Commercial P-Channel Power VDMOSFET as X-ray Dosimeter †

The possibility of using commercial p-channel power vertical double-diffused metal-oxidesemiconductor field-effect transistors (VDMOSFETs) as X-ray sensors is investigated in this case study. In this aspect, the dependence of sensitivity on both the gate voltage and the mean energy for three X-ray beams is examined. The eight gate voltages from 0 to 21 V are applied, and the dependence of the sensitivity on the gate voltage is well fitted using the proposed equation. Regarding X-ray energy, the sensitivity first increases and then decreases as a consequence of the behavior of the mass energy-absorption coefficients and is the largest for RQR8 beam. As the mass energy-absorption coefficients of SiO2 are not found in the literature, the mass energy-absorption coefficients of silicon are used. The behavior of irradiated transistors during annealing at room temperature without gate polarization is also considered.


Introduction
The idea of using p-channel metal-oxide-semiconductor field-effect transistor (MOSFET), or shorter MOS transistor, as a pMOS dosimeter of ionizing radiation is very old [1], and the basic concept of pMOS dosimeter is to convert the threshold voltage shift, ∆V T , induced by irradiation, into absorbed radiation dose, D. The pMOS dosimeter advantages, in comparison with other dosimetric systems, include immediate, non-destructive read out of dosimetric information, extremely small size of the sensor element, the ability to permanently store the absorbed dose, wide dose range, very low power consumption, compatibility with microprocessors, and competitive price (especially if cost of the read-out system is taken into account). The disadvantages are a need for calibration in different radiation fields ("energy response"), relatively low resolution (starting from about 1 rad), and nonreusability.
There are many investigations of the effect of gamma radiation [9,10,23], protons [5,23], and heavy-ions [6,24] but not the effect of X rays on commercial MOSFETs, to the best of our knowledge. Additionally, their ability to be used as dosimeters of X rays has not been investigated, to our knowledge. X-rays are much more complex and complicated than gamma rays [25] because they are polyenergetic, but the transistor responses are highly dependent on energy from the X-ray spectrum. Many laboratories do not have an X spectrometer but use mean energy and/or a half-value layer as X-beam parameter(s).
In this case study, we investigate the sensitivity, as a main dosimetric parameter, of commercial p-channel VDMOSFETs to X-rays depending on different positive voltages at the gate (a zero gate voltage case was presented in [26]). This transistor type is potentially suitable for radiation dosimetry because it has a relatively thick oxide of about 100 nm. The dependence of sensitivity on X-ray energy is also investigated using three different beam energies. The behavior of densities of positive radiation-induced fixed traps (FTs) in the gate oxide and switching traps (STs) near and at the interface during X-ray irradiation is examined [27,28]. The recovery of the threshold voltage of irradiated transistors during their annealing at room temperature without gate voltage (spontaneous annealing) is also investigated as another dosimetric parameter.

Experimental Details
The IRF9520 commercial p-channel VDMOSFETs, mounted in TO-220 plastic packaging, having about 100 nm oxide thickness and pre-irradiation threshold voltage of V T0 = 2.9 V, were used. The transistors were irradiated at room-temperature with X-rays to the value of the air kerma of K air = 50 Gy at the Vinča Institute of Nuclear Science, Belgrade, Serbia (a Hopewell Design Beam Irradiator model x80-225 was used). The voltages at the gate during irradiation were V G,irr = 0 V, 3 V, 6 V, 9 V, 12 V, 15 V, 18 V and 21 V, while the drain and source were grounded (in the case of V G,irr = 0 V, all pins of transistors were grounded).
Air kerma, K air , was measured directly with the dosimetric system containing the PTW UNIDOS Webline electrometer and Exradin A3 ionization chamber. The transistors were irradiated at a distance of 35 cm, but K air was measured at a distance of 50 cm, and then K air was recalculated for a distance of 35 cm using the quadratic law.
Three RQR radiation qualities (RQR3, RQR8, and RQR10) were used. The mean energies were calculated by SpekCalc software that is free of charge for research purposes [29]. The characteristics of X-ray beams, the mean energies and air kerma rates are given in Table 1. Table 1. The X-ray beam type, tube potential (U p ), tube current (I p ), mean energy (E mean ), and air kerma rate (DK air ). During irradiation, an automatic system for measuring the electrical transfer characteristics was used [26,30]. This system contains the custom-made switching and bias unit (SABU) [30], and for these experiments a specially designed printed circuit board with relays (PCBR) [26], in which the eight VDMOSFETs were placed, was implemented. The PCBR is connected with SABU via two DSUB cables-one DSUB-25 is for relay control, and the other DSUB-9 is for transistors biasing. The SABU contains a PIC16F887 microcontroller that communicates with the PC via an FTDI chip. The source-measure unit (Keithley 2400 SMU) is connected to the computer via USB-GPIB interface card. The entire system (SABU, PCBR, and SMU) is controlled by the PC using a custom-written program in C#. The block diagram of experimental setup is displayed in Figure 1. and the other DSUB-9 is for transistors biasing. The SABU contains a PIC16F887 microcontroller that communicates with the PC via an FTDI chip. The source-measure unit (Keithley 2400 SMU) is connected to the computer via USB-GPIB interface card. The entire system (SABU, PCBR, and SMU) is controlled by the PC using a custom-written program in C#. The block diagram of experimental setup is displayed in Figure 1. After irradiation, the spontaneous annealing (SA), representing the room-temperature annealing without a gate voltage (VG,sa = 0 V), was performed up to 3500 h.

X-ray Beam
The gate and drain were short-connected during the electrical characteristic measurements. The drain-source current, IDS, was forced, and the gate voltage, VG, was measured. The threshold voltage, VT, is determined from the electrical transfer characteristics in saturation as the intersection between VG axis and the extrapolated linear region of the (IDS) 1/2 -VG curves using the least-square method performed in the Octave 6.2.0 program [31]. For p-channel MOSFETs, VT is negative, but in the whole paper the absolute values of VT are used.
Since the MGT is an electrical measurement technique that does not really recognize the physical location of the traps but recognizes the electrical activity of created traps, we usually use ∆Nft and ∆Nst as they better reflect the electrical response of the traps, compared to the more commonly used quantities, which imply the physical location of the traps: the density of oxide traps (the traps in the oxide), ∆Not, and the density of interface states (the states exactly at the SiO2/Si interface), ∆Nit.
The traps, created by any stress (radiation, electric fields, temperature, etc.), which do not capture the carriers (charge) from the channel (i.e., do not exchange carriers After irradiation, the spontaneous annealing (SA), representing the room-temperature annealing without a gate voltage (V G,sa = 0 V), was performed up to 3500 h.
The gate and drain were short-connected during the electrical characteristic measurements. The drain-source current, I DS , was forced, and the gate voltage, V G , was measured. The threshold voltage, V T , is determined from the electrical transfer characteristics in saturation as the intersection between V G axis and the extrapolated linear region of the (I DS ) 1/2 -V G curves using the least-square method performed in the Octave 6.2.0 program [31]. For p-channel MOSFETs, V T is negative, but in the whole paper the absolute values of V T are used.
The threshold voltage shift, ∆V T , is: The midgap-subthreshold technique (MGT) that determines the components of ∆V T of fixed traps (FTs), ∆V ft , and of switching traps (STs), ∆V st , was used [32]. ∆V T during irradiation and annealing can be presented as: Using ∆V ft and ∆V st , the areal densities of FTs, ∆N ft [cm −2 ], STs, and ∆N st [cm −2 ], respectively, can be found [32]: where C ox = ε ox /t ox is the gate oxide capacitance per unit area, ε ox = 3.45 × 10 −13 F/cm is the silicon-dioxide permittivity, and e is the electron charge. Since the MGT is an electrical measurement technique that does not really recognize the physical location of the traps but recognizes the electrical activity of created traps, we usually use ∆N ft and ∆N st as they better reflect the electrical response of the traps, compared to the more commonly used quantities, which imply the physical location of the traps: the density of oxide traps (the traps in the oxide), ∆N ot , and the density of interface states (the states exactly at the SiO 2 /Si interface), ∆N it .
The traps, created by any stress (radiation, electric fields, temperature, etc.), which do not capture the carriers (charge) from the channel (i.e., do not exchange carriers (charge) with the channel) within the time frame of the electrical MG measurement, represent the FTs. The traps, created by any stress, which capture the carriers (charges) from the channel (exchange carriers (charges) with the channel) within the time frame of the electrical MG measurement, represent the STs [31].
The STs consist of traps created in the oxide but very near the SiO 2 /Si interface, called the slow switching traps (SSTs) or border traps, and of traps created exactly at the SiO 2 /Si interface, called fast-switching traps (FSTs), true-interface traps (true interface states), or simply-interface traps (states). The correlation between the densities of these traps is [33]: where ∆N sst is the density of SSTs and ∆N fst is the density of FSTs. It is obvious that ∆N ot includes the FTs and SSTs but ∆N it only includes FSTs, and the correlations are

Results and Discussion
The results of the threshold voltage shift, ∆V T , during irradiation with V G,irr = 21 V (maximum gate polarization used), for all three X-ray beams, are shown in Figure 2. The case with the minimum value of the gate polarization of V G,irr = 0 V (zero gate polarization) was considered in [26]. All used gate polarizations, including zero gate polarization, show the same behavior.
The STs consist of traps created in the oxide but very near the SiO2/Si interface, called the slow switching traps (SSTs) or border traps, and of traps created exactly at the SiO2/Si interface, called fast-switching traps (FSTs), true-interface traps (true interface states), or simply-interface traps (states). The correlation between the densities of these traps is [33]: where ΔNsst is the density of SSTs and ΔNfst is the density of FSTs. It is obvious that ∆Not includes the FTs and SSTs but ∆Nit only includes FSTs, and the correlations are ΔNot = ΔNft + ΔNsst and ∆Nit = ∆Nst − ∆Nsst = ΔNfst.

Results and Discussion
The results of the threshold voltage shift, ∆VT, during irradiation with VG,irr = 21 V (maximum gate polarization used), for all three X-ray beams, are shown in Figure 2. The case with the minimum value of the gate polarization of VG,irr = 0 V (zero gate polarization) was considered in [26]. All used gate polarizations, including zero gate polarization, show the same behavior.
It was shown that the dependence of ∆VT on Kair for VG,irr = 0 V is linear up to the investigated air kerma of 50 Gy [26]: where S is the sensitivity of the transistors to radiation. Linearity is expected to increase with increasing gate polarization. Here, it is proven that the ∆VT = f(Kair) dependence for all used gate polarizations is linear according to Equation (5) (shown only for VG,irr = 21 V in Figure 2), and r-square (r 2 ) correlation coefficients of linear regression are higher than 0.99 for all cases. Table 2 shows the sensitivity of irradiated VDMOSFETs.   It was shown that the dependence of ∆V T on K air for V G,irr = 0 V is linear up to the investigated air kerma of 50 Gy [26]: where S is the sensitivity of the transistors to radiation. Linearity is expected to increase with increasing gate polarization. Here, it is proven that the ∆V T = f (K air ) dependence for all used gate polarizations is linear according to Equation (5) (shown only for V G,irr = 21 V in Figure 2), and r-square (r 2 ) correlation coefficients of linear regression are higher than 0.99 for all cases. Table 2 shows the sensitivity of irradiated VDMOSFETs.
Our investigations have shown that the following simple function can fit very well the dependence of ∆V T on V G,irr, at certain dose [34].
where ∆V T,sat is the saturation value of ∆V T , and r and s are the positive constants. Consequently, a similar equation can be used to fit the dependence of S on V G,irr : where S sat is the saturation value of S, and a and b are the positive constants. Figure 3 shows that the fitting of sensitivity using Equation (7) is good. The parameters of Equation (7), obtained as a result of fitting shown in Figure 3, are given in Table 3. Our investigations have shown that the following simple function can fit very well the dependence of ∆VT on VG,irr, at certain dose [34].
where ΔVT,sat is the saturation value of ΔVT, and r and s are the positive constants. Consequently, a similar equation can be used to fit the dependence of S on VG,irr: where Ssat is the saturation value of S, and a and b are the positive constants. Figure 3 shows that the fitting of sensitivity using Equation (7) is good. The parameters of Equation (7), obtained as a result of fitting shown in Figure 3, are given in Table 3.  (7). The dependence of the density of FTs and ∆Nft on Kair for VG,irr = 21 V is shown in Figure 4. ∆Nft is the highest for the RQR8 beam but the lowest for RQR3. ∆Nft also shows this behavior for the other used polarizations (not shown), except for VG,irr = 0 V, analyzed in [26], where ∆Nft is also the highest for the RQR8 beam but almost the same for the other two beams. Figure 5 shows that ∆Nst is about 50% less than ∆Nft for VG,irr = 21 V, and ∆Nst is the highest for RQR3 and the lowest for RQR10. VG,irr = 0 V shows opposite behavior, and ∆Nst is the highest for the RQR10 beam but the lowest for RQR3 [26].  The dependence of the density of FTs and ∆N ft on K air for V G,irr = 21 V is shown in Figure 4. ∆N ft is the highest for the RQR8 beam but the lowest for RQR3. ∆N ft also shows this behavior for the other used polarizations (not shown), except for V G,irr = 0 V, analyzed in [26], where ∆N ft is also the highest for the RQR8 beam but almost the same for the other two beams. Figure 5 shows that ∆N st is about 50% less than ∆N ft for V G,irr = 21 V, and ∆N st is the highest for RQR3 and the lowest for RQR10. V G,irr = 0 V shows opposite behavior, and ∆N st is the highest for the RQR10 beam but the lowest for RQR3 [26].   ∆Nft = f(VG,irr) dependence is not linear, and it is not possible to find a simple parameter similar to sensitivity by which we could easily consider the dependence of ∆Nft on VG,irr. Therefore, ∆Nft at a certain Kair should be considered, and it is best to take the last point during irradiation, i.e., Kair = 50 Gy. The same goes for ∆Nst = f (VG,irr). The values of ∆Nft at 50 Gy are presented in Figure 6, showing that the highest density is for RQR8 and the lowest for the RQR3 beam. This behavior corresponds to the sensitivity shown in Figure  3. However, ∆Nst does not show any clear dependence on VG,irr as ∆Nft (Figure 7). ∆Nft is twice as large as ∆Nst and has a more dominant effect on ∆VT than ∆Nst. Although ∆Nft contribution to ∆VT is still significant, it is much lower than in the case of gamma radiation of VDMOSFETs, when ∆Nft is usually more than five times higher than ∆Nst [31,35].   ∆Nft = f(VG,irr) dependence is not linear, and it is not possible to find a simple parameter similar to sensitivity by which we could easily consider the dependence of ∆Nft on VG,irr. Therefore, ∆Nft at a certain Kair should be considered, and it is best to take the last point during irradiation, i.e., Kair = 50 Gy. The same goes for ∆Nst = f(VG,irr). The values of ∆Nft at 50 Gy are presented in Figure 6, showing that the highest density is for RQR8 and the lowest for the RQR3 beam. This behavior corresponds to the sensitivity shown in Figure  3. However, ∆Nst does not show any clear dependence on VG,irr as ∆Nft (Figure 7). ∆Nft is twice as large as ∆Nst and has a more dominant effect on ∆VT than ∆Nst. Although ∆Nft contribution to ∆VT is still significant, it is much lower than in the case of gamma radiation of VDMOSFETs, when ∆Nft is usually more than five times higher than ∆Nst [31,35]. ∆N ft = f (V G,irr ) dependence is not linear, and it is not possible to find a simple parameter similar to sensitivity by which we could easily consider the dependence of ∆N ft on V G,irr . Therefore, ∆N ft at a certain K air should be considered, and it is best to take the last point during irradiation, i.e., K air = 50 Gy. The same goes for ∆N st = f (V G,irr ). The values of ∆N ft at 50 Gy are presented in Figure 6, showing that the highest density is for RQR8 and the lowest for the RQR3 beam. This behavior corresponds to the sensitivity shown in Figure 3. However, ∆N st does not show any clear dependence on V G,irr as ∆N ft (Figure 7). ∆N ft is twice as large as ∆N st and has a more dominant effect on ∆V T than ∆N st . Although ∆N ft contribution to ∆V T is still significant, it is much lower than in the case of gamma radiation of VDMOSFETs, when ∆N ft is usually more than five times higher than ∆N st [31,35]. Electronics 2022, 11, x FOR PEER REVIEW 7 of 12   Figure 8 shows the dependence of ∆Nft at Kair = 50 Gy on mean beam energy, Emean. The behavior is the same for all applied voltages, as in the case of VG,irr = 21 V shown in Figure 4, including zero polarization [26].    Figure 8 shows the dependence of ∆Nft at Kair = 50 Gy on mean beam energy, Emean. The behavior is the same for all applied voltages, as in the case of VG,irr = 21 V shown in Figure 4, including zero polarization [26].   Figure 8 shows the dependence of ∆N ft at K air = 50 Gy on mean beam energy, E mean . The behavior is the same for all applied voltages, as in the case of V G,irr = 21 V shown in Figure 4, including zero polarization [26].
The absorbed dose, D, in matter represents the mean energy absorbed per unit mass of irradiated matter at the point of interest, and for a constant incident radiation flux it is defined as follows: where E ab is the mean absorbed energy in the matter and m is the mass of the matter. Taking into account the mechanisms of creating traps in the oxide during irradiation [31], it is absolutely clear that ∆N ft depends on the energy absorbed in the gate oxide (SiO 2 ). Based on Equation (8), it follows that ∆N ft directly depends on the absorbed dose in SiO 2 and D SiO2 . If all X-ray photons have the same energy corresponding to the mean energy, E mean , then only one type of interaction effect will be involved (the photoelectric effect for these mean energies [31]). However, it should be borne in mind that it is a polyenergetic radiation spectrum that also includes radiation photons of lower and higher energies, so for some energies the Compton effect is dominant.   Figure 8 shows the dependence of ∆Nft at Kair = 50 Gy on mean beam energy, Emean. The behavior is the same for all applied voltages, as in the case of VG,irr = 21 V shown in Figure 4, including zero polarization [26].  The absorbed dose in matter is related to the kerma in air via the equation [31]: where (µ me (E)) matter and (µ me (E)) air are the mass energy-absorption coefficients of the matter and air, respectively. These coefficients are energy-dependent, and for SiO 2 Equation (9) can be written as where (µ me (E)) SiO2 represents the mass energy-absorption coefficients of SiO 2 . Unfortunately, we were not able to find the values for (µ me (E)) SiO2 in the literature. Therefore, instead of (µ me (E)) SiO2 , we used the mass energy-absorption coefficients of silicon, (µ me (E)) Si , given in Ref. [36]. This difference can be significant for energies less than 100 keV. In Figure 9, the (µ me (E)) Si /(µ me (E)) air ratio in terms of beam energy is shown. If we compare the results from Figure 9 with the results from Figure 8, it can be concluded that they do not agree. Namely, on the basis of Figure 9, the sensitivity is expected to decrease with the mean X-ray energy in considered range from 32.57 to 56.70 keV. The reason for this discrepancy between the results from Figures 8 and 9 may lie in the fact that either (µ me (E)) Si coefficients for silicon are not suitable to be used for SiO 2 or/and the mean energy is not a true indicator of the X-ray beam. The absorbed dose, D, in matter represents the mean energy absorbed per unit mass of irradiated matter at the point of interest, and for a constant incident radiation flux it is defined as follows: where Eab is the mean absorbed energy in the matter and m is the mass of the matter. Taking into account the mechanisms of creating traps in the oxide during irradiation [31], it is absolutely clear that ∆Nft depends on the energy absorbed in the gate oxide (SiO2). Based on Equation (8), it follows that ∆Nft directly depends on the absorbed dose in SiO2 and DSiO2.
If all X-ray photons have the same energy corresponding to the mean energy, Emean, then only one type of interaction effect will be involved (the photoelectric effect for these mean energies [31]). However, it should be borne in mind that it is a polyenergetic radiation spectrum that also includes radiation photons of lower and higher energies, so for some energies the Compton effect is dominant.
The absorbed dose in matter is related to the kerma in air via the equation [31]: where (µme(E))matter and (µme(E))air are the mass energy-absorption coefficients of the matter and air, respectively. These coefficients are energy-dependent, and for SiO2 Equation (9) can be written as where (µme(E))SiO2 represents the mass energy-absorption coefficients of SiO2. Unfortunately, we were not able to find the values for (µme(E))SiO2 in the literature. Therefore, instead of (µme(E))SiO2, we used the mass energy-absorption coefficients of silicon, (µme(E))Si, given in Ref. [36]. This difference can be significant for energies less than 100 keV. In Figure 9, the (µme(E))Si/(µme(E))air ratio in terms of beam energy is shown. If we compare the results from Figure 9 with the results from Figure 8, it can be concluded that they do not agree. Namely, on the basis of Figure 9, the sensitivity is expected to decrease with the mean X-ray energy in considered range from 32.57 to 56.70 keV. The reason for this discrepancy between the results from Figures 8 and 9 may lie in the fact that either (µme(E))Si coefficients for silicon are not suitable to be used for SiO2 or/and the mean energy is not a true indicator of the X-ray beam. Another characteristic of dosimeters, in addition to sensitivity, is fading, f. This shows the recovery of the transistor threshold voltage after irradiation, during annealing at room Figure 9. (µ me (E)) silicon /(µ me (E)) air ratio versus X-ray photon energy. Another characteristic of dosimeters, in addition to sensitivity, is fading, f. This shows the recovery of the transistor threshold voltage after irradiation, during annealing at room temperature without gate polarization (so-called spontaneous annealing, SA). The fading can be found as [34] where V T (0) is the threshold voltage after irradiation, i.e., at the beginning of SA; V T (t) is the threshold voltage during SA; V T0 is the threshold voltage before irradiation; ∆V T (0) is the threshold voltage shift after irradiation, i.e., at the beginning of SA; and ∆V T (t) is the threshold voltage shift during SA. During SA after gamma irradiation, ∆V T (t) usually decreases, which gives the positive fading that increases [34]. Otherwise, ∆V T (t) can also increase (reverse annealing), giving the negative fading. Figure 10 shows that the obtained fading is negative for all samples, which is opposite to the case of gamma radiation.
Electronics 2022, 11, x FOR PEER REVIEW 9 of 12 temperature without gate polarization (so-called spontaneous annealing, SA). The fading can be found as [34] ) 0 ( where VT(0) is the threshold voltage after irradiation, i.e., at the beginning of SA; VT(t) is the threshold voltage during SA; VT0 is the threshold voltage before irradiation; ∆VT(0) is the threshold voltage shift after irradiation, i.e., at the beginning of SA; and ∆VT(t) is the threshold voltage shift during SA. During SA after gamma irradiation, ∆VT(t) usually decreases, which gives the positive fading that increases [34]. Otherwise, ∆VT(t) can also increase (reverse annealing), giving the negative fading. Figure 10 shows that the obtained fading is negative for all samples, which is opposite to the case of gamma radiation. Looking at Figures 3 and 10, it cannot be concluded which transistor has the best dosimetric characteristics. Since the sensitivity and fading are the only dosimetric parameters, we introduce a new dosimetric parameter, Golden Ratio, GR, that connects these two parameters: where S is the sensitivity and f(tmax) is the fading at the last point of SA (in our case, tmax ≈ 3500 h, i.e., about 5 months). The higher GR represents better dosimetric characteristics of the transistor that should have a large S and a small f (GR should be as high as possible). This means that GR can be used as a good parameter to compare different transistors or to examine the effect of operating conditions (e.g., as in our case, different gate voltages).
The GR is displayed in Figure 11, showing that the highest GR (the best dosimetric characteristic) is for RQR8 and VG,rad = 12 and 15 V. Looking at Figures 3 and 10, it cannot be concluded which transistor has the best dosimetric characteristics. Since the sensitivity and fading are the only dosimetric parameters, we introduce a new dosimetric parameter, Golden Ratio, GR, that connects these two parameters: where S is the sensitivity and f (t max ) is the fading at the last point of SA (in our case, Electronics 2022, 11, x FOR PEER REVIEW 10 of 12 Figure 11. ∆Nst at Kair = 50 Gy versus gate voltage during irradiation.

Conclusions
In this case study, the possibility of using commercial p-channel power vertical double-diffused metal-oxide-semiconductor field-effect transistors (VDMOSFETs) as X-ray sensors is investigated. This is important because VDMOSFETs are potentially suitable for radiation dosimetry because they have a relatively thick oxide. The results show that the ∆VT = f(Kair) dependence of threshold voltage shift, ∆VT, on air kerma, Kair, is linear up to the used air kerma of 50 Gy for all used gate polarizations. The r-square (r 2 ) correlation coefficients of linear regression are higher than 0.99 for all cases. The fitting of dependence of the sensitivity, S, on the gate polarization, VG,irr, applied during irradiation and using the proposed equation is good. The density of FTs, ∆Nft, is the highest for RQR8 but the lowest for the RQR3 beam. The density of STs, ∆Nst, does not show any clear dependence on VG,irr as ∆Nft. ∆Nft is two times higher than ∆Nst, having a more dominant effect on ∆VT than ∆Nst. However, the effect of STs on ∆VT is more significant than in the case of gammaradiation, where ∆Nft is usually more than five times higher than ∆Nst. The mass energyabsorption coefficients for silicon-dioxide, (µme(E))SiO2, have not been found in the literature, and the mass energy-absorption coefficients for silicon, (µme(E))Si, are used for ∆Nft on Kair dependence explanation. However, there is a discrepancy between the experimental results and theoretical predictions. As a consequence, either the (µme(E))Si coefficients for silicon are not suitable to be used for SiO2 and/or the mean energy is not a proper indicator of the X-ray beam. All transistors show the negative fading during spontaneous annealing, which is not the case with gamma-radiation. The newly proposed dosimetry parameter, called the Golden Ratio, GR, is a very useful tool for comparing different dosimeter conditions.

Conclusions
In this case study, the possibility of using commercial p-channel power vertical doublediffused metal-oxide-semiconductor field-effect transistors (VDMOSFETs) as X-ray sensors is investigated. This is important because VDMOSFETs are potentially suitable for radiation dosimetry because they have a relatively thick oxide. The results show that the ∆V T = f (K air ) dependence of threshold voltage shift, ∆V T , on air kerma, K air , is linear up to the used air kerma of 50 Gy for all used gate polarizations. The r-square (r 2 ) correlation coefficients of linear regression are higher than 0.99 for all cases. The fitting of dependence of the sensitivity, S, on the gate polarization, V G,irr , applied during irradiation and using the proposed equation is good. The density of FTs, ∆N ft , is the highest for RQR8 but the lowest for the RQR3 beam. The density of STs, ∆N st , does not show any clear dependence on V G,irr as ∆N ft . ∆N ft is two times higher than ∆N st , having a more dominant effect on ∆V T than ∆N st . However, the effect of STs on ∆V T is more significant than in the case of gamma-radiation, where ∆N ft is usually more than five times higher than ∆N st . The mass energy-absorption coefficients for silicon-dioxide, (µ me (E)) SiO2, have not been found in the literature, and the mass energy-absorption coefficients for silicon, (µ me (E)) Si, are used for ∆N ft on K air dependence explanation. However, there is a discrepancy between the experimental results and theoretical predictions. As a consequence, either the (µ me (E)) Si coefficients for silicon are not suitable to be used for SiO 2 and/or the mean energy is not a proper indicator of the X-ray beam. All transistors show the negative fading during spontaneous annealing, which is not the case with gamma-radiation. The newly proposed dosimetry parameter, called the Golden Ratio, GR, is a very useful tool for comparing different dosimeter conditions.