# Fileset

[ps_98_4_045701.pdf](https://mdr.nims.go.jp/filesets/40cfc6ef-6ffc-4414-a11d-ca56ec21c5e0/download)

## Creator

[H Amekura](https://orcid.org/0000-0003-2148-8431), K Narumi, A Chiba, Y Hirano, K Yamada, S Yamamoto, N Ishikawa, N Okubo, M Toulemonde, Y Saitoh

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Mechanism of ion track formation in silicon by much lower energy deposition than the formation threshold](https://mdr.nims.go.jp/datasets/66d773c7-db45-49f0-9c27-a7c7c85c9cb3)

## Fulltext

Mechanism of ion track formation in silicon by much lower energy deposition than the formation thresholdPhys. Scr. 98 (2023) 045701 https://doi.org/10.1088/1402-4896/acbbf5PAPERMechanism of ion track formation in silicon bymuch lower energydeposition than the formation thresholdHAmekura1,∗ , KNarumi2, AChiba2, YHirano2, KYamada2, S Yamamoto2 , N Ishikawa3 , NOkubo3,MToulemonde4 andY Saitoh21 National Institute forMaterials Science (NIMS), Tsukuba, Ibaraki 305-0003, Japan2 National Institutes forQuantumScience andTechnology (QST), Takasaki, Gunma 370-1292, Japan3 JapanAtomic EnergyAgency (JAEA), Tokai, Ibaraki 319-1195, Japan4 Centre de Recherche sur les Ions, les Matériaux et la Photonique, CIMAP-GANIL, Normandie University CEA, CNRS, Caen, 14000,France∗ Author towhomany correspondence should be addressed.E-mail: amekura.hiroshi@nims.go.jpKeywords:C60 ion, ion track, swift heavy ion, silicon, synergy effect, track recrystallizationAbstractMechanismof the ion track formation in crystalline silicon (c-Si) is discussed, particularly under 1–9MeVC60 ion irradiation. In this energy region, the track formationwas not expected because theenergyEwasmuch lower than the threshold ofEth= 17MeVdetermined by extrapolation fromhigher energy data in the past literature. The track formation is different between irradiations of C60ions and ofmonoatomic ions: The tracks were observed under 3MeVC60 ion irradiation but notunder 200MeVXe ions, while both the irradiations have the same electronic stopping (Se) of 14 keVnm−1 butmuch higher nuclear stopping (Sn) for the former ions. The involvement of Sn is suggestedfor the C60 ions.While the inelastic thermal spike (i-TS) calculations predict that the high energymonoatomic ion irradiation forms the tracks, the tracks have never been experimentally detected,suggesting quick annihilation of the tracks by highly enhanced recrystallization in c-Si. Exceptions areC60 ions of 1–9MeV,where the track radii arewell reproduced by the i-TS theorywith assuming themelting transition. Collisional damage induced by the high Sn fromC60 ions obstructs therecrystallization in c-Si. Then the tracks formed by themelting transition survive against therecrystallization. This is a new type of the synergy effect between Se and Sn, different from the already-knownmechanisms, i.e., the pre-damage effect and the unified thermal spike.While c-Si was believedas a radiation-hardmaterial in the Se regimewith high Se threshold, this study suggests that c-Si has alow Se threshold but with efficient recrystallization.1. IntroductionWhen a high energy heavy ion in the electronic stopping regime, i.e., swift heavy ion (SHI) [1–3], is injected intosome solids, a damaged region of cylindrical shapewith high aspect ratio is formed along the nearly straighttrajectory of the ion, which is called a latent ion track [4, 5]. The track formation is governed by the electronicenergy deposition processes. In fact, the diameters of the tracks increase with increasing the electronic energydeposition (Se). However, the diameters exhibit threshold behaviors at low Se, belowwhich the tracks are nolonger formed. The threshold value Se,th strongly depends onmaterial species [6]. Limited but relativelymanymaterials show the ion tracks [7].According to the inelastic thermal spike (i-TS)model [8], the tracks are considered as regions transientlymolten or vaporized by energy deposited fromSHIs. The threshold is ascribed to the energy required for themelting or vaporization transition, i.e., the sumof latent heats and integrated heat capacities. However, it isrecently pointed out that the track diameters are determined fromnot only the diameters of themolten/vaporized regions but also the recrystallization processes [9]. Furthermore, it is also pointed out that the trackOPEN ACCESSRECEIVED13October 2022REVISED27 January 2023ACCEPTED FOR PUBLICATION14 February 2023PUBLISHED6March 2023Original content from thisworkmay be used underthe terms of the CreativeCommonsAttribution 4.0licence.Any further distribution ofthis workmustmaintainattribution to theauthor(s) and the title ofthework, journal citationandDOI.© 2023TheAuthor(s). Published by IOPPublishing Ltdhttps://doi.org/10.1088/1402-4896/acbbf5https://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0003-0407-0033https://orcid.org/0000-0003-0407-0033https://orcid.org/0000-0002-2217-3645https://orcid.org/0000-0002-2217-3645mailto:amekura.hiroshi@nims.go.jphttps://crossmark.crossref.org/dialog/?doi=10.1088/1402-4896/acbbf5&domain=pdf&date_stamp=2023-03-06https://crossmark.crossref.org/dialog/?doi=10.1088/1402-4896/acbbf5&domain=pdf&date_stamp=2023-03-06http://creativecommons.org/licenses/by/4.0http://creativecommons.org/licenses/by/4.0http://creativecommons.org/licenses/by/4.0formations by the synergy effects between Se and the nuclear energy deposition (Sn) are observed in somematerials [3, 10–12], while the track formation ismostly governed by Se,Crystalline silicon (c-Si) is one of themost importantmaterials in today’s technology. Thismaterial is knownas a radiation-hardmaterial in the electronic stopping regime: Any swift heavymonoatomic ions do not form iontracks in c-Si, whatever high energy the ions have [13–15]. Toulemonde et al [13] studied the ionfluencedependence of the electric resistivity of c-Si under irradiationswith various Se between 3.7 keV nm−1 and 14 keVnm−1 and concluded that defect formation by electronic excitation is inefficient in c-Si.Mary et al evaluated c-Siirradiatedwith 3.5GeVXe (Se= 8.8 keV nm−1) [14] and 3.6GeVU ions (23.7 keVnm−1) [15] by the deep-leveltransient spectroscopy (DLTS), and concluded that the irradiations introduced point defects only, whoseconcentrationwas explained by the nuclear collisions only. Neither the track formation nor the point defectformation via the Se process was observed. It should be noted that the 3.6GeVU ions [15], whichMary et alutilized, was close to the Bragg peak, i.e., the highest Se value in c-Si attainable by SHIs.However, it was still lowerthan the Se threshold of the track formation in c-Si of∼30 keVnm−1 [16].Despite these observations, some scientists reported the track formations in c-Si withmonoatomic SHIs,whichwere later regarded as uncertain. Furuno et al [17] formed Sifilms of 5 nm thickwith the very small grainsizes of typically 1 nmby evaporation, irradiated themwith 207MeVAu ions (Se= 17 keVnm−1), and observeddiscontinuous tracks by TEM.Dunlop et al [18] criticized the observations since the Sifilmswith the grain sizesof 1 nm showmuch differentmaterial properties from the bulk crystalline Si. Therefore, thework by Furunoet al evidences the track formation in Si nano-aggregates, but not in bulk crystalline Si. Furthermore, Itoh et alregarded in their paper that Furuno et al observed the track formation in amorphous Si, whichwas inducedwithlower Se threshold than crystalline Si [6].Srivastava et al irradiated c-Si wafers with 100MeVAu ions (Se= 12 keVnm−1). They observed the surfacecraters byAFM [19] but not ion tracks directly, while the craters can be formed by the tracks. Because of thelimited spatial resolution of AFM, the observed surface structures were typically∼150 nmwide, while the trackdiameter of c-Si should be 10 nmwide or less. Since the evidence by Srivastava et al is indirect and ambiguous, itis not possible to conclude the track formation in c-Si.The track formation in c-Si was succeeded in utilizing fullerene (C60) ions, since aC60 ion providesmuchhigher energy deposition than the heaviestmonoatomic ions ofU. Since all the sixty C atoms are injected intoc-Si at the same time at almost the same position, i.e., within the diameter of C60molecule of 0.7 nm, roughlysixty times greater energy is deposited than the carbonmonoatomic ion does. To calculate the electronic andnuclear stopping power Si (i= e or n) of C60 ions at the energy E, i.e., Si (E, C60), a following relationshipwasassumed [20],( ) ( ) ( ) ( )/= =S E C S E C i e or n, 60 60, 1i i60 1where Si (E, C1) denotes the Si value of Cmonoatomic ions at the energy E, which is calculated fromSRIM2013code [21].In the late 1990s, Canut et al [22] andDunlop et al [18] simultaneously succeeded in producing ion tracks inc-Si using 30 and 40MeVC60 ions from theOrsay facility in France.With decreasing the energy from40MeV,30MeV, and to 20MeV [16], the trackmean diameter decreased from10.5 nm, 8.4 nm, and to 6.0 nm. (For faircomparison, the Se and Sn values of theOrsay irradiationswere recalculated by SRIM2013 [21] from the ionenergy and equation (1), since the stopping powers depend on the version of SRIM code). The relationshipbetween the squared track radii and the electronic stopping power Se of C60 ions is plotted infigure 1. Straightlines infigure 1 indicate following relation:( ) ( )= -R C S S 2e e th2,whereR,C, and Se,th denote the track radius, a proportional coefficient, and the Se threshold, respectively. Therelation (2) has been justified in other semiconductors of Ge, GaAs, and InP irradiatedwithC60 cluster ions [23].From theOrsay data (open circles), the Se threshold of∼30 keVnm−1, i.e., theC60 energy of 17MeV, isextrapolated as shown infigure 1. Consequently, no track formation could be expectedwithC60 irradiations at17MeV and lower.However, as shown by closed symbols infigure 1, we have observed track formation underC60 irradiation at 1–6MeV [24], which ismuch lower energy than the threshold of 17MeV extrapolated fromtheOrsay data [16, 18, 22] . It should be noted again that the tracks were observed in c-Si even under 1MeVC60irradiation, while the track sizes decrease with the energy [24]. Following three observations also should benoted: (i) themean track radius at 6MeV (∼5 nm) is larger than that at 20MeV (∼3 nm), while the latter hashigher energy than the former. (ii)The tracks formed by the irradiations atE� 6MeV also follow the relation(2), while the threshold Se,th ismuch lower as 4.2 keV nm−1 [24]. (iii)As clearly shown infigure 1, the Sedependence of the track radii formed inOrsay and that in Takasaki do not overlapwith each other. If both thedata fromTakasaki and fromOrsay fall on the same curve, the trackmean radii should decrease between 6MeVand 20MeV. It was one of themotivations for the additional irradiation at 9MeV.2Phys. Scr. 98 (2023) 045701 HAmekura et alIn this paper, themechanism of this phenomenon, i.e., the track formation in c-Si withC60 ion irradiation ofmuch lower energies of 1–9MeV than the previously extrapolated threshold of 17MeV, is discussed based onthe data shown in the previous paper [24] and newdata shown in this paper.2. ExperimentalSamples of single crystalline siliconwere cut from commercially available Si wafers of p-type conduction(boron-doped) grown by theCzochralskimethod, with resistivity of∼1Ω cm, surface orientation of<1 1 1>,and thickness of∼0.38mm.The samples weremechanically cut into 3mm× 4mm rectangles, which arehereafter called bulk samples. The bulk sampleswere immersed in hydrofluoric acid to remove surface oxides.The trackswere observed by transmission electronmicroscopy (TEM). Two different configurations of TEMsamples (pre-thinned and post-thinned)were prepared from the bulk samples. The pre-thinned samples werethinned down froma bulk samplewith 30 keVGa focused ion beam (FIB)milling to a thickness of∼100 nm,whichwere held onTEMgrids. Then the pre-thinned samples on the TEMgrids were irradiated byC60 ionswithan incident angle of 7° from the surface normal, to evaluate the diameters of the tracks. In the case of the post-thinned samples, bulk samples were irradiated byC60 ionswith the incident angle of 7° from the surface normalof the 3mm× 4mm face, and the cross-sectional samples were thinned down to a thickness of∼100 nmby FIBto observe the depth profiles of the ion tracks. See [24] for details. To identify the surface position of the post-thinned samples, a thin layer of Pt was deposited on the sample surface before the FIBmilling.Irradiation of C60 ionswas conducted at the Takasaki AdvancedRadiation Research Institute (TARRI), oftheNational Institutes forQuantumScience andTechnology (QST), using a 3MV tandem accelerator and anewly developed high-fluxC60 negative ion source [25]. C60 ionswith charge state of+1 (C60+ )were utilized for1–6MeV irradiations, while thosewith+2 (C602+)were utilized for 9MeV irradiation.While themagneticmassseparation of ionswas applied, it does notmatter for singly charged ions.However, it is difficult for the doublychargedC60 ions to exclude themixture of fragmented ionswith the samem/q, i.e., 4.5MeVC30+ ions and 9MeVC C602+ ions.However, evaluation of the beamwith a semiconductor detector confirmed that the signal from4.5MeVC30+ ionswas almost negligible compared to 9MeVC602+ ions.The samples weremostly irradiated to lowfluences of 5× 1010–1× 1011 C60 cm−2 to avoid overlaps betweenthe tracks. For precise control of the lowfluence, the ion fluxwas reduced to below 50 pA throughmesh-typeattenuators and an aperture of 3mm in diameter, while using the high-flux ion source [25]. The incident anglewas set to 7° from the surface normal to avoid channeling effects. In fact, the channeling of C60 ionswereobserved in quartz (SiO2) crystal, while the sizes of the crystal channels were smaller than those of C60 ions [26].For comparison, some samples were irradiatedwith 200MeVXe14+ ions from the tandemaccelerator in theJapanAtomic energy Agency (JAEA), Tokai Research andDevelopment Center.Figure 1.The electronic stopping power Se dependence of squared track radiiR2 formed byC60 ion irradiations. Open and closedcircles indicate the data observed inOrsay (E= 20–40MeV) [16, 22] andTakasaki (E� 6MeV) [24], respectively. For reference, theC60 ion energy and the track radiusR are indicated in the top and right axes, respectively. Solid lines indicate relationsfitted by theequation (2). Reproduced from [24]CCBY4.0.3Phys. Scr. 98 (2023) 045701 HAmekura et alhttps://creativecommons.org/licenses/by/4.0/TEMobservation of the two different configurations (the pre- and the post-thinned)was conducted using aJEM-2100microscope (JEOL)with an operation voltage of 200 kV. According to past literature, the tracks in c-Siwere recrystallizedwith prolonged TEMobservation [18]. Careful observations were performed tominimize theelectron beam current and observation time.3. ResultsTEM images of c-Si irradiatedwith 9MeVC602+ ions are exhibited infigure 2, where (a)–(c) and (d)(e) showirradiated pre-thinned and post-thinned samples, respectively. The observation angle offigure 2(a)was 0° fromthe surface normal but those offigures 2(b) and (c)were 30°. Figure 2(a) clearly exhibitsmany black dots, whichare ascribed to the cross-sections of the tracks. The number density of the black dotswas 4× 1010 cm−2, which iscomparble to the ionfluence of 5× 1010 cm−2, confirming that the observed dots are ion tracks. Themost of thetracks exhibit elliptical shapes, rather than true circles, with themajor axes pointing the same direction. Thiscould be due to the irradiationwith an incident angle of 7° from the surface normal.With increasing theobservation angle (i.e., tilting), the track images are divided into twoparts; i.e. white circles and black rods, asFigure 2.Bright field TEM images of ion tracks in c-Si formed by 9MeVC602+ ion irradiations to the pre-thinned samples (a)-(c) andthe post-thinned samples (d)(e). The observation anglewas 0° for (a)(d)(e) and 30° for (b)(c) from the surface normal. Black thicklayers in (d)(e) are deposited Pt layers for surfacemarker. In (b) and (c), the entrances and themain bodies of the tracks are visible aswhite circles and black rods, respectively. Lessmodified regions, i.e., gaps, are observed between the entrances and themain bodies asshown in (b)(c) but not in (d)(e).4Phys. Scr. 98 (2023) 045701 HAmekura et alshown infigures 2(b) and (c). They are observed as pairs in themost cases and are ascribed to the entrances andthemain bodies of the tracks, respectively. Similar images were reported in YIG crystals irradiatedwith 40.2MeVC603+ ions [27].An interesting observationwas that lessmodified region, i.e., a gap, existed between thewhite entrance andthe black body. The same gapswere reported in YIG irradiatedwith 40.2MeVC603+ ions [27], but not clear forc-Si irradiatedwith 30MeVC602+ ions [18]. These gaps were observed inmany tracks, and themeanwidthwasroughly∼8 nm in the plane of the figure. Since the observation angle was 30°, themean gap along the tracks was∼8 nm sin−1(30°)=∼16 nm. Figure 2(d) and (e) exhibit depth profiles of the tracks observed in the post-thinned samples. The gapswere not clearly observed infigure 2(d) and (e). This discrepancy has not beenclarified yet. Possibly the gaps are due to the diffraction contrast, since the entrances and the bodies appear inwhite and black, respectively.Themean track diameter under the 9MeV irradiationwas determined as 11.9± 1.7 nm,which is larger thanthat under 6MeV irradiation. A decrease in the track radiuswith the ion energy, as expected infigure 1, was notobserved.4.Discussion4.1. Involvement of SnFigure 3 compares TEM images of c-Si irradiatedwith (a) 3MeVC60+ ions and (b) 200MeVXe14+ ions. Both theions have the same Se of 14 keV nm−1 butmuch different Sn of 3.7 keVnm−1 and 0.05 keV nm−1 for 3MeVC60ion and 200MeVXe ion, respectively. The Se of 14 keV nm−1 ismuch lower than the track formation thresholdof∼30 keVnm−1 [16]. Even at the same value of Se of 14 keVnm-1, which ismuch lower than the thresholdreported in past literature [16], the tracks were observed under 3MeVC60 irradiation but not under 200MeVXeirradiation. This observation clearly indicates that there is another factor to control the formation of the iontracks except Se. Possible factors are the nuclear energy deposition Sn and the ion velocity. However, as shown insub-section 4-3, the effect of the ion velocity is calculated by the i-TSmodel. It turns out that the difference in theion velocity cannot explain the appearance/disappearance of the tracks.Figure 4 shows Se, Sn, andwhether the tracks are formed or not, for six different ion species and energies atwhich the experiments were carried out. Track ‘Yes’ and ‘No’ infigure 4 denote the appearance anddisappearance of the tracks, respectively. It is obvious fromfigure 4 that Se is not a good indicator to decidewhther the tracks are formed or not.While 3.6GeVU ions have relatively high Se, they do not form any tracks.Contrarty, 1MeVC60 ions form ion tracks, although they havemuch lower Se than 3.6GeVU and even 200MeVXe ions. Rather Sn could be a better indicator: If we set a threshold value of Sn for track formation at, e.g., 0.5 keVnm−1, all the experimental results in these six cases are explainedwithout any exceptions. This factmay indicatethat small but certain amount of Sn (>0.5 keV nm−1) is a pre-requisite for the track formation in c-Si. Furtherdiscussionwhether Sn is a better indicator or not is given in the next sub-section.4.2. Closer involvement of SeAs shown infigure 4, the Sn looks a good indicator whether the tracks are formed or not.However, the observedion tracks (see figures 2(b)–(e)) show cylindrical shapes, not the nearly spherical shapes like collision cascades.This observation supports that the track formation is still governed by the Se related processes. In fact, figure 5Figure 3.Bright field TEM images of pre-thinned c-Si samples irradiatedwith (a) 3MeVC60+ and (b) 200MeVXe14+ ions. (b)wasreproducedwith permission from [24]CCBY4.0. The fluencewas 5× 1010 ions cm−2 for both the cases. Tracks are observed in (a)but not in (b). Both the irradiations have the same Se, but different Sn.5Phys. Scr. 98 (2023) 045701 HAmekura et alhttps://creativecommons.org/licenses/by/4.0/shows the energy dependences of Se and Sn in c-Si irradiatedwithC60 ions, whichwere calculated byequation (1), in addition to the dependence of themean track diameter. In the energy region between 1 and 10MeV,wheremost of our experiments were conducted, Sn decrease but Se increases with the ion energy. Themean track diameter also increases with the energy. As shown infigure 4, certain amounts of Sn is indispensableto the track formation.However,figure 5 shows that an increase of Sn (with decreasing E) results in the decreaseof the track diameter. Rather the track diameter increases similarly with Se.We consider that the track formation itself is governed by the Se-related processes as similar as theconventional SHI irradiations. However, a certain amounts of Sn is required to activate track formationprocesses or to protect tracks against the track-annihiration processes such as recrystallization.4.3. Explanation from the Inelastic Thermal SpikeModelHowdoes the i-TSmodel explain the quite high threshold (∼30 keVnm−1) of the track formation in c-Si ?Chettah et al calculated the radii of themolten tracks and of the vaporized tracks in c-Si induced by the i-TSFigure 4.Values of Se and Sn, andwhether tracks are formed or not, are plotted for six different ion species and energies. The values ofthemonoatomic ionswere calculated fromSRIM2013 [21] and those of theC60 ionswere done from the equation (1) and SRIM2013.Track ‘Yes’ and ‘No’ in thefigure denote the appearance and the disappearance of the tracks, respectively.Figure 5. Ion energy dependences of electronic and nuclear energy deposition Se and Sn in c-Si with C60 ions, whichwere calculatedwith equation (1) and SRIM2013 [21]. The dependence of the track diameter is indicated by circles with error bars.6Phys. Scr. 98 (2023) 045701 HAmekura et aleffects for various Se values [28], and compared themwith those of the ion tracks observed under 20–40MeVC60irradiations. As shown infigure 6, themelting curves were plotted for two different velocities of 0.07MeV/u and5MeV/u, and the vaporization curves for 0.04MeV/u and 5MeV/u. In these calculations, the velocity effect istaken into account. From the calculations, the threshold value for themelting transitionwas estimated to 3.5keVnm−1 and 5.7 keV nm−1 for the velocities of 0.07MeV/u and 5MeV/u, respectively. Those of thevaporization transitionwas estimated to 25 keVnm−1 and 48 keVnm−1 for the velocities of 0.04MeV/u and 5MeV/u, respectively.Most of the swift heavymonoatomic ion (SHMI) irradiations have carried out at the Se values lower than 24keVnm−1, as indicated by closed triangles infigure 6. This is because Se of∼24 keVnm−1 was attained underirradiation ofGeVU ionswhich are the heaviest (quasi) stable ions. They are close to the Braggmaximumof Se,i.e., the highest available Se value in c-Si.Meanwhile, the experiments indicated that no ion tracks are formed inc-Si with any SHMI irradiations at Se∼24 keVnm−1 or lower as indicated by the triangles infigure 6.However,the i-TS calculations indicate that themelting region is formed even at the Se values higher than∼4 keVnm−1 forthe veolocity of 0.07MeV/u. This discrepancy between the experiments and the i-TS calculations can be solvedif we assume the annihilation of the tracks. In fact, Chadderton proposed perfect expitaxial recrystallization ofthemolten tracks in c-Si [29], since efficient recrystallizationwas also observed in c-Si under low energy ionirradiation [29]. In thismodel, themolten tracks are formed in c-Si by SHMIs. After the formation of themoltenregions by the SHMI irradiation, themolten regions recover by the perfect epitaxial recrystallization in c-Si.Therefore, when c-Si is irradiatedwith SHMIs, themolten regions are transiently formed but they are perfectlyrecrystallizedwith cooling. Ion tracks are no longer observed after then.However, the ion track formation has been already reported in c-Si withC60 irradiations inOrsay[16, 18, 22]. In this case, high energies of 20, 30, and 40MeVwere applied. As indicated by closed circles infigure 6, the relationship between the track radius and Sematchedwith the radii of the vaporized regions, ratherthan those of themolten regions. It indicates that the tracks observed in c-Si are formed via the vaporization, butnot themelting. Evenwith the highly efficient recrystallization in c-Si, the perfect recovery of the vaporizedregions are difficult. Consequently, the ion tracks were observed under high energy C60 irradiation performed atOrsay (20–40MeV).What happens underC60 irradiations in the energy regions between 1 and 9MeV ? The data of the track radiiversus Se in the energy of 1–9MeV are plotted by open circles infigure 6. Surprisingly these data points well fallon the curve of the radii of themolten regions. Therefore, the track formation under 1–9MeVC60 irradiationcan be ascribed to themolten transition in c-Si by the i-TS effects. Up to now, no data except ours fall on the radiiof themolten regions because of the highly efficient recrystallization.We consider that the certain amount of Snobstructs the efficient recrystallization in c-Si, while details have not been clarified.Using Rutherfordbackscattering spectrometry (RBS), Shen et al studied damage in c-Si irradiatedwithC60 ions of 100–530 keV, inwhich Sn of C60 ion reaches amaximum [30]. They observed that the damagewas strongly enhanced by theFigure 6.Electronic stopping power dependence of the radii of themelting regions and of the vaporized regions calculated by theinelastic thermal spike (i-TS)model [28]. Themean radii of the tracks formed inOrsay and those in this study are indicated by closedand open circles, respectively. Closed triangles indicate the results ofmonoatomic swift heavy ion (SHI) irradiations [13–15, 24]including 3.5GeVXe, 3.6GeVU, and 200MeVXe ions, neither of whichwas successful in forming tracks.7Phys. Scr. 98 (2023) 045701 HAmekura et alcluster effect: comparingwith a carbonmonomer ion of the same velocity (8.8 keV), C60 ion of 530 keVgenerated 7700 timesmore displacements and reduced the displacement energy [30], indicating the formationof the spikes. Such nuclear disorder could obstruct the recrystallization and enhace the survival ratio of the tracksin c-Si. According to our 9MeVC60 irradiation to c-Si, the track areal density (4× 1010 tracks cm−2)wascomparable to the ionfluence (5× 1010 ions cm−2) , indicating the track survival ratio of almost unity.Asmentined in sub-section 4-1, 200MeVXe irradiation does not form the tracks in c-Si but 3MeVC60irradiation does, while both the irradiations have the same Se. The second governing factor could be Sn or the ionvelocity. In fact, the velocity effect on the track sizes was calculated and shown infigure 6 for themeltingtransition at 5MeV/u and 0.07MeV. The difference between the curves at 5MeV/u and 0.07MeV/u is rathersmall and difficult to explain the apparence/disappearance of the tracks.While the tracks are formed in both the energy regions of 1–9MeV and 20–40MeV, the properties of thetracks in the two regions can be different with each other. Asmentionedwithfigure 1, the Se dependence of thetrack radii formed inOrsay and that in Takasaki do not overlapwith each other. This difference could beascribed to the different properties of the track formation in 1–9MeV and 20–40MeV. Recently, Länger et al[31] reported negative evidence on the recrystallization of the tracks in c-Si under 1.14GeVU ion irradiation. Atthemoment, we have no idea tomerge it with ourmodel.4.4. Categorization of the synergy effects for track fromationFollowing the discussion up to the previous sub-section, we have come to a conclusion that the track formationin c-Si under 1–9MeVC60 ion irradiation requires both Se and Sn for generatingmolten regions and reducingthe recrstallization of the tracks, respectively. Therefore, the tracks in the present case are formed by a synergyeffect between Se and Sn. Up to now, various synergy effects between Se and Sn have been reported [3, 10–12]:Herewe discuss the syergy effect influencing the track formation only, with help of the i-TS theory.We don'tdiscuss the recovery of point defects by Se [10].The i-TSmodel is described by coupled heat diffusion equations for the electronic and the atomicsubsystems as shown in equations (3a) and (3b), whereCi,Ki,Ti , andAi (i= e, a) denote the specific heat,thermal conductivity, temperature, and source term in the electronic (i= e) and atomic (i= a) subsystems,respectively. These two equations are bound by the electron-lattice couplingG. The point defect density plays animportant role, which is assumed tomostly depend on Sn and thefluenceΦ, as shown in equation (3c).( ) ( ( ) ) ( )( ) ( ) ( )¶¶=  ⋅  - - +C nTtK n T G n T T A S a3e dee d e d e a e e( ) ( ( ) ) ( )( ) ( ) ( )¶¶=  ⋅  + - +C nTtK n T G n T T A S b3a daa d a d e a n n( ( ) ) ( )= Fn n S S c, , 3d d n e( ( ) ( ( ))) ( )=R R T r F S S d, , 3tr tr a recryst n eSince the point defect density nd is reduced [10] or enhanced under high Se, the density nd also depends on Se.However, this effect is not considered here. All the quantitiesCi (nd),Ki (nd), (i= e, a) andG (nd) are assumed todepend on nd.While it is not described explicitly in literature, themean track radiusRtr is a function of the spatialdistribution of the atomic temperatureTa(r), as shown in equation (3d).Because themean track radiusRtr is reduced under efficient recrystallization, it is also the function of therecrystallization efficency Frecryst. Since the purpose of the equations is to show conceptial categorization of thedifferent sources of the synergy effects, themathematical completeness of these eqations is not discussed here.Three types of the synergy effects are known as shown in table 1: thefirst type of the synergy effect is knownas the pre-damage effect. It is known that previously introduced nuclear collisional damage enhances the i-TSeffect, which results in formation of larger tracks than thosewithout the pre-damage [11]. This effect is explainedfrom equations (3a–3d), sinceKe,Ka andG are the function of nd. The increase in nd turns to the decrease in thethermal conductivitiesKa and probablyKe. Consequently the deposited energy from the ion is confined insmaller region, which results in highermaximum temperature thanwithout the pre-damage. Also the increasein nd turns to the increase in the couplingG, which results inmore efficient energy transfer from the electronic tothe atomic subsystembefore the energy diffusion in the electronic subsystem.However, this type of the effectscannot explain the present phenomenon, since our targetmaterial Si was a single crystal before theC60irradiation. Also thefluencewas so low that overlaps of the tracks were negliglble. Therefore the ‘pre-damage’does not exist in the present case. The ‘pre-damage’mechanism is excluded. (However, if the i-TS heating by oneion is enhancedwith the nuclear damage by the same ion, i.e., in situ-damage, the conclusionmay change.)The second type is the collateral heating of Se and Sn, i.e., the unified thermal spike (u-TS)model: in theconventional i-TSmodel for SHIs, the energy from the ionwas deposited to the electronic subsystemonly,because the source term for the atomic subsystem,An(Sn) in equation (3b), was excluded. The second synergyeffect, i.e., the u-TS, is inducedwith the inclusion of the nuclear source termAn(Sn).8Phys. Scr. 98 (2023) 045701 HAmekura et alTable 1.Threemechanisms of the synergy effects between Se and Sn for ion track formation.Name of the synergy effectParameters playingroles Mechanism Inconsistency with the present phenomenon ReferencesPre-damage effect Ka,Ke andG Damage introduced in the sample before the ion irradiation reduces the thermalconductivityKa, which results in localization of heat near the track. Damagealso enhances the electron-phonon couplingG. Both increase the latticetemperature of tracks comparedwith the non-damaged case.Because of the lowfluence, overlaps of tracks are negligible. Therefore,the pre-damage does not exist.[11, 23]Unified thermal spike(u-TS)An(Sn) In the i-TSmodel, only the electronic subsystem is heated by ions viaAe(Se). Theatomic subsystem is indirectly heated via the couplingG. In the u-TS, theatomic subsystem is also directly heated viaAn(Sn).The nuclear heating effectAn increases with Sn. As shown infigure 5, thetrack radii, however, increase with decreasing Sn. The observed energydependence cannot be explained by the present effect.[3]Recrystalization of tracks Frecryst In Si, once-formed-tracks are easily annihilated by recrystalization. Because ofhigh Sn,C60 ion irradiation introduces high concentration of defects, whichobstruct the recrystallization. Therefore, certain portion of the tracks are sur-vived and are observed.No inconsistency. This work9Phys.Scr.98(2023)045701HAmekuraetalThe nuclear heating effectAn increases with Sn.However, the observed dependence on the track radii wasopposed to the expectation. As shown infigure 5, Sn decreases with increasing the ion energy and the track radiiincrease with decreasing Sn. In fact, while we have carried out preliminary calculations with the unified thermalspikemodel [3], the energy dependence of the track radii as shown infigure 5was not reproduced.In the third type, themean track radius is determined fromnot only the spatial profile of the atomictemperature but also the efficiency of the recrystallization Frecryst. The efficiency Frecryst is a function of Sn andprobably of Se.While the details of thismodel have not been clarified yet, thismodel explains, at themoment, thepresent phenomenon better than others.While c-Si was believed as a radiation-hardmaterial in the Se regimewith high Se threshold, this study suggests that c-Si has a low Se threshold butwith efficient recrystallization.5. ConclusionsIt is known that nomonoatomic SHIs can form ion tracks in c-Si. ExceptionswereC60 cluster ion irradiation of20–40MeV, either ofwhich providesmuchhigher electronic energydeposition than anymonoatomic SHIs. Sincethemean trackdiameter decreasedwith decreasing the ion energy from40 to 20MeV, itwas expected fromanextrapolation that no tracks couldbeen formedbelow the thresholdofSe,th∼30 keVnm−1 (Eth∼ 17MeV).Nevertheless, wehave observed that the tracks are formedunder 1–9MeVC60 ion irradiations, all ofwhich aremuch lower than the extrapolated threshold of∼17MeV. In this paper, some attemptsweremade tounderstandthis phenomenon.Track formationwas comparedbetween irradiations of 200MeVXe ions and 3MeVC60irradiation, both ofwhichhave the same electronic stopping Se of 14 keVnm−1 butmuchdifferent nuclearstopping Sn of 0.05 keVnm−1 and3.7 keVnm−1, respectively. Trackswere only observed under 3MeVC60irradiation,which indicates the involvement of Sn for the track formation, i.e., the synergy effect. The resultswerecomparedwith the i-TS calculations,which have clarified that the velocity effect does not playmajor roles.According to the i-TS calculations, the track formation under 20–40MeVC60 irradiation is ascribed to thevaporization in c-Si, while the track formation via themelting transition,which is accessible bymonoatomic SHIirradiation, has never been observed probably due to thequick recovery of the tracks by efficient recrystallization inc-Si. Collisional damagedue to a certain amount of Sn under 1–9MeVC60 irradiationdisturbs the recrystallizationof c-Si, which results in the survival of the tracks formedby themelting transitions. Since thismechanism isdifferent from the knownsynergy effects of the pre-damage effect and theu-TS, this can be a new type of thesynergy effect between Se and Sn for track formation.While c-Si was believed as a radiation-hardmaterial in the Seregimewith highSe threshold, this study suggests that c-Si has a low Se thresholdbutwith efficient recrystallization.AcknowledgmentsApart of the studywas supported by the Inter-organizational Atomic EnergyResearchProgram through anacademic collaborative agreement among JAEA,QST, andUniv. of Tokyo. The authors are grateful to the crewofthe accelerator facilities atQST-Takasaki and at JAEA-Tokai for their help.HAwas supported by JSPS-KAKENHIGrant number 22K04990.TEMobservationwas performedusing the facility of theNIMSTEMstation.Data availability statementThe data that support thefindings of this study are available upon reasonable request from the authors.Authors contributionsAC, YH,KY,KN, andY S have developed theMeVhigh-fluxC60 ion beam.HAprepared samples. Y S, AC,YH, S Y andKNconducted C60 ion irradiation.N I andNOconducted 200MeVXe irradiation.HA conductedTEMobservation.MT supplied information on the past literature and valuable suggestions. All the authorsjoined in discussion of the results and contributed tomanuscript preparation.Additional informationNo supplementary information is attached.10Phys. Scr. 98 (2023) 045701 HAmekura et alCompeting interestsThe authors declare no competing interests.ORCID iDsHAmekura https://orcid.org/0000-0003-2148-8431SYamamoto https://orcid.org/0000-0003-0407-0033N Ishikawa https://orcid.org/0000-0002-2217-3645References[1] AvasthiDK andMehtaGK2011 Swift Heavy Ions forMaterials Engineering andNanostructuring (Berlin, Heidelberg, NewYork:Springer)[2] AmekuraH,Chen F and Jia Y 2020 Ion Irradiation of Dielectrics for Photonic Applications (Singapore: SpringerNature)Chap. 5[3] ToulemondeM,WeberW J, Li G, ShutthanandanV, Kluth P, YangT,WangY andZhang Y 2011 Synergy of nuclear and electronicenergy losses in ion-irradiation processes: the case of vitreous silicon dioxide Phys. Rev. B 83 054106[4] YoungDA1958 Etching of radiation damage in lithium fluorideNature 182 375[5] Silk ECHandBarnes R S 1959 Examination offission fragment trackswith an electronmicroscope Philos.Mag. 4 970[6] ItohN,DuffyDM,Khakshouri S and StonehamAM2009Making tracks: electronic excitation roles in forming swift heavy ion tracksJ. Phys. Condens.Matter 21 474205[7] WeschWandWendler E (ed) 2016 Ion BeamModification of Solids - Ion-Solid Interaction and RadiationDamage (Basel, Switzerland:Springer International Publishing) 61[8] DufourC andToulemondeM2016 Ion BeamModification of Solids edWWesch and EWendler (Basel, Switzerland: SpringerInternational Publishing) 63[9] RymzhanovRA,MedvedevN,O’Connell J H, Janse vanVuurenA, SkuratovVA andVolkov AE 2019Recrystallization as thegoverningmechanismof ion track formation Sci. Rep. 9 3837[10] Zinkle S J, SkuratovVA andHoelzerDT2002On the conflicting roles of ionizing radiation in ceramicsNucl. Instrum.Methods Phys.Res., Sect. B 191 758[11] WeberW J, Zarkadoula E, PakarinenOH, SachanR, ChisholmMF, Liu P, XueH, Jin K andZhang Y 2015 Synergy of elastic andinelastic energy loss on ion track formation in SrTiO3 Sci. Rep. 5 7726[12] Thomé L,Debelle A,Garrido F, Trocellier P, Serruys Y, VelisaG andMiro S 2013Combined effects of nuclear and electronic energylosses in solids irradiatedwith a dual-ion beamAppl. Phys. Lett. 102 141906[13] ToulemondeM,Dural J, NouetG,Mary P,Hamet J F, BeaufortMF,Desoyer J C, BlanchardC andAuleytner J 1989High energy heavyion irradiation of siliconPhysica Status Solidi (a) 114 467[14] Mary P, Bogdanski P,NouetG andToulemondeM1989Defects created by 3.5GeV xenon ions in siliconAppl. Surf. Sci. 43 102[15] Mary P, Bogdanski P, ToulemondeM, Spohr R andVetter J 1992Deep-level transient spectroscopy studies ofU-irradiated siliconNucl.Instrum.Methods Phys. Res., Sect. B 62 391[16] Colder A, Canut B, LevaloisM,Marie P, Portier X andRamos SMM2002 Latent track formation inGaAs irradiatedwith 20, 30, and 40MeV fullerenes J. Appl. Phys. 91 5853[17] Furuno S,OtsuH,HojouK and Izui K 1996Tracks of high energy heavy ions in solidsNucl. Instrum.Methods Phys. Res., Sect. B 107 223[18] DunlopA, JaskierowiczG andDella-Negra S 1998 Latent track formation in silicon irradiated by 30MeV fullerenesNucl. Instrum.Methods Phys. Res., Sect. B 146 302[19] Srivastava PC,GanesanV and SinhaOP 2002AFM study of swift gold ion irradiated siliconNucl. Instrum.Methods Phys. Res., Sect. B187 220[20] Bouneau S, Brunelle A, Della-Negra S, Depauw J, JacquetD, Le Beyec Y, PautratM, FallavierM, Poizat J C andAndersenHH2002Verylarge gold and silver sputtering yields induced by keV toMeV energy Aun clusters (n= 1–13)Phys. Rev. B 65 144106[21] Ziegler J F, Biersack J P andZieglerMD2008 SRIM -The Stopping andRange of Ions inMatter (Chester,MD,USA: SRIMCo.)[22] Canut B, Bonardi N, Ramos SMMandDella-Negra S 1998 Latent tracks formation in silicon single crystals irradiatedwith fullerenesin the electronic regimeNucl. Instrum.Methods Phys. Res., Sect. B 146 296[23] KamarouA,WeschW,Wendler E,Undisz A andRettenmayrM2008Radiation damage formation in InP, InSb, GaAs, GaP, Ge, and Sidue to fast ions Phys. Rev. B 78 054111[24] AmekuraH et al 2021 Ion tracks in silicon formed bymuch lower energy deposition than the track formation threshold Sci. Rep. 11 185[25] ChibaA,Usui A,HiranoY, YamadaK,NarumiK and Saitoh Y 2020Novel approaches for intensifying negative C60 ion beams usingconventional ion sources installed on a tandem acceleratorQuantumBeamScience 4 13[26] AmekuraH,NarumiK, Chiba A,HiranoY, YamadaK, Yamamoto S and Saitoh Y 2022 Incident angle dependent formation of iontracks in quartz crystal withC60+ ions: big ions in small channelsQuantumBeam Science 6 4[27] DunlopA, JaskierowiczG, Jensen J andDella-Negra S 1997Track separation due to dissociation ofMeVC60 inside a solidNucl.Instrum.Methods Phys. Res., Sect. B 132 93[28] ChettahA, KucalH,Wang ZG,KacM,MeftahA andToulemondeM2009Behavior of crystalline silicon under huge electronicexcitations: a transient thermal spike descriptionNucl. Instrum.Methods Phys. Res., Sect. B 267 2719[29] Chadderton LT 2003Nuclear tracks in solids: registration physics and the compound spikeRadiat.Meas. 36 13[30] ShenH, BrinkC,Hvelplund P, Shiryaev S, Shi P andDavies J A 1997 Fullerene ion (C60+ ) damage in Si at 25 °CNucl. Instrum.MethodsPhys. Res., Sect. B 129 203[31] LängerC, Ernst P, BenderM, SeverinD, TrautmannC, SchlebergerM andDürrM2021 Single-ion induced surfacemodifications onhydrogen-covered Si(001) surfaces—significant difference between slowhighly charged and swift heavy ionsNew J. Phys. 23 09303711Phys. Scr. 98 (2023) 045701 HAmekura et alhttps://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0003-2148-8431https://orcid.org/0000-0003-0407-0033https://orcid.org/0000-0003-0407-0033https://orcid.org/0000-0003-0407-0033https://orcid.org/0000-0003-0407-0033https://orcid.org/0000-0002-2217-3645https://orcid.org/0000-0002-2217-3645https://orcid.org/0000-0002-2217-3645https://orcid.org/0000-0002-2217-3645https://doi.org/10.1103/PhysRevB.83.054106https://doi.org/10.1038/182375a0https://doi.org/10.1080/14786435908238273https://doi.org/10.1088/0953-8984/21/47/474205https://doi.org/10.1038/s41598-019-40239-9https://doi.org/10.1016/S0168-583X(02)00648-1https://doi.org/10.1038/srep07726https://doi.org/10.1063/1.4801518https://doi.org/10.1002/pssa.2211140205https://doi.org/10.1016/0169-4332(89)90197-9https://doi.org/10.1016/0168-583X(92)95263-Qhttps://doi.org/10.1063/1.1467962https://doi.org/10.1016/0168-583X(95)00813-6https://doi.org/10.1016/S0168-583X(98)00509-6https://doi.org/10.1016/S0168-583X(01)00931-4https://doi.org/10.1103/PhysRevB.65.144106https://doi.org/10.1016/S0168-583X(98)00512-6https://doi.org/10.1103/PhysRevB.78.054111https://doi.org/10.1038/s41598-020-80360-8https://doi.org/10.3390/qubs4010013https://doi.org/10.3390/qubs6010004https://doi.org/10.1016/S0168-583X(97)00390-Xhttps://doi.org/10.1016/j.nimb.2009.05.063https://doi.org/10.1016/S1350-4487(03)00094-5https://doi.org/10.1016/S0168-583X(97)00286-3https://doi.org/10.1088/1367-2630/ac254d 1. Introduction 2. Experimental 3. Results 4. Discussion 4.1. Involvement of Sn 4.2. Closer involvement of Se 4.3. Explanation from the Inelastic Thermal Spike Model 4.4. Categorization of the synergy effects for track fromation 5. Conclusions Acknowledgments Data availability statement Authors contributions Additional information Competing interests References