# Fileset [Materialia_2025.pdf](https://mdr.nims.go.jp/filesets/90899071-9792-46ab-a04a-5bd9fef09654/download) ## Creator [H. Amekura](https://orcid.org/0000-0003-2148-8431), K. Narumi, A. Chiba, Y. Hirano, K. Yamada, S. Yamamoto, Y. Saitoh ## Rights This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [An extraordinarily low-energy threshold of less than 60 keV for ion track formation in silicon](https://mdr.nims.go.jp/datasets/c82821bb-0806-4e9c-add0-880031b5480b) ## Fulltext An extraordinarily low-energy threshold of less than 60 keV for ion track formation in siliconAn extraordinarily low-energy threshold of less than 60 keV for ion track formation in siliconH. Amekura a,*, K. Narumi b, A. Chiba b, Y. Hirano b, K. Yamada b, S. Yamamoto b, Y. Saitoh ba National Institute for Materials Science (NIMS), Tsukuba, 305-0003, Japanb Takasaki Institute for Advanced Quantum Science, National Institutes for Quantum Science and Technology (QST), Takasaki, 370-1292, JapanA R T I C L E I N F OKeywords:Ion trackC60 ionSiliconCluster effectSwift heavy ionA B S T R A C TThe impingement of a C60 cluster ion upon a solid can realize the temporospatially correlated injection of sixty C atoms to the solid at the same time and place with a molecular dimension of 0.7 nm in diameter. This could result in ion track formation that differs from that of conventional monatomic ion irradiation. Although no ion tracks have been observed in Si even under high-energy 3.6-GeV monatomic U ion irradiation, certain tracks have been found in Si under low-energy 1-MeV C60 ion irradiation. Here, we investigated track formation under an irradiation of less than 1 MeV: (i) With a decrease in energy, the diameters and lengths of the tracks decreased; however, the length decreased more steeply than the diameter. (ii) Although the tracks were fuzzily perceived down to 60-keV irradiation, no tracks were observed under 30-keV irradiation, except for an extended damage zone. Furthermore, we observed (iii) track formation below the electronic stopping threshold, and (iv) track length extension due to “the acceleration effect” of cluster-ion irradiation at low energies. (v) Finally, the approximated linearity between the track volume and C60 energy is discussed.1. IntroductionCrystalline Si is one of the most investigated materials, particularly regarding its ion–solid interactions in the energy range from sub-keV to several MeV. This is because ion implantation into Si is one of the most important processes in fabricating micro-/nano-integrated circuits for information technologies [1]. Nevertheless, ion track formation in crystalline Si under high-energy heavy ions of nearly 1 MeV/amu or higher, which are called swift heavy ions (SHIs), has remained controversial [2–14].Although various SHI irradiations have been attempted to find track formation in Si [2,3], tracks have never been observed even when irradiated with high-energy 3.6-GeV U ions (electronic energy loss Se =23.7 keV/nm) [3]. This is close to the Bragg peak, i.e., the highest Se attainable in Si by monatomic SHIs (m-SHIs). It should be noted that the reported Se values are shown herein after recalculation using the SRIM 2013 code [15]. This indicates that ion tracks are not formed in Si by m-SHIs; however, tracks have been observed in Si under 30- and 40-MeV C60 fullerene cluster ion irradiation in the Orsay facility, France [4,5]. The 30- and 40-MeV C60 ions afford a high Se of 42.7 and 50.0 keV/nm in Si, respectively. Thus, many researchers believed that not observing track formation in Si under m-SHI irradiation is ascribable to the considerably high Se threshold in Si, which cannot be overcome by m-SHIs, except by extremely high Se delivered by C60 ions. Considering that 60 carbon atoms from a C60 molecule were simultaneously injected into a solid, a significantly higher Se was obtained even with C60 ions having tens MeV [16–18].Furthermore, the pioneer papers of the first observation of tracks in Si using C60 ions by Canut et al. [4] and Dunlop et al. [5] have already pointed out the importance of the velocity effect. Much slower velocity of C60 ions compared to that of m-SHIs may induce much higher excitation density for the track formation in former ions. The inelastic thermal spike (i-TS) calculations [19] by Chettah et al. [6], which include the velocity effect, however, suggest that the calculated velocity effect is not high enough to explain the completely different track formations between C60 ions and m-SHIs if the tracks are formed by melting.The i-TS calculations raised further the mystery of the ion tracks in Si [6]. Following the melting criterion for the track formation, the Se threshold was estimated as low as ~5 keV/nm. This quite low threshold is inconsistent with all of the past experiments where the tracks were formed only higher than 25 keV/nm. The experimental results under * Corresponding author at: National Institute for Materials Science (NIMS), 3-13 Sakura, Tsukuba, 305-0003, Japan.E-mail address: amekura.hiroshi@nims.go.jp (H. Amekura). Contents lists available at ScienceDirectMaterialiajournal homepage: www.elsevier.com/locate/mtlahttps://doi.org/10.1016/j.mtla.2024.102317Received 26 August 2024; Accepted 9 December 2024 MTLA 39 (2025) 102317 Available online 9 December 2024 2589-1529/© 2024 The Author(s). Published by Elsevier B.V. on behalf of Acta Materialia Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). mailto:amekura.hiroshi@nims.go.jpwww.sciencedirect.com/science/journal/25891529https://www.elsevier.com/locate/mtlahttps://doi.org/10.1016/j.mtla.2024.102317https://doi.org/10.1016/j.mtla.2024.102317http://creativecommons.org/licenses/by/4.0/20–40 MeV C60 irradiations were rather reproduced by the vaporization criterion. Then, raised questions are (i) “why the melting zones do not transform to the ion tracks but disappear” and (ii) “whether the prerequisites of the present i-TS model are applicable to semiconductor Si or not.” Similar results were reported from another group using the i-TS model with Monte Carlo electron dynamics [7], instead of Waligorski distribution [20], indicating that the discrepancy between the calculations and experiments is not accidental but could be due to an intrinsic imperfection of the i-TS model presumed.To answer the question (i), the recrystallization of tracks in Si was proposed [8]. Since the recrystallization of Si is often observed under low energy ion irradiation, i.e., the nuclear stopping regime, the same phenomenon can be induced on the electronic stopping regime [8]. While the tracks are transiently formed in Si via the melting, soon the tracks disappear by the recrystallization of Si before experimental observation begins.Regarding (ii), one of the imperfections of the i-TS model was pointed out: In the i-TS model, the carrier relaxation via the bandgap is not considered [21]. This assumption sounds too crude to obtain reliable results, while many successes were reported from the track formations in bandgap materials, i.e., many insulators and some semiconductors [19]. Duffy and coworkers extended the i-TS model including the carrier relaxation via bandgap [21]. Since the calculations became much more difficult than the standard i-TS model, some rough approximations were introduced. Assuming the electron-phonon relaxation time of 0.4 ps, the experimental results of 30–40 MeV C60 irradiations have been reproduced by the melting criterion with the Se threshold of 25 keV/nm [21]. This was inconsistent with our results in the previous paper where the tracks were formed under 1–9 MeV C60 irradiations, i.e., Se = 7.5–21.3 keV/nm [9]. Improvements of the ion track calculations applicable to Si were also discussed by other authors [22,23], including the non-thermal melting model [23].One of the recent remarkable observations was reported by Dürr et al. [10], who irradiated hydrogen-terminated Si surface with m-SHIs. While they observed the H-terminated Si surface by Scanning Tunneling Microscope (STM) after SHI irradiation, they occasionally observed loss of one or two atoms only. If a melting track would be formed in Si, the terminated hydrogen atoms on the surface of several nm in diameter could be lost, since the Si-H bonds are easily ruptured at such high temperatures [10]. Since the hydrogen loss from the surface is an irreversible process, the lost hydrogen atoms have never returned even if the perfect recrystallization of Si would be induced after cooling. Therefore, their results are inconsistent with the melting (and vaporization) in Si.In our recent publications, we reported track formation in Si under C60 irradiations in the range of 1–9 MeV [9,11], which has considerably lower energies than the C60 irradiation of 20–40 MeV performed in the Orsay facility [4,5]. Nevertheless, tracks were formed in Si under 1-MeV C60 ion irradiation (Se = 7.5 keV/nm), while 3.6-GeV monatomic U ion irradiation (23.7 keV/nm) does not.This paper reports the investigation of track formation in Si irradiated with C60 ions in the energy region below 1 MeV (i.e., 30–750 keV), as we successfully observed ion tracks under 1-MeV C60 irradiation in previous studies [9,11]. Since the acceleration of C60 ions to less than 1 MeV was difficult for a 3-MV tandem accelerator, a 400-kV single-ended ion implanter was used here. Although Si is known to be tolerant to track formation by m-SHI irradiation, tracks were observed down to 60-keV C60 ions (Se = 1.8 keV/nm). The extrapolated Se threshold from the C60 irradiation data of 1–9 MeV was ~4 keV/nm; therefore, track formation under 60-keV C60 irradiation (Se = 1.8 keV/nm) cannot be explained by Se only. A contribution from the nuclear energy deposition (Sn) or something else cannot be excluded. At low energies, the track lengths increase beyond those expected from the ion range of individual ions, which can be a manifestation of “the acceleration effect” of cluster ions [24,25]. The approximated linearity between the track volume and ion energy is discussed.2. ExperimentalSamples of single crystalline Si were cut from commercially available wafers of p-type conduction (boron-doped) with a resistivity of ~1 Ω cm, grown via the Czochralski method. The samples were mechanically cut into 3 mm × 4 mm rectangles, which were called bulk samples. The bulk samples were immersed in hydrofluoric acid to remove surface oxide.The tracks were evaluated by transmission electron microscopy (TEM), and two configurations of TEM samples were prepared [9,11,26]. Top-view samples were obtained by thinning down an unirradiated bulk sample to a thickness of less than ~100 nm using 30-keV Ga focused ion beam (FIB) milling and held on TEM grids. The top-view samples on the grids were irradiated with C60 ions at an incident angle of 7◦ from the surface normal, to observe the track diameters by TEM.Side-view samples were obtained by irradiating the 3 mm × 4 mm faces of other bulk samples with C60 ions at an incident angle of 7◦ from the surface normal. Thereafter, the side-view samples were picked up from the irradiated surfaces and thinned down along the C60 beam by FIB to observe the depth profiles of the ion tracks. To identify the surface location of the side-view samples, a thin Pt layer was deposited on the sample surfaces prior to the FIB thinning. An amorphous C layer was subsequently deposited over the Pt layer to protect it from FIB milling.The irradiation of C60 ions was conducted at the Takasaki Institute for Advanced Quantum Science, of the National Institutes for Quantum Science and Technology (QST). A 400-kV single-ended ion implanter and a 3-MV tandem accelerator were used for energy ranges of 30–750 keV and 1–9 MeV, respectively. This study focused on the former energy range. The details of irradiation in the latter energy range are available elsewhere [9,11].C60 ions of 30–120, 200–540, and 750 keV were accelerated under the maximum voltage of 400 kV using the different charge states of C60+ , C602+, and C603+, respectively. The C60 ions of 1–6 MeV and 9 MeV were accelerated by the 3 MV tandem accelerator using the charge states of C60+ and C602+, respectively. The energies and the initial charge states were summarized in Table 1. The fluence was set to 5 × 1010 or 1 × 1011 C60/ cm2 to avoid the overlap of the tracks. To improve the beam homogeneity, the C60 beams were horizontally and vertically scanned at frequencies of 89 and 502 Hz, respectively. An ion flux was adjusted between 0.3 and 1 nA, with an irradiation area of ~0.5 cm2.TEM observation was conducted using a JEOL JEM-2100 microscope, with an operating voltage of 200 kV. Approximately fifty tracks each were examined to determine either the mean diameter and the mean length for every ion energy. According to past literature [5], the tracks in Si were recrystallized with prolonged TEM observation. Careful observations were performed to minimized the electron current and observation time. It was confirmed that any apparent changes were not Table 1 Comparison of the experimental initial charges Qin of C60 ions and the effective charges Qeff calculated by Shima’s formula [30]. The numbers with underline indicate the regions where Qeff ~ Qin.C60 energy (MeV) Qin Qeff Qeff / Qin9 +2 13.3 6.666 +1 10.9 10.94 +1 8.97 8.973 +1 7.78 7.782 +1 6.37 6.371 +1 4.53 4.530.75 +3 3.92 1.310.5 +2 3.21 1.610.4 +2 2.87 1.440.2 +1 2.04 2.040.12 +1 1.58 1.580.06 +1 1.12 1.120.03 +1 0.790 0.790H. Amekura et al. Materialia 39 (2025) 102317 2 induced during the observation.The stopping powers of m-SHI were calculated using the SRIM 2013 code [15]; those of the C60 ion were determined using the following relationship: Si(E,C60) = γiNSi(E /N,C1) (1) where i = e (electronic) [16], and i = n (nuclear) [27]; N = 60 was presumed for C60 ions. Eq. (1) shows that the stopping power of a C60 ion is equal to γiN times that of a monatomic C ion with the same velocity as the C60 ion. Although γi = 1 is frequently assumed, the assumption of γe ~ 1 was recently bolstered by Kaneko’s calculations [17], which concluded that γe was approximated as a constant of 0.8 between 2- and 10-MeV C60 ions in carbon foil. Here, γe = 1 was assumed in Eq. (1) to maintain consistency with our previous papers [9,11,18,26].Since the SRIM code was used to determine the stopping powers, the attainment to the effective charges was assumed. However, this is not trivial for m-SHIs [28]. How about C60 ions? Furthermore, since very short tracks, which are formed by low-energy C60 ions, are one of the main concerns of the present work, the charge equilibrium thickness should be estimated. Toulemonde [29] studied the equilibrium thickness of m-SHIs, and proposed a relationship between the specific energy Ep (MeV/u) and the thickness of carbon stripper foil X66 required for the charge equilibrium as, X66[μg/cm2] = 5.0(Ep[MeV/u])1.5. (2) In the original paper [29], he used the pre-factor of 2.5 instead of 5.0. However, since he suggested in the same paper to double the value for certainty, we used the pre-factor of 5.0. Of course, since this relationship is determined form the data between 1 and 44 MeV/amu, it is not guaranteed to apply slow C60 ions of much lower than 1 MeV/amu. However, the application of this relationship could provide a rough estimation. When Ep = 1 MeV/amu, the foil of 5 μg/cm2, i.e., 23 nm in thickness, is required, which sounds reasonable. The amorphous carbon density of 2.2 g/cm3 was used. In the case of our highest energy of 9 MeV C60 ion (0.0125 MeV/u), the foil of 0.006 μg/cm2, i.e., 0.03 nm in thickness, was calculated. While this thickness was calculated in a carbon foil, which could be different in Si, the charge equilibrium could be attained also in Si within a considerably thin surface layer, which is much shorter than the observed track lengths. The most parts of the tracks are formed under the charge equilibrium.The effective charges Qeff of C60 ions were estimated from the ion velocities v with applying the formula proposed by Shima et al. [30], i.e., Qeff = Z1[1 − exp(− 1.25vr +0.32v2r − 0.11v3r)]g(Z2) (3) with vr = 0.608(v / vB)/Z0.451 (4) g(Z2) = 1 − 0.0019(Z2 − 6)v0.5r + 10− 5(Z2 − 6)2vr (5) where Z1, Z2, and vB denote the charge numbers of the projectile and of the target, and the Bohr velocity, respectively. The effective charges Qeff Fig. 1. Side-view bright-field transmission electron microscopy (BF-TEM) images of ion tracks in Si, which were irradiated with C60 ions of energies ranging from 9 MeV to 30 keV. The samples were irradiated to a fluence of 1 × 1011 C60/cm2 except to 5 × 1010 C60/cm2 at 750 keV and 9 MeV. The black thin layers are Pt films deposited as surface markers. The P-layers are protection layers against FIB, made of deposited amorphous C.H. Amekura et al. Materialia 39 (2025) 102317 3 of C60 ions in various energies were calculated and compared with the experimental initial charges Qin as shown in Table 1.Since the ratio Qeff / Qin for 750 keV C60 ions or less is approximated to ~1.4, the ions were injected with the charges relatively close to the effective ones. Charge redistributions to the equilibriums could be modest. Contrary, since the ratio Qeff / Qin is much higher than the unity for 1 MeV C60 ions or higher energies, relatively large charge redistributions were induced within a shallow surface layer.3. ResultsFig. 1 shows side-view bright-field TEM (BF-TEM) images of ion tracks in Si. The samples were irradiated with C60 ions of energies ranging from 30 keV to 9 MeV. A fluence of 1 × 1011 C60/cm2 was applied, except 5 × 1010 C60/cm2 for 750 keV and 9 MeV. The thin black layer located approximately at the center of each figure was a Pt film deposited as a surface marker. Protection layers (P-layers), made of amorphous C, against FIB thinning were deposited over the Pt layers.Ion tracks were observed as black cylinders close to the other side of the Pt layers. The longest cylinders with the highest aspect ratio (AR) were observed at the highest energy of 9 MeV. With a decrease in the ion energy, the AR of the tracks decreased, i.e., the track length steeply decreased, but the diameter gradually decreased.With a decrease in energy, the AR of the tracks decreased, i.e., the shapes became slightly rounder, probably indicating a crossover from the electronic cylindrical tracks to nuclear spherical tracks. With a decrease in energy to 120 keV or lower, the tracks did not appear cylindrical but rather elongated semi-spherical. However, isolated tracks with low ARs were perceived down to 60 keV. A nearly continuous damaged layer, instead of isolated tracks, was observed beneath the Pt layer under 30-keV irradiation. Thus, isolated tracks were no longer observed under 30-keV irradiation.Fig. 2 shows the top-view images of the ion tracks in Si, with white dots representing the tracks. The colors of the dots were confirmed to change from white to black with the defocusing of TEM, indicating that the dots were due to the Fresnel contrast and have lower density than the matrix, attributable to the ion tracks. The white dots were easily observed down to 120 keV. As the dots became smaller, the images became less clear but were still observed under an irradiation of 60 keV. However, they were not observed under 30-keV irradiation.Figs. 1 and 2 show that ion tracks were formed down to 60-keV irradiation but not under 30-keV irradiation. Instead, a continuous damaged layer was observed under 30-keV irradiation, as shown in Fig. 1(f).After analyzing the TEM images of the ion tracks, the mean track length (L), mean track diameter (D), and their standard deviations (SDs) were determined and are plotted in Fig. 3 against the ion energy. L and D were determined from the side- and top-view TEM images, respectively. The ion energy (E) dependences were fitted by power-law dependences with adjustments in the exponents: L∝EP with P = 0.397 (6) D∝EQ with Q = 0.209. (7) Fig. 2. Top-view BF-TEM images of ion tracks in Si, which were formed with C60 ion irradiation of energies of 750–30 keV. The samples were irradiated to a fluence of 1 × 1011 C60/cm2 except to 5 × 1010 C60/cm2 at 750 keV. The ion tracks are indicated as white dots. Tracks were not detected at 30 keV.H. Amekura et al. Materialia 39 (2025) 102317 4 The exponent of the track length L (P = 0.397), exceeded that of diameter D (Q = 0.209). Thus, L increased more steeply than D. Considering that the AR is defined as L/D, AR = L/D ∼ EP− Q ∼ E0.188. (8) The AR increased with an increase in E, as confirmed in Fig. 1. The tracks formed at higher (lower) energies exhibited shapes with a higher (lower) AR.In our previous publication [11], high resolution TEM (HR-TEM) observation was applied to a Si sample irradiated with 6 MeV C60 ions. A damaged crystalline track, but not amorphous, was observed. However, it needs caution to perform this kind of observation, because the film thickness should thinner than the track length [26], hopefully less than (the mean track length) – 2 × (SD). Otherwise, an amorphous track shows lattice fringes from deeper crystalline layer than the track length [26]. Therefore, this kind of observation is not easily applicable to samples irradiated with lower energy C60 ions than 6 MeV. To confirm the damage crystalline nature of the ion tracks formed by 6 MeV C60 ions, Rutherford backscattering spectrometry/Channeling (RBS/C) measurements were conducted and have supported the HR-TEM result [11].4. Discussion4.1. Nonelectronic contribution to track formationFig. 4 shows the Se dependence of the squared mean track radii, i.e., R2. We previously reported [9,11] that the R2 between 1 and 9 MeV was well fitted with an empirical law [31]: R2 = C(Se − Se,th)(9) where C and Se,th indicate a proportional coefficient and Se threshold of 4.2 keV/nm, respectively. This empirical law is indicated by a broken line in Fig. 4. The solid curve represents the Se dependence of the R2 calculated from the inelastic thermal spike (i-TS) model while assuming the melting criterion [6]. The i-TS curve slightly overestimated the track radii, possibly because the partial recrystallization of the tracks in Si [8] was not presumed in the i-TS model. However, the extrapolated threshold from the i-TS curve was comparable with that from the empirical law (Eq. (9)). Both curves vanished around ~4 keV/nm. Hereinafter, the extrapolated threshold is described as ~4 keV/nm. C60 ions of 60, 120, and 200 keV afforded Se values of 1.8, 2.6, and 3.2 keV/nm, respectively, i.e., all of them were below the threshold of ~4 keV/nm. Even if they were below the Se threshold, the tracks were experimentally confirmed under 60-, 120-, and 200-keV irradiation.Fig. 5 shows the ion energy dependence of the track diameter and energy losses. The dependence of the diameter between 750 keV and 9 MeV was consistent with that of the Se (solid curve). However, the decrease in the diameter slowed at 500 keV, whereas the Se decreased more steeply. Around 300 keV, the Se decreased to the threshold value of ~4 keV/nm, which was determined from an extrapolation in Fig. 4. As previously described, the track formation below 300 keV could not be attributed to the Se only. To compensate for the decrease in the Se with a decrease in energy, the nuclear energy loss (Sn) increased and became more dominant than the Se at ~700 keV and below. Larger diameters were observed at 200 and 400 keV than those at 500 keV. The compensating Sn or the synergy effect between the Se and Sn was Fig. 3. Ion energy (E) dependence of the mean track length (L, circles) and mean diameter (D, triangles) in Si irradiated with C60 ions, determined from the side- and top-view TEM images, respectively. The circles (triangles) and bars show the mean values ± standard deviations, respectively. The solid and broken lines indicate the least squares fitting of the power laws of L ∝ E 0.397 and D ∝ E 0.209, respectively.Fig. 4. Squared mean track radii (R2) versus electronic energy deposition (Se) of C60 ions in Si. The circles and bars show the mean values ± standard deviations, respectively. The broken line indicates the empirical rule of R2 = C(Se – Se,th), which was optimized with data between 1 and 9 MeV [11]. The solid curve indicates the Se dependence of R2 calculated from the inelastic thermal spike (i-TS) model [6].Fig. 5. The ion energy dependence of the mean track diameter in Si irradiated with C60 ions is shown by circles and bars, indicating the mean values ±standard deviation, respectively. The energy dependences of Se, Sn, and (Se +Sn), calculated from Eq. (1), are indicated by solid, broken, and dotted curves, respectively.H. Amekura et al. Materialia 39 (2025) 102317 5 probably the driving force of the track formation below the Se threshold of ~4 keV/nm. However, a preliminary unified thermal spike (u-TS) calculation predicted that the track radii should increase with decreasing the C60 energy from 6 MeV to 1 MeV, which was completely inconsistent with our experiments.Some discontinuities are observed in the energy dependence of the track diameter as shown in Fig. 5, between 120 keV and 200 keV, 400 keV and 500 keV, 750 keV and 1 MeV. However, they cannot be explained by the jumps of the incident charge state of C60 ions: As already described in the Experimental section, the energies (the incident charge states) were 1 MeV (+1), 750 keV (+3), 500 keV (+2), 400 keV (+2), 200 keV (+1), and 120 keV (+1). While there is a jump on the track diameter from 1 MeV to 750 keV (+1 to +3), but no jump from 750 keV to 500 keV (+3 to +2). Furthermore, a jump was observed from 500 keV to 400 keV (+2 to +2), while the charge state was maintained. Moreover, a jump was not observed from 400 keV to 200 keV (+2 to +1) while the charge state changed. Again, a jump was observed from 200 keV to 120 keV (+1 to +1) while the charge state did not change.4.2. Cluster track length and monatomic ion rangeThe ion energy E dependence of the mean track length L in Si is again shown in Fig. 6. Although it has already been shown in Fig. 3, L was fitted by a power law of L ∝ E 0.379.As previously mentioned, we presumed the validity of Eq. (1). Thus, the energy-loss processes of each C atom constituting a C60 ion were assumed the same as those of a monatomic C ion, i.e., the independent energy-loss processes of each C atom irrespective of the formation of a C60 molecule. One of the consequences of the independent energy-loss processes for C atoms forming a C60 molecule is that the ion ranges of the C atoms forming the C60 molecule should be comparable to those of monatomic C ions separately injected into Si. The corresponding ion range (Rp) of monatomic C ions with the same velocity as the C60 ions was calculated using the SRIM 2013 code [15] and shown by a broken curve in Fig. 6. The calculated Rp was considerably longer than the experimental mean track length (L) at 1 MeV or above but became shorter than L at 200 keV or below.The Rp is the mean depth where injected ions are stopped. Contrarily, an injected ion should be so energetic within the ion track that the Se of the ion always overcomes the track formation threshold, Se,th. The considerably shorter track length compared with the Rp is quite common in different materials, such as yttrium iron garnet (YIG) [32] irradiated with MeV C60 ions. Dunlop et al. [32] mentioned that a difference between C60 ions and m-SHIs is whether the fragmentation of the ions is induced or not. If a C60 ion is destroyed into pieces by multiple nuclear collisions with Si atoms in the target but the distances among them are considerably shorter than the delta-electron ranges, the fragmented parts are still regarded as the same ion maintaining the track. When the distances among the fragments exceed the delta-electron ranges, the fragmented parts are no longer regarded as the same ion; thus, the track must be interrupted. The track continuity condition of the Se threshold is applied to each fragment: i.e., the Se of each fragment should exceed the threshold Se,th even after fragmentation. Thus, the track length being considerably shorter than the ion range is reasonably understood.The Rp steeply decreased with a decrease in the ion energy (Fig. 6). The ratio of C60 ions that reached the Rp before being affected by the fragmentation may have increased. Thus, the track length decreased less steeply than the Rp (Fig. 6).However, the track length being longer than the ion range observed at 200 keV or less (Fig. 6) was a bit unexpected. However, it has been observed that C atoms that form C60 molecular ions are implanted deeper into a solid than isolated monatomic C ions with the same velocity [25]. Morita et al. compared the ranges of the same-velocity ions of 30 keV C60+ and 0.5 keV C+ monomer ions in Si via high-resolution Rutherford backscattering spectrometry (HR-RBS) [25]. The former and latter ranges were 6.1 and 4.0 nm, respectively. Since the experimental conditions of Morita et al. (30 keV C60+ ion irradiation to Si detected by HR-RBS) were quite similar to those of the present observations (60–200 keV C60+ ion irradiation to Si detected by TEM), the track-length enhancement observed in the present work can be ascribed to the same origin.Morita et al. ascribed the range enhancement to “the acceleration effect” of the cluster ion irradiation [25]; i.e., the leading ions are accelerated and injected deeper by being pushed by the trailing ions [24]. Historically the range enhancement of cluster ions was discussed by Sigmund and ascribed to “the clearing-the-way (CTW) effect” [33,34]; i.e., the leading ions clear away the target atoms for deeper injection of the trailing ions. However, the CTW effect is induced only when M1 > M2, where M1 and M2 denote the elemental masses of the incident and the target ions, respectively. The CTW effect is not induced when M1 < M2. Yamamura and Muramoto, however, showed that the range enhancement was induced even when M1 < M2 using Monte Carlo simulations, while the enhancement was lower compared to the case of M1 > M2 [24]. Since the CTW effect cannot explain the enhancement in the case of M1 < M2, another mechanism, i.e., the acceleration effect, was proposed [24]. Tracks longer than the ion range of isolated monatomic C ions, which were observed in the present work, were ascribed to “the acceleration effect.”4.3. Energy dependence of mean track volumeFig. 7 shows the ion energy dependence of the mean track volume (V), which was simply determined from the mean radius (R) and L through the following relationship: V = πR2L (10) As shown by a solid line in Fig. 7, the data points were well fitted by a power law of V∝E0.871. (11) The exponent of 0.871 was close to unity; thus, the data points were fitted while assuming the linear law of V∝E, (12) as shown by a broken line in Fig. 7, which also provides excellent agreement. If the exponent can be approximated to unity, i.e., the track Fig. 6. The ion energy (E) dependence of the mean track length (L) in Si irradiated with C60 ions is shown by circles and bars, indicating the mean values ± standard deviations, respectively. The solid line indicates the least squares fitting of the power law of L ∝ E 0.397. The broken curve indicates the ion range of the monatomic C ion in Si with the same velocity as the C60 ion, calculated using the SRIM 2013 code [15].H. Amekura et al. Materialia 39 (2025) 102317 6 volume is assumed to be proportional to the ion energy, a significantly simpler scenario could be applied for the track formation. Aoki et al. conducted molecular dynamics (MD) simulations of the impacts of Ar cluster ions on Si surfaces, with a cluster size of 13–3000 atoms and acceleration energy of 0.5–55 keV [35]. They reported that the penetration depth of the cluster ions, which corresponds to the L in the present study, was proportional to the cubic root of the acceleration energy, i.e., E1/3. Thus, the crater volume was linearly proportional to E.As previously described, the track length is determined by a series of complex processes, such as the fragmentation of C60 molecules by multiple collisions, which increase the distance and decrease the interactions among the fragments. However, if the mean track volume, V (track length L), was assumed to be proportional to the ion energy (E) (cubic root of the energy, E1/3), L can be easily estimated as L ∼ E1/3. (13) Of course, this is not correct since the experimental results indicate that L ∼ E0.397, (14) as shown in Fig. 3. However, Eq. (13) could provide a crude but useful clue to estimating L. Table 2 summarizes the power-law exponents of the track length, diameter, and volume. From the linear fitting of V[nm3] = 868E[MeV], (15) shown in Fig. 7, a track volume of 868 nm3 was expected for each 1 MeV C60 ion, in which 8.67 × 104 bonds of Si exist. If the energy of 1 MeV was equally shared by the Si bonds in the aforementioned track volume, one bond received the energy of 11.2 eV, which was sufficient for bond rupture.4.4. Comparison with past studiesShen et al. studied the damage in Si induced by 100–530 keV C60 ion irradiation via RBS/C measurements [36]. We evaluated track formation not only in the energy region evaluated by Shen et al. (100–530 keV) but also in a considerably wider energy region (30 keV to 9 MeV). Shen et al. irradiated to a fluence between 2 × 1011 and 5 × 1012 C60/cm2, which was slightly higher than the present study of 5 × 1010 or 1 × 1011 C60/cm2.Fig. 5 shows the energy dependences of Se and Sn, indicating that the Sn exceeded the Se below 700 keV. In the region studied by Shen et al. (100–530 keV), the Sn was always higher than the Se. However, the Se was not negligible compared with the Sn. While Shen et al. interpreted their experimental results as efficient damage production via collision cascades and spike formation [36], the results of Shen et al. should be regarded as not a purely Sn-dominant region but Sn-dominant with a non-negligible Se region. In fact, the present study always observed cylindrical damage regions, which can be called ion tracks at high-energy while changing the ion energy from 9 MeV (Se-dominant region) to 60 keV (Sn-dominant). No clear transition from electronic ion tracks (cylindrical) to nuclear collision cascades (spherical) was detected.In the previous paper [9], we discussed that tracks are formed under C60 irradiation, but not under m-SHIs even at the same Se range. The i-TS model of the melting criterion including the velocity effect cannot explain the experimental results of m-SHIs [6]. Furthermore, the i-TS calculations well reproduced the Se dependence of track diameter under MeV C60 ion irradiation [9], while experiments showed that tracks were not formed at the same Se values under m-SHI irradiation.To explain these behaviors, we extended the track recrystallization model proposed by Chadderton [8]. After m-SHI irradiation, tracks were not observed because the recrystallization of tracks had been promptly induced as proposed by Chadderton. Similar disappearance of the tracks by the recrystallization was proposed in MgO from the MD simulations [37]. We additionally assumed the track recrystallization was inhibited by defects introduced by Sn-related processes. It should be noted again that Sn delivered by C60 ions is much higher than that of m-SHIs. The tracks in Si are formed and stabilized by the synergy effect of Se and Sn under C60 irradiation, but not by the u-TS effect.Two other synergy effects are known [9], i.e., the pre-damage effect [31] and the u-TS model [38]. Since the tracks are formed in virgin Si samples, the pre-damage effect does not play a role in the present case. The u-TS model was applied to Si irradiated with C60 ions. A preliminary result showed the track diameter increased with decreasing the ion energy from 6 MeV to 1 MeV, which was completely different from our experimental observation. The u-TS model is also excluded. (The recrystallization model is not consistent with the observation of hydrogen loss from the hydrogen-terminated Si irradiated with m-SHIs [10]. We need to look for a more suitable model.)Even taking into account the low energy behaviors in the present work, the role of Sn does not mostly change but a minor addition: As shown in Fig. 4, the squared track radii R2 follow the relation R2 = C (Se – Se,th) at 500 keV and higher, where C and Se,th denote the proportional constant and the Se threshold, respectively. Since the threshold Se,th was ~4 keV/nm, the tracks should not be formed below this threshold. However, the tracks are formed even at 200 keV or less, which are not due to the pure-Se origin but probably assisted by Sn.Even at the low energies, the main role of Sn is the same as the high energies, i.e., the introduction of defects to prevent the track recrystallization. However, a minor portion of energy delivered by the Sn-related processes additively contribute to decrease the track formation threshold Se,th.5. ConclusionsIon track formation in crystalline Si induced by C60 ion irradiation was investigated within 30–750 keV using a 400-kV single-ended ion Fig. 7. Ion energy (E) dependence of the mean track volume (V) in Si irradiated with C60 ions. The circles and bars show the mean volumes ± standard deviations, respectively. The solid and broken lines indicate the least squares fitting of a power law of V ∝ E 0.871 and linear law of V ∝ E, respectively.Table 2 Exponents of power-law dependences, which were assumed for the ion energy (E) dependences of the mean length (L), mean diameter (D), and mean volume (V) of the tracks.Track length L ∝ E P P = 0.397Track diameter D ∝ E Q Q = 0.209(Aspect ratio AR = L/D ∝ E P-QP > Q → higher AR for higher E.)Track volume V ∝ E R R = 0.871H. Amekura et al. Materialia 39 (2025) 102317 7 implanter, in addition to our previous study between 1 and 9 MeV using a 3-MV tandem accelerator [9,11]. With a decrease in the ion energy from 9 MeV, the track length and diameter decreased, although the length decreased more steeply than the diameter. Although the tracks, i. e., localized damaged regions, were perceived down to 60-keV irradiation, they were not observed; however, a weak continuous damaged region was observed under 30-keV irradiation.The Se threshold of the track formation was estimated using two methods: the i-TS theory and the empirical squared radius law. Although both of them suggested a Se threshold of ~4 keV/nm, tracks were formed even at 1.8 keV/nm, i.e., below the threshold, indicating a contribution from the nuclear collisional processes.The ion track length (L) of C60 ions was compared with the ion range (Rp) of monatomic C ions with the same velocity. Although the latter was longer than the former above 400 keV, the former became longer than the latter below 400 keV. The enhancement of L in the low-energy region can be attributed to “the acceleration effect” of the cluster-ion irradiation, whereas the reduction in L in the high-energy region was attributed to the fragmentation of C60 ions through multiple collisions with the Si matrix. The experimental results indicated that the track volume was roughly proportional to the incident C60 energy but not exactly. This approximated linearity could provide a crude but useful clue to estimating the track length.Declaration of generative ai in scientific writingNo generative AI has been used in the preparation of this paper.PreprintsAn earlier version is available at SSRN: https://ssrn.com/abstract =4944996.FundingThis work was supported by JSPS-KAKENHI Grant number 22K04990.CRediT authorship contribution statementH. Amekura: Conceptualization, Investigation, Writing – original draft, Writing – review & editing. K. Narumi: Conceptualization, Investigation, Methodology, Writing – review & editing. A. Chiba: Methodology, Validation. Y. Hirano: Methodology, Validation. K. Yamada: Methodology, Validation. S. Yamamoto: Methodology, Formal analysis. Y. Saitoh: Methodology, Validation.Declaration of competing interestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.AcknowledgmentsA part of the study was supported by the Inter-organizational Atomic Energy Research Program through an academic collaborative agreement among JAEA, QST, and the Univ. of Tokyo. The authors are grateful to the crew of the accelerator facilities at QST-Takasaki for their help. HA was supported by JSPS-KAKENHI Grant number 22K04990. This work was supported by “Advanced Research Infrastructure for Materials and Nanotechnology in Japan (ARIM)” of the Ministry of Education, Culture, Sports, Science and Technology (MEXT). Proposal Numbers JPMXP1223NM5040 and JPMXP1224NM5073.References[1] K. 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