*3.4. TiN*

The XRD patterns are shown in Figure 7 for unirradiated and irradiated TiN films on the SiO<sup>2</sup> glass substrate. As already mentioned in Section 2, (111) and (200) diffraction peaks are observed and the XRD intensity decreases due to ion impact. Figure 8 shows XRD intensities normalized to those of unirradiated TiN films on SiO<sup>2</sup> glass, C-Al2O<sup>3</sup> and R-Al2O<sup>3</sup> substrates as a function of the ion fluence. It is seen that the XRD intensity degradation is nearly the same for the diffraction planes of (111) and (200) on SiO2, and for (111) on C-Al2O3. The XRD intensity degradation is less sensitive to the ion impact for the diffraction plane (220) on the R-Al2O<sup>3</sup> substrate (~30% smaller than that for (111) and (200) on SiO2, and for (111) on C-Al2O3). The XRD intensity degradation per unit fluence YXD for (111) and (200) diffractions is given in Table 5, together with sputtering yields and stopping powers (TRIM1997 and SRIM2013). No appreciable change in the lattice parameter is observed, as shown in Figure 7. Similarly to the SiO2, ZnO and Fe2O<sup>3</sup> cases, the appropriate energy, E − Se`/2, ` = film thickness of ~170 nm is taken into account, and the energy is close to that for sputtering, in which the energy loss of the carbon foil of 100 nm is considered. The X-ray (Cu-kα) attenuation length LXA is obtained to be 11.8 µm [80], and the attenuation depth is 3.7, 4.3 and 6.0 µm for diffraction angles of 36.6◦ , ~43◦ and 61◦ , respectively; thus, the X-ray attenuation correction is insignificant.

**Figure 7.** XRD patterns of TiN film on SiO<sup>2</sup> glass substrate: unirradiated (•) and irradiated by 100 MeV Xe at 0.72 <sup>×</sup> <sup>10</sup><sup>12</sup> cm−<sup>2</sup> (*+*).

**Figure 8.** XRD intensity normalized to unirradiated films of TiN as a function of ion fluence for 60 MeV Ar (, ♦), 90 MeV Ni (H, +, , T ), 100 MeV Xe (o, x, ) and 200 MeV Xe (N, •) ions. Diffraction plane (111) at diffraction angle of ~36.6◦ is indicated by , H, o and N for SiO<sup>2</sup> substrate, (200) at ~43◦ by ♦, +, x and • for SiO<sup>2</sup> substrate, (111) by for C-Al2O<sup>3</sup> substrate and (220) at ~61◦ by T and for R-Al2O<sup>3</sup> substrate. Linear fit is indicated by dotted lines. An estimated error of XRD intensity is 10%.



The characteristic length (LEQ) is estimated to be 4.5, 4.4, 4.2 and 4.0 nm for 60 MeV Ar+7, 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 0.43 (60 MeV Ar+7), 0.44 (90 MeV Ni+10), 0.46 (100 MeV Xe+14) and 0.48 (200 MeV Xe+14) [83,84]. Here, σ1L = σ1L(Ti) + σ1L(N), and the ionization potential I<sup>P</sup> and Neff are (I<sup>P</sup> = 143 eV and Neff = 1) for Ar+7 , with those described in Section 3.1 for Ni+10 and Xe+14. LEQ is much smaller than the film thickness, and hence the charge-state effect is insignificant.

It is found that sputtered Ti collected in the carbon foil is proportional to the ion fluence, as shown in Figure 9 for 60 MeV Ar, 90 MeV Ni, 100 MeV Xe and 200 MeV Xe ions. The sputtering yield of Ti is obtained using the collection efficiency of 0.34 in the carbon foil collector [47] and the results are given in Table 5. Sputtered N collected in the carbon foil is obtained to be 0.4 <sup>×</sup> <sup>10</sup><sup>14</sup> and 0.44 <sup>×</sup> <sup>10</sup><sup>14</sup> cm−<sup>2</sup> with an estimated error of 20% for 200 MeV Xe at 0.22 <sup>×</sup> <sup>10</sup><sup>12</sup> cm−<sup>2</sup> and 60 MeV Ar at 2.8 <sup>×</sup> <sup>10</sup><sup>12</sup> cm−<sup>2</sup> , respectively, and this is comparable with the Ti areal density of 0.4 <sup>×</sup> <sup>10</sup><sup>14</sup> cm−<sup>2</sup> (200 MeV Xe) and 0.475 <sup>×</sup> <sup>10</sup><sup>14</sup> cm−<sup>2</sup> (60 MeV Ar). The results imply stoichiometric sputtering, due to the collection efficiency of N in the carbon foil collector of 0.35 [55], which is close to that of Ti. Thus, the total sputtering yield (Ti + N) is obtained by doubling Ysp (Ti) in Table 5. The sputtering yields of TiN (YEC) due to elastic collisions can be estimated assuming that YEC is proportional to the nuclear stopping power. Here, the proportional constant is obtained to be ~1.6 nm/keV using the experimental yields of 0.527 (0.6 keV Ar) and 0.427 (0.6 keV N) [94] and 0.7 (0.5 keV Cd) [88]. Ysp(TiN)/YEC ranges from 2.5 <sup>×</sup> <sup>10</sup><sup>3</sup> to 6 <sup>×</sup> <sup>10</sup><sup>3</sup> . The XRD intensity degradations YXD and Ysp(Ti + N) are plotted as a function of the electronic stopping power S<sup>e</sup> in Figure 10. It appears that both fit to the power-law: YXD = (0.0224Se) 1.26 and Ysp = (1.17Se) 1.95. The exponents are comparable for XRD intensity degradation and sputtering.

**Figure 9.** Areal density of sputtered Ti from TiN on SiO<sup>2</sup> substrate collected in carbon foil vs. ion fluence for 60 MeV Ar (), 89 MeV Ni (∇), 99 MeV Xe (o) and 198 MeV Xe (∆) ions. An estimated error of areal density is 20%.

**Figure 10.** XRD intensity degradation YXD (10−<sup>12</sup> cm<sup>2</sup> ) (o, +) and sputtering yields Ysp (Ti + N) (, x) vs. electronic stopping power Se (keV/nm). Se is calculated by TRIM1997 (o, ) and by SRIM2013 (+, x). Power-law fits are indicated by dotted lines: YXD = (0.0224Se) 1.26 and Ysp = (1.17Se) 1.95 .
