Modiﬁcation of SiO 2 , ZnO, Fe 2 O 3 and TiN Films by Electronic Excitation under High Energy Ion Impact

: It has been known that the modiﬁcation of non-metallic solid materials (oxides, nitrides, etc.), e.g., the formation of tracks, sputtering representing atomic displacement near the surface and lattice disordering are induced by electronic excitation under high-energy ion impact. We have investigated lattice disordering by the X-ray diffraction (XRD) of SiO 2 , ZnO, Fe 2 O 3 and TiN ﬁlms and have also measured the sputtering yields of TiN for a comparison of lattice disordering with sputtering. We ﬁnd that both the degradation of the XRD intensity per unit ion ﬂuence and the sputtering yields follow the power-law of the electronic stopping power and that these exponents are larger than unity. The exponents for the XRD degradation and sputtering are found to be comparable. These results imply that similar mechanisms are responsible for the lattice disordering and electronic sputtering. A mechanism of electron–lattice coupling, i.e., the energy transfer from the electronic system into the lattice, is discussed based on a crude estimation of atomic displacement due to Coulomb repulsion during the short neutralization time (~fs) in the ionized region. The bandgap scheme or exciton model is examined. 0.1%) and nearly zero at ~1 × 10 12 cm − 2 for 200 MeV Xe, 100 MeV Xe and 90 MeV Ni ion impact. The dependence of the lattice parameter change on the ion ﬂuence and S e is complicated, and is to be investigated.

Besides track formation and electronic sputtering, lattice disordering (the degradation of X-ray diffraction (XRD) intensity) with lattice expansion (an increase in the lattice parameter) by high-energy ions has been observed for the polycrystalline films of SiO 2 [70] and WO 3 [58], and lattice disordering with lattice compaction for those of Cu 2 O [57], CuO [59], Fe 2 O 3 [60], Cu 3 N [61] and Mn-doped ZnO [71]. Only lattice disordering has been observed for the ultra-thin films of WO 3 [72]. It should be noted that a comparison between high-energy and low-energy ion impact effects is important. Lattice expansion has been observed for a few keV D ion irradiation on Fe 2 O 3 [73], and this can be understood by the incorporation of D into non-substitutional sites (incorporation or implantation effect). Thus, lattice expansion by medium-energy ions (100 keV Ne) on Fe 2 O 3 [60] could be understood by Ne incorporation and/or interstitial-type defects generated by ion impact, with a possible stabilization by incorporating Ne in the film, whereas lattice compaction has been observed for a 100 MeV Xe ion impact on Fe 2 O 3 [60]. It should be noted that the incorporation of ions in thin films does not take place for high-energy ions, since the projected range of ions (R p ) is much larger than the film thickness (e.g., R p of 14 µm for 100 MeV Xe in SiO 2 ), unless the thickness is too large. The lattice expansion due to the incorporation effect has been observed for a few keV H and D irradiation at a low fluence on WNO x with x ≈ 0.4, whereas lattice compaction has been observed at a high fluence of D [74]. Peculiarly, lattice expansion at a low ion fluence and compaction at a high fluence, as well as disordering, have been reported for medium-energy (100 keV Ne and N) and high-energy (100 MeV Xe and 90 MeV Ni) ion impact on WNO x [75,76]. One speculation is that the lattice compaction is due to vacancy-type defects generated by ion impact, which is to be investigated. Furthermore, a drastic increase in electrical conductivity has been observed for Cu 3 N [61], Mn-doped ZnO [71] and WNO x with x ≈ 0.4 [75,76]. The conductivity increase is ascribed to the increase in the carrier concentration and mobility.
There are a few reports on the S e dependence of the XRD intensity degradation per unit fluence (Y XD ) for SiC and KBr [56] and WO 3 [72]. Y XD is found to follow the power-law fit: Y XD = (B XD S e ) N XD , B XD being a material-dependent constant and the exponent N XD being comparable with the Nsp of the electronic sputtering. The results imply that similar mechanisms operate for lattice disordering and electronic sputtering. It is of interest to compare the S e dependence of lattice disordering with that of electronic sputtering for materials other than those mentioned above. In this paper, we have measured the lattice disordering of SiO 2 , ZnO, Fe 2 O 3 and TiN films, and the sputtering of TiN. The XRD results are compared with the sputtering. The exciton model is examined and scaling parameters are explored for representing electronic excitation effects.

Materials and Methods
XRD has been measured using Cu-k α radiation. Accuracy of the XRD intensity is estimated to be approximately 10%, based on the variation of repeated measurements. Rutherford backscattering (RBS) has been performed with MeV He ions for evaluation of film thickness and composition. Similarly, accuracy of the RBS is estimated considering the variation of the repeated measurements. High-energy ion irradiation has been performed at room temperature and normal incidence. Irradiation of high-energy ion with lower incident charge than the equilibrium charge without carbon foil is often employed for the samples of XRD measurement; however, the effect of non-equilibrium charge incidence does not come into play because the length for attaining the equilibrium charge is much smaller than the film thickness, as described for each material in Section 3. SiO (100), (002), (004) and (202) diffraction of hexagonal-tridymite structure [70]. The strong peak at 69 • is Si(004) and peak at 33 • is possibly Si(002). Film thickness is~1.5 µm and the composition is stoichiometric (O/Si = 2.0 ± 5%) by RBS of 1.8 MeV He. Film density is taken to be the same as that of amorphous-SiO 2 (a-SiO 2 ), since it has been derived to be 2.26 gcm −3 from XRD results, which is close to that of a-SiO 2 (2.2 gcm −3 ) Pure ZnO films have been prepared on MgO (001) substrate by using a radio frequency magnetron sputtering (RFMS) deposition method with ZnO target, and it has been reported that the dominant growth orientation is (001) and (100) of hexagonal-wurtzite structure depending on the substrate temperature of 350 • C and 500 • C during the film growth, respectively [71,77,78]. The composition is stoichiometric, i.e., O/Zn = 1.0 ± 0.05, and film thickness is~100 nm by He RBS. Here, the density is taken to be 4.2 × 10 22 Zn cm −3 (5.67 gcm −3 ).
Preparation and characterization methods of Fe 2 O 3 films are described in [60]. Briefly, Fe 2 O 3 films have been prepared by deposition of Fe layers on SiO 2 -glass and C-plane cut Al 2 O 3 (C-Al 2 O 3 ) substrates using a RFMS deposition method with Fe target (99.99%) and Ar gas, followed by oxidation at 500 • C for 2-5 hr in air. According to RBS of 1.4-1.8 MeV He ions, the composition is stoichiometric (O/Fe = 1.5 ± 0.1) and film thickness used in this study is~100 nm. Here, the density of 3.96 × 10 22 Fe cm −3 (5.25 gcm −3 ) is employed. Diffraction peaks have been observed at~33 • and 36 • , and crystalline structure has been identified as hexagonal Fe 2 O 3 (hematite or α-Fe 2 O 3 ). These correspond to (104) and (110) diffraction planes.
TiN films have been prepared on SiO 2 -glass, C-plane cut Al 2 O 3 (C-Al 2 O 3 ) and R-plane cut Al 2 O 3 (R-Al 2 O 3 ) substrates at 600 • C using a RFMS deposition method with Ti target (99.5%) and high purity N 2 gas. RBS of 1.4-1.8 MeV He ions shows that the composition is stoichiometric (N/Ti = 1.0 ± 0.05) and that the film thickness used in this study is~170 nm (deposition time of 1 hr). Here, the density of 5.25x10 22 Ti cm −3 (5.4 gcm −3 ) is employed. Diffraction peaks have been observed at 36.6 • , 42.6 • and~77 • on SiO 2 glass and C-Al 2 O 3 . Crystalline structure has been identified as a cubic structure and these correspond to (111), (200) and (222) diffractions [79]. Diffraction intensity of (111) is larger than that of (200) on SiO 2 glass, and diffraction of (111) on C-Al 2 O 3 is very intensive. TiN on R-Al 2 O 3 has preferential growth orientation of (220) of a cubic structure (diffraction angle at~61 • ). Sputtered atoms are collected in the carbon foil (100 nm) and the sputtered atoms are analyzed by RBS to obtain the sputtering yields [54] (carbon collector method).

SiO 2
The XRD intensity at the diffraction angle of~22 • (the most intensive (002) diffraction of hexagonal-trydimite) normalized to that of as-grown SiO 2 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 (Y XD ) 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 D obtained by RBS-channeling (RBS-C) technique and TEM [5]) are compared with Y XD in Figure 2, and it appears that both agree well for S e > 10 keV. A discrepancy between A D and Y XD is seen for S e < 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 (Y XD ) 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 (L XA ) of Cu-k α (8.0 keV) is obtained to be 128 µm [80] and the attenuation depth (L XA ·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 × 10 12 cm −2 is found to be nearly independent of the electronic stopping power.   [46], (x) from (Matsnami et al.) [47,48], (♦) from (Arnoldbik et al.) [49] and (+) from (Toulemonde et al.) [51]. S e is calculated using SRIM2013, and power-law fits of Y XD ((0.0545S e ) 2.9 ) and Y sp ((0.62S e ) 3.0 ) are indicated by blue and black dotted lines, respectively. Power-law fit (•) Y XD ((0.055S e ) 3.4 , TRIM1997) and Y sp ((0.58S e ) 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 2 films. Ion, incident energy (E in MeV), XRD intensity degradation (Y XD ), appropriate E* (MeV) considering the energy loss in the film and electronic stopping power in keV/nm (S e *) appropriate for Y XD (see text). S e from SRIM2013. The deviation ∆S e * = (S e */S e (E) − 1) × 100 is also given. The electronic stopping power (S e *) 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., S e * = S e (E*) with E* = E(incidence) − S e (E) × 0.75 µm ( Table 1). The correction for the film thickness on S e 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 (L EQ = 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 σ 1L (10 −16 cm 2 ) 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 × 10 22 Si cm −3 ) being the density, and (target atomic number) 2/3 dependence being included. Here, σ 1L = σ 1L (Si) + 2σ 1L (O), ionization potential I P = 321 eV [85,86] with the number of removable electrons N eff = 8 and I P = 343 eV with N eff = 12 are employed for Ni +10 and Xe +14 . L EQ is much smaller than the film thickness and hence the charge-state effect is insignificant.

Ion
The sputtering yields Y sp of SiO 2 (normal incidence) are summarized in Table 2 for the comparison of the S e dependence of the XRD degradation yields Y XD . 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 e by CasP (version 5.2) differs~30% from that by SRIM 2013. Figure 2 shows the S e dependence of the XRD degradation yields Y XD and Y sp . Both Y XD and Y sp fit to the power-law of S e , and the exponents of XRD degradation N XD = 2.9 and N sp = 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 e calculated using earlier versions of TRIM/SRIM (TRIM1985 to SRIM2010) [45][46][47][48][49]51], and the plot using earlier versions give the same exponent (N sp = 3) with a 6% smaller constant B sp 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-SiO 2 , films and single-crystal-SiO 2 (c-SiO 2 ) [45][46][47][48], even though the density of c-SiO 2 is larger by 20% than that of a-SiO 2 , whereas much smaller yields (by a factor of three) have been observed for c-SiO 2 [51]. The discrepancy remains in question. Sputtering yields Y EC , which are due to elastic collision cascades, is estimated assuming Y EC 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]. Y EC is given in Table 2 and it is shown that Ysp/Y EC ranges from 44 (5 MeV Cl) to 3450 (210 MeV Au). Table 2. Sputtering data of SiO 2 (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 (S e ), nuclear stopping power (S n ), projected range (R p ) and sputtering yield (Y SP ). S e , S n and R p are calculated using SRIM2013. (S e (E*)/S e (E) − 1), (S n (E*)/S n (E) − 1) and (R p (E*)/R p (E) − 1) in % are given in the parentheses after S e (E*), S n (E*) and R p (E*), respectively. Y SP in the parenthesis is for SiO 2 films. S e (E) by CasP is also listed. Y EC is the calculated sputtering yield due to elastic collisions. In order to obtain the stopping powers (S) for the non-metallic compounds, such as SiO 2 , described above, we apply the Bragg's additive rule, e.g., S(SiO 2 ) = 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 (I Bethe ) 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 I Bethe of 330 eV [92], and hence the small increase in I Bethe 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., N 2 , O 2 ), 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.

ZnO
The XRD intensity at a diffraction angle of~34 • ((001) diffraction) and 32 • ((100) diffraction) normalized to those of unirradiated ZnO films on the MgO substrate is shown in Figure 3 as a function of the ion fluence for 90 MeV Ni +10 , 100 MeV Xe +14 and 200 MeV Xe +14 ion impact. It appears that the XRD intensity degradation is nearly independent of the diffraction planes. The XRD intensity degradation per unit fluence Y XD is given in Table 3, together with sputtering yields [54], stopping powers and projected ranges (SRIM2013). The X-ray (Cu-kα) attenuation length L XA is obtained to be 36.6 µm [80] and the attenuation depth is 11 and 10 µm for the diffraction angle of~34 • and 32 • , respectively; thus, the X-ray attenuation correction is unnecessary. It appears that the appropriate energy for the Y XD vs. S e plot, E − S e /2, where = a film thickness of~100 nm, is nearly the same as E* for sputtering, in which the energy loss of a carbon foil of 100 nm is considered. Similarly to the case of SiO 2 , the characteristic length (L EQ ) is estimated to be 4.  [83,84]. Here, σ 1L = σ 1L (Zn) + σ 1L (O), and the ionization potential I P and N eff are described in Section 3.1. Again, L EQ is much smaller than the film thickness and the charge-state effect is insignificant.  Table 3. XRD data of ZnO films. Ion, incident energy (E in MeV), XRD intensity degradation (Y XD ), E* = E − ∆E (energy loss in carbon foil of 100 nm) (MeV) and electronic (S e *) and nuclear (S n *) stopping powers in keV/nm and projected range R p * (µm) at E* calculated using SRIM2013. Sputtering yield Y sp from [54]. Sputtering yield by 100 keV Ne ion is also given.  Figure 4 shows the XRD intensity degradation Y XD vs. electronic stopping power (S e ) (SRIM2013 and TRIM1997) together with the sputtering yields Y sp vs. S e . Both Y XD and Y sp follow the power-law fit and the exponent for Y XD using TRIM1997 gives a slightly larger value than that using SRIM2013. The exponent of lattice disordering is nearly the same as that of sputtering. The change in the lattice parameter ∆ c appears to scatter, and roughly −0.2% and −0.1% with an estimated error of 0.1% are obtained for (100) and (002) diffractions by 100 MeV Xe at 10 × 10 12 cm −2 , assuming that ∆ c is proportional to the ion fluence. ∆ c is obtained at −0.3% for (002) diffraction by 200 MeV Xe at 5 × 10 12 cm −2 , and no appreciable change in the lattice parameter is observed by 90 MeV Ni ions at 40 × 10 12 cm −2 ; more data are desired. and S e (SR2013, x) is also shown. Sputtering yield from [54]. Power-law fits to Ysp: (0.175 S e ) 1.57 for both S e from TRIM1997 and SR2013 is indicated by green dotted line.

Fe 2 O 3
The XRD intensity at a diffraction angle of~33 • and 36 • (corresponding to diffraction planes of (104) and (110)) normalized to those of unirradiated Fe 2 O 3 films on C-Al 2 O 3 and SiO 2 glass substrates as a function of the ion fluence is shown in Figure 5 for 90 MeV Ni +10 , 100 MeV Xe +14 and 200 MeV Xe +14 ion impact. It appears that the XRD intensity degradation is nearly independent of the diffraction planes and substrates. The XRD intensity degradation per unit fluence Y XD is given in Table 4, together with the sputtering yields [60] and stopping powers (SRIM2013). The X-ray (Cu-kα) attenuation length L XA is obtained to be 8.8 µm [80] and the attenuation depth is 2.5 and 2.7 µm for the diffraction angle of~33 • and 36 • , respectively, which are much larger the film thickness of~100 nm and thus the X-ray attenuation correction is unnecessary. The appropriate energy for the XRD vs. S e plot, using half-way approximation (E − S e /2) with the film thickness of 100 nm, again gives nearly the same as E* for sputtering, in which the energy loss of the carbon foil of 100 nm is taken into account.  [60]. Linear fit is indicated by dotted lines. An estimated error of XRD intensity is 10%. Table 4. XRD data of Fe 2 O 3 films. Ion, energy (E in MeV), XRD intensity degradation (Y XD ), E* = E-∆E (energy loss in carbon foil of 100 nm) (MeV) and electronic (S e *) and nuclear (S n *) stopping powers in keV/nm and projected range R p * (µm) calculated using SRIM2013. Sputtering yield Y sp from [60]. Results by low energy (100 keV Ne) ion are also given.  [83,84]. Here, σ 1L = σ 1L (Fe) + 1.5σ 1L (O). L EQ is much smaller than the film thickness and the charge-state effect does not come into play. Figure 6 shows XRD intensity degradation Y XD vs. electronic stopping power (S e ) (SRIM2013 and TRIM1997) together with the sputtering yields Y sp vs. S e . Both Y XD and Y sp follow the power-law fit and the exponent using TRIM1997 gives a slightly larger fit than those using SRIM2013. The exponent of lattice disordering is two times larger than that of sputtering (N sp is exceptionally close to unity, in contrast to the SiO 2 and ZnO cases). The change in the lattice parameter appears to scatter depending on the substrate and diffraction planes, and is not proportional to the ion fluence. The average of the lattice parameter change in the (104) and (110)

TiN
The XRD patterns are shown in Figure 7 for unirradiated and irradiated TiN films on the SiO 2 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 2 glass, C-Al 2 O 3 and R-Al 2 O 3 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 SiO 2 , and for (111) on C-Al 2 O 3 . The XRD intensity degradation is less sensitive to the ion impact for the diffraction plane (220) on the R-Al 2 O 3 substrate (~30% smaller than that for (111) and (200) on SiO 2 , and for (111) on C-Al 2 O 3 ). The XRD intensity degradation per unit fluence Y XD 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 SiO 2 , ZnO and Fe 2 O 3 cases, the appropriate energy, E − S e /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 L XA 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.    (111) and (200) diffraction on SiO 2 and C-Al 2 O 3 , substrates, Y XD for (220) diffraction on R-Al 2 O 3 in the parenthesis, E* = E − ∆E (energy loss in carbon foil of 100 nm) (MeV) and electronic (S e *) and nuclear (S n *) stopping powers in keV/nm and projected range R p * (µm) calculated using SRIM2013 and sputtering yield Y sp of Ti. S e * (TRIM1997) is given in parenthesis. The characteristic length (L EQ ) is estimated to be 4.  [83,84]. Here, σ 1L = σ 1L (Ti) + σ 1L (N), and the ionization potential I P and N eff are (I P = 143 eV and N eff = 1) for Ar +7 , with those described in Section 3.1 for Ni +10 and Xe +14 . L EQ is much smaller than the film thickness, and hence the charge-state effect is insignificant.

Ion
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 × 10 14 and 0.44 × 10 14 cm −2 with an estimated error of 20% for 200 MeV Xe at 0.22 × 10 12 cm −2 and 60 MeV Ar at 2.8 × 10 12 cm −2 , respectively, and this is comparable with the Ti areal density of 0.4 × 10 14 cm −2 (200 MeV Xe) and 0.475 × 10 14 cm −2 (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 Y sp (Ti) in Table 5. The sputtering yields of TiN (Y EC ) due to elastic collisions can be estimated assuming that Y EC 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]. Y sp (TiN)/Y EC ranges from 2.5 × 10 3 to 6 × 10 3 . The XRD intensity degradations Y XD and Y sp (Ti + N) are plotted as a function of the electronic stopping power S e in Figure 10. It appears that both fit to the power-law: Y XD = (0.0224S e ) 1.26 and Y sp = (1.17S e ) 1.95 . The exponents are comparable for XRD intensity degradation and sputtering.

Comparison of Lattice Disordering with Sputtering
The electronic stopping power (S e ) dependence of lattice disordering Y XD , together with electronic sputtering, is summarized in Table 6, recognizing that most of the data have used TRIM1997. Results using SRIM2013 and TRIM1997 are compared in Section 3. Both exponents of the power-law fits are similar for SiO 2 , ZnO, Fe 2 O 3 , TiN and WO 3 films, as well as for KBr and SiC. As mentioned in Section 3, it can be seen that the exponent of the lattice disordering N XD is comparable with that of sputtering N sp , except for Fe 2 O 3 , in which N sp is exceptionally close to unity, as in the case of Cu 2 O (N sp = 1.0) [56] and CuO (N sp = 1.08) [59]. The similarity of the exponent of lattice disordering and sputtering for SiO 2 , ZnO, Fe 2 O 3 , TiN, WO 3 , KBr and SiC imply that both phenomena originate from similar mechanisms, despite the fact that small displacements and annealing and/or the reduction in disordering via ion-induced defects are involved in the lattice disordering, whereas large displacements are involved in sputtering. The result of Fe 2 O 3 indicates that the electronic excitation is more effective for lattice disordering. In the case of CuO, N XD is nearly zero [59]. In Table 6, Y XD (10 −12 cm 2 ) at S e = 10 keV/nm and Y XD /Y sp (×10 −15 cm 2 ) are listed. It is found that the ratio Y XD /Y sp is an order of 10 −15 cm 2 , except for ZnO, where the sputtering yields are exceptionally small. More data of lattice disordering would be desired for further discussion. Table 6. Summary of electronic stopping power (S e in keV/nm) dependence of lattice disordering Y XD = (B XD S e ) NXD for the present results of SiO 2 , ZnO, Fe 2 O 3 and TiN films, and sputtering yields Y sp = (B sp S e ) Nsp of the present result for TiN. Lattice disordering and sputtering yields of WO 3 film from [58,72], those of KBr and SiC from [56] and sputtering yields of SiO 2 , ZnO and Fe 2 O 3 (see Section 3). Constant B XD and B sp and the exponent N XD and N sp are obtained using TRIM1997 and those using SRIM2013 are in parentheses. Y XD at S e = 10 keV and Y XD /Y sp (10 −15 cm 2 ) are given.

Electron-Lattice Coupling
Three models have been suggested for atomic displacement induced by electronic excitation: Coulomb explosion (CE) [3,4], thermal spike (TS) [50] and exciton model [30,[95][96][97]. The neutralization time of the ionized region along the ion path is generally too short, and the fraction of the charged sputtered ions is small, e.g., 100 MeV Xe ions on SiO 2 glass [48]. Hence, the CE model is unsound. However, a small atomic separation during the short time might be enough for electron-lattice coupling (a key for electronic excitation effects), which will be discussed later. A crude estimation of the evaporation yield for SiO 2 based on the TS model appears to be far smaller than the experimental sputtering yield [55] and thus the TS model is also unsound. Moreover, the electron-lattice coupling or transfer mechanism of electronic energy into the lattice is not clear in the model. In the exciton model, the non-radiative decay of self-trapped excitons (STX, i.e., localized excited-state of electronic system coupled with lattice) leads to atomic displacement. According to the exciton model (or bandgap scheme), it is anticipated that the energy of the atoms in motion from the non-radiative decay of STX is comparable with the bandgap, leading to a larger sputtering yield with a larger bandgap, discarding the argument for the efficiency of STX generation from the electron-hole pairs, which is inversely proportional to the bandgap. This bandgap scheme is examined below. The effective depth contributing to the electronic sputtering of WO 3 has been obtained to be 40 nm, which is nearly independent of S e [98], which would shed light on understanding the electronic sputtering; therefore, more data are desired.
The electronic sputtering yield Y sp super-linearly depends on the electronic stopping power (S e ), and Y sp at S e = 10 keV/nm is taken to be a representative value, which is plotted as a function of the bandgap (E g ) in Figure 11 from [56], including the present TiN result. The optical absorbance (defined as log 10 (I o /I), I o and I being the incident and transmitted photon intensities) of TiN films are measured, and the direct bandgap E g is obtained to be 4.5 eV for a film thickness of 25-50 nm, which decreases to 2.8 eV for a film thickness of~180 nm by using the relation: (absorbance • photon energy) 2 is proportional to photon energy-E g . The thickness dependence of E g is under investigation by considering the influence of the reflectivity, film growth conditions and experimental problems, such as stray light, etc. A large variation has been reported for E g , 4.0 eV (film thickness of 260 nm on Si substrate) ( [101]. In this study, E g is taken to be 4 eV and this choice is tolerable in the following discussion. It has been reported that the bandgap is reduced by 0.06 eV under a 400 KeV Xe ion implantation at 10 16 cm −2 [99]. High-energy ion impact effects on optical properties are under way. It can be observed that the bandgap scheme seems to work for E g > 3 eV [56]. A large deviation (two orders of magnitude) from the upper limit (dashed line indicated in Figure 11) is observed for ZrO 2 , MgO, MgAl 2 O 4 and Al 2 O 3 . The existence of STX is known for limited materials, rare gas solids, SiO 2 and alkali halides [30,95,96]. The STX does not exist for MgO and probably does not exist for Al 2 O 3 [102]. The deviation for MgO and Al 2 O 3 could be explained by the non-existence of STX. The numbers of electron-hole pairs leading to STX are inversely proportional to E g , which could be a reason for the dependence of the sputtering yields for E g < 3 eV. In any case, the single parameter of the band gap is insufficient for the explanation of the bandgap dependence of the sputtering yields. Figure 11. Sputtering yield at S e = 10 keV/nm vs. bandgap. Data from [56], TiN (present result) and LiF data from [62]. Dotted line is a guide for eyes (E g > 3 eV).
Martin et al. [102] argued that STX exists for materials with small elastic constants. Following this suggestion, sputtering yields are plotted as a function of the elastic constant (C 11 ) in Figure 12. Here, C 11 [107], 135 (CuO) [108], 388 (Si 3 N 4 ) as an average of the values [109,110], 345 (polycrystalline-AlN) [111], which is smaller by 16% than 410 (AlN single crystal) [112], 234 (Cu 3 N) [113], 500 (SiC) [114] and 625 (TiN) [115]. It can be observed for oxides (the most abundant data are available at present) that Y sp decreases exponentially with an increase in the elastic constant for C 11 < 300 GPa, except for MgO and ZrO 2 . Y sp for nitrides and SiC is larger than that for oxides at a given C 11 , and these are to be separately treated. It can be understood that the elastic constant represent the resistance of lattice deformation by electronic energy deposition. However, a single parameter, either the bandgap or elastic constant, is not adequate, and at least one more parameter is necessary. Furthermore, parameters other than those mentioned above are to be explored. More data for nitrides, alkali halides and especially carbides are desired. Finally, a mechanism for the electron-lattice coupling is discussed. In an ionized region along the ion path, Coulomb repulsion leads to atomic motion, which is not adequate to cause sputtering because of its short neutralization time. Nevertheless, displacement comparable with the lattice vibration amplitude (one tenth of the average atomic separation, d av of~0.25 nm for a-SiO 2 ) is highly achievable during the neutralization time. As a first step, the time required for the Si + -O + displacement of 0.025 nm (one tenth of d av ) from d av is estimated to be~15 fs using a formula [116]. Also, the time is estimated to be~15 fs and~12 fs for the Zn + -O + displacement of 0.02 nm from d av of 0.2 nm in ZnO and for the Ti + -N + displacement of 0.02 nm from d av of 0.2 nm in TiN, respectively. A similar situation has been reported for the Fe + -O + displacement of 0.01 nm in Fe 2 O 3 (~7 fs) [60], the K + -Br + displacement of 0.01 nm in KBr (~9 fs) and the Si + -C + displacement of 0.01 nm in SiC (~6 fs). These suggest a possibility that a small displacement comparable with the lattice vibration amplitude caused by Coulomb repulsion during the short neutralization time leads to the generation of a highly excited-state coupled with the lattice (h-ESCL), and h-ESCL is considered to be equivalent to STX or multi STX. The non-radiative decay of h-ESCL leads to atomic displacement (a larger displacement results in sputtering and smaller displacement results in phonon generation or lattice distortion).

Conclusions
We have measured the lattice disordering of polycrystalline SiO 2 , ZnO, Fe 2 O 3 and TiN films, as well as the sputtering yield of TiN, by high-energy ion impact. It is found that lattice disordering is caused by electronic excitation and the degradation of the XRD intensity fits to the power-law on the electronic stopping power. The exponent in the fit of the XRD degradation is comparable with that of the electronic sputtering yield for these films, as well as the published results of WO 3 , KBr and SiC, implying that both lattice disordering and sputtering originate from similar mechanisms. In the case of Fe 2 O 3 , on the other hand, the exponent of the lattice disordering is larger by twice than that of the sputtering (the exponent for the sputtering is close to unity). The exciton mechanism seems to work for Eg > 3 eV, with some exceptions, and the elastic constant is examined as another scaling parameter for the electronic sputtering yields. A possibility of electronlattice coupling is discussed based on a crude estimation that an atomic displacement comparable with the vibration amplitude due to Coulomb repulsion during the short neutralization time in the ionized region along the ion path can be attainable and, thus, the generation of a highly excited state coupled with the lattice is highly achievable, resulting in atomic displacement.