**3.1. Main characteristics of the databases**

An example of the computed databases is given in **Table 3** for a target composed of GaAs material and subjected to atmospheric neutron irradiation. As illustrated in this sample composed of nine events, each neutron-interaction event is described in two or several successive lines: the first line gives the event number, the energy of the incident neutron at the origin of the event, the Cartesian coordinates of the reaction vertex, and the number of secondary products generated; the following lines give for each secondary product the nature of this product, its mass and atomic numbers, its initial energy just after emission/production, and the Cartesian coordinates of its momentum. In the first line of the database sample shown in **Table 3**, the event #11369 corresponds to a neutron elastic interaction with an As nucleus of the semiconductor lattice, giving a recoil As with an energy of 58 keV.

**Table 4** summarizes the main size characteristics of the computed databases for the six semiconductor materials listed in **Table 1** and subjected to 100 million of atmospheric neutrons each. Five size parameters (or metrics) are reported in **Table 4** to quantify the different databases in terms of neutron-semiconductor interactions: the number (fraction) of elastic and inelastic events, the total number of events, the total number of generated secondary products with energy above the energy threshold Eth given in **Table 1**, and, finally, the average number of secondary ions produced in the case of inelastic events. **Figures 2** and **3** also graphically represent the fractions of elastic and inelastic events and the total number of interaction events and generated secondary products, respectively. All these results lead to the following remarks:


**Figure 2** shows the fraction of elastic and inelastic events for the different semiconductor materials. We can distinguish three different behaviors with low (< 30%, Ge and GaAs), intermediate

> (40–60%, Si and GaN), and high (> 60%, C and SiC) elastic event rates; the presence of low-Z elements such as C and N, respectively, in SiC and GaN leads to increase elastic interactions in

> **Table 4.** Main characteristics of the neutron event databases generated for the six semiconductor materials considered

**Target material Si Ge C (diamond) 4H–SiC GaN GaAs**

3788 (27.7)

9898 (72.3)

**Total number of events 13,400 13,686 38,517 21,161 21,258 14,722**

30,536 (79.2)

Susceptibility of Group-IV and III-V Semiconductor-Based Electronics to Atmospheric Neutrons…

7981 (20.8) 13,771 (65.1)

7390 (34.9)

18,989 20,527 48,357 29,067 32,011 21,758

2.02 1.69 2.23 2.07 1.83 1.66

8303 (39.1)

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12,955 (60.9)

4119 (28)

123

10,603 (72)

(59.1)

(40.9)

In addition, **Figure 3** shows the total number of interaction events (elastic + inelastic) and the total number of secondary products generated in the different targets. For Si, Ge, and GaAs, this last quantity is in the same order of magnitude (with Si < Ge < GaAs that follows the rule that neutron nuclear interaction probability with the elements is even higher than the atomic number is). For GaN and SiC and as previously mentioned, the presence of low-Z elements, C and N, respectively, increases the number of elastic events and indirectly increases the total number of secondary products. Finally, carbon-diamond material dominates this comparison in terms of the number of events/products due to its high power of neutron moderation.

**Figure 4** shows the number of events as a function of the number of secondary products generated during the different interaction events. We call this last quantity secondary product

**Si Ge C SiC GaAs GaN**

**Figure 2.** Fraction of elastic and inelastic events for the six semiconductor targets irradiated with atmospheric neutrons.

Elastic events Inelasc events

these last materials with respect to the elastic rates observed for Si and GaAs.

**3.2. Nature of the secondary products**

**Event fracon (%)**

Number of elastic events (fraction, %) 7918

Number of inelastic events (fraction, %) 5482

**Total number of secondary products** 

Average number of secondary ions produced in inelastic events

**(E > E**th**)**

in this work.


**Table 3.** Sample (nine events) extracted from the computed database corresponding to GaAs target material subjected to atmospheric neutron irradiation.

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**Table 4.** Main characteristics of the neutron event databases generated for the six semiconductor materials considered in this work.

(40–60%, Si and GaN), and high (> 60%, C and SiC) elastic event rates; the presence of low-Z elements such as C and N, respectively, in SiC and GaN leads to increase elastic interactions in these last materials with respect to the elastic rates observed for Si and GaAs.

In addition, **Figure 3** shows the total number of interaction events (elastic + inelastic) and the total number of secondary products generated in the different targets. For Si, Ge, and GaAs, this last quantity is in the same order of magnitude (with Si < Ge < GaAs that follows the rule that neutron nuclear interaction probability with the elements is even higher than the atomic number is). For GaN and SiC and as previously mentioned, the presence of low-Z elements, C and N, respectively, increases the number of elastic events and indirectly increases the total number of secondary products. Finally, carbon-diamond material dominates this comparison in terms of the number of events/products due to its high power of neutron moderation.

### **3.2. Nature of the secondary products**

• Diamond shows a very different behavior than the other materials since it is an excellent neutron moderator (better than graphite). This explains the extremely elevated number of elastic events as compared to other materials: ×8 with respect to Ge, ×7 with respect to

• Silicon carbide, which can be viewed as a "mixture" of Si and C at the atomic level, shows an intermediate behavior between Si and C with a quasi ×2 number of elastic events due to

**Figure 2** shows the fraction of elastic and inelastic events for the different semiconductor materials. We can distinguish three different behaviors with low (< 30%, Ge and GaAs), intermediate

**Event Energy (MeV)of the (x, y, z) coordinates of the vertex Number of Number incident neutron of the interaction event products 11369** 1 1.938009e+00 -3.123114e+00 2.128556e+00 -2.043811e-03 1 As75[0.0] 75 33 5.865383e-02 4.466775e-01 4.319914e-01 7.834939e-01 **Product A Z Energy (MeV) (ux, uy, uz) coordinates of the momentum vector** 

**Table 3.** Sample (nine events) extracted from the computed database corresponding to GaAs target material subjected

**11370** 1 2.383369e+02 -1.712552e+00 -2.155406e+00 -2.719637e-03 3 proton 1 1 8.546443e+01 -5.270216e-01 -1.286384e-01 8.400597e-01 alpha 4 2 1.383653e+01 2.459101e-02 -1.145710e-01 -9.931107e-01 Ni62[0.0] 62 28 2.160926e+00 8.943092e-02 -1.490662e-01 9.847748e-01 **11371** 1 2.638142e+01 -3.206409e+00 -4.575562e+00 9.494563e-03 1 Ga68[0.0] 68 31 6.260841e-01 1.892272e-01 -2.680785e-01 9.446306e-01 **11372** 1 2.074821e+02 4.896602e+00 -4.752904e+00 6.255025e-04 2 proton 1 1 1.893323e+02 1.776401e-01 2.641910e-02 9.837408e-01 Zn68[0.0] 68 30 1.562386e-01 -9.659646e-01 9.698920e-03 2.584925e-01 **11373** 1 7.875999e+00 -1.735542e+00 4.719762e+00 -5.800941e-03 1 Ga69[0.0] 69 31 2.959972e-01 3.094430e-02 9.454495e-02 9.950395e-01 **11374** 1 1.114444e+02 4.558722e+00 -4.191099e+00 9.470209e-03 2 proton 1 1 6.645712e+00 -4.477549e-01 -6.883188e-01 -5.707301e-01 Zn64[0.0] 64 30 3.507131e+00 3.622407e-01 1.244171e-01 9.237435e-01 **11375** 1 1.541558e+02 2.595860e-01 1.292310e+00 5.783486e-03 2 proton 1 1 3.268971e+01 -3.472904e-02 -3.481138e-01 9.368088e-01 Ge74[0.0] 74 32 4.819644e-01 -9.020135e-01 3.033525e-01 -3.071628e-01 **11376** 1 3.974678e+01 6.775934e-01 4.367106e+00 -9.091089e-03 2 alpha 4 2 7.800831e+00 7.650253e-01 3.799136e-01 5.200019e-01 Cu64[0.0] 64 29 1.066644e+00 -5.057675e-01 -4.010571e-01 7.637751e-01 **11377** 1 2.877963e+02 -1.109289e+00 1.109673e+00 -8.077168e-03 4 proton 1 1 6.803890e+01 2.508779e-01 -6.180162e-01 7.450612e-01 proton 1 1 1.804781e+01 -3.496855e-01 -7.349503e-01 -5.810061e-01 deuteron 2 1 1.321282e+01 -5.108815e-01 -4.381425e-01 7.396156e-01 Zn66[0.0] 66 30 9.454173e-01 9.760912e-01 2.947766e-04 2.173610e-01

GaAs, and ×4 with respect to Si.

122 Numerical Simulations in Engineering and Science

the presence of C.

to atmospheric neutron irradiation.

**Figure 4** shows the number of events as a function of the number of secondary products generated during the different interaction events. We call this last quantity secondary product

**Figure 2.** Fraction of elastic and inelastic events for the six semiconductor targets irradiated with atmospheric neutrons.

• Multi-fragment reactions with M ≥ 4 represent a small but non-negligible part of the events for all semiconductors except for diamond: 3.6% for Si, 4.9% for Ge, 4.6% for GaAs, 5.0% for GaN, and 3.2% for SiC against only 2.8% for C. These large multiplicity events are important because they can produce a single event that potentially impacts several sensitive volumes in a component or a circuit. With respect to silicon, Ge, GaAs, and GaN show a

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125

**Figures 5** and **6** provide a detailed analysis of the production of these secondary ions, target per target, and as a function of the atomic number of the products. Z is ranging from 1 (proton) to the highest atomic number of the element(s) present in the target material: 6 for carbon,

**Figure 5.** Number of secondary products produced in Si, C (diamond), and SiC as a function of their atomic number (for

x 20 microns).

100 million atmospheric incident neutrons on a volume target of 1 cm<sup>2</sup>

slightly higher probability for such large multiplicity events.

14 for silicon, 32 for germanium, 31 for GaN, and 33 for GaAs.

**Figure 3.** Total numbers of interaction events and secondary products referenced in the different computed databases.

**Figure 4.** Number of events as a function of the number of secondary products (also called secondary product shower multiplicity) for the six semiconductor materials (for 100 million atmospheric incident neutrons on a volume target of 1cm2 x 20 microns).

shower multiplicity (M) because each event can be considered at the origin of a shower of ionizing products: a multiplicity of one (i.e., one product emitted) corresponds to elastic events; larger multiplicities correspond to the production of two or more secondary products during nuclear reactions.

From **Figure 4**, we can formulate the following observations:


• Multi-fragment reactions with M ≥ 4 represent a small but non-negligible part of the events for all semiconductors except for diamond: 3.6% for Si, 4.9% for Ge, 4.6% for GaAs, 5.0% for GaN, and 3.2% for SiC against only 2.8% for C. These large multiplicity events are important because they can produce a single event that potentially impacts several sensitive volumes in a component or a circuit. With respect to silicon, Ge, GaAs, and GaN show a slightly higher probability for such large multiplicity events.

**Figures 5** and **6** provide a detailed analysis of the production of these secondary ions, target per target, and as a function of the atomic number of the products. Z is ranging from 1 (proton) to the highest atomic number of the element(s) present in the target material: 6 for carbon, 14 for silicon, 32 for germanium, 31 for GaN, and 33 for GaAs.

x 20 microns).

**0**

**10000**

**Number of**

**interactions or products**

**20000**

**30000**

**40000**

**50000**

**60000**

124 Numerical Simulations in Engineering and Science

nuclear reactions.

lium arsenide.

**Number of events**

1cm2

**12345678 9 10 11 12 13 14 15**

**Si Ge C SiC GaN**

Interactions (elastic + inelastic)

**Si Ge C SiC GaAs GaN**

**GaAs**

Secondary products

**Secondary product shower mulplicity**

**Figure 3.** Total numbers of interaction events and secondary products referenced in the different computed databases.

**Figure 4.** Number of events as a function of the number of secondary products (also called secondary product shower multiplicity) for the six semiconductor materials (for 100 million atmospheric incident neutrons on a volume target of

shower multiplicity (M) because each event can be considered at the origin of a shower of ionizing products: a multiplicity of one (i.e., one product emitted) corresponds to elastic events; larger multiplicities correspond to the production of two or more secondary products during

• For all targets, the number of reactions monotonously decreases when increasing M. This number of reactions goes to zero above M = 6 for carbon (diamond), M = 10 for silicon, M = 12 for germanium and silicon carbide, M = 13 for gallium nitride, and M = 15 for gal-

• For M > 9, the event statistic is therefore relatively weak and may be dependent of the number of incident neutrons. Pushing the statistics beyond 100 million neutrons may give slightly different results for these limits in terms of secondary product shower multiplicity.

From **Figure 4**, we can formulate the following observations:

**Figure 5.** Number of secondary products produced in Si, C (diamond), and SiC as a function of their atomic number (for 100 million atmospheric incident neutrons on a volume target of 1 cm<sup>2</sup> x 20 microns).

comes from the limited number of high-energy incident neutrons, due to the 1/E nature of the spectrum of **Figure 1** and to the finite value of the high-energy limit (10<sup>5</sup> MeV) considered for

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127

**Figures 7**–**10** provide a detailed analysis of the secondary ions produced during neutron interactions in the different target materials in terms of initial energy (when products are

**Figure 7.** Histograms in energy for recoil nuclei, protons, and alpha particles induced by neutron interactions in the

different targets.

simulation; certain reaction channels being not present in the computed databases.

released), linear energy transfer (LET), and range in the target material.

**3.3. Detailed analysis in terms of energy, LET, and range**

**Figure 6.** Number of secondary products produced in Ge, GaAs, and GaN as a function of their atomic number (for 100 million atmospheric incident neutrons on a volume target of 1 cm2 x 20 microns).

For the six materials, the most frequent produced secondary particles are the recoil products due to neutron elastic interactions with the nuclei of the semiconductor lattice, followed by protons in the second position and alpha particles in the third one (in the case of compound materials, recoil nuclei concern the two different species: Si and C recoil products for SiC, Gas and As for GaAs, and Ga and N for GaN). All the other products are systematically less produced than these three categories of products.

This observation justifies why in the following analysis (paragraph 3.3), all produced particles will be divided in four classes: recoil products, protons, alpha particles, and other products.

Also shown in **Figure 5**, beryllium (Z = 4) is the less produced product for silicon target, lithium (Z = 3) for diamond, and fluor (Z = 9) for SiC. Finally, note that in **Figure 6**, an axis-break has been introduced because no secondary product is created between Z = 3 and 19 for Ge, between Z = 4 and 22 (except Z = 16 and 19) for GaAs, and between Z = 7 and 21 for GaN. For these large Z elements (31 for Ga, 32 for Ge, and 33 for As), the absence of fragments in these ranges of Z comes from the limited number of high-energy incident neutrons, due to the 1/E nature of the spectrum of **Figure 1** and to the finite value of the high-energy limit (10<sup>5</sup> MeV) considered for simulation; certain reaction channels being not present in the computed databases.

### **3.3. Detailed analysis in terms of energy, LET, and range**

For the six materials, the most frequent produced secondary particles are the recoil products due to neutron elastic interactions with the nuclei of the semiconductor lattice, followed by protons in the second position and alpha particles in the third one (in the case of compound materials, recoil nuclei concern the two different species: Si and C recoil products for SiC, Gas and As for GaAs, and Ga and N for GaN). All the other products are systematically less

**Figure 6.** Number of secondary products produced in Ge, GaAs, and GaN as a function of their atomic number (for 100

x 20 microns).

This observation justifies why in the following analysis (paragraph 3.3), all produced particles will be divided in four classes: recoil products, protons, alpha particles, and other

Also shown in **Figure 5**, beryllium (Z = 4) is the less produced product for silicon target, lithium (Z = 3) for diamond, and fluor (Z = 9) for SiC. Finally, note that in **Figure 6**, an axis-break has been introduced because no secondary product is created between Z = 3 and 19 for Ge, between Z = 4 and 22 (except Z = 16 and 19) for GaAs, and between Z = 7 and 21 for GaN. For these large Z elements (31 for Ga, 32 for Ge, and 33 for As), the absence of fragments in these ranges of Z

produced than these three categories of products.

million atmospheric incident neutrons on a volume target of 1 cm2

126 Numerical Simulations in Engineering and Science

products.

**Figures 7**–**10** provide a detailed analysis of the secondary ions produced during neutron interactions in the different target materials in terms of initial energy (when products are released), linear energy transfer (LET), and range in the target material.

**Figure 7.** Histograms in energy for recoil nuclei, protons, and alpha particles induced by neutron interactions in the different targets.

LET and range have been obtained from SRIM [12] simulation using numerical functions developed from a behavioral modeling of SRIM Tables [13]. These generalized functions LET(Z, A, E target) and Range(Z, A, E target) have been written in C++ and allow us to calculate the two quantities for any given ion defined by the triplet (Z, A, E energy) and for the semiconductor targets Si, Ge, C, SiC, GaAs, and GaN.

All histograms shown in **Figures 7**–**10** have been constructed using linear bins with constant bin widths corresponding to the minimum value of the x-axis scale. Curves have been also smoothed in frequency in order to give a more readable aspect to the different distributions.

**Figure 8.** Histograms in LET for recoil nuclei, protons, and alpha particles induced by neutron interactions in the different targets.

**Figure 7** shows the histograms in energy for recoil nuclei, protons, and alpha particles induced by neutron interactions in the six targets. We note a certain similarity between the curves

**Figure 9.** Histograms in range for recoil nuclei, protons, and alpha particles induced by neutron interactions in silicon,

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• Recoil products have systematically a distribution peaking at low energies (1 MeV) and ranging between 1 and 30 MeV for C, 1 and 10 MeV for Si and SiC, 1 to 7–8 MeV for GaAs and GaN, and 1 to 5 MeV for Ge. The high limit in energy of recoil nuclei distributions is much lower

• Fragments other than protons and alpha particles show a more broaden distribution than that of recoil products, with a maximum close to 1 MeV and ranging up to a few tens of MeV.

related to the different materials:

germanium, and diamond targets.

than the atomic number Z, which is higher.

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LET and range have been obtained from SRIM [12] simulation using numerical functions developed from a behavioral modeling of SRIM Tables [13]. These generalized functions LET(Z, A, E target) and Range(Z, A, E target) have been written in C++ and allow us to calculate the two quantities for any given ion defined by the triplet (Z, A, E energy) and for the semiconductor

All histograms shown in **Figures 7**–**10** have been constructed using linear bins with constant bin widths corresponding to the minimum value of the x-axis scale. Curves have been also smoothed in frequency in order to give a more readable aspect to the different

**Figure 8.** Histograms in LET for recoil nuclei, protons, and alpha particles induced by neutron interactions in the

targets Si, Ge, C, SiC, GaAs, and GaN.

128 Numerical Simulations in Engineering and Science

distributions.

different targets.

**Figure 9.** Histograms in range for recoil nuclei, protons, and alpha particles induced by neutron interactions in silicon, germanium, and diamond targets.

**Figure 7** shows the histograms in energy for recoil nuclei, protons, and alpha particles induced by neutron interactions in the six targets. We note a certain similarity between the curves related to the different materials:


• Alpha particles show a clear peak distribution ranging from 1 MeV to a few tens of MeV and with a maximum around 7–10 MeV, except for C and SiC (around 3 MeV). Above 10 MeV, alpha particles are the most numerous with protons.

vertex position. In the same way as observed in **Figure 7**, distributions of **Figure 8** show similari-

• Heavy products composed of recoil nuclei and fragments other than protons and alpha

• Recoil product LET values are distributed following a very sharp (peaked) distribution

• Protons, which are the lightest but the more energetic particles, are characterized by the

• Alpha particles exhibit intermediate LET values, with a peak distribution centered in the

To complete previous results, **Figures 9** and **10** show the range distributions of all products, always partitioned in four classes. On the one hand, recoil and other (heavy) products exhibit the shorter ranges, in the deca-nanometer domain and up to a maximum of a few microns. On the other hand, light products, i.e., protons and alpha particles, show much longer ranges up to a few hundreds of microns for the most energetic alpha particles and ranges up to a few

From results shown in **Figures 8**–**10**, we can logically conclude that recoil nuclei and heavy fragments other than protons and alpha particles are susceptible to induce single events in a very short range from their emission point and with a relative high efficiency, due to their

On the contrary, protons and alpha particles are characterized by lower LET values but with longer ranges in the different semiconductor materials. Consequently, they are susceptible to induce single events farther from their emission point than heavy fragments up to distances

This last paragraph examines the consequences of neutron interactions in the different targets in terms of electron-hole pair generation and fundamental mechanism at the origin of single events in electronics. From the computed databases, we calculated in **Figure 11** the total energy deposited by all the secondary products in the different target materials. Although it is a purely theoretical value, this total amount of deposited energy by ionization process is in the range of 10<sup>11</sup> eV for 100 million incident neutrons, which gives an average value in the range of keV per incident neutron, more precisely 1.7 keV for Si, 2.85 keV for Ge, 3.07 keV for C, 2.33 keV for SiC, 2.6 keV for GaAs, and 3.74 keV for GaN. This quantity is found to be

Dividing this total energy deposited by all the secondary products by the average energy for creation of an electron-hole pair (given in **Table 1**) gives, for each target material, the upper theoretical limit of the total amount of electron–hole pairs induced by neutrons (via the secondary products). This quantity is shown in **Figure 12** for the different target materials. Also, normalized per incident neutron, this corresponds to 472 e–h pairs for Si, 983 for

of hundred microns for alpha particles and several millimeters for protons.

minimum for the silicon target and maximum for GaN (**Figure 11**).

**3.4. Consequences in terms of electron-hole pair generation and single events**

)) for all targets.

Susceptibility of Group-IV and III-V Semiconductor-Based Electronics to Atmospheric Neutrons…

)).

)).

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particles exhibit the highest LET values, in the range 1 to 10 MeV/(mg/cm<sup>2</sup>

ties from a target to another:

centered at approximately 3 MeV/(mg/cm<sup>2</sup>

range 0.1 to a 1 MeV/(mg/cm<sup>2</sup>

millimeters for high-energy protons.

initial high LET values.

lowest LET values, from 0.01 to a few 0.1 MeV/(mg/cm<sup>2</sup>

)).

• Protons exhibit a large distribution with a maximum around a few MeV (Si, SiC, C) or 10 MeV (Ge, GaAs, GaN) and with a large tail distribution ranging up to several hundreds of MeV (up to 1 GeV for C). Protons clearly dominate in number from 20 MeV to 1 GeV with respect to all other particles.

**Figure 8** shows the same data of **Figure 7** but expressed in LET. This transformation has the advantage to show the ionizing power of secondary products just after their release at interaction

**Figure 10.** Histograms in range for recoil nuclei, protons, and alpha particles induced by neutron interactions in silicon carbide, gallium arsenide, and gallium nitride targets.

vertex position. In the same way as observed in **Figure 7**, distributions of **Figure 8** show similarities from a target to another:

• Alpha particles show a clear peak distribution ranging from 1 MeV to a few tens of MeV and with a maximum around 7–10 MeV, except for C and SiC (around 3 MeV). Above

• Protons exhibit a large distribution with a maximum around a few MeV (Si, SiC, C) or 10 MeV (Ge, GaAs, GaN) and with a large tail distribution ranging up to several hundreds of MeV (up to 1 GeV for C). Protons clearly dominate in number from 20 MeV to 1 GeV with respect

**Figure 8** shows the same data of **Figure 7** but expressed in LET. This transformation has the advantage to show the ionizing power of secondary products just after their release at interaction

**Figure 10.** Histograms in range for recoil nuclei, protons, and alpha particles induced by neutron interactions in silicon

carbide, gallium arsenide, and gallium nitride targets.

10 MeV, alpha particles are the most numerous with protons.

to all other particles.

130 Numerical Simulations in Engineering and Science


To complete previous results, **Figures 9** and **10** show the range distributions of all products, always partitioned in four classes. On the one hand, recoil and other (heavy) products exhibit the shorter ranges, in the deca-nanometer domain and up to a maximum of a few microns. On the other hand, light products, i.e., protons and alpha particles, show much longer ranges up to a few hundreds of microns for the most energetic alpha particles and ranges up to a few millimeters for high-energy protons.

From results shown in **Figures 8**–**10**, we can logically conclude that recoil nuclei and heavy fragments other than protons and alpha particles are susceptible to induce single events in a very short range from their emission point and with a relative high efficiency, due to their initial high LET values.

On the contrary, protons and alpha particles are characterized by lower LET values but with longer ranges in the different semiconductor materials. Consequently, they are susceptible to induce single events farther from their emission point than heavy fragments up to distances of hundred microns for alpha particles and several millimeters for protons.
