#
Commercial P-Channel Power VDMOSFET as X-ray Dosimeter^{ †}

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

^{†}

## Abstract

**:**

_{2}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.

## 1. Introduction

_{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.

## 2. Experimental Details

_{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}, 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.

_{G,sa}= 0 V), was performed up to 3500 h.

_{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.

_{T}, is:

_{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:

_{ft}and ∆V

_{st}, the areal densities of FTs, ∆N

_{ft}[cm

^{−2}], STs, and ∆N

_{st}[cm

^{−2}], respectively, can be found [32]:

_{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.

_{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}.

_{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]:

_{sst}is the density of SSTs and ΔN

_{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 ΔN

_{ot}= ΔN

_{ft}+ ΔN

_{sst}and ∆N

_{it}= ∆N

_{st}− ∆N

_{sst}= ΔN

_{fst}.

## 3. Results and Discussion

_{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.

_{T}on K

_{air}for V

_{G,irr}= 0 V is linear up to the investigated air kerma of 50 Gy [26]:

_{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.

_{T}on V

_{G,irr,}at certain dose [34].

_{T}

_{,sat}is the saturation value of ΔV

_{T}, and r and s are the positive constants.

_{G,irr}:

_{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.

_{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].

_{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].

_{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].

_{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}.

_{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.

_{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

_{me}(E))

_{SiO2}represents the mass energy-absorption coefficients of SiO

_{2}.

_{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 Figure 8 and Figure 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.

_{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.

_{max}) is the fading at the last point of SA (in our case, t

_{max}≈ 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 V

_{G,rad}= 12 and 15 V.

## 4. Conclusions

_{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.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**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}).

X-ray Beam | U_{p} (kV) | I_{p} (mA) | E_{mean} (keV) | DK_{air} (mG/s) |
---|---|---|---|---|

RQR3 | 50 | 30 | 32.57 | 9.28 |

RQR8 | 100 | 30 | 50.82 | 26.45 |

RQR10 | 150 | 30 | 56.70 | 30.31 |

V_{G} (V) | S_{RQR3} (mV/Gy) | S_{RQR}_{8} (mV/Gy) | S_{RQR}_{10} (mV/Gy) |
---|---|---|---|

0 | 6.76 | 7.78 | 7.13 |

3 | 19.46 | 22.21 | 20.50 |

6 | 24.10 | 27.50 | 25.68 |

9 | 28.33 | 32.18 | 28.57 |

12 | 30.38 | 34.36 | 32.28 |

15 | 30.27 | 38.81 | 35.00 |

18 | 33.90 | 42.91 | 38.36 |

21 | 34.61 | 42.63 | 38.33 |

X-ray Beam | S_{sat} (mV/Gy) | a | b |
---|---|---|---|

RQR3 | 0.0343 | 0.7868 | 0.8447 |

RQR8 | 0.0457 | 0.8040 | 0.8907 |

RQR10 | 0.0403 | 0.7980 | 0.8805 |

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**MDPI and ACS Style**

Ristić, G.S.; Ilić, S.D.; Veljković, S.; Jevtić, A.S.; Dimitrijević, S.; Palma, A.J.; Stanković, S.; Andjelković, M.S.
Commercial P-Channel Power VDMOSFET as X-ray Dosimeter. *Electronics* **2022**, *11*, 918.
https://doi.org/10.3390/electronics11060918

**AMA Style**

Ristić GS, Ilić SD, Veljković S, Jevtić AS, Dimitrijević S, Palma AJ, Stanković S, Andjelković MS.
Commercial P-Channel Power VDMOSFET as X-ray Dosimeter. *Electronics*. 2022; 11(6):918.
https://doi.org/10.3390/electronics11060918

**Chicago/Turabian Style**

Ristić, Goran S., Stefan D. Ilić, Sandra Veljković, Aleksandar S. Jevtić, Strahinja Dimitrijević, Alberto J. Palma, Srboljub Stanković, and Marko S. Andjelković.
2022. "Commercial P-Channel Power VDMOSFET as X-ray Dosimeter" *Electronics* 11, no. 6: 918.
https://doi.org/10.3390/electronics11060918