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[H. Amekura](https://orcid.org/0000-0003-2148-8431), [K. Narumi](https://orcid.org/0000-0001-8569-0108), A. Chiba, Y. Hirano, K. Yamada, S. Yamamoto, Y. Saitoh, [H. Segawa](https://orcid.org/0000-0002-7198-8410)

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[A model reasoning low-energy track-formation and enhanced nuclear energy loss in Si irradiated with C60 ions](https://mdr.nims.go.jp/datasets/13b0ff7d-90c8-44e1-aa4c-5272327f57dc)

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A model reasoning low-energy track-formation and enhanced nuclear energy loss in Si irradiated with C60 ionsA model reasoning low-energy track-formation and enhanced nuclear energy loss in Si irradiated with C60 ions☆H. Amekura a,* , K. Narumi b , A. Chiba b, Y. Hirano b, K. Yamada b, S. Yamamoto b, Y. Saitoh b,  H. Segawa aa National Institute for Materials Science (NIMS), Tsukuba 305-0003, Japanb National Institutes for Quantum Science and Technology (QST), Takasaki 370-1292, JapanA R T I C L E  I N F OKeywords:Ion trackC60 ionSiliconSynergy effectCluster effectA B S T R A C TIon energy dependence of track radius in Si was investigated under C60 ion irradiation between 30 keV and 9 MeV. The tracks were observed from 9 MeV down to 60 keV but not at 30 keV. The track radius gradually decreased with decreasing the energy from 9 MeV to 500 keV, showing a tentative increase around 300 keV followed by further decrease. Both (i) the track formation at exceptionally low energies and (ii) the non- monotonic energy dependence of the track radius, are explained by the ion energy dependence of electronic and nuclear energy losses of C60 ions in Si, i.e., the cluster-ion energy loss (CIEL) model.1. IntroductionSince ion implantation/irradiation to Si is recognized as one of the most important processes in fabricating micro-/nano-integrated circuits for information technology, the ion–solid interactions in Si have been extensively studied particularly in the energy range from sub-keV to several MeV [1]. While the ion track formation has been observed in many materials under heavy-ion irradiation in the energy range of tens MeV or higher, which are often called swift heavy ion (SHI) irradiation, the track formation in crystalline Si has, however, remained controversial. To extend the applicability of high energy heavy ions in the range of tens MeV and higher to the Si micro-/nano-technology, the understanding of the ion–solid interaction between Si and ions in this energy region, particularly concerning the ion track formation, is significant.Although various SHI irradiations have already been attempted to Si [2,3], no ion tracks have ever been formed under up to high-energy 3.6- GeV U ion irradiation (electronic energy loss Se = 24 keV/nm) [3]. These ions correspond to the Bragg peak region, in which the highest Se attainable by monatomic SHIs (m-SHIs) is induced. These observations indicate that any of m-SHIs cannot form ion tracks in Si. However, it does not mean that ions other than m-SHIs cannot form ion tracks in Si. In fact, 30- and 40-MeV fullerene C60 cluster-ions (Se of 43 and 50 keV/ nm in Si, respectively) succeeded in forming ion tracks in Si [4,5]. After then, many researchers believed that the failures of the track formation in Si under m-SHI irradiation were ascribed to the limitation of Se available against the quite high Se threshold in Si, which cannot be overcome by any of m-SHIs but C60 ions with delivering extremely high Se. Since sixty carbon atoms from a C60 molecule were injected into a solid at almost the same time and the same nanometric region, an extremely higher Se was provided even with C60 ions of only tens MeV [6–8].It should be, however, noted that both Canut et al. [4] and Dunlop et al. [5], who independently observed the first track formation in Si under C60 irradiation, have also pointed the importance of the velocity effect. Much slower velocity of C60 ions compared to the m-SHIs may induce much higher excitation density for the track formation at the expense of more localized excitation volume.Chettah et al. carried out the inelastic thermal spike (i-TS) calculations [9] in Si irradiated with C60 ions with including the velocity effect [10]. However, they suggested that the calculated velocity effect was not high enough to explain the completely different track formation behaviors between C60 ions and m-SHIs, if the tracks were formed by melting [10]. According to their calculations [10], the Se threshold was estimated as low as ~ 4 keV/nm for C60 ions under the melting criterion of the track formation. This quite low threshold looks inconsistent with all the past experiments where the tracks were not formed at least less than 30 keV/nm. These two thresholds, 4 and 30 keV/nm, which are ☆ This article is part of a special issue entitled: ‘2025 REI-22 Conference’ published in Nuclear Inst. and Methods in Physics Research, B.* Corresponding author at: 3-13 Sakura, Tsukuba 305-0003, Japan.E-mail address: amekura.hiroshi@nims.go.jp (H. Amekura). Contents lists available at ScienceDirectNuclear Inst. and Methods in Physics Research, Bjournal homepage: www.elsevier.com/locate/nimbhttps://doi.org/10.1016/j.nimb.2026.166225Received 14 February 2026; Received in revised form 24 May 2026; Accepted 12 June 2026  Nuclear Instruments and Methods in Physics Research B 579 (2026) 166225 Available online 17 June 2026 0168-583X/© 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). https://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0001-8569-0108https://orcid.org/0000-0001-8569-0108mailto:amekura.hiroshi@nims.go.jpwww.sciencedirect.com/science/journal/0168583Xhttps://www.elsevier.com/locate/nimbhttps://doi.org/10.1016/j.nimb.2026.166225https://doi.org/10.1016/j.nimb.2026.166225http://creativecommons.org/licenses/by/4.0/quite different from each other, were assumed as the thresholds at low and high velocity limits. However, it is quite difficult to reproduce these two widely different thresholds from the i-TS calculations [10]. In fact, Se,th of 6 keV/nm was estimated for the high velocity of 5 MeV/u (i.e., 3.6 GeV U ion) [10], which is comparable to the low velocity value of ~4 keV/nm. Therefore, Chettah et al. suggested the boiling criterion for the track formation in Si under m-SHI irradiation, instead of the melting criterion [10]. Another origin of the inconsistency on the Se,th of Si could be ascribed to the recrystallization of the ion tracks [11]: In this model, the Se,th of Si is assumed to be not so high. Therefore, the tracks are easily created in Si. However, because of the highly enhanced recrystallization, the created tracks are rapidly annihilated. Consequently, no tracks are observed in Si after irradiation by any m-SHIs with any energy.However, the recrystallization model has not been broadly accepted yet, but still under debate. In fact, Länger et al. reported negative evidence for the recrystallization model in Si [12]. Further studies are necessary to clarify why no tracks are formed in Si under m-SHI irradiation.Contrary, our experimental results show the ion tracks are formed and survived in Si under C60 ion irradiation without the annihilation due to the recrystallization. We tentatively ascribed the track survival without the annihilation due to the recrystallization in Si under C60 irradiation to relatively high nuclear energy deposition Sn [13]. While Sn is negligibly low under m-SHI irradiation, it is relatively high under C60 irradiation. Damage generated by Sn of C60 ions could disturb the recrystallization of the tracks [13].It seems that the melting criterion describes better the track formation in Si under C60 ion irradiation less than 9 MeV [13–15]. It should be noted that the threshold Se, th of ~ 4 keV/nm is consistent with our recent study [15], where the ion tracks were traced with decreasing the C60 ion energy from 9 MeV to 30 keV. Cylindrical damage zones with high aspect ratios (ARs) formed under 9 MeV irradiation, decrease their diameters, lengths and ARs, with decreasing the ion energy [15]. While something like tracks were observed down to 60 keV irradiation, no discernible localized structures like tracks were observed under 30 keV irradiation [15].In this paper, some experimental results are examined from the energy dependence of the electronic and nuclear energy losses (Se and Sn) of C60 ions. Hereafter, it is called “the cluster-ion energy loss (CIEL) model” and is applied to; (i) why the ion tracks are formed in low energy down to 60 keV under C60 ion irradiation, and (ii) the inconsistency of the track formation threshold energy between the prediction of the i-TS model (300 keV) and the experimental observation (60 keV). The CIEL model also predicts that Sn is enhanced around the track threshold. While the track formation down to 300 keV is ascribed to the purely Se processes, the formation below 300 keV cannot be explained except the synergy effect of Se and Sn.2. ExperimentalThe experimental conditions were the same as the previous paper [15]. Samples of single crystalline Si (boron-doped p-type) were cut from commercially available wafers with a resistivity of ~1 Ω cm. The samples were immersed in hydrofluoric acid before the irradiation to remove surface oxide. 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). C60 ions between 30 and 750 keV were accelerated using a 400-kV single-ended ion implanter with the different charge states of C60+ , C602+, and C603+. The C60 ions between 1 and 9 MeV were accelerated by the 3 MV tandem accelerator. To avoid the overlap of the track, the ion fluence was set to 5 × 1010 or 1 × 1011 C60/ cm2. The ion tracks were evaluated by transmission electron microscopy (TEM) with an operating voltage of 200 kV (JEOL JEM-2100). Focused ion beam (FIB) milling with 30 keV Ga ions were applied for the thinning of the TEM samples.3. The cluster-ion energy loss (CIEL) modelFig. 1 shows calculated energy dependences of Se and Sn in Si irradiated with (a) C60 ions and (b) monatomic Xe ions. The energy losses of Xe ion in Si were evaluated from SRIM 2013 code [16] and plotted in Fig. 1(b). Those of C60 ions, Se (E, C60) and Sn (E, C60), were evaluated and plotted in Fig. 1(a) under the approximation that the energy losses of a C60 ion with the energy E are comparable to 60 times of those of a monatomic carbon ion with the same velocity, i.e., E/60, Se (E, C60) = 60 Se (E/60, C1), (1)                                                        Sn (E, C60) = 60 Sn (E/60, C1). (2)                                                       These relationships were proposed for the electronic ones from Ref. [6] and the nuclear ones from Ref. [7], respectively. Se (Xe) is plotted again in Fig. 1(a) by a broken curve for comparison with that of C60 ion, Se (C60), which clearly indicates that Se (C60) is much higher than Se (Xe) due to the enhancement described by eq. (1).The horizontal broken lines in Fig. 1 indicate Se,th, i.e., the threshold value of Se, which corresponds with the lowest Se value to induce thermal melting for track formation. Because of the velocity effect [17], the Se,th value could weakly depend on the energy. However, according to Chettah et al. [10], Se,th calculated at the low energy 0.07 MeV/u and at the high energy 5 MeV/u were ~4 keV/nm and ~ 6 keV/nm, respectively. The energy dependence of Se,th in Si can be approximated by the horizontal line.In the case of Xe irradiation to Si, as shown in Fig. 1(b), the Se curve crosses with Se,th line at the threshold energy Eth of ~15 MeV. This is inconsistent with the experimental observations, because ion tracks Fig. 1. Ion energy dependence of electronic energy loss Se and nuclear energy loss Sn in Si, irradiated with (a) C60 ions and (b) monatomic Xe ions. Horizontal broken lines indicate Se,th, i.e., the lowest energy loss required to induce the thermal melting for track formation. For comparison, Se of Xe ion is also plotted in (a) by a broken curve. Arrows indicate the electronic track formation thresholds.H. Amekura et al.                                                                                                                                                                                                                               Nuclear Inst. and Methods in Physics Research, B 579 (2026) 166225 2 have never been observed in Si under m-SHI irradiation up to 3.6 GeV U ions. However, as already described in Introduction, this inconsistency is reasonable and can be ascribed to the recrystallization of the tracks under m-SHI irradiation [11], because the track recrystallization is not included in the CIEL model. Rather, Fig. 1(b) could be intuitive to understand similar situations that happened in many materials where ion tracks are formed under m-SHIs irradiation, i.e., much lower Sn than Se at the threshold energy Eth.Tracks are formed in the energy region where Se is higher than Se,th. In the case of monatomic ions (Fig. 1(b)), the Sn value is much lower than Se at the threshold energy Eth, which is indicated by a downward arrow at Se = Se,th. Consequently, the behaviors around the (electronic) track formation threshold under m-SHI irradiation are determined by Se- related processes only. The monotonic decrease in the track radius with decreasing the Se is a typical consequence in many materials under m- SHI irradiation.As shown in Fig. 1(a), Se (C60) is much higher than Se (Xe). Consequently, the energy at the cross-point between Se(C60) and Se,th, i.e., the threshold energy Eth, considerably shifts to low energy side. Using the Se,th of ~ 4 keV/nm, which was the value derived in the previous paper, Eth was estimated to be 300 keV. It means that ion track formation, which was known as a high energy phenomenon, is realized at low energies under C60 irradiation.In the case of the monatomic ions, Sn was negligible to Se at Eth, as shown in Fig. 1(b). However, Sn overcomes Se at Eth in the case of C60 irradiation as shown by an upward arrow in Fig. 1(a). The behaviors of tracks around the Se threshold may strongly be influenced by the cooperation of high Sn under C60 irradiation.It has been often suggested that the existence of the non-negligible Sn when comparing the irradiation effects of C60 ions and m-SHIs, both of which provide comparable Se. The origins of the non-negligible Sn are considered as following: (a) originally low energies of constituent C atoms of C60 ions and (b) the Sn enhancement due to the simultaneous injection of 60 carbon atoms as described as eq. (2). However, we here propose the third one: (c) Sn enhancement due to the huge low-energy shift of the threshold energy Eth, which is induced via eq. (1).4. Experimental resultsFig. 2 shows the electronic energy loss Se dependence of the experimental mean-track-raii of Si irradiated with C60 ions. The corresponding C60 ion energy is shown close to each data point. Two significant behaviors are observed: (1) Even at the low C60 ion energy of 60 keV, i. e., Se = 1.8 keV/nm, ion tracks of 1.6 nm in the mean radius are formed. (2) With decreasing the ion energy from 9 MeV, the mean radius monotonically decreases down to 500 keV. However, with further decrease, the radius increases once and decreases again. The non- monotonic decrease of the track radius with Se is exceptional. In many materials, monotonic changes in the radii with Se have been reported [18].Regarding (1), ion track formation was known as one of the high energy phenomena, but the tracks were observed down to extremely low energy of 60 keV. The track formation at low energy is well supported by the CIEL model as shown in Fig. 1.Regarding (2), similar behaviors, i.e., non-monotonic Se dependence of the track radius was reported by Toulemonde, et al., in amorphous SiO2 irradiated with Au ions ranging from 300 keV to 185 MeV (Se =0.71 − 16.2 keV/nm and Sn = 3.2 − 0.16 keV/nm) [19]. According to them, the track radius of SiO2 decreased with decreasing the Au energy from 185 MeV to 10 MeV, but increased from 10 MeV to 300 keV. They suggested the track formation in SiO2 via the synergy effect of Se and Sn, since Sn increases with decreasing the energy. As shown in Fig. 1, Sn is enhanced around the track formation threshold in Si irradiated with C60 ions. The synergy effect between Se and Sn is expected for the track formation also in Si irradiated with C60 ions.5. DiscussionWhile the predicted threshold energy Eth was 300 keV from the relationship Se(E) = Se,th, the tracks were observed down to 60 keV irradiation. The difference between 60 and 300 keV could be ascribed to the enhanced Sn around the Se threshold. The Se dependence of the track radius R of semiconductors under C60 ion irradiation is described by an empirical rule [20],R2 = C (Se – Se,th), (3).where C denotes a proportional factor. The data points shown in Fig. 2 were replotted in Fig. 3 with Se versus squared R, i.e., R2. When the data points follow the relationship indicated by eq. (3), they fall on a straight line in the plot of Fig. 3. In fact, the data points between 500 keV and 9 MeV are well fitted by a straight broken line as shown in Fig. 3. This observation indicates that the track formation between 500 keV and 9 MeV is mainly due to the Se-related process. The fitted value of Se,th, was 4.2 keV/nm.A solid curve shows calculated results from the i-TS model [10]. While the i-TS model slightly overestimate the track radii, the extrapolated threshold Se,th reached to ~3.5 keV/nm, in good agreement with the value extrapolated by eq. (3). In this paper, Se,th of ~ 4 keV/nm is used. It should be noted that squared track radius R2 increased again below 500 keV and then decreased and disappeared at 30 keV. The behaviors below 500 keV irradiation cannot be explained by the monotonic decay of the electronic stopping Se only. Rather, the deviation of the data points from eq. (3) below 500 keV probably indicates a change in the track formation mechanism from higher to lower than 500 keV. Since Sn increases in this energy region, the peak in R2 at 300 keV could be ascribed to the synergy effect of Se and Sn.While we have assumed the constant Se,th independent of the ion energy in Si in this discussion, which is a good approximation as discussed in section 3, the model can be extended for variable Se,th including the large velocity effect. The Se,th increases mostly with the ion energy. Consequently, the two effects discussed here become more significant.Fig. 2. Electronic energy loss Se dependence of the experimental mean-track- radii in Si irradiated with C60 ions. Corresponding ion energies are shown in the figure. Solid curves are guides to the eye, indicating the qualitative consequences from the CIEL model.H. Amekura et al.                                                                                                                                                                                                                               Nuclear Inst. and Methods in Physics Research, B 579 (2026) 166225 3 6. ConclusionsThe mean track radii of Si were evaluated by TEM by changing the ion energy of C60 ions from 30 keV to 9 MeV. The tracks were observed down to 60 keV but not at 30 keV irradiation. In many materials under monatomic-ion irradiation, tracks are formed in higher energy than tens MeV or more. The track formation under tens keV irradiation is unusual. However, this phenomenon is described by the large low energy shift of the threshold energy Eth, which is ascribed to much higher Se of C60 ions. Furthermore, the low energy shift of Eth also results in a shift of the threshold to the enhanced Sn peak. The track formation around the threshold could be largely modified by the enhanced Sn. In the case of Si, the track radius monotonically decreased with decreasing the ion energy from 9 MeV. However, the tracks turned to an increase below 500 keV but soon decreased and disappeared. From the empirical rule, eq. (3), the track formation higher than ~500 keV is explained by the Se-related processes. However, the track formation below ~500 keV cannot be explained by the purely Se-related processes alone. The synergy effect between Se and Sn is suggested, which is favorable since the Sn is largely enhanced around the threshold under C60 ion irradiation.CRediT authorship contribution statementH. Amekura: Writing – review & editing, Writing – original draft, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. K. Narumi: Writing – review & editing, Methodology, Investigation, Conceptualization. A. Chiba: Methodology, Investigation. Y. Hirano: Methodology. K. Yamada: Methodology. S. Yamamoto: Methodology, Investigation. Y. Saitoh: Supervision, Methodology. H. Segawa: Supervision, Project administration, Funding acquisition.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 25K08531. 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 JPMXP1225NM5095 and JPMXP1226NM5009.Declaration of generative AI in scientific writing.No generative AI has been used in the preparation of this paper.Preprints.No preprints have been shared.FundingThis work was supported by JSPS-KAKENHI Grant number 25K08531.References[1] K. Suzuki, Ion Implantation and Activation, Vol. 1, Bentham Science Publishers, 2013, 10.2174/97816080578181130101.[2] M. Toulemonde, J. Dural, G. Nouet, P. Mary, J.F. Hamet, M.F. Beaufort, J.C. Desoyer, C. Blanchard, J. Auleytner, High Energy Heavy Ion Irradiation of Silicon, physica status solidi (a) 114 (1989) 467–473, https://doi.org/10.1002/ pssa.2211140205.[3] P. Mary, P. Bogdanski, M. Toulemonde, R. Spohr, J. Vetter, Deep-level transient spectroscopy studies of U-irradiated silicon, Nucl. Instrum. Methods Phys. Res., Sect. B 62 (1992) 391–393, https://doi.org/10.1016/0168-583X(92)95263-Q.[4] B. Canut, N. Bonardi, S.M.M. Ramos, S. Della-Negra, Latent tracks formation in silicon single crystals irradiated with fullerenes in the electronic regime, Nucl. Instrum. Methods Phys. Res., Sect. B 146 (1998) 296–301, https://doi.org/10.1016/S0168- 583X(98)00512-6.[5] A. Dunlop, G. Jaskierowicz, S. Della-Negra, Latent track formation in silicon irradiated by 30 MeV fullerenes, Nucl. Instrum. Methods Phys. Res., Sect. B 146 (1998) 302–308, https://doi.org/10.1016/S0168-583X(98)00509-6.[6] D. Ben-Hamu, A. Baer, H. Feldman, J. Levin, O. Heber, Z. Amitay, Z. Vager, D. Zajfman, Energy loss of fast clusters through matter, Phys. Rev. A 56 (1997) 4786–4794, https://doi.org/10.1103/PhysRevA.56.4786.[7] S. Bouneau, A. Brunelle, S. Della-Negra, J. Depauw, D. Jacquet, Y. Le Beyec, M. Pautrat, M. Fallavier, J.C. Poizat, H.H. Andersen, Very large gold and silver sputtering yields induced by keV to MeV energy Aun clusters (n = 1–13), Phys. Rev. B 65 (2002) 144106, https://doi.org/10.1103/PhysRevB.65.144106.[8] T. Kaneko, MeV Cluster Ion Beam-Material Interaction, Quantum Beam Sci. 6 (2022) 6, https://doi.org/10.3390/qubs6010006.[9] C. Dufour, M. Toulemonde, Models for the description of track formation, in: W. Wesch, E. Wendler (Eds.) Ion Beam Modification of Solids, Springer, 2016, pp. 63–104, https://doi.org/10.1007/978-3-319-33561-2_2.[10] A. Chettah, H. Kucal, Z.G. Wang, M. Kac, A. Meftah, M. Toulemonde, Behavior of crystalline silicon under huge electronic excitations: a transient thermal spike description, Nucl. Instrum. Methods Phys. Res., Sect. B 267 (2009) 2719–2724, https://doi.org/ 10.1016/j.nimb.2009.05.063.[11] L.T. Chadderton, Nuclear tracks in solids: registration physics and the compound spike, Radiat. Meas. 36 (2003) 13–34, https://doi.org/10.1016/S1350-4487(03)00094- 5.[12] C. Länger, P. Ernst, M. Bender, D. Severin, C. Trautmann, M. Schleberger, M. Dürr, Single-ion induced surface modifications on hydrogen-covered Si(001) surfaces—significant difference between slow highly charged and swift heavy ions, New J. Phys. 23 (2021) 093037, https://doi.org/10.1088/1367-2630/ac254d.[13] H. Amekura, K. Narumi, A. Chiba, Y. Hirano, K. Yamada, S. Yamamoto, N. Ishikawa, N. Okubo, M. Toulemonde, Y. Saitoh, Mechanism of ion track formation in silicon by much lower energy deposition than the formation threshold, Phys. Scr. 98 (2023) 045701, https://doi.org/10.1088/1402-4896/acbbf5.[14] H. Amekura, M. Toulemonde, K. Narumi, R. Li, A. Chiba, Y. Hirano, K. Yamada, S. Yamamoto, N. Ishikawa, N. Okubo, Y. Saitoh, Ion tracks in silicon formed by much lower energy deposition than the track formation threshold, Sci. Rep. 11 (2021) 185, https://doi.org/10.1038/s41598-020-80360-8.[15] H. Amekura, K. Narumi, A. Chiba, Y. Hirano, K. Yamada, S. Yamamoto, Y. Saitoh, An extraordinarily low-energy threshold of less than 60 keV for ion track formation in silicon, Materialia 39 (2025) 102317, https://doi.org/10.1016/j. mtla.2024.102317.[16] J.F. Ziegler, J.P. Biersack, M.D. Ziegler, SRIM - the Stopping and Range of Ions in Matter, SRIM Co., Chester, MD, 2008.[17] A. Meftah, F. Brisard, J.M. Costantini, M. Hage-Ali, J.P. Stoquert, F. Studer, M. Toulemonde, Swift heavy ions in magnetic insulators: a damage-cross-section Fig. 3. Data shown in Fig. 2 were plotted with Se versus R2, where R2 denotes the squared mean track radius. The data following with the eq. (3) are observed on a straight line in the figure. The broken line indicates a linear fitting of the data higher than 500 keV. The solid curve indicates calculated results from the i-TS model by Chettah et al [10]. Reproduced from Ref. [15] by the Creative Commons CC-BY license.H. Amekura et al.                                                                                                                                                                                                                               Nuclear Inst. and Methods in Physics Research, B 579 (2026) 166225 4 http://refhub.elsevier.com/S0168-583X(26)00226-0/h0005http://refhub.elsevier.com/S0168-583X(26)00226-0/h0005https://doi.org/10.1016/0168-583X(92)95263-Qhttps://doi.org/10.1016/S0168-583X(98)00512-6https://doi.org/10.1016/S0168-583X(98)00512-6https://doi.org/10.1016/S0168-583X(98)00509-6https://doi.org/10.1103/PhysRevA.56.4786https://doi.org/10.1103/PhysRevB.65.144106https://doi.org/10.3390/qubs6010006https://doi.org/10.1016/j.nimb.2009.05.063https://doi.org/10.1016/j.nimb.2009.05.063https://doi.org/10.1016/S1350-4487(03)00094-5https://doi.org/10.1016/S1350-4487(03)00094-5https://doi.org/10.1088/1367-2630/ac254dhttps://doi.org/10.1088/1402-4896/acbbf5https://doi.org/10.1038/s41598-020-80360-8https://doi.org/10.1016/j.mtla.2024.102317https://doi.org/10.1016/j.mtla.2024.102317http://refhub.elsevier.com/S0168-583X(26)00226-0/h0080http://refhub.elsevier.com/S0168-583X(26)00226-0/h0080velocity effect, Phys. Rev. B 48 (1993) 920–925, https://doi.org/10.1103/ PhysRevB.48.920.[18] G. Szenes, General features of latent track formation in magnetic insulators irradiated with swift heavy ions, Phys. Rev. B 51 (1995) 8026–8029, https://doi.org/10.1103/ PhysRevB.51.8026.[19] M. Toulemonde, W.J. Weber, G. Li, V. Shutthanandan, P. Kluth, T. Yang, Y. Wang, Y. Zhang, Synergy of nuclear and electronic energy losses in ion-irradiation processes: the case of vitreous silicon dioxide, Phys. Rev. B 83 (2011) 054106, https://doi.org/ 10.1103/PhysRevB.83.054106.[20] A. Kamarou, W. Wesch, E. Wendler, A. Undisz, M. Rettenmayr, Radiation damage formation in InP, InSb, GaAs, GaP, Ge, and Si due to fast ions, Phys. Rev. B 78 (2008) 054111, https://doi.org/10.1103/PhysRevB.78.054111.H. Amekura et al.                                                                                                                                                                                                                               Nuclear Inst. and Methods in Physics Research, B 579 (2026) 166225 5 https://doi.org/10.1103/PhysRevB.48.920https://doi.org/10.1103/PhysRevB.48.920https://doi.org/10.1103/PhysRevB.51.8026https://doi.org/10.1103/PhysRevB.51.8026https://doi.org/10.1103/PhysRevB.83.054106https://doi.org/10.1103/PhysRevB.83.054106https://doi.org/10.1103/PhysRevB.78.054111 A model reasoning low-energy track-formation and enhanced nuclear energy loss in Si irradiated with C60 ions 1 Introduction 2 Experimental 3 The cluster-ion energy loss (CIEL) model 4 Experimental results 5 Discussion 6 Conclusions CRediT authorship contribution statement Declaration of competing interest Acknowledgments Funding References