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This work focuses on the radiation response of Group IV (Si, Ge, SiC, diamond) and III-V (GaAs, GaN, GaP, GaSb, InAs, InP, InSb, AlAs) semiconductors subjected to D–D (2.45 MeV) and D–T (14 MeV) neutrons. The response of each material has been systematically investigated through a direct calculation using nuclear cross-section libraries, MCNP6, and Geant4 numerical simulations. For the semiconductor materials considered, we have investigated in detail the reaction rates per type of reaction (elastic, inelastic, and nonelastic) and proposed an exhaustive classification and counting of all the neutron-induced events and secondary products as a function of their nature and energy. Several metrics for quantifying the susceptibility of the related semiconductor-based electronics to neutron fusions have been finally considered and discussed.
Aix-Marseille University, CNRS, University of Toulon, Faculté des Sciences, Marseille Cedex, France
Daniela Munteanu
Aix-Marseille University, CNRS, University of Toulon, Faculté des Sciences, Marseille Cedex, France
*Address all correspondence to: daniela.munteanu@univ-amu.fr
1. Introduction
At the horizon of 2035 and beyond, the very large electronic equipment for command and diagnostic operations of future fusion power machines, such as ITER, the international thermonuclear experimental reactor [1], will embrace a wide variety of semiconductors materials. Indeed, new materials, such as SiC, Ge, GaN, or GaAs, are envisaged to progressively replace the traditional silicon of microelectronics for high temperature, high performance, or high-speed electronics/optoelectronics applications [2, 3, 4, 5]. These equipment will be directly or partially (behind radiation shielding) exposed to a complex radiation field due to primary fusion neutrons created in the core of the plasma and then transported outside the machine [6]. These neutrons are produced in the deuterium–tritium (D–T) reaction that has been identified as the most efficient for fusion devices [7]:
D+T→4He3.52MeV+n14.07MeVE1
However, one must also consider deuterium–deuterium (D–D) reaction because this less efficient fusion reaction will be used to study, during the development and commissioning of future machines, their operation before introducing tritium fuel. D–D fusion following the two main reactions with equal probability of occurrence:
D+D→3He0.82MeV+n2.45MeVE2
D+D→T1.01MeV+p3.02MeVE3
For future fusion power machines, the radiative reliability issue for the envisaged new material-based electronics arises now, even if—(i) most of these components have not yet been manufactured and tested, and (ii) the design and the integration of machine electronics equipment will not take place for many years. In such a long-term development, numerical simulation offers a very promising solution to anticipate, in the first step at the material level, this reliability issue for semiconductors whose radiative response is little or poorly known.
In the direct continuation of our previous works [8, 9, 10] that investigated the atmospheric radiation response of a wide variety of semiconductors, the present chapter focuses on the radiation response of Group IV (Si, Ge, SiC, diamond) and III-V (GaAs, GaN, GaP, GaSb, InAs, InP, InSb, AlAs) semiconductors subjected to D–D (2.45 MeV) and D–T (14 MeV) neutrons.
In this work, the response of each material has been systematically investigated through a direct calculation using nuclear cross-section libraries, MCNP6, and Geant4 numerical simulations. In the following, for the 12 semiconductor materials considered, we will investigate in detail the reaction rates per type of reaction (elastic, inelastic, and nonelastic) and propose an exhaustive classification of all the neutron-induced secondary products as a function of their nature and distribution in the energy. Implications for quantifying the susceptibility of these related semiconductor-based electronics to neutron fusions will be finally presented and discussed.
Table 1 summarizes the natural isotopic abundance of the different chemical elements entering the composition of the studied semiconductor materials. Nitrogen, phosphorus, and arsenic have only a single natural isotope which simplifies the calculations to come for these elements. On the contrary, the other elements have two (C, N, Ga, In, Sb), three (Si), and up to five (Ge) different natural isotopes. Nevertheless, for C and N, the relative weight of the minority isotope is less than or around the percent, so we can consider that the natural carbon and nitrogen consist only of the simple isotopes 12C and 14N, respectively, with a very good approximation. The other isotopes listed in Table 1 must be considered with their respective weight in atomic composition for correctly simulating the neutron response of the natural materials to which they relate.
Symbol
Z
Nuclide (100×Z+A format)
Natural abundance (%)
C
6
6012
98.93
6013
1.07
N
7
7014
99.6
7015
0.4
Al
13
13027
100
14028
92.22
Si
14
14029
4.68
14030
3.09
P
15
15031
100
Ga
31
31069
60.1
31071
39.9
32070
20.52
32072
27.45
Ge
32
32073
7.76
32074
36.52
32076
7.75
As
33
33075
100
In
49
49115
95.7
49113
4.3
Sb
51
51121
57.4
51123
42.6
Table 1.
Natural abundance of nuclides related to the materials studied in this work. Z refers to the atomic number, A to the atomic mass.
Table 2 reports the value of the energy bandgap, the number of atoms per square centimeter, the density, and the value of the energy for electron-hole pair creation in bulk material for the 12 semiconductors studied in this work. Due to their atomic composition and crystallographic structure, all these materials are denser than Si (2.33 g/cm3) and three materials exhibit a much larger number of atoms per square centimeter than Si—SiC, diamond, and GaN. This can have a direct consequence on the number of neutron interactions per unit volume of the material, as discussed in the following. In addition, seven materials (SiC, diamond, GaAs, AlAs, InP, GaN, and GaP) exhibit a bandgap larger than Si and logically, a larger electron-hole pair creation energy (3.6 eV for Si) [10], four materials (Ge, InAs, GaSb, and InSb) are low-bandgap semiconductors (< 1eV) with lower electron-hole pair creation energy than Si. The electrical consequences of this important parameter are discussed in Section 5.
Material
Bandgap at 300 K (eV)
Number of atoms per cm3 ( ×1022)
Density (g/cm3)
E-h pair creation energy Eeh (eV)
Si
1.124
5.0
2.329
3.6
Ge
0.661
4.42
5.3267
2.9
SiC (4H)
3.23
9.64
3.21
7.8
Diamond
5.47
17.6
3.515
12
GaAs
1.42
4.42
5.32
4.8
AlAs
2.16
4.42
3.76
6.8
InP
1.34
3.96
4.81
4.5
InAs
0.36
3.59
5.67
1.8
GaSb
0.73
3.53
5.61
2.7
InSb
0.17
2.94
5.78
1.1
GaN
3.39
8.85
6.15
8.9
GaP
2.26
4.94
4.138
6.8
Table 2.
Main properties of the semiconductors considered in this study. From Ref. [8, 10].
3. Direct evaluation of semiconductor susceptibility to fusion neutrons
The susceptibility of the different semiconductors to neutron irradiation can be firstly evaluated via the calculation of the number of neutron-material interactions under 2.45 or 14 MeV neutrons. This can be performed via a direct analytical calculation using neutron cross-section library data; we considered here the TENDL-2021 nuclear data library [11]. The number of interactions in the target at a fixed neutron energy E is simply given by:
N(E)=∑ifiσi(E)×10−24×NV×e×ME4
where σi is the value at energy E of the cross section for isotope i (in barn), fi is the fraction of isotope i in the target isotopic composition, e is the target thickness, NV is the number of atoms per unit volume, and M is the number of incident monoenergetic neutrons; in this work, fixed to the arbitrary value of 5 × 108 for standardization purpose (introduced in other previous studies [8, 9, 10], M initially corresponds to the number of atmospheric neutrons impacting a surface of 1 cm2 at sea level exposed to natural radiation during 25 × 106 h).
Figure 1 illustrates the extraction from TENDL-2021 library data of the neutron cross-section values at 2.45 and 14 MeV for two different isotopes. Total, elastic, and inelastic data, respectively, correspond to reaction type numbers MT = 1, 2, and 4 in the standardized ENDF format [12]. When it is not available, the cross-section value for the sum of all nonelastic channels (MT = 3) is obtained by subtracting elastic + inelastic cross sections to the total cross section.
Figure 1.
Example of neutron cross sections (total, elastic and inelastic) extracted from TENDL-2021 nuclear data library [11] for the isotopes 32-Ge-070 (left) and 51-Sb-123 (right).
As the result of this analytical evaluation using Eq. (4), Table 3 gives the total number of interaction events in a target (1cm2 × 20 μm) composed of a single chemical element with an isotope distribution corresponding to the natural abundance (Table 1) and subjected to 2.45 or 14 MeV neutrons. Values reported in Table 3 correspond to a normalized value NV = 1.0 × 1022 at/cm3 for all targets.
Total number of interaction events in a target (1cm2 × 20 μm) composed of a single chemical element with an isotope distribution corresponding to the natural abundance (Table 1) and subjected to 2.45 or 14 MeV neutrons. Values are calculated from Eq. (4) with a normalized value NV = 1.0 × 1022 at/cm3 for all targets.
From the data of Table 3, it is now easy to evaluate the neutron response for any material composed of these elements. Figure 2 shows the results of this evaluation for the different semiconductor materials, considering their stoichiometry and their exact number of atoms per square centimeter, given in Table 2. All numerical values for Figure 2 are detailed in the Appendix (Table 6). From the results of Figure 2, we can formulate the following observations:
Elastic and inelastic interactions dominate for all materials at 2.45 MeV whereas nonelastic interactions represent very roughly one-third of the total number of events at 14 MeV.
All studied materials exhibit a larger total number of interaction events than silicon, both at 2.45 and 14 MeV.
Two semiconductors, C (diamond) and GaN show the largest neutron susceptibility at these two energies, followed by SiC.
Diamond at 2.45 MeV exhibits a pure and extremely high elastic response; this behavior is due to the combination of an important elastic cross section (1.62 barn at 2.45 MeV) and the highest NV value (1.76 × 1023 at/cm3) between all materials.
Only a single material, GaN, demonstrates a frank higher response at 14 MeV than at 2.45 MeV in terms of total events (elastic + inelastic + nonelastic), due to an elevated number of nonelastic events, the highest at 14 MeV for all materials.
AlAs exhibits the smallest neutron response after silicon.
Figure 2.
Number of elastic, inelastic, and nonelastic interaction events in a target (1cm2 × 20 μm) composed of natural semiconductors and subjected to 5 × 108 neutrons of 2.45 or 14 MeV. Values are deduced from Table 3 considering the stoichiometry and the exact number of atoms per square centimeter for each material given in Table 2. Numerical values for this graph are reported in the appendix (Table 6).
All these results are now investigated in detail in the next section via more complete numerical simulations.
The neutron susceptibility of the studied materials has been in-depth analyzed using the Monte Carlo radiation transport codes Geant4 (version 10.07 patch 02, G4NDL4.6 neutron library [13, 14, 15]) and MCNP6 (version 6.2 [16, 17]). In a similar way to previous analytical estimations, natural semiconductor targets (1 cm2 × 20 μm) have been subjected to incoming 2.45 or 14 MeV neutrons perpendicularly to their largest surface. The same number of 5 × 108 incident neutrons has been considered for each simulation run.
For Geant4, a simulation run produces a single output file containing all the information related to the neutron interaction events in the target material—nature of the interaction, spatial coordinates of the reaction vertex, and exhaustive list of secondary particles produced during the interaction (energy and emission direction vector for each of these emitted particles). A post-treatment eliminates all gamma photons, neutral and light particles (e−, e+, η), not able to induce significant single-event effects in electronics.
For MCNP6 simulation, PTRAC card options were activated to obtain, for each event, the nature and the coordinates of the vertex of the interaction and the final energy of the neutron after the interaction. It is thus possible to count and to discriminate interactions as a function of the target atom and as a function of their nature (elastic, inelastic, and nonelastic).
4.2 Numbers of interaction events at 2.45 and 14 MeV
Figures 3 and 4 show the number of interaction events for the different semiconductor targets subjected to 2.45 and 14 MeV neutrons, respectively. All the numerical values for these two figures are reported in Table 6 of the Appendix. These results show a good agreement, on one hand, between analytical and numerical estimations, and, on the other hand, between Geant4 and MCNP6 results. If we consider the total number of interaction events (Table 6), analytical and numerical results agree within 6% on average at 2.45 MeV and within 2.4% on average at 14 MeV. Between Geant4 and MCNP6 results, agreements are better, within 3% on average at
Figure 3.
Number of elastic, inelastic, and nonelastic events estimated by Geant4 and MCNP6 as a function of the nature of the target material for 2.45 MeV incoming neutrons.
Figure 4.
Number of elastic, inelastic, and nonelastic events estimated by Geant4 and MCNP6 as a function of the nature of the target material for 14 MeV incoming neutrons.
2.45 MeV and within 1.6% on average at 14 MeV. The best agreement is obtained for diamond, GaN, and GaAs at 14 MeV, the largest difference is for GaP at 2.45 MeV, with 11.5% of the variation between Geant4 and MCNP6, the number of elastic events being larger than 14% for Geant4 with respect to MCNP6. Globally, one can see that the different sets of results agree very satisfactorily.
In the following and because Geant4 can track all particles and, consequently, give more exhaustive information about secondaries than MCNP6, we will explore in detail the distributions and characteristics of secondaries produced in the interaction events at both 2.45 and 14 MeV from Geant4 results.
4.3 Detailed analysis at 2.45 MeV
Figures 5–7 shows the energy histograms of the secondaries produced by 2.45 MeV neutrons in the targets composed of the different natural semiconductor materials under investigation. In the particular case of C (diamond), shown in Figure 5, all secondaries are exclusively elastic carbon recoil nuclei. They form a continuum from zero to a maximum energy Emax theoretically equal to [18]:
Figure 5.
Energy histograms of secondaries produced in the diamond target by 2.45 MeV neutrons and obtained from Geant4 and MCNP6 simulations. All secondaries are elastic recoil nuclei.
Figure 6.
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of Si, Ge, GaAs, SiC, AlAs, InAs, InSb, and GaSb semiconductor materials.
Figure 7.
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of GaP, InP, and GaN semiconductor materials.
Emax=4×E×A(A+1)2E5
where A is the mass number of the target nucleus and E is the energy of the incident neutrons. Here, for carbon, A = 12 and with E = 2.45 MeV, we obtain a theoretical value of Emax = 0.696 MeV, in excellent agreement with the cutoff value of 0.7 MeV extracted from Figure 5. This figure also shows a direct comparison between MCNP6 and Geant4 simulation results because, in the case of elastic events, it is possible from MCNP6 output data to compute the energy distribution of recoil nuclei; an estimation unfortunately not possible for inelastic and nonelastic events.
Figures 6 and 7 show Geant4 results for the other target materials. For Si, Ge, SiC, AlAs, GaAs, InAs, InSb, and GaSb (Figure 6), 2.45 MeV neutrons produce quasi exclusively, via elastic, inelastic, and nonelastic interactions, secondaries with the same atomic number than one of the elements of the target. The heavier the recoil nucleus or secondary product, the more the distribution is shifted toward the lower energies. This shift is more marked as the difference in atomic number is greater, for example for InP (Z = 15 and 49). Only three materials, i.e., GaN, GaP, and InP, show (Figure 7) a significant production of secondaries at 2.45 MeV that differ from target elements:
For GaP and InP, the presence of phosphorus makes possible the nonelastic reaction 31P(n,p)31Si that produces a proton with mean energy around 890 keV. Following this reaction scheme, 980 protons are emitted in GaP and 755 in InP. 31P(n,p)31Si represents 88% (resp. 28%) of the nonelastic interactions in GaP (resp. in InP).
For GaN, the presence of nitrogen makes possible the two nonelastic reactions 14N(n,α)11B and 14N(n,p)14C that respectively produce an alpha particle (around 1.6 MeV) and a proton (around 2.7 MeV). 4555 alphas and 614 protons are emitted following these two reaction schemas. 14N(n,α)11B and 14N(n,p)14C, respectively, represent 84 and 11% of the nonelastic interactions in GaN.
In addition to the previous analysis, Figure 8 (left) gives, for each material, the sum of the initial kinetic energy for all produced secondaries (we recall here that neutrons, gamma rays, and light particles, such as electrons or positrons are not considered, only charged particles with Z ≥ 1 are considered). Such a quantity represents the energy susceptible to be deposited by all these secondaries in the considered target if they are totally stopped (after transferring the totality of their kinetic energy, essentially by ionization process). This energy amount is the highest for C (about 105 MeV), followed by SiC, GaN, Si, and GaP (all above 104 MeV); it is minimum for InSb (around 3 × 103 MeV). Figure 8 (right) gives the average energy conveyed per particle for the four categories of secondaries. The consequence of this result on the electrical point-of-view and in the framework of single-event effect occurrence is be discussed in Section 5.
Figure 8.
Left: Sum of the kinetic energy of all secondaries produced by 2.45 MeV in the different targets (charged particle with Z ≥ 1). Right: Average particle energy per particle type (same legend as for the left figure).
4.4 Detailed analysis at 14 MeV
Figures 9 and 10 show the energy histograms of the secondaries produced by 14 MeV neutrons in the different targets. Contrary to the previous case at 2.45 MeV, a significant number of nonelastic reaction channels is opened at this higher neutron energy. The ratio of the number of nonelastic reactions with respect to the total number of events varies from about 5% in the case of C up to 38% for InP; it is around 33% for Si. These nonelastic reactions produce several types of ions, protons, and alpha particles—their respective numbers are given in Table 4 which also indicates the number of secondary ions produced characterized by the same atomic number as target nuclei. This last category includes, of course, all recoil nuclei produced in elastic and inelastic reactions but also ions produced in certain nonelastic reactions, for example, in the (n,n’γ) or (n,2n’γ) reactions that are increasingly frequent when increasing the atomic number of the target element. These nonelastic reactions give a final nucleus with a lighter mass with respect to the initial impacted nucleus (for example, 74Ge(n,2n)73Ge or 115In(n,2n)113In, etc.).
Figure 9.
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of GaN, GaP, GaAs, GaSb, InSb, InP, InAs, and AlAs III-V semiconductor materials.
Figure 10.
Energy histograms of secondaries produced by 2.45 MeV neutrons in targets of Si, SiC-4H, Ge, and C (diamond) Group-IV semiconductor materials.
Target
Number of ions with the same Z as target nuclei
Number of protons, deuterons, and tritons
Number of alpha particles
Number of other ions
Si
58,293 (Si)
16,815
10,245
22,968
Ge
107,913 (Ge)
1910
1042
2152
C
222,165 (C)
2
11,460
11,445
SiC
56,611 (Si) + 60,415 (C)
16,376
13,101
25,577
AlAs
26,836 (Al) + 52,924 (As)
10,003
3186
5530
GaAs
51,729 (Ga) + 52,697 (As)
3238
806
1713
GaN
102,776 (Ga) + 59,190 (N)
9377
7295
12,278
GaP
57,127 (Ga) + 26,396 (P)
19,439
4126
7938
GaSb
40,309 (Ga) + 53,776 (Sb)
1874
438
1105
InAs
53,690 (In) + 42,455 (As)
1409
237
1094
InP
58,842 (In) + 20,892 (P)
13,994
2814
5725
InSb
43,067 (In) + 44,737 (Sb)
458
54
484
Table 4.
Number of secondaries produced by 14 MeV neutrons in the different targets.
For the good understanding of Figures 9 and 10, Table 5 indicates the main nonelastic reactions leading to the production of protons and alpha particles. The energy ranges of the ejected particles are also reported. Protons, deuterons, and tritons (Z=1) are produced in large numbers in six materials, by order of importance—GaP, Si, SiC, InP, AlAs, and GaN. The main reactions for these targets are the following (we indicated in parenthesis the energy threshold of the reactions): 31P(n,n’p)30Si (7.5 MeV), 31P(n,p)31Si (0.7 MeV), 31P(n,d)30Si (5.2 MeV), 28Si(n,p)28Al (4 MeV), 27Al(n,p)27Mg (1.9 MeV), 14N(n,d)13C (5.7 MeV). Protons and deuterons are also observed in smaller numbers in the other materials, i.e., GaAs, Ge, GaSb, InAs, and InSb. Only two tritons are observed for C, they are produced in the rare reaction 13C(n,t)11B. Concerning alpha particles (Z=2), they are produced in large or significant numbers in seven materials—SiC, C, Si, GaN, GaP, InP, and AlAs. The main reactions for these targets are the following—28Si(n,α)25Mg (2.7 MeV), 12C(n,α)9Be (6.2 MeV), 14N(n,α)11B (0.17 MeV), 31P(n,α)28Al (2 MeV), 27Al(n,α)24Na (3.2 MeV). Traces of alpha particles are also observed in Ge, GaAs, GaSb, and InSb.
Element
Main reactions for α, p or d production (14 MeV neutrons)
Energy range of the ejected particle
C
12C(n,α)9Be
0.2–7 MeV
N
14N(n,α)11B 14N(n,d)13C 14N(n,p)14C
0.01–14 MeV 0.1–9 MeV 5–12 MeV
Al
27Al(n,α)24Na 27Al(n,p)27Mg
1.8–14 MeV 0.4–13 MeV
Si
28Si(n,d)27Al 28Si(n,p)28Al 28Si(n,α)25Mg
10–50 keV (peak at 34 keV) 2–10 MeV 0.5–13 MeV
P
31P(n,α)28Al 31P(n,n’p)30Si
0.2–12 MeV 0.4–11 MeV
Ga
69Ga(n,α)66Cu 69Ga(n,p)69Zn
4–14 MeV 0.01–14 MeV
Ge
70Ge(n,α)67Zn 70Ge(n,p)70Ga
4–14 MeV 1.5–13 MeV
As
75As(n,α)72Ga 75As(n,p)75Ge
4–14 MeV 1–13 MeV
In
115In(n,p)115Cd
10–14 MeV
Sb
123Sb(n,p)123Sn
12–14 MeV
Table 5.
Main reactions for proton, deuteron, or alpha particle production in the nonelastic interactions of 14 MeV neutrons with target elements. The energy ranges of the ejected particles are also indicated (see Figures 9 and 10 for visualization).
Figure 11 (left) shows the sum of the kinetic energy of all secondaries produced by 14 MeV in the different targets. Figure 11 (right) gives the average energy conveyed per particle for the four categories of secondaries. Protons and alphas are of prime importance in the radiation response of these materials insofar as they convey a very important part of the total kinetic energy; this part is predominant in the case of five materials—Si, SiC, AlAs, GaN, and GaP. As compared to Figure 8 (left) obtained for 2.45 MeV neutrons, the amplification factor of the total kinetic energy at 14 MeV for all secondaries is minimal for C (×2.5) and InSb ((×3.5) and maximal for InP, GaP, AlAs (around ×10), and Si (×14.3).
Figure 11.
Left: Sum of the kinetic energy of all secondaries produced by 14 MeV in the different targets (charged particle with Z ≥ 1). Right: Average particle energy per particle type (same legend as for the left figure).
5. Implication for electronics subjected to fusion neutrons
In this last section, we examine the previous results in light of the mechanisms of creation of single-event effects (SEEs) in electronics subjected to fusion neutrons. We recall here that these SEEs are initiated by neutron-matter interactions in four main steps—(1) interactions produce secondary fragments or recoil nuclei from target nuclei. (2) The produced ion(s) interact(s) with material to generate free charge carriers via the production of electron and hole pairs. (3) Electrons and holes are transported by drift-diffusion mechanisms through the circuit materials (oxides and semiconductors) up to a sensitive node (reversely biased junctions); free carriers also recombine during their transport. (4) The collected charge on a sensitive node can significantly alter its voltage that leads to a change in device or circuit operation. This voltage glitch may propagate through the circuit. The present work allows us to provide quantitative information on steps 1 and 2 in so far as from step 3, it would be necessary to consider the circuit architecture, the applied polarizations, and the transport and recombination properties of the materials. In the following, we examine the different materials in light of the number of interactions and of the number of e-h pairs created on average per interaction.
Concerning the first metric, the number of SEEs susceptible to be created in an electronic circuit (of the same geometry as the target for simplicity) is at most equal to the number of interaction events that can deposit enough energy, i.e., create a sufficient electrical charge able to disturb the circuit operation (in the case of an SRAM memory, this minimum amount of charge susceptible to upset a memory cell is called a critical charge). This number of SEEs is not easy to evaluate but it can be upper bounded by the number of events that can deposit energy and therefore generate an electrical charge greater than or equal to the critical charge of the circuit. To roughly estimate this metric from the histogram of the energies/charges deposited per event, a simple transformation is necessary, as illustrated in Figure 12. Figure 12 (left) shows the energy histograms (frequency and cumulative frequency histograms) for all the events produced by 2.45 MeV and 14 MeV neutrons in GaP. The relationship between energy (bottom scale) and charge (top scale) considers the energy value of the creation of electron-hole pairs, as given in Table 2.
Figure 12.
Left: Histogram and cumulative histogram of the energy deposited per event for all interaction events in GaP target. Right: Reversed cumulative histogram from the left figure expressed in charge deposited per event (MeV).
At fixed energy or charge, the cumulative frequency histogram directly indicates the number of events for which the total energy deposited is below this value. In practice, it is more convenient to have the complementary value, i.e., the number of events above this value is plotted in Figure 12 (right), and directly expressed in electrical charge instead of energy. Applying this transformation to all targets gives the ensemble of cumulative histograms, as shown in Figures 13 and 14.
Figure 13.
Reversed cumulative histogram of the energy deposited per event for all interaction events in GaP, GaN, InSb, GaSb, InP, AlAs, GaAs, and InAs targets subjected to 2.45 MeV and 14 MeV neutrons. For a fixed value of the deposited charge, the curves give the number of interactions able to deposit at most this energy in the corresponding target.
Figure 14.
Reversed cumulative histogram of the energy deposited per event for all interaction events in Si, Ge, SiC, and C (diamond) targets subjected to 2.45 MeV and 14 meV neutrons. For a fixed value of the deposited charge, the curves give the number of interactions able to deposit at most this energy in the corresponding target.
These figures can be directly used to estimate the number of events able to deposit an electrical charge superior to a given value. From this data and knowing a minimum of geometric and electrical characteristics of the circuit to be evaluated from a radiative point of view (number and geometry of the sensitive volumes, critical charge, etc.), it would be possible, in future studies, to estimate the number of events susceptible to produce SEEs at both 2.45 and 14 MeV.
Figures 13 and 14 provide also other interesting information about the difference in the neutron susceptibility of a given material at these two energies—the greater this difference, the more the material, and therefore, the circuit based on this semiconductor will be likely to present a significant difference in its radiative SEE response. This difference can be appreciated following two criteria—the respective amounts of events at the lowest charge deposited per event (here at 10−2 fC) and the “distance” between the shoulders of the curves at the highest charge values. For example, a circuit based on diamond or GaN semiconductor may logically presents less difference between its SEE responses at 2.45 MeV and 14 MeV than a circuit based on germanium, InSb, or InAs. Of course, this difference in neutron sensitivity is also dependent on the critical charge value of the considered circuit. In the case of GaAs, for example, a circuit with a 10 fC of critical charge should be quasi-immune to
2.45 MeV neutrons but sensitive to 14 MeV. To go further in this analysis and be quantitative, it would be of course necessary to consider the cumulative histograms of the charge collected at each event. The passage from the deposited charge to the collected charge requires numerical simulations on a given architecture and modeling of transport, recombination, and collection mechanisms, a work currently in progress.
Concerning the second metric, Figure 15 gives the number of e-h pairs created in average per interaction for the different targets at the two neutron energies. At 2.45 MeV, this value is minimum for AlAs (78,000) and maximum for diamond (29,000) and Si (27,000). The average level and the relative low dispersion of these values indicate that recoil nuclei, very widely produced in these elastic and inelastic reactions, deposit small amounts of charges over very short distances of a few nanometers to a few hundred nanometers (data not shown). At 14 MeV, the results of Figure 15 (right) show higher values (approximately ×3 to × 12 for the different materials, and × 20 for Si) due to the contributions of nonelastic reactions that produce the most energetic secondaries, notably protons and alpha particles. Surprisingly and contrary to the case of irradiation with atmospheric neutrons [10], Silicon sensibly differs from the other materials at 14 MeV since it has the greatest multiplying factor between
Figure 15.
The average number of e-h pairs created per interaction event in the different targets subjected to 2.45 MeV (left) and 14 MeV (right) neutrons.
2.45 and 14 MeV. This is due to a relatively low number of events (86 kilo events) at this energy with respect to the other semiconductors (Table 6) combined with an important level of production of protons and alpha particles (Table 3) and also with an energy value of e-h pair creation inferior to the average value (around 5 eV) for all materials (Table 2). The other materials which exhibit high values are SiC, GaP, and InP. Statistically, in these four materials, a neutron-target interaction at 14 MeV will deposit more charge than in the other materials, which potentially makes these events more threatening for the creation of SEEs. The balance between all these factors is, therefore, not obvious when one remains at the only “material” level for these studies. This point requires numerical simulations at the circuit level to go further in the investigation of the level of SEE in electronics based on these different materials.
This work explored the radiation response of Group IV (Si, Ge, SiC, diamond) and III-V (GaAs, GaN, GaP, GaSb, InAs, InP, InSb, AlAs) semiconductors subjected to D–D (2.45 MeV) and D–T (14 MeV) neutrons. This first study was limited to the level of the neutron response of bulk materials, an essential step to be able, subsequently, to study the response of electronic components and circuits based on these materials. The response of each semiconductor has been systematically investigated through a direct calculation using nuclear cross-section libraries, MCNP6, and Geant4 numerical simulations. The counting of reaction rates per type of reaction (elastic, inelastic, nonelastic), as well as the classification of all neutron-induced secondary products as a function of their nature and energy, gives a first very complete picture of the behavior of these materials in a fusion environment under D–D or D–T neutrons. Although all studied materials exhibit a larger total number of interaction events than silicon, both at 2.45 and 14 MeV, there is nothing to conclude at this stage that they will present a larger response in terms of SEEs at circuit level since this higher neutron susceptibility only relates to the overall number of events and not to the production of the most energetic particles, such as protons or alpha particles. Moreover, such a higher neutron response may be compensated by other mechanisms at the electronics level, for example, a higher energy value of e-h pair creation (which has the effect of reducing the charge deposited) or higher carrier mobility (which can increase the performance of transistors and strengthen the resilience of circuits to single events). Future studies at the circuit level, following a methodology similar to a first study carried out on GaN subjected to atmospheric neutrons [19], will be largely based on the interaction event databases compiled during this first work and will provide more quantitative information to precisely assess the D–D and D–T neutron radiation response of future circuits based on these alternative materials to the classical silicon of microelectronics.
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Written By
Jean-Luc Autran and Daniela Munteanu
Reviewed: 04 February 2022Published: 17 April 2022
Open access peer-reviewed chapter
