A MOSFET-Based Method for Measuring Peak Kilovoltage (kVp) in Diagnostic X-Ray Beams

Peak kilovoltage (kVp) is an X-ray tube parameter that can influence the radiograph image quality and therefore, if the kVp is different from the nominal value, it can provide an unnecessary radiation dose to the patient if the examination has to be repeated. Therefore, some radiation protection institutions and health organizations (ICRP, IAEA) make recommendations to monitor kVp in medical diagnostic X-ray equipment in clinics and hospitals. There are some methods for measuring kVp in diagnostic X-ray beams, and the most common is the well-known two-sensor method, which uses two filters to attenuate the radiation beam, and it is based on the measurement of each identical sensor. The purpose of this article is to present a method for non-invasive measurement of kVp in medical diagnostic X-ray beams using the MOSFET device. Actually, MOSFET is well known as a detector for ionizing radiation dosimetry mainly in radiotherapy beams. Recently, MOSFET has also been used as dosimeter in diagnostic X-ray beams. In this work it will be shown a kVp measurement technique with MOSFET, which does not use the attenuation factor of the radiation filters, but instead takes advantage of the effect of the device package itself, known as the buildup cap effect. The results show that even with damage to the device exposed to radiation, MOSFET can be used as sensor for kVp measurement.


I. INTRODUCTION
T HE PEAK kilovoltage (kVp) of X-ray tubes used in clinics and hospitals is an important parameter to be monitored following recommendations made by some international organizations (e.g., IAEA, ICRP) [1], [2]. Actually, the kVp of an X-ray tube normally used in radiodiagnosis is a parameter that can influence the quality of the radiographic image and therefore can lead the patient to receive unnecessary radiation doses if the exam is repeated due to a blurred image, for example. This can occur mainly on older radiographic equipment, which is widely operational in Latin American and African countries, for instance. However, presenting an innovative technique may also have applications in other kVp measurement processes, even if it is not for clinical X-ray equipment.
Generally, the most common method for measuring kVp in X-ray tubes of clinical equipment is to use two identical radiation sensors, each with a radiation filter in front of the sensor [3], [4], [5], [6]. It is a non-invasive measurement technique with two sensors and radiation attenuation filters with different thicknesses, x 1 and x 2 . As in radiodiagnosis the exposures are made with pulses of the order of tens or hundreds of milliseconds then, to avoid systematic errors [5], the X-ray pulse must be performed simultaneously on both sensors, and the result can be obtained by means of calculations as described in the literature [4], [5], [6], [7] (Fig. 1).
The method mentioned above is well known [4] and the kVp is basically estimated by (1), where S 1 and S 2 are the current signals (nA) from each sensor, x 1  thickness of each radiation attenuation filter (mm), C 1 and C 2 correspond to the regression coefficients [3], [4], [5].
Actually, this method is based on determining the intensity I x of a filtered spectrum such as that emitted by a typical X-ray tube [6], [7], [8], given by: where I 0 corresponds to the unfiltered X-ray beam, E max is the maximum energy of the emitted photons, f (E) is the distribution function of photons with energies between E and E + dE, μ(E) is the linear attenuation coefficient of the filter material for the energy E, and x is the filter thickness. Silberstein [8] was the first to correlate I x with the Laplace transform making: to obtain: By using the Laplace transform shifting property it results in: where, μ 0 is the linear attenuation coefficient for E max , and G(x) is a function that can be chosen appropriately to be able to reconstruct the filtered X-ray spectrum I x [6], [7], [8], since E max is correlated to kVp by: where q e is the electron charge. However, Herrnsdorf [3] showed that, in fact, it is not necessary to reconstruct the spectrum to obtain the kVp. Instead, one can use the concept of effective attenuation coefficient, μ eft , and the exponential attenuation equation: According to Lindström [9], μ eft is correlated with both mean and effective energies of the X-ray spectrum and it can be assumed that: Assuming that each filter x 1 and x 2 produces, respectively, I x1 and I x2 as a function of μ ef t , and also that S 1 and S 2 correspond to I x1 and I x2 , respectively, from (7) we have that: Combining (8) with (9) then results in (1). In this article it will be shown that if the sensors are two identical MOSFETs the technique presented based on (1) also works. However, the main purpose in this paper is to demonstrate experimentally that there is another way to measure the kVp of an X-ray tube without the need for two radiation filters. Before presenting the method, some information about the process of interaction of X-ray photons with the device is briefly discussed next.
Normally, the kVp value is chosen on the clinical X-ray equipment panel depending on the patient's weight. In medical diagnostic radiology these values can vary between 70 kV and 150 kV, depending on the type of organ to be radiographed and also on the type of equipment and the manufacturer. For the range 70-150 kV one can assume that the effective energy varies approximately between 50 keV and 100 keV where Compton effect is predominant [10], [11], [12], [13]. In fact, photon interactions occur with both the device package and the semiconductor chip and as both the package and the semiconductor material are of low atomic numbers then the probability of the Compton effect predominates for the energy range used in diagnostic X-ray beams [13]. Furthermore, there also are the Rayleigh and photoelectric effects, the latter occurring due to the photons scattered in the Compton effect, i.e., photons with lower energy. Actually, the package works as a build-up cap, which is a well-known effect [14]. Due to numerous interactions, an electron rain is generated in the MOSFET as shown in Fig. 2 [15]. Therefore, instead of beam attenuation, there is a build-up cap effect, which makes the signal to be measured stronger, i.e., the current in the semiconductor device, i d (t), increases. In the MOSFET, i d signal is the drain current and can be measured in real-time during the X-ray pulse, shown next.

A. MOSFET BIASING, SIGNAL MEASUREMENT AND AMMETER
The MOSFET biasing circuit is simple as shown in Fig. 3a. Analyzing a MOSFET switching curve (Fig. 3b), there is  a cutoff region (I D ≈ 2 nA), a small range of V GS where switching occurs, and a saturation region with the current I D = V DS /R D . Therefore, V GS = 2.0 V bias was chosen before the switching region for the following reasons: 1) X-ray irradiation on the MOSFET produces a shift in the curve to the left [16], [17]; 2) Switching region can generate signals with strong statistical fluctuation; 3) At the saturation (I D ≈ 20 μA) the sensitivity to the radiation is practically null, i.e., the drain current due to X-ray pulse can be much less than the saturation current.
During the X-ray pulse, the electron rain coming from package and chip itself generates a drain current called I DX , to associate with the time interval in which the X-ray pulse occurs. That is, due to V DS bias the signal i d (t) = I DX is generated. Without X-ray beam the drain current is simply called I D . To measure simultaneously two device samples an EFF1705 source-meter [18], Scients , was used. Basically, it is a 0.1 nA resolution two-channel electronic system for measuring I DX and I D , and supply V DS and V GS .   Table 1 shows the device characteristics (mechanical and electrical). Information about the package thickness and its material (Ecopack) can be found in [19], [20].

B. MOSFETS
Actually, the way found to perform an innovative method for measuring kVp with MOSFETs was to choose devices that are commercially available in two different types of packages. This means that both MOSFET devices have to be electrically identical (chip area, oxide thickness, drainsource resistance, capacitances, etc.) and can have different mechanical characteristics, specifically different packages, e.g., the thickness of the package between the device face and the chip face (Thickness in Table 1) [19], [20].

C. EXPERIMENTAL SETUP AND X-RAY PULSES
A clinical diagnostic X-ray equipment, Polymat Plus 30/50, Siemens , was used to perform the experiments. For measurements using the most common method, Fig. 1 illustrates the experimental setup: two identical devices and each with a filter of different thicknesses: x 1 = 1.0 mm and x 2 = 2.0 mm. The distance between the X-ray source and the sensors was set to be d = 32.5 cm, for all experiments. The X-ray tube parameters can be chosen according to Table 2.

D. MEASUREMENT PROCEDURES
First, it was evaluated how is the signal behavior of a standard detector (10X5-6 ion chamber, Radical ) for the following X-ray tube parameters: 1600 ms exposure time for all experiments; 100 mAs and 200 mAs workloads; and varying the potential (kVp) from 52 kV up to 125 kV. The dose rate is proportional to the current signal produced by the sensor in each X-ray pulse [11], [15]. In each graph presented in the results each point corresponds to an average of 3 measurements. A total of 12 MOSFETs were used in all experiments as each measurement was performed in duplicate (two MOSFET samples).
The second procedure aimed to verify the repeatability in the I DX measurement. The following X-ray tube parameters were taken: 1600 ms, 100 mAs, 102 kV. The experiments do not involve patients and for that reason after each X-ray pulse the clinical equipment had to be cooled down during 3 min (by technical recommendation), and therefore 180 measurements of I D were taken, so each point corresponds to an average of 180 readings. This timeout for the X-ray pulses also allows for some annealing to occur on the MOSFET. Actually, the value of I D after each X-ray pulse corresponds practically to the ionization damage in the silicon oxide of the device, which generates a parasitic electric field as a function of the accumulated radiation dose. Therefore, it makes a shift in the MOSFET switching curve, which is a well-known effect [16], [17].
Knowing that there is repeatability on I DX measurements, the third part of the experiments is correlated with the first part, which consists of comparing the MOSFET response with the response of the standard detector. A comparison of the results of two identical MOSFETs was also performed.
One of the methods in this paper is to verify if the MOSFET could be used in the usual two-sensor technique, i.e., it was placed radiation filters with different thicknesses on two electrically and mechanically identical devices. This procedure will lead us to conclude whether the MOSFET can be used by the known two-sensor method (see Fig. 1).
The fifth method performed in this work is basically the main one. Two electrically identical MOSFETs with different packages were exposed to the X-ray pulses without radiation attenuation filters as shown in Fig. 4. The X-ray tube parameters were: 1600 ms; 100 mAs; and varying the potential from 52 kV up to 125 kV.
Finally, our last experiment is to analyze how much scattering from the inherent radiation filter of the clinical equipment can reach the MOSFET under test. This can be done by varying the area of the radiation field in the X-ray equipment itself to perform I DX measurements for each selected radiation field size. Scattered photons can make an additional contribution to measurements and thus produce a systematic error [14]. As the EFF1705 resolution is 0.1 nA, and in all the data the relative uncertainty were always less than 2%, a constant marker size was chosen to represent the error bar size, which is always smaller than the marker size.

III. RESULTS AND DISCUSSION
Firstly, Fig. 5 shows how the signal produced by the ion chamber behaves. It can be seen that the response of the standard sensor varies practically linearly with kVp. Regarding the workload, one can verify that by doubling the workload, the response also practically doubles. For example, the dose rate is 43 mGy/s for 102kV@100mAs, and about 82 mGy/s for 102kV@200mAs. As the Xray pulse time is constant (1.6 s) then the X-ray tube current, I XRT , corresponds to 62.5 mA and 125 mA, respectively. The current in the sensor is proportional to I XRT [11], [15]. Fig. 6a shows results of I DX measurements for a sequence of 30 X-ray pulses (≈ 69 mGy each pulse), therefore the x-axis corresponds to ≈ 2.1 Gy accumulated radiation dose. It can be seen that there is repeatability in the measurements. In this set of I DX measurements, the highest value of relative uncertainty was less than 1.5%. During the same sequence of X-ray pulses it was followed how I D varied. The graph in Fig. 6b indicates that I D increases about 200%, which corresponds to the ionization damage produced on the device during the irradiation. Fig. 7 shows the MOSFET response to the X-ray pulses from the clinical equipment, and comparing with the standard sensor (Fig. 5) the similarity of behavior of both sensors can be noticed, it was expected [15]. The graph in Fig. 8 shows two identical MOSFET samples irradiated simultaneously to compare their responses. Basically, the difference in the curves consists in the sensitivity of each MOSFET, as in all types of sensor. In this case it is due to very small electrical and mechanical differences in their characteristics. Fig. 9 demonstrates that, regardless of the workload, the MOSFET can be used as a sensor if the usual dual-sensor technique is preferred. However, as I DX is higher for a workload of 200 mAs one can conclude that it is better to make the measurements by selecting a higher workload to minimize the relative uncertainties.     in Table 3, where C 1 and C 2 correspond to the regression of equation (10), i.e., it corresponds to the x-axis versus the y-axis (the inverse problem function).
The main result of this work is shown in Fig. 11 where two electrically identical MOSFETs with different packages are irradiated without radiation attenuation filters in front of each device. In a simple comparison of Fig. 9 with Fig. 11 it is observed in the second one I DX measurements are stronger without radiation filters even if a lower workload is selected. For example, the MOSFET produces I DX ≈ 92 nA for 100mAs@102kV without radiation filter, whereas with the 1 mm and 2 mm thick filter it produces I DX ≈ 40 nA and I DX ≈ 33 nA, respectively. Therefore, even performing the measurements with a workload of 100 mAs, a signal gain of more than 6dB is obtained in the experiment made without radiation filters.
The last results of this paper are in Table 4 and Table 5. The first one presents the fraction of radiation scattered by the inherent radiation filtration of the clinical equipment. Note that the contribution of scattered photons reaches 9.2% (≈1-40.2/44.3) comparing the X-ray beam of 196 cm 2 with that of 1 cm 2 , i.e., the scattering elimination is 9.2%. This leads us to conclude that the measurement of kVp must be performed with the collimated radiation beam, practically covering only the device area, to minimize the uncertainties and avoid a systematic error due to scattering. Table 5 shows two sets of relative uncertainties obtained in the experiment of Fig. 8. As the uncertainties (type B) of the X-ray generator and source-meter are 1% and 0.5%, respectively, it can be stated that the uncertainties u 1 and u 2 , obtained from each device MOSFET1 and MOSFET2, respectively, are compatible with the expected value of type A uncertainties.  Finally, looking at the setup of the usual method in [4], it can be seen that there are radiation filters with their other required parts. Thus, from the point of view of kVp meter design, the proposed method presents less complexity, since there is a current signal gain and the technique becomes simpler. Also, from an industrial design point of view, it can be said that such an innovative technique implies an improvement in the economic factor of production.

IV. CONCLUSION
A non-invasive method based on electrically identical MOSFETs with different packages for measuring the potential (kVp) of diagnostic X-ray tube was presented. The usual method is based on the ratio of measurements from two identical sensors each with a radiation attenuation filter positioned in front of the device. The method proposed in this work does not use radiation filters, but instead uses the build-up cap effect, its own package, to obtain a signal gain and consequently achieve lower measurement uncertainties. The results showed that it is an innovative and valid technique. Also, the data obtained lead to the conclusion that it is more efficient to perform the measurements with a collimated X-ray beam.