It can be seen from Fig. 10 that the agreement of the calculated sensitivity with the measured ones seems excellent except with the one obtained with amplifier gain of 400 and discrimination level of 0.125 V, for which the discrimination-level setting might be too low and the measured sensitivity might so as be interfered by the noise. As explained above, the air-induced electrons in the calibration field might have significant contribution to the measured sensitivity of the bare photodiode and, therefore, measured sensitivity should be somewhat higher than that of calculation. Looking at the characteristic data of the S1723-06 photodiode|11~ it is found that the depletion layer at 30 V bias voltage should be about 150 ||micro~meter~ instead of 200 ||micro~meter~ modeled in the EGS4 calculation. If this correction were taken into account, the calculated sensitivity should approach the correct trend of showing a value somewhat lower than that of measurement. VI. CONCLUSIONS From this study the following conclusions will be expressed: The energy response of the PIN silicon photodiode detector is very different from the exposure response function. Therefore, adequate compensation filter is necessary for the digital dosimeter with the photodiode detector. The setting of the discrimination level has strong influence to the sensitivity of the photodiode in the low-energy region up to several hundreds of keV. The thickness of the active layer has a proportional effect on the sensitivity of the photodiode in the low-energy region up to several hundreds of keV. In the high-energy region the effect diminishes gradually up to 10 MeV. The area of the active volume has indeed straight proportional effect on the sensitivity of the photodiode. With the compensation filter of 0.15-mm Cu + 0.21-mm Sn or of 0.9-mm Cu, the PIN silicon photodiode personal dosimeter has a fairly constant sensitivity within |+ or -~20% in the energy range between about 50 and 200 keV. It is, therefore, advisable to be used in the radiation environment of typical X-ray facilities. With the compensation filter of 6- to 10-mm Pb, the sensitivity of the PIN silicon photodiode shows fairly constant up several hundreds keV to 10 MeV and drops drastically at low energies. Therefore, it may find adequate application in the radiation environment of nuclear power plants. The agreement of the energy response of the PIN silicon photodiode between the results of the Monte Carlo calculation and the experimental measurement is fairly good. VII. REFERENCES |1~ C. J. Umbarger, M. A. Wolf, and G. Entine, A Totally New Pocket Radiation Chirper, Health Physics, 36, 455-458, 1979. |2~ R. Nowotny, A Silicon-Diode Pocket Radiation Chirper, Health Physics 44, 158-160, 1983. |3~ Rad-21(ALNOR), ALNOR, Alnor Oy, Turku Finland. |4~ GAMMACOM M4200(R. A. Stephen), England. |5~ DMC-10 and DMC-90, MGP, France. |6~ DOX-SI Digited Dosimeter, Saphymo Physiotechnie, France. |7~ W. Von Ammon and H. Herzer, The production and Availability of High Resistivity Silicon for Detector Application, Nucl. Instr. and Meth. in Physics Research 226, 94, 1984. |8~ J. Kemmer, Improvement of Detector Fabrication by the Planar Process, Nucl. Instr. and Meth. in Physics Research 226, 89, 1984. |9~ H. H. Tseng and H. F. Chang, Energy Compensation Characteristics of Cu and Sn on Low Cost Si Photodiodes for |Gamma~(x) Dosimetry Applications, IEEE Trans. Nucl. Sci., vol 39, no. 5, p.1523, 1992. |10~ W. R. Nelson, H. Hirayama, and D. W. O. Rogers, The EGS4 code System, SLAC-265, 1985. |11~ HAMAMATSU Photodiodes 1991 CATALOG, Hamamatsu Photonics K. K., Solid State Division, 1126-1, Ichino-cho, Hammatsu City 435, Japan.