**3. Results and Discussion**

*3.1. SiO<sup>2</sup>*

The XRD intensity at the diffraction angle of ~22◦ (the most intensive (002) diffraction of hexagonal-trydimite) normalized to that of as-grown SiO<sup>2</sup> films on Si(001) is shown in Figure 1 as a function of the ion fluence for 90 MeV Ni+10, 100 MeV Xe+14 and 200 MeV Xe+14 ion impact. The XRD intensity of the irradiated sample normalized to that of the unirradiated sample is proportional to the ion fluence to a certain fluence. Deviation from the linear dependence for the high fluence could be due to the overlapping effect. As observed in latent track formation (e.g., [5,6]), electronic excitation effects extend to a region (approximately cylindrical) with a radius of several nm and a length of the projected range or film thickness, and thus ions may hit the ion-irradiated part for a high ion fluence (called the overlapping effect). As described below, the XRD degradation yield per unit ion fluence (YXD) is reduced at a high fluence, and this could be understood as thermal annealing and/or a reduction in the disordered regions via ion-induced defects (recrystallization [26]). The damage cross-sections (A<sup>D</sup> obtained by RBS-channeling (RBS-C) technique and TEM [5]) are compared with YXD in Figure 2, and it appears that both agree well for S<sup>e</sup> > 10 keV. A discrepancy between A<sup>D</sup> and YXD is seen for S<sup>e</sup> < 10 keV, and the reason for this is not understood. In addition, sputtering yields are often reduced, and this is unlikely to be explained by the annealing effect. Therefore, the reasons for the sputtering suppression at a high fluence remain in question. The XRD degradation yields (YXD) per unit ion fluence are obtained and given in Table 1. The film thickness has been obtained to be ~1.5 µm, using 1.8 MeV He RBS. The attenuation length (LXA) of Cu-k<sup>α</sup> (8.0 keV) is obtained to be 128 µm [80] and the attenuation depth (LXA·sin(22◦/2)) = 24.3 µm. The film thickness (~1.5 µm) is much smaller than the attenuation depth and thus no correction is necessary for the XRD intensity. The lattice expansion or increase in the lattice parameter of 0.5% with an estimated error of 0.2% at 1 <sup>×</sup> <sup>10</sup><sup>12</sup> cm−<sup>2</sup> is found to be nearly independent of the electronic stopping power.

**Figure 1.** XRD intensity from (002) diffraction plane at ~22◦ normalized to as-grown films of SiO<sup>2</sup> as a function of ion fluence for 90 MeV Ni (•), 100 MeV Xe (o, ∆) and 200 MeV Xe (x) ions. Data of 90 MeV Ni (•) and 100 MeV Xe (∆) are from [70]. Linear fit is indicated by dashed lines. An estimated error of XRD intensity is 10%.

**Figure 2.** XRD degradation per unit fluence YXD of polycrystalline SiO<sup>2</sup> film (o, present result) and sputtering yield Ysp (x) of amorphous (or vitreous)-SiO<sup>2</sup> (, x)) and film of SiO<sup>2</sup> (N, , x, ♦, +) as a function of electronic stopping power (Se). Data (, N) from (Qiu et al.) [45], () from (Sugden et al.) [46], (x) from (Matsnami et al.) [47,48], (♦) from (Arnoldbik et al.) [49] and (+) from (Toulemonde et al.) [51]. Se is calculated using SRIM2013, and power-law fits of YXD ((0.0545Se) 2.9) and Ysp ((0.62Se) 3.0) are indicated by blue and black dotted lines, respectively. Power-law fit (•) YXD ((0.055Se) 3.4, TRIM1997) and Ysp ((0.58Se) 3.0, TRIM1985 through SRIM2010) from [47,48,51] are indicated by black and green dashed lines. Damage cross sections () are obtained by RBS-C and () by TEM from [5].

**Table 1.** XRD data of SiO<sup>2</sup> films. Ion, incident energy (E in MeV), XRD intensity degradation (YXD), appropriate E\* (MeV) considering the energy loss in the film and electronic stopping power in keV/nm (Se\*) appropriate for YXD (see text). S<sup>e</sup> from SRIM2013. The deviation ∆Se\* = (Se\*/Se(E) − 1) × 100 is also given.


The electronic stopping power (Se\*) appropriate for XRD intensity degradation is calculated using SRIM 2013, using a half-way approximation that the ion loses its energy for half of the film thickness (~0.75 µm), i.e., Se\* = Se(E\*) with E\* = E(incidence) − Se(E) × 0.75 µm (Table 1). The correction for the film thickness on S<sup>e</sup> appears to be a few percent. It is noticed that the incident charge (Ni+10, Xe+14) differs from the equilibrium charge (+19, +25 and +30 for 90 MeV Ni, 100 MeV Xe and 200 MeV Xe, respectively (Shima et al.) [81], and +18.2, +23.9 and +29.3 (Schiwietz et al.) [82]), both being in good agreement. Following [64], the characteristic length (LEQ = 1/(electron loss cross-section times N)) for attaining the equilibrium charge is estimated to be 8.7, 8.3 and 7.9 nm for 90 MeV Ni+10, 100 MeV Xe+14 and 200 MeV Xe+14, respectively, from the empirical formula of the single-electron loss cross-section σ1L (10−<sup>16</sup> cm<sup>2</sup> ) of 0.52 (90 MeV Ni+10), 0.55 (100 MeV Xe+14) and 0.57 (200 MeV Xe+14) [83,84], N (2.2 <sup>×</sup> <sup>10</sup><sup>22</sup> Si cm−<sup>3</sup> ) being the density, and (target atomic number)2/3 dependence being included. Here, σ1L = σ1L(Si) + 2σ1L(O), ionization potential I<sup>P</sup> = 321 eV [85,86] with the number of removable electrons Neff = 8 and I<sup>P</sup> = 343 eV with Neff = 12 are employed for Ni+10 and Xe+14. LEQ is much smaller than the film thickness and hence the charge-state effect is insignificant.

The sputtering yields Ysp of SiO<sup>2</sup> (normal incidence) are summarized in Table 2 for the comparison of the S<sup>e</sup> dependence of the XRD degradation yields YXD. There are various versions of TRIM/SRIM starting in 1985, and in this occasion, the results used the latest version of SRIM2013 are compared with those earlier versions. Firstly, the correction on the stopping power and projected range for carbon foils (20–120 nm), which have been used to achieve the equilibrium charge incidence, is less than a few %, except for low-energy Cl ions (several %). Secondly, S<sup>e</sup> by CasP (version 5.2) differs ~30% from that by SRIM 2013. Figure 2 shows the S<sup>e</sup> dependence of the XRD degradation yields YXD and Ysp. Both YXD and Ysp fit to the power-law of Se, and the exponents of XRD degradation NXD = 2.9 and Nsp = 3 (sputtering) are almost identical, indicating that the same mechanism is responsible for lattice disordering and sputtering. Further plotted is the sputtering yields vs. S<sup>e</sup> calculated using earlier versions of TRIM/SRIM (TRIM1985 to SRIM2010) [45–49,51], and the plot using earlier versions give the same exponent (Nsp = 3) with a 6% smaller constant Bsp in the power-law fit (20% smaller in the sputtering yields). This means that the plot and discussion using SRIM2013 do not significantly differ from those using the earlier versions of TRIM/SRIM. One notices that no appreciable difference in sputtering yields is observed among a-SiO2, films and single-crystal-SiO<sup>2</sup> (c-SiO2) [45–48], even though the density of c-SiO<sup>2</sup> is larger by 20% than that of a-SiO2, whereas much smaller yields (by a factor of three) have been observed for c-SiO<sup>2</sup> [51]. The discrepancy remains in question. Sputtering yields YEC, which are due to elastic collision cascades, is estimated assuming YEC is proportional to the nuclear stopping power, discarding the variation of the α-factor (order of unity) depending on the ratio of target mass over ion mass (Sigmund) [87]. The proportional constant is obtained to be 2.7 nm/keV using the sputtering yields by low-energy ions (Ar and Kr) (Betz et al.) [88]. YEC is given in Table 2 and it is shown that Ysp/YEC ranges from 44 (5 MeV Cl) to 3450 (210 MeV Au).

**Table 2.** Sputtering data of SiO<sup>2</sup> (normal incidence). Ion, incident energy (E in MeV), energy (E\* in MeV) corrected for the energy loss in carbon foils (see footnote), electronic stopping power (Se), nuclear stopping power (Sn), projected range (Rp) and sputtering yield (YSP). Se, S<sup>n</sup> and R<sup>p</sup> are calculated using SRIM2013. (Se(E\*)/Se(E) − 1), (Sn(E\*)/Sn(E) − 1) and (Rp(E\*)/Rp(E) − 1) in % are given in the parentheses after Se(E\*), Sn(E\*) and Rp(E\*), respectively. YSP in the parenthesis is for SiO<sup>2</sup> films. Se(E) by CasP is also listed. YEC is the calculated sputtering yield due to elastic collisions.


Equilibrium charge has been obtained by using carbon foils of 120 nm [45], 25 nm [46], 100 nm [47,48], 20 nm [49] and 50 nm [51].

In order to obtain the stopping powers (S) for the non-metallic compounds, such as SiO2, described above, we apply the Bragg's additive rule, e.g., S(SiO2) = S(Si) + 2S(O) and S of the constituting elements is calculated using TRIM/SRIM and CasP codes. Before moving to the discussion of the Bragg's deviation, the accuracy of S is briefly mentioned. It is estimated to be 8% (Be through U ions in Ag) near the maximum of S (~0.8 MeV/u) [66], 17% (K to U ions in Au) (Paul) [89]. Besenbacher et al. have reported no difference between solid and gas phases for 0.5–3 MeV He ion stopping in Ar with an experimental accuracy of 3% [90], and this could be understood by the fact that the binding energy (cohesive energy) of solid Ar is too small (0.08 eV (Kittel) [91]), compared with the ionization potential (IBethe) of 188 eV [92], to affect the stopping. On the other hand, Arnau et al. have reported a large deviation (~50% near the stopping power maximum at ~50 keV) for proton stopping between solid and gas phases of Zn, and the deviation reduces ~10% at ~1 MeV [93]. The cohesive energy of 1.35 eV [91] is much smaller than the mean ionization potential IBethe of 330 eV [92], and hence the small increase in IBethe cannot explain the Bragg's deviation of Zn. They have argued that the difference in the 4s into 4p transition probability and screening effect between solid and gas phases are responsible. Both TRIM/SRIM and CasP codes are based on the experiments of conveniently available solid targets and molecular gas (e.g., N2, O2), and thus it is anticipated that the binding effect is included to some or large extent and that the Bragg's deviation is not serious for nitrides and oxides, and is roughly 10% or less at around 1 MeV/u.
