Ionizing and non-ionizing kerma factors in silicon for China Spallation Neutron Source neutron spectrum

NUCLEAR ENERGY SCIENCE AND ENGINEERING

Ionizing and non-ionizing kerma factors in silicon for China Spallation Neutron Source neutron spectrum

Xiao-Ming Jin，

Yan Liu，

Chun-Lei Su，

Wei Chen，

Chen-hui Wang，

Shan-Chao Yang，

Xiao-Qiang Guo

Nuclear Science and Techniques

Vol.30, No.9

Article number 143

Published in print 01 Sep 2019

Available online 16 Aug 2019

DOI：10.1007/s41365-019-0664-5

61100

The quantification of ionizing and non-ionizing energy deposition plays a critical role in precision neutron dosimetry and in the separation of the displacement damage effects and ionizing effects induced by neutron radiation on semiconductor devices. In this report, neutrons generated by the newly built China spallation neutron source (CSNS) are simulated by Geant4 in semiconductor material silicon to calculate the ionizing and non-ionizing kerma factors. Furthermore, the integral method is applied to calculate neutron-induced ionizing at the CSNS and non-ionizing kerma factors according to the standard neutron nuclear database and the incident neutron spectrum. In addition, thermoluminescence dosimeters are utilized to measure the ionizing energy deposition and six series of bipolar junction transistors are used to measure the non-ionizing energy deposition based on their neutron damage constants. The calibrated kerma factors that were experimentally measured agreed well with the simulation and integral calculation results. This report describes a complete set of methods and fundamental data for the analysis of neutron-induced radiation effects at the CSNS on silicon-based semiconductor devices.

Neutron radiationKermaIonizing energyNon-ionizing energyCSNS

1 Introduction

The kerma factor is defined as the sum of the initial kinetic energies of all the charged particles liberated by indirectly ionizing particles (for example, neutrons) in a volume element containing a unit mass of the specified material. The energy deposition per unit mass of the target material is the product of the fluence and the kerma factor. It is widely used in neutron radiation to quantitatively separate the ionizing and non-ionizing energy deposition [1-5]. For semiconductor devices, neutron-induced radiation effects mainly include displacement damage, total ionizing dose (TID) effects, and single event effects (SEE). It has been proved that the displacement damage is equated with the non-ionizing kerma factor, so the 1 MeV equivalent neutron fluence has been commonly adopted for different neutron spectrum for decades [6,7]. Similarly, the TID and SEE are equated with the ionizing kerma factor of neutrons, which are directly related to the ionizing energy deposition induced by secondary ions owing to the interaction of incident neutrons with device materials [8-11].

The CSNS, located at Dongguan, Guangdong province in China, is the first spallation neutron source ever built in China and produces neutron spectra that are very similar to that of terrestrial neutrons. This scientific facility was initially opened to general users in 2018, and it has become one of the most significant neutron sources in China in terms of neutron radiation effects testing on semiconductor devices in avionics and spacecraft. Given that most semiconductor devices are manufactured using silicon-based CMOS and bipolar technology, the ionizing and non-ionizing kerma factors in silicon are very important in the quantitative analysis of displacement damage and ionizing effects respectively, as the fundamental data for neutron-induced radiation effects. Therefore, it is essential that the kerma factors should be confirmed for CSNS neutrons.

A comprehensive set of theoretical calculation methods and experimental calibration methods are proposed in this report to quantify the ionizing and non-ionizing kerma factors in silicon. Initially, ionizing and non-ionizing kerma factors are calculated using Geant4 simulation and the integral method respectively. Moreover, thermoluminescence dosimeters are first calibrated using a standard Co-60 gamma irradiation source and are then irradiated in the CSNS neutron field to measure the ionizing dose and to calculate the experimental ionizing kerma factors. BJT transistors were first calibrated for their neutron damage constant in 1 MeV equivalent neutron fluence at Xi’an pulsed reactor (XAPR) [12] at the Northwest Institute of Nuclear Technology in China, were irradiated in the CSNS neutron field to calculate the experimental non-ionizing kerma factors via the normalization of the damage constant to 1 MeV neutron fluence.

2 Theoretical calculation

The CSNS is designed to deliver a proton beam with a kinetic energy of 1.6 GeV at a repetition rate of 25 Hz to a tungsten target [13,14]. A tantalum (0.3 mm) clad and water-cooled sliced tungsten target (11 pieces, 65 cm in total length, cross-section: 170 × 70 mm²) is in use at the CSNS [15]. The investigations were performed at endstation 2# at a distance of 76 m from the tungsten target. Fig. 1 shows the neutron energy spectrum at the sample position of endstation 2# of the CSNS. It was provided by CSNS staff using FLUKA 2011.2x software developed by European Organization for Nuclear Research. Approximately 14% of neutrons have energies from 0.28 eV to 0.1 MeV, 40% are from 0.1 MeV to 1 MeV, 41% are from 1 MeV to 20 MeV, and 5% are above 20 MeV. Two types of theoretical calculation methods including Geant4 simulation and the integral method were utilized to calculate the ionizing and non-ionizing kerma factors for the CSNS neutron beam based on the incident neutron spectrum.

Fig. 1.

Neutron energy spectrum at endstation 2# of the CSNS.

2.1 Geant4 simulation

The geometrical structure established in Geant4 simulation consists of seven layers of silicon dielectric (Fig. 2). According to the feature size of current semiconductor technology, each layer is 100 μm in length and width, and 20 μm in thickness. The direction of the incident neutrons is perpendicular to the surface of the first silicon layer and the position of these neutrons is uniformly sampled in the x and y coordinates. The energy of the incident neutron is sampled from the initial neutron flux (Fig. 1). There are 252 continuous energy bins extending from 0.283 eV to 373.2 MeV. For each energy interval, the probability to initialize the energy of the incident neutron as the mean value of E_i-1 and E_i is P_i, which is calculated using equation (1):

Fig. 2.

Geometrical model for neutron transportation in silicon.

P_{i} = \frac{\int_{E_{i - 1}}^{E_{i}} Ф (E) d E}{\int_{E_{min}}^{E_{max}} Ф (E) d E},

(1)

where Φ(E) is the differential neutron flux for the CSNS neutrons, E_min is 0.283 eV, and E_max is 373.2 MeV.

A comprehensive set of physics lists are chosen to simulate the behavior of neutron transportation in silicon. Each physics list consists of a set of physics processes and cross-sections for calculating total cross-sections for a certain range of validity. The hadronic interactions were described by the QGSP_BIC_HP, the electromagnetic effects by the G4EmStandardNR, the decay process by the G4DecayPhysics, and the neutron interactions by the G4_NeutronHP. Moreover, the binary cascade model is implemented as an accurate intranuclear cascade model utilizing a realistic nucleon distribution model for the target nucleus, and the probability of collisions is based on the impact parameters between the incident particle and each of the target nucleons [16-18].

Ionization energy deposition is mainly due to electromagnetic processes due to secondary charged nucleons and nuclear fragments. Non-ionizing energy deposition is mainly attributed to the interaction of incident neutrons with target atoms and the Coulomb interaction of secondary charged nucleons with target atoms. Given that the thickness of silicon is much thinner than the range of incident neutrons in silicon, the energy deposition is uniformly distributed in each silicon layer and the cumulative ionizing and non-ionizing energy loss increases linearly with the thickness of silicon, as shown in Fig. 3. The ionizing and non-ionizing kerma factors can be calculated by the following equations:

Fig. 3.

Variation of the CSNS neutron-induced ionizing and non-ionizing energy deposition as a function of the thickness of silicon.

K_{NIEL} = \frac{1}{ρ} \frac{1}{N} \frac{d E_{NIEL}}{d x},

(2)

K_{IEL} = \frac{1}{ρ} \frac{1}{N} \frac{d E_{IEL}}{d x},

(3)

where K_NIEL is the non-ionizing kerma factor, K_IEL is the ionizing kerma factor, N is the total sampling number for incident neutrons, and ρ is the density of silicon. In this work, N = 10⁷, ρ = 2.32 g/cm³, and (dE/dx)/N is equal to the slope of the zero-crossing linear fitting. Finally, Geant4 simulation results yield K_NIEL = 3.03 × 10^-13 Gy(Si)·cm² and K_IEL = 1.83 × 10^-12 Gy(Si)·cm².

2.2 Integral method

The kerma factor for CSNS neutrons via the integral method is calculated based on equations (4) and (5) as follows:

K_{NIEL} = \int_{E_{min}}^{E_{max}} Ф (E) K_{NIEL} (E) d E,

(4)

K_{IEL} = \int_{E_{min}}^{E_{max}} Ф (E) K_{IEL} (E) d E,

(5)

where K_NIEL is the non-ionizing kerma factor for the CSNS neutrons, K_IEL is the ionizing kerma factor for the CSNS neutrons, E is the neutron energy, Φ(E) is the differential neutron flux for the CSNS neutrons, K_NIEL(E) is the non-ionizing kerma factor as a function of neutron energy E, K_IEL(E) is the ionizing kerma factor as a function of neutron energy E, E_min is the minimum energy of the CSNS neutrons, and E_max is the maximum neutron energy of the CSNS neutrons.

The kerma factors as a function of neutron energy are shown in Fig. 4. The non-ionizing kerma factors as a function of neutron energy are from the table of the silicon displacement function in ASTM E722-14 [4], and ionizing kerma function is obtained by subtracting the non-ionizing kerma function from the total kerma function for silicon, as indicated in Caswell's paper [5]. Finally, using the integral method, it was determined that K_NIEL = 2.96 × 10^-13 Gy(Si)·cm² and K_IEL = 1.81 × 10^-12 Gy(Si)·cm², exhibiting a good agreement with the Geant4 simulation results.

Fig. 4.

Ionizing and non-ionizing kerma factors in silicon as a function of neutron energy.

To further study the contribution of different neutron energy bands to the average kerma factor, the normalization of the integral of K(E)Φ(E) with respect to E as a function of neutron energy is shown in Fig. 5 for both non-ionizing and ionizing kerma functions. In the CSNS neutron spectrum, neutrons above 0.1 MeV account for 86% of the incident neutrons. These neutrons induce almost all the ionizing and non-ionizing energy deposition in silicon.

Fig. 5.

Normalization of integral of K(E)Φ(E) with respect to E as a function of the neutron energy.

3 Experimental verification

Experimental measurements were conducted to validate the simulation and calculation results at the sample position of endstation 2# at a distance of 76 m from the tungsten target. To validate the ionizing kerma factor, thermoluminescence dosimetry was applied to obtain the ionizing dose under CSNS neutron irradiation. To validate the non-ionizing kerma factor, the neutron damage constants for a series of BJT transistors were measured in the CSNS neutron radiation environment.

3.1 Thermoluminescence dosimetry

Sensitive lithium fluoride based thermoluminescence detectors (TLDs) doped with magnesium and titanium (⁷LiF: Mg, Ti) was used to measure the absorbed radiation doses under CSNS neutron irradiation from fractions of μGy up to approximately the kGy range. The response of TLDs owing to neutron radiation is related to the neutron-induced ionizing dose deposition and the concomitant photon-induced ionizing dose deposition [19,20]. The neutron-induced ionizing kerma factor could be calculated using the following equation:

\frac{\bar{R}}{s} = \frac{\frac{1}{m} \sum_{i = 1}^{m} R_{i}}{s} = K_{IEL} Ф_{n} + d_{p} t_{r} + B,

(6)

where R_i is the post-radiation readout value of the i-th TLD by the thermoluminescence dosimeter reader, s is the TLD coefficient of the linear fitting slope of the average TLD calibration curve, m is the sample size of the TLDs (20 samples), K_IEL is the ionizing kerma factor for CSNS neutrons, Ф_n is the total irradiated neutron fluence of the TLDs ((4.52 ± 0.45) × 10¹¹ n/cm²), d_p is the ionizing dose rate of the concomitant photons ((2.62 ± 0.02) × 10^-7 Gy(Si)/s measured by the CSNS staff), t_r is the total irradiated time of the TLDs ((3.23 ± 0.0001) × 10⁵ s), and B is the ionizing dose of the natural background radiation ((1.07 ± 0.01) × 10^-3 Gy(Si) measured by additional TLDs).

The 20 TLD samples were calibrated at the Co-60 gamma radiation facility to determine the TLD coefficient, s. The calibration measurements were performed at multiple doses up to 200 ± 1 Gy(Si). Fig. 6 represents the variation of the average readout value of the 20 TLD samples with the ionizing dose. This curve has good linearity between 0 and 100 ± 1 Gy(Si). Thus, its linearity upper limit is 100 ± 1 Gy(Si). The TLD coefficient s is the linear fitting slope of the average TLD calibration curve by equation (7):

Fig. 6.

The average readout value of the 20 TLDs versus ionizing dose for calibration measurements of TLD at Co-60.

\bar{R} (D) = \frac{1}{m} \sum_{i = 1}^{m} R_{i} (D) = s \cdot D,

(7)

where D is the ionizing dose, R_i(D) is the readout value of the i-th TLD by the thermoluminescence dosimeter reader at ionizing dose D, and $\bar{R} (D)$ is the average readout value of the 20 samples at ionizing dose D. The TLD coefficient was determined to be 20.35 ± 0.17 Gy(Si)^-1 based on the linear fitting of measurements below 100 ± 1 Gy(Si).

In the CSNS experiment, the TLD samples were irradiated up to a total neutron fluence of (4.52 ± 0.45) × 10¹¹ n/cm² at the sample position of endstation 2# for a distance of 76 m from the tungsten target, and the average readout value of the 20 TLDs $\bar{R}$ was 19.76 ± 0.12. Three additional TLD samples were placed in a natural radiation environment, accompanying the 20 TLD samples for neutron radiation testing during the entire experiment and transportation. The ionizing dose of the natural background radiation B was (1.07 ± 0.01) × 10^-3 Gy(Si), as the average ionizing dose of the three TLDs. Therefore, based on thermoluminescence dosimetry, it was determined that the experimental K_IEL was (1.96 ± 0.20) × 10^-12 Gy(Si)·cm² using equation (6). This result is consistent with the theoretical calculation results.

3.2 Calibration of the BJT neutron damage constant

The radiation effects on BJTs and the displacement damage effects in silicon devices have been actively studied for almost six decades. One of the major achievements of the early studies on radiation effects was the development of the Messenger–Spratt equation, which demonstrates that the change in the current gain due to neutron irradiation is described as follows:

Δ \frac{1}{β} = \frac{1}{β (Ф)} - \frac{1}{β (0)} = k Ф,

(8)

where β(0) is the pre-radiation current gain, β(φ) is the post-radiation current gain, k is the neutron damage constant, and Ф is the neutron fluence [21]. In general, the mechanisms responsible for gain degradation in BJTs are attributable to displacement damage related to non-ionizing energy deposition [22]. Therefore, the constant k_CSNS for the CSNS and the k_1MeV for XAPR could be described as follows:

\frac{k_{CSNS}}{k_{1 MeV}} = \frac{K_{NIEL} (CSNS)}{K_{NIEL} (1 MeV)},

(9)

where k_CSNS and k_1MeV are the constants that are determined from the linear fitting of the experimental results using equation (8) for the CSNS and XAPR respectively. K_NIEL(CSNS) is the non-ionizing kerma factor for the CSNS neutron spectrum, K_NIEL(1MeV) is equal to 3.27 × 10^-13 Gy(Si)·cm² (converted from 95 MeV·mb in silicon according to ASTM e722-14 [4]).

The BJTs used for the radiation experiments were manufactured via a 0.8 um bipolar process by the State Key Laboratory of Analog Integrated Circuit, Chongqing, China. Table 1 summarizes the main features of six types of BJTs, including the transistor structure, emitter area, base region width, and base doping concentration.

The bipolar transistors information

Description	Structure	Emitter area (µm²)	Base region width (µm)	Base doping (cm^-3)
PNP 1	Lateral	35 × 24	12	1.5 × 10¹⁵
PNP 2	Substrate	66 × 28	11	1.5 × 10¹⁵
PNP 3	Substrate	72 × 28	10	1.5 × 10¹⁵
NPN 1	Vertical	250 × 20	11	8.0 × 10¹⁷
NPN 2	Vertical	40 × 20	11	8.0 × 10¹⁷
NPN 3	Vertical	50 × 50	5	8.0 × 10¹⁷

During neutron irradiation, all the pins were shorted to ground. In the test interval after neutron exposure, the gain parameters of the transistors were measured using an HP4156A semiconductor parameter analyzer. For the PNP transistors, the collector was grounded, the emitter was biased to 2 V and the base voltage was swept from 2 V to 1 V. For the NPN transistors, the emitter was grounded, the collector was biased to 2 V and the base voltage was swept from 0 V to 1 V. The current gain β is the ratio of the collector current (fixed at 2 × 10^-5 A for PNP and 6 × 10^-4 A for NPN) and base current. Fig. 7 shows the variation of 1/β with the neutron fluence at the CSNS and XAPR. The neutron fluence at the XAPR is 1 MeV equivalent neutron fluence. The experimental results illustrate a good linear relationship of △1/β and the neutron fluence. The lateral PNP (PNP 1) is the most sensitive, the substrate PNPs (PNP 2 and 3) are the second most sensitive, and the vertical NPNs (NPN 1, 2, and 3) are the least sensitive in this study due to differences in the BJT structures. Linear fitting between △1/β and the neutron fluence facilitates the calculation of the neutron damage constant k for each BJT for the CSNS and XAPR respectively.

Fig. 7.

Current gain degradation versus the increasing neutron fluence at the CSNS and the XAPR for the bipolar transistors.

Fig. 8 shows the neutron damage constants at the CSNS versus the XAPR for six types of BJTs. The slope of the linear fitting is 0.94 ± 0.03. Using equation (9), this slope indicates the ratio of the non-ionizing kerma factors between the CSNS and the XAPR. Therefore, the calibration method for the BJT neutron damage constant indicates that K_NIEL(CSNS) is (3.06 ± 0.10) × 10^-13 Gy(Si)·cm².

Fig. 8.

Neutron damage constant k at the CSNS versus k at the XAPR for bipolar transistors. The slope of the linear fit represents the ratio of the non-ionizing kerma factors between the CSNS and the XAPR.

4 Discussion

As shown in table 2, the non-ionizing and ionizing kerma factors for the CSNS neutrons are compared with the theoretical calculations and experimental validation. The difference is within 3.3 % for non-ionizing kerma factors and 6.7 % for ionizing kerma factors. The neutron-induced displacement damage effects, especially for bipolar electronic devices, depend on the non-ionizing energy deposition, which is the product of the neutron fluence and non-ionizing kerma factor. Similarly, neutron-induced ionizing effects (for example, TID and SEE) depend on the ionizing energy deposition, which is the product of the neutron fluence and the ionizing kerma factor, especially for CMOS electronic devices. More importantly, the characterization of neutron radiation effects in electronic devices based on kerma factors facilitates uniformity of the interpretation and evaluation of the results of neutron irradiation via sources of different neutron energy spectra. As such, it is convenient to normalize the incident neutron fluence from a source to an equivalent monoenergetic neutron fluence (for example, 1 MeV equivalent neutron fluence) that is applicable to a particular semiconductor material (for example, silicon).

Comparison of kerma factors between theoretical calculation and experimental validation for CSNS neutrons

Method	Non-ionizing kerma (Gy·cm²)	Ionization kerma (Gy·cm²)
Geant4 simulation	3.03 × 10^-13	1.83 × 10^-12
Integral method	2.96 × 10^-13	1.81 × 10^-12
Thermoluminescence dosimetry	-	(1.96 ± 0.20) × 10^-12
BJT neutron damage constant	(3.06 ± 0.10) × 10^-13	-

5 Conclusion

A comprehensive set of theoretical calculation methods and experimental calibration methods were presented to obtain and validate the neutron-induced non-ionizing and ionizing kerma factors in silicon. The experimental calibration results agree well with the theoretical results for the CSNS neutron spectrum. This consistency demonstrates that both the Geant4 simulation and the integral method for the standard database are appropriate approaches for the theoretical determination of the kerma factors. From an experimental perspective, the thermoluminescence dosimetry and the calibration method for the BJT neutron damage constant facilitate the determination of the ionizing and non-ionizing kerma factors respectively. For the study of radiation effects on semiconductor devices, the kerma factors allow us to separately quantify the non-ionizing and ionizing energy deposition for a specified neutron fluence. The non-ionizing energy deposition is directly related to the displacement damage effects, especially for bipolar semiconductor devices, while the ionizing energy deposition is directly related to the TID and SEE effects, especially for CMOS semiconductor devices.

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