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

Abstract

The possibility of using commercial p-channel power vertical double-diffused metal-oxide-semiconductor 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.

1. 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.

Power MOSFETs attract attention when they are stressed by electric fields [2,3], when they are operating in ionizing radiation fields [4,5,6,7,8], and as potential gamma radiation dosimeters [9,10,11]. Otherwise, many applications of power MOSFETs need to be radiation-hardened [12]. In addition, the influence of ionizing radiation on some MOSFETs containing different materials [13,14,15,16,17,18,19] and on some commercial electronic devices [20,21,22] has been investigated.

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.

2. 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. 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	Up (kV)	Ip (mA)	Emean (keV)	DKair (mG/s)
RQR3	50	30	32.57	9.28
RQR8	100	30	50.82	26.45
RQR10	150	30	56.70	30.31

.

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.

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:

$$\Delta V_T=V_T-V_{T0}.$$

(1)

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:

$$\Delta V_T=\Delta V_{ft}+\Delta V_{st}.$$

(2)

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]:

$$\Delta N_{ft}=\frac{C_{ox}}{e}\Delta V_{ft}, \to \Delta N_{st}=\frac{C_{ox}}{e}\Delta V_{st}.$$

(3)

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 SiO₂/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 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]:

$$\Delta N_{st}=\Delta N_{sst}+\Delta N_{fst},$$

(4)

where ΔN_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

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.

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]:

$$\Delta V_T=S\cdot K_{air},$$

(5)

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 (r²) correlation coefficients of linear regression are higher than 0.99 for all cases.

Table 2. The sensitivity, S, of irradiated VDMOSFETs.

VG (V)	SRQR3 (mV/Gy)	SRQR8 (mV/Gy)	SRQR10 (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

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].

$$\Delta V_T(V_G)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\Delta V_{T,sat}(1-r\cdot s^{V_{G,irr}})\hspace{0.17em}\hspace{0.17em}\hspace{0.17em},$$

(6)

where ΔV_T,sat is the saturation value of ΔV_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:

$$S(V_G)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=S_{sat}(1-a\cdot b^{V_G,irr})\hspace{0.17em}\hspace{0.17em}\hspace{0.17em},$$

(7)

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. The parameters of Equation (7) for three beams.

X-ray Beam	Ssat (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

.

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].

∆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].

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:

$$D=\frac{E_{ab}}{m}\hspace{0.17em}\left(\frac{Gy}{kg}\right),$$

(8)

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 (SiO₂). Based on Equation (8), it follows that ∆N_ft directly depends on the absorbed dose in SiO₂ 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.

The absorbed dose in matter is related to the kerma in air via the equation [31]:

$$D=\frac{{({\mu }_{me}(E))}_{\mathrm{matter}}}{{({\mu }_{me}(E))}_{\mathrm{air}}}{K}_{air},$$

(9)

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 SiO₂ Equation (9) can be written as

$$D_{Si{O}_2}=\frac{{({\mu }_{me}(E))}_{{\mathrm{SiO}}_2}}{{({\mu }_{me}(E))}_{\mathrm{air}}}{K}_{air},$$

(10)

where (µ_me(E))_SiO2 represents the mass energy-absorption coefficients of SiO₂.

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 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 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 temperature without gate polarization (so-called spontaneous annealing, SA). The fading can be found as [34]

$$f\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\frac{V_T(0)\hspace{0.17em}-\hspace{0.17em}{V}_T(t)}{V_T(0)\hspace{0.17em}-\hspace{0.17em}{V}_{T0}}\hspace{0.17em}\hspace{0.17em}=\frac{\Delta V_T(0)-\Delta V_T(t)}{\Delta V_T(0)},$$

(11)

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.

Looking at Figure 3 and Figure 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:

$$GR\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\frac{S}{f(t_{max})}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em},$$

(12)

where S is the sensitivity and f(t_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

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 ∆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 (r²) 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 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.