Ion tracks in silicon formed by much lower energy deposition than the track formation threshold

Damaged regions of cylindrical shapes called ion tracks, typically in nano-meters wide and tens micro-meters long, are formed along the ion trajectories in many insulators, when high energy ions in the electronic stopping regime are injected. In most cases, the ion tracks were assumed as consequences of dense electronic energy deposition from the high energy ions, except some cases where the synergy effect with the nuclear energy deposition plays an important role. In crystalline Si (c-Si), no tracks have been observed with any monomer ions up to GeV. Tracks are formed in c-Si under 40 MeV fullerene (C60) cluster ion irradiation, which provides much higher energy deposition than monomer ions. The track diameter decreases with decreasing the ion energy until they disappear at an extrapolated value of ~ 17 MeV. However, here we report the track formation of 10 nm in diameter under C60 ion irradiation of 6 MeV, i.e., much lower than the extrapolated threshold. The diameters of 10 nm were comparable to those under 40 MeV C60 irradiation. Furthermore, the tracks formed by 6 MeV C60 irradiation consisted of damaged crystalline, while those formed by 40 MeV C60 irradiation were amorphous. The track formation was observed down to 1 MeV and probably lower with decreasing the track diameters. The track lengths were much shorter than those expected from the drop of Se below the threshold. These track formations at such low energies cannot be explained by the conventional purely electronic energy deposition mechanism, indicating another origin, e.g., the synergy effect between the electronic and nuclear energy depositions, or dual transitions of transient melting and boiling.


Results
The open symbols in Fig. 1a show the ion track diameters in c-Si, formed by C 60 ion irradiation (E ≥ 25 MeV), as reported in past literature 7,8,13 . The energy dependencies of the electronic and nuclear stopping powers, S e and S n , of C 60 ions in c-Si are plotted in Fig. 1b, which were approximated as the sum of sixty independent carbon monomer ions with the energy of (E/60) each, and expressed as, where i = n (nuclear) or e (electronic) 14 . The monomer stopping power S i (E/60, C 1 ) was derived from SRIM 2013 15 . At E > 20 MeV, S e is more than 10 times greater than S n , and the former increases with the energy while the latter decreases. Canut et al. 7 plotted the squared radius of the ion tracks (R 2 ) versus S e , and confirmed the square root law:  www.nature.com/scientificreports/ where S e,th and C denote the threshold stopping of ~ 30 keV/nm and a prefactor constant, respectively. The square root law (2a) is a phenomenological law and has a following relation with the analytical thermal spike (ATS) model 16 : The ATS model gives where S e,th and a(0) denote the threshold S e for the track formation and the initial width of the radial distribution of temperature in the track, respectively. When (S e / S e,th ) = (1 + x), where x ≪ 1 , the relation ln (1 + x) ~ x is hold. Then, ln (S e /S e,th ) is approximated by (S e /S e,th -1), the square root law (2a) is derived: However, because of different S e dependence between the square root law and the ATS, the deviation between them becomes larger with increasing S e as shown in Fig. S-1 in the supplementary materials.
The validity of the square root law was confirmed by Kamarou, et al. in various semiconductors including InP, GaAs, Ge, and Si, irradiated with high energy C 60 ions 17 . Following the tradition, the square root law is applied in this paper.
In the above-cited studies, the stopping power was calculated using, e.g., TRIM 97 18 . In this study, the previous stopping power values were recalculated using the latest code SRIM 2013 15 . The S e,th of 30 keV/nm is extrapolated using SRIM 2013. However, different values of S e,th of 37 keV/nm 17 and 32 keV/nm 7 were calculated from the same experimental data using various TRIM codes.
As shown in Fig. 1a, the fitting by Eq. (2a) well matched the data points. Note that the abscissa is not plotted with S e but with the energy. Following the extrapolation, the track radius becomes null at ~ 17 MeV 7 ; that is, no tracks were formed below ~ 17 MeV. While the square root law (2a) could be a rough approximation, the existence of the S e threshold is a typical behavior of latent ion tracks formed in materials by SHI irradiation, which is ascribed to the melting heat in the inelastic thermal spike (i-TS) model 19 . Figure 1a shows that ion tracks of ~ 10 nm in diameter were observed under 6 MeV C 60 irradiation, far below the hitherto-reported threshold of ~ 17 MeV 7 (hereafter termed the 'electronic threshold'). It should be noted that the track diameters at 6 MeV were comparable to those at 40 MeV, and larger than those at 30 MeV. These (3a) R 2 = a(0) 2 ln S e /S e,th , S e < 2.7S e,th , (3b) R 2 = a(0)/2.7S e,th S e . S e > 2.7S e,th (4) R 2 = a(0) 2 (S e − S e,th )/S e,th .  www.nature.com/scientificreports/ facts indicate that there is a mechanism for energy deposition not only from S e but probably also from S n , since S e monotonously decreased but S n increased with decreasing energy as shown in Fig. 1b. Figure 2 shows bright-field transmission electron microscopy (TEM) images of irradiated c-Si samples. As described in the Methods section, we prepared TEM specimens in two different configurations, i.e., pre-thinned (planar) and post-thinned (cross-sectional). Figure 2a shows a planar image (i.e., a pre-thinned sample) of c-Si irradiated with 6 MeV C 60 + ions. Dark dots of ~ 10 nm in diameter are observed. The sample was irradiated with an incident angle of 7° to avoid channeling. Since cos (7°) ~ 0.993, the deformed circular images of the tracks could not be due to the non-normal incidence. In all the observed pre-thinned samples, the areal density of the tracks was in the same order of the magnitude as the ion fluence. Figure 2b shows a 30°-tilted image of the same sample (in a lower magnification). The nearly circular dots in Fig. 2a turned to cylinders in Fig. 2b, supporting the fact that the dark regions are ion tracks. Figure 2c shows a cross-sectional (post-thinned) image of a sample irradiated with 6 MeV C 60 + ions, which indicates the depth profiles of the ion tracks. The black layer is a deposited Pt layer for a surface marker. Many tracks were observed but they were almost free from overlaps. The three different configurations of observations (planar, inclined planar, and cross-section) firmly confirm the formation of the ion tracks. The track lengths showed some variation with the mean length of 66.3 nm and the standard deviation of 7.9 nm. While many hillocks were observed in quartz (SiO 2 ) crystal irradiated with the same conditions 20 , the hillocks were not observed in the case of c-Si.
Furuno et al. reported that the tracks could be formed in low-quality evaporated films of Si under 207 MeV Au 13+ irradiation (S e = 17 keV/nm) 21 . Since this report 21 was inconsistent with other observations in crystalline Si 4,5 , the track formation was ascribed to the low-quality (low thermal conductivity, high electron-phonon coupling, etc.) of the evaporated Si films (probably in an amorphous phase). However, our observation of the tracks cannot be attributed to bad quality of the samples. Our samples were commercial available crystalline Si. Possibly, the pre-thinned samples (e.g., Fig. 2a) could be slightly damaged since they were thinned by focused ion beam (FIB) of 30 keV Ga + before C 60 irradiation. However, the same tracks are also observed in the postthinned samples (Fig. 2c), which were not damaged with FIB before C 60 irradiation. This fact confirmed that the damage in the pre-thinned samples were minimum and probably negligible. Furthermore, the track formation under 1-6 MeV C 60 irradiation, which we observed, is an intrinsic phenomenon, not induced by pre-damage.
Figure 2d-f show the tracks formed by 4 MeV C 60 + ion irradiation. Compared to the tracks formed by 6 MeV ions, these tracks (4 MeV) were slightly smaller and shorter. Track formation in c-Si was also confirmed with C 60 + ions of 3, 2, and 1 MeV. Figure 2g,h show the track formation with 1 MeV C 60 + ion irradiation, in the prethinned (g) and post-thinned (h) configurations, respectively. With decreasing the ion energy to 1 MeV, both the diameter and length of the tracks decreased compared to higher energies.
It should be noted that the shapes of the ion tracks formed by 1 MeV ions are not straight as those formed by higher energies. As well known, the high electronic energy deposition S e forms damage regions of straight cylinders, while the high nuclear energy deposition S n forms more random and extended collision cascades. As shown in Fig. 1b, a 1 MeV C 60 ion has comparable high S e and high S n . The formed tracks could be skewed tracks as observed in Fig. 2h, as the consequence of both the contributions of S e and S n . Figure 2i shows a pre-thinned sample irradiated with 200 MeV Xe 14+ ions (S e = 14 keV/nm and S n = 0.05 keV/ nm); the S e value being comparable to that of the 4 MeV C 60 ions (S e = 15 keV/nm and S n = 3 keV/nm). However, no tracks were observed in this case, indicating the importance of the non-negligible S n contribution (i.e., the synergy effect) for the track formation.

Discussion
The data shown in Fig. 1a, i.e., the energy dependence of the track diameters, were plotted with squared radius R 2 versus the electronic stopping power S e in Fig. 3. The S e was derived from Eq. (1). Both the high energy data (E ≥ 25 MeV) and the low energy one (E ≤ 6 MeV) are well fitted with the square root laws but different parameter values, i.e., where the superscripts L and H denote the low and high energy region, respectively. The threshold stoppings were S e,th L = 4.2 keV/nm and S e,th H = 30 keV/nm for E ≤ 6 MeV and E ≥ 25 MeV, respectively. The high energy threshold was ten times higher than the low energy one. Particularly, the threshold of 4.2 keV/nm was extraordinarily low. Itoh et al. have collected the S e thresholds of 43 materials in their paper 22 . Among the 43 materials, those having the thresholds less than 4.2 keV/nm (our case at E ≤ 6 MeV) are limited to only four materials: SiO 2 (2 keV/nm), a-Ge (3 keV/nm), LiF (4 keV/nm), and BaFe 12 O 19 (4 keV/nm) 22 . Since c-Si is known to have very high threshold, something unusual could happen under the C 60 ion irradiation at E ≤ 6 MeV.
Contrary, the prefactor for the low energy (C L = 1.28 nm 3/2 /keV 1/2 for E ≤ 6 MeV) and that for the high energy (C H = 1.17 nm 3/2 /keV 1/2 for E ≥ 25 MeV) are almost the same, irrespective of much different energy regions. According to the i-TS model, the threshold S e,th relates to the heat for the melting. The similar values of the prefactor C for high and low energy regions indicate that the track radius increases in almost the same manner with the additional S e , i.e., (S e -S e,th ), irrespective of S e,th . Almost the same value of C L and C H could be a reasonable consequence, because the material is the same, i.e., c-Si. On the other hand, the large difference in the threshold S e,th indicates that the melting (or the boiling) is induced with very low value of S e in the low energy region, where S n is not negligible. Therefore, there must be an additional heat source except S e . The strongly reduced threshold could be ascribed to much more efficient heat source rather than the S e but probably S n . For reference, a data point of 200 MeV Xe ion is also shown in Fig. 3, which has similar S e with 4 meV C 60 ion but much lower S n . Clearly the tracks are not formed under 200 MeV Xe irradiation. www.nature.com/scientificreports/ Since the tracks formed by the high energy (E ≥ 25 MeV) are ascribed to the electronic energy deposition, one might consider that the tracks by the low energy (E ≤ 6 MeV) could be formed by the purely nuclear energy deposition, e.g., the collision cascades. However, the low energy tracks (E ≤ 6 MeV) also depend on S e via the square root law as shown in Fig. 3, indicating that S e plays an important role even in the low energy region (E ≤ 6 MeV). Figure 4a shows the track lengths determined from the post-thinned samples by closed circles. Here we need to recall the definition of two quantities: Ion range (projected range) is the depth where implanted ion terminates, while the track length is the length of the modified region formed by an ion. Even beyond the track length, the ion goes further without forming track. The ion range is longer than the track length. The track termination of swift monomer ion is induced when the S e of the ion decreases below the threshold. Contrary, in the case of C 60 ions, there is another channel for the track termination, i.e., the fragmentation of the C 60 ions 8 . Also there are two mechanisms for the fragmentation: (i) Coulomb repulsion between ionized carbon atoms constituting a C 60 molecule 8 and (ii) collisions of carbon atoms constituting a C 60 molecule with Si matrix 8 . Dunlop et al. concluded that the latter (C-Si collisions) are the dominant process for the fragmentation of 30 MeV C 60 ion irradiation 8 . Since the latter process become more dominant for lower energy, the fragmentation processes in our experiments (E = 1-6 MeV) are mostly governed by the C 60 -Si collisions.
If a C 60 molecule is assumed as 60 independent single C ions with the same energies of E/60, the ion range R P of a C 60 ion can be approximated by the ion range of the single C ion with the same velocity, i.e., The right-hand side of the Eq. (5), R P (E/60, C 1 ), i.e., the projected range of single carbon ion in c-Si with the energy of E/60, was calculated by SRIM 2013 15 . The calculated ion ranges were plotted in Fig. 4a, which were much longer than the ion tracks observed by TEM. Figure 4b shows the depth profiles of the electronic energy deposition S e induced by a C 60 ion, which were calculated by Eq. (1). The track lengths are indicated by rectangles with error bars. The incident S e values of 6 MeV C 60 ion at the surface of c-Si is 18.4 keV/nm, which decreases to 18.2 keV/nm at the depth of 66 nm where the track terminated. The incident S e value of 4 MeV C 60 at the surface is 16.3 keV/nm, which is much lower than the S e value at the end of the track of 6 MeV C 60 ion (18.2 keV/nm). Even though, tracks of 57 nm long in average are formed under 4 MeV C 60 irradiation. In the case of 1 MeV C 60 irradiation, the incident S e at the surface is 8.5 keV/nm, which is less than a half of the S e value at the end of the 6 MeV C 60 track (18.2 keV/nm). However, tracks of 33 nm long in average are formed. From these observations, it is concluded that the termination of the tracks is not induced when the S e value becomes below the threshold value but probably when the fragmentation of the C 60 cluster is induced. When a C 60 ion is divided into N fragments, each fragment has S e /N in average, which results in drastic reduction of the S e . Figure 5 exhibits high-resolution (HR) planar TEM images of ion tracks in c-Si irradiated with C 60 ions of (a) 30 MeV 8 and (b) 6 MeV. While a nearly circular track was observed in Fig. 5b, a striking observation was that the track region also exhibited lattice fringes, coincided with the unirradiated region, i.e., a defective crystalline track.   8 . Since they irradiated c-Si with 30 MeV C 60 ions, the samples could be much more damaged than our samples irradiated with 6 MeV C 60 ions. Much quicker recrystallization could be induced in our cases.
Another possibility is due to much shorter length of our tracks: The mean track length was 66.3 nm for 6 MeV C 60 ions, which is thinner than the TEM sample (~ 100 nm thick). Since the tracks terminate inside the TEM samples, the remaining crystalline parts deeper than the track-length would contribute for the fringes. However, the HR-TEM images are so clear that this explanation seems less plausible. Up to now, a lot of studies To confirm the defective crystalline tracks, Rutherford backscattering spectrometry and channeling (RBS/C) measurements were carried out. Figure 6a exhibits RBS/C spectra of random and aligned configurations of an unirradiated sample, and of the aligned configurations of the samples irradiated with 6 MeV C 60 + ions at three different fluences. With increasing the fluence, the surface peak around 330 channel, which is due to the scattering by the tracks, increased but does not reached at the random level. The numbers in parentheses indicate the track coverage ratio (TCR) at the surface, which is defined as where R and Φ denote the mean radius of the ion track and the C 60 fluence, respectively.
The intensity of the surface peak was plotted with the fluence in Fig. 6b. From the track radius shown in Fig. 1a, TCR reaches at 100% at the fluence of 1.3 × 10 12 C 60 /cm 2 , where almost all the surface of the sample is covered by the tracks. If the tracks could be amorphous, the surface peak intensity would reach the random level and would saturate at TCR ~ 100%. However, the experiments showed that the surface peak intensity reached at only ~ 46% of the random level at TCR of 100% and that the intensity monotonically increased even beyond the TCR of 100%. It should be noted that even ~ 46% of the random level could indicate significant disorder, defects or possibly partial amorphization. However, HR-TEM image (Fig. 5b) does not show any evidence of partial amorphization.
Furthermore, the surface peak increased to the fluence to 4 × 10 12 C 60 /cm 2 (TCR = 320%), where the multiple overlaps of the tracks are expected. Even though, the surface peak intensity did not reach at the random level of the RBS/C measurements. Consequently, these observations support the formation of defective crystalline ion tracks, rather than amorphous ones, under 6 MeV C 60 ion irradiation.
At the beginning, we considered that the tracks observed in Fig. 5b were originally amorphous but crystallized by electron beam irradiation under HR-TEM observation. However, the samples used for the RBS/C measurements were not irradiated by electron beam but only 2 MeV He + ions. Consequently, the crystallinity of the ion tracks has been confirmed by two different methods, i.e., HR-TEM and RBS/C, which further supports that the defective crystalline tracks in c-Si are not a consequence of improper experimental procedures but an intrinsic nature of this system.
Szenes and Toth 23 irradiated yttrium-iron-garnet (YIG) Y 3 Fe 5 O 12 with C 60 ions of 3.5, 5, and 7 MeV, and observed the ion track formation. To evaluate the synergy effect of S e and S n on track formation, they applied an effective stopping power defined by with a coefficient K of 2.2 for the YIG. Kitayama et al. 24 irradiated amorphous SiN films with 540 keV C 60 2+ ions, and evaluated the synergy effect on the electronic and collisional sputtering. To explain the data, they used K = 2.5. We have adopted this formalism. As shown in Fig. 1b, even assuming K = 3, S eff is less than the electronic threshold of 30 keV/nm at 6 MeV. If K = 5 is assumed, S eff becomes greater than the threshold of 30 keV/nm at 6 MeV, i.e., the track formation is approved. In this case, however, S eff at 1 MeV is higher than at 6 MeV, which is (6) TCR = πR 2 � (7) S eff = S e + K S n , www.nature.com/scientificreports/ inconsistent with the larger track diameters at 6 MeV than those at 1 MeV. This is because Eq. (7) is an empirical rule, which holds in limited energy region only. If it would hold also in very low energy where S e < < S n , the effective stopping power S eff could inconsistently be ~ KS n , which should be higher than S n since K > 1. A transition from 6 to 1 MeV could happen because the track shapes at 6 MeV are nearly straight (Fig. 2c) but those at 1 MeV are skewed cylinder shapes (Fig. 2h). Different spatial distributions of S e (straight cylinders) and S n (skewed cylinder) could reduce the synergy effect efficiency, which has already been reported in zircon 25 . While the mechanism of the track formation at 1-6 MeV is still an open question, we suggest two issues: (i) As pointed by Weber et al. 9 , the track radii became larger in pre-damaged samples. For C 60 ions of 1-6 MeV, S n is not negligible to S e . The damage formed by S n assists the track formation by S e . Since the fluence is low, the track formation by S e assisted by S n is induced by the same ion. This is not the pre-damage effect but the "insitu" damage effect. Another issue is that Chettah et al. 13 proposed the boiling transition for the track formation at 30-40 MeV C 60 ions from the analysis of the inelastic thermal spike model. We speculate that the tracks by www.nature.com/scientificreports/ the melting transition could not been observed because of the perfect recrystallization under SHI irradiation where S n is negligible. We attribute the track formation under 30-40 MeV C 60 irradiation to the boiling transition. Contrary, non-negligible S n under 1-6 MeV C 60 irradiation prevents the perfect recrystallization at the melting transition, which results in the track formation by the melting transition.

Summary
The ion energy dependence of track formation in c-Si, and the relevant stopping powers, are schematically summarized in Fig. 1c. The C 60 irradiation higher than 25 MeV, S n is much less than S e . Consequently the synergy effect is not expected (i.e., S e > S e,th > > S n ). The damage formation is governed only by S e . When S e decreases below the threshold, i.e., S e < S e,th , tracks are expected to be no longer formed. (This is only due to the extrapolation). However, a further decrease in the energy results in an increase in S n , activating the synergy effect: Tracks are formed once again at 1-6 MeV. With further decreasing energy, the contribution of S n increases further, finally resulting in cascade-like tracks being observed at 1 MeV. While the S e,th determined from the square root law at E ≥ 25 MeV was reasonably high as 30 keV/nm, the S e,th at E ≤ 6 MeV was 4.2 keV/nm, which is extraordinarily low and inconsistent with the fact that c-Si is insensitive to SHIs. There must be another heat source other than S e , but probably S n for C 60 irradiations at E ≤ 6 MeV. However, it should be noted that the track diameters at low energy (E ≤ 6 MeV) depend on S e via the square root law. It seems that the S e plays an important role in the track formation also at low energy (E ≤ 6 MeV). Purely nuclear origin, such as the collision cascades are excluded, while it does not mean to exclude the synergy effects between S e and S n . The track length is determined not by a decrease of S e , but by the fragmentation of C 60 molecules. Another scenario is that the track formations at 6 MeV and those at 30 MeV could be ascribed to the melting and boiling transitions, respectively. Whilst the tracks by the melting transition are fully recrystallized under SHI irradiations, the recrystallization is hindered due to non-negligible nuclear collision contribution.

Methods
C 60 ion irradiation. The irradiation of C 60 + ions was conducted at the Takasaki Advanced Radiation Research Institute (TARRI), of the National Institutes for Quantum and Radiological Science and Technology (QST), using a 3 MV tandem accelerator and a newly developed high-flux C 60 negative ion source. The samples were mostly irradiated to a low fluence of 5 × 10 10 C 60 /cm 2 to avoid overlaps between the tracks. For precise control of the low fluence, the ion flux was reduced to below 50 pA through an aperture of 3 mm in diameter, while using the high-flux ion source. The incident angle was set to 7° to avoid any channeling effect. Since cos (7°) = 0.993, beams deviating from the normal incidence did not significantly modify the shapes of the tracks. For comparison, some samples were irradiated with 200 MeV Xe 14+ ions from the tandem accelerator in the Japan Atomic energy Agency (JAEA), Tokai Research and Development Center.
Sample preparation. Silicon samples were cut from commercially available Si wafers of p-type conduction (boron-doped), with resistivity of ~ 1 Ωcm, surface orientation of < 1 1 1 > , and thickness of ~ 0.38 mm. The samples were mechanically cut into 3 mm × 4 mm rectangles, which are hereafter called bulk samples. The bulk samples were immersed in hydrofluoric acid to remove the surface oxide.
Two different TEM specimens (pre-thinned and post-thinned) were prepared from the bulk samples. In the case of the post-thinned samples, a group of bulk samples were irradiated by a C 60 + beam with an incident angle of 7° to the 3 mm × 4 mm faces, and the TEM specimens were milled down to a thickness of ~ 100 nm to observe the depth profile of the ion tracks. The TEM specimens were fabricated with 30 keV Ga focused ion beam (FIB) milling. To identify the surface position in the cross-sectional configuration, a thin layer of Pt was deposited on the sample surface before the FIB milling. The other bulk samples (pre-thinned) were first milled down to a thickness of ~ 100 nm, and then irradiated with C 60 + ions with an incident angle of 7° to observe the track faces. See TEM observation. TEM observation of both configurations (i.e., the depth and planar profiles) was conducted using a JEOL JEM-2100 microscope (with a LaB 6 thermal emission e-gun). HRTEM observation was carried out using JEOL JEM-2100F microscope (with a Schottky-type field emission e-gun). Both the acceleration voltages were 200 kV. According to past literature, the tracks in c-Si were recrystallized with prolonged TEM observation. Careful observations were performed to minimize the electron beam current and TEM observation time.
Rutherford backscattering spectrometry and channeling (RBS/C) measurements. He + ions of 2 MeV from a single-end accelerator in QST-Takasaki were used. The beam size was 1 mm in diameter and the scattering angle was 165°. Scattered ions were monitored by a surface-barrier detector, with the accumulated charge of 10 μC for a spectrum.

Data availability
The datasets and materials generated during the current study are available from the corresponding author on reasonable request.