Incident Angle Dependent Formation of Ion Tracks in Quartz Crystal with C₆₀⁺ Ions: Big Ions in Small Channels

Abstract

Quartz (SiO₂) crystals possess intrinsic columnar pores perpendicular to (0001) surfaces, consisting of three- and six-membered ring (3MR and 6MR) structures of Si and O atoms. The diameters of the larger pores, i.e., 6 MRs, are ~0.49 nm, while the diameters of fullerene (C₆₀) ions are 0.7 nm, i.e., larger than either type of the pores. Transmission electron microscopy observation evidenced approximately two times longer ion tracks in the channeling condition, i.e., 0° incidence to (0001) surface, than an off-channeling condition, i.e., 7° incidence in this case, under 6 MeV C₆₀ ion injection. The track length at the 0° incidence decreases more steeply than that at the 7° incidence with decreasing the energy from 6 MeV to 1 MeV. Finally, the track lengths at the 0° and 7° incidences become comparable, i.e., the channeling-like effect disappears at 1 MeV irradiation. This study experimentally indicates that the channeling-like effect of C₆₀ ions is induced in quartz crystals, while the sizes of the channels are smaller than the C₆₀ ions.

1. Introduction

When an ion is injected into a crystal along some special directions, the ion range is drastically extended compared to the random incidence. This phenomenon is called “ion channeling”, and is utilized for broad applications of ion beams, including analyses [1]. However, the channeling of cluster ions in solids has an intrinsic limitation—as the sizes of the channels are determined from the lattice structures and the geometry between the ion beam and the crystals, and much larger channels than the usual ones are not easily attained, particularly in inorganic solids. On the other hand, the sizes of cluster ions can be more easily enlarged. Consequently, we may encounter situations where the sizes of the projectiles are larger than any of the channels in a solid.

Figure 1a schematically depicts atomic structures of the low temperature phase (trigonal) of quartz crystal (SiO₂), looking from the <0001> direction. As shown in Figure 1a, the (0001) plane of the quartz consists of three-membered rings (3MRs) and six-membered rings (6MRs), which are composed of three pairs and six pairs of Si-O atoms, respectively. While the cross-section of 6MR is not circles but dodecagons, distance between diagonal Si pairs of 0.4916 nm gives an approximate diameter for the 6MR pores. In Figure 1a, a fullerene (C₆₀) ion, with a diameter of 0.7 nm, is also depicted in the same scale as the (0001) plane of quartz. From the geometrical constraints, it looks impossible for a C₆₀ ion to enter the quartz crystal from the <0001> direction without destructing the crystal structures of quartz and/or the C₆₀ molecule itself. In fact, C₆₀ molecules are broken to fragments inside of solids via collisions between constituent atoms in the solid and constituent C atoms in C₆₀ molecules, or via Coulomb repulsions between ionized C atoms in C₆₀ molecules [2].

Figure 1b exhibits the crystal structures of quartz looking from the direction of 7°-tilted from the <0001> direction. While only three atomic layers are depicted, the channels of 3MRs are almost closed. Those of 6MRs are still open by half. However, with additional plots of two or three layers, the 6MR channels are also closed. Therefore, tilting of 7° corresponds to an off-channeling condition.

In this paper, the lengths of ion tracks in quartz crystal formed by the 1–6 MeV C₆₀ ion irradiations were evaluated by transmission electron microscopy (TEM) observations and were compared between two different incident angles of 0° (channeling condition) and 7° (off-channeling condition). There are a huge number of reports on ion irradiation effects in crystalline quartz [4,5,6,7,8,9,10,11,12,13,14,15]. Here, ion track formation in quartz is reported, where the ion tracks are damaged regions of cylindrical shapes induced by irradiations of swift heavy ions (SHI) or cluster ions [16,17]. The ion tracks in crystalline quartz induced with SHI irradiation have been extensively studied [7,11,12,13,14]. In addition, the track formation with C₆₀ cluster ion irradiation has been studied [2,18,19,20,21,22]. Recently, Amekura et al. reported track formation in crystalline quartz [23] and crystalline silicon [24] using several MeV C₆₀ ion irradiation. As each of single C₆₀ ion deposited a huge energy along its trajectory, the observation of ion tracks by TEM corresponds to the observation of the trajectory of each single C₆₀ ion. However, the tracks are not recorded when the C₆₀ energy decreases below the threshold or when the C₆₀ ion is fragmented into much smaller parts.

The conventional channeling of monomer ions is well described by the continuum model proposed by Lindhard [25]. In the case of the monomer ions, there is enough space to change the trajectories freely in the channels. Interacting with the atomic rows around the channel, the ion traverses almost the center of the channel, where core electrons from the surrounding atom rows cannot reach. Furthermore, nuclear collisions between the channeling ions and the surrounding atoms seldom occur. However, in the case of C₆₀ ions, the 6 MR channel is fully occupied by many simultaneously injected C atoms. This situation is much different from the channeling of the monomer ions. Because of the geometrical restriction of the many simultaneously injected C atoms, certain C atoms may stay in the center of the channel where the interaction is rather weak, but the other many C atoms are pushed close to the surrounding atomic rows. The latter atoms are suffered by strong interactions not only with the core electrons, but by the nuclear collisions with atomic rows around the channels. Furthermore, as the 6MR channel is smaller than the C₆₀ ion, a certain portion of C atoms from a C₆₀ molecule cannot enter the same 6MR channel and inject into neighboring 6MRs and/or 3MRs. in addition, these atoms may be suffered by nuclear collisions. Therefore, the present phenomenon, i.e., the transport of C₆₀ ions, which strongly depends on the incident angle of the C₆₀ ions, is not exactly the same as the channeling of the monomer ions. Here, we call the present phenomenon the channeling-like effect.

2. Materials and Methods

Samples of 3 mm × 4 mm × 0.5 mm were mechanically cut from commercially available z-cut quartz (SiO₂) single crystals. The faces of 3 mm × 4 mm, which are parallel to the (0001) plane, were irradiated with C₆₀⁺ ions with an incident angle of 0° or 7° from the surface normal. The irradiation of C₆₀⁺ ions was conducted at the Takasaki Advanced Radiation Research Institute (TARRI) of the National Institutes for Quantum Science and Technology (QST) using a 3 MV tandem accelerator with proper charge-exchanger gas [26] and a newly developed high-flux C₆₀ negative ion source [27]. The samples were irradiated at one of the energies of 1, 2, 3, 4 and 6 MeV, to a fluence between 5 × 10¹⁰ and 5 × 10¹¹ C₆₀/cm². For precise control of the low fluences, the ion flux was reduced to a-few-tens of pA through mesh-type attenuators and an aperture of 3 mm in diameter, while using the high-flux ion source.

After irradiation, a thin Pt layer was deposited on the irradiated surface of the sample as a surface marker for cross-sectional TEM observation. Then, the samples were thinned down to a thickness of ~100 nm for electron beam transmission by using 30 keV Ga⁺ focused ion beam (FIB) milling. TEM observation was conducted using JEOL JEM-2100 and JEM-2100F microscopes with an operation voltage of 200 kV. The samples were irradiated with five different energies of C₆₀ ions between 1 and 6 MeV at the two different incident angles of 0° and 7°, i.e., at nine different conditions. An image of only one TEM sample with 4 MeV irradiation of 7° incidence has been published in a previous paper [23].

3. Experimental Results

Figure 2 shows bright field cross-sectional TEM images of quartz crystals irradiated with 6 MeV C₆₀ ions, with an incident angle of (a) 0° and (b) 7° from the surface normal. The black thin layer in each image is a Pt layer deposited for the surface marker. Many thin cylindrical structures are observed in Figure 2b at the bulk side of the Pt layer, which are ion tracks. We have already reported in [23] the ion track formation in crystalline quarts under 4 MeV C₆₀ ion irradiation with an incident angle of 7°. In addition, the hillock formation has been reported in [23]. While we showed a TEM image irradiated with 4 MeV C₆₀ ions of 7° incidence in the previous paper, here, similar hillocks were observed in the image irradiated with 6 MeV C₆₀ ions of 7° incidence, as shown in Figure 2b. The incident angle dependence has never been reported anywhere before.

A thick layer at the vacuum side of the Pt layer is a deposited carbon layer for supporting against the FIB milling. At the normal incidence (a), a surface damage zone which does not show any tracks inside is observed between the bottom side of the Pt layer and the track layer where many tracks are observed. While many crystalline TEM samples change the image contrast with small tilting, the surface damage zones do not change the contrast. Therefore, we consider that the zone is amorphous or highly damaged. At the 7° incidence (b), the surface damage zone was not observed, or it was very thin if it even existed. However, this is not a common feature. In some cases, thicker surface damage zones were observed even at the 7° incidence.

In Figure 2b, many black dots are observed at the vacuum side of the Pt layer. Judging from the contrast of the image, the dots themselves are made of Pt. Maybe hillocks were formed on the surface of the quartz sample by C₆₀ irradiation, and they were covered by deposited Pt with mostly maintaining their shapes. As the Pt layer was thicker by accident in the 0° incidence sample (a), fine information of the irradiated surface could be washed out. While the image in Figure 2b was irradiated with 6 MeV C₆₀ ions, a similar image was also reported under 4 MeV C₆₀ irradiation in our previous paper [23].

In order to determine the mean track length, we made the following assumption: The tracks are formed even inside of the surface damage zone, while they are not visible because of the amorphous or strongly damaged nature of the damage zone. Observation of ion tracks by TEM requires crystallinity of the matrix materials. While the tracks are observed in quartz, i.e., a crystalline form of SiO₂ [7,13], they are not possible in amorphous SiO₂ [28]. The disappearance of the ion tracks in quartz crystal with the amorphization is reported in the supplementary material of Ref. [23]. Here, we define the length of the tracks as the distance from the bottom of the Pt layer to the tails of the tracks, including the thickness of the insensitive layer. In this definition, the mean track length of the 0° incidence was 202 ± 30 nm under 6 MeV C₆₀ irradiation, roughly double of the length of the 7° incidence of 124 ± 19 nm. The ion energy dependences of the track length are plotted for the two different incident angles of 0° and 7° in Figure 3a. The results at 4 MeV were qualitatively the same with those at 6 MeV, except for a decrease in the mean track length. The mean length under 4 MeV irradiation decreased to 153 ± 23 nm at the 0° incidence, which was still double of the length at the 7° incidence, i.e., 87 ± 13 nm.

Figure 3a clearly indicates that the track length clearly decreased with changing the incident angle from 0° to 7° at the same energies. This behavior is regarded as the channeling-like effect of C₆₀ ions through the quartz crystal, while the 6MRs and 3MRs of quartz were smaller than the diameters of C₆₀ ions.

With decreasing the energy of the incident C₆₀ ions as shown in Figure 3, the track length of the 0° incidence decreased more steeply than that of the 7° incidence. Consequently, the length difference between the 0° and the 7° incidences decreased with decreasing the C₆₀ energy. At 1 MeV C₆₀ irradiation, the track length of the 0° incidence and that of the 7° incidence become comparable within experimental error.

The energy dependence of the electronic and nuclear stopping powers (S_e and S_n) of C₆₀ ions was estimated from the relation [29,30]:

S_i(E, C₆₀) = N·S_i(E/N, C₁)

(1)

where i = e (electronnic) or i = n (nuclear), and N = 60 is presumed for C₆₀ ions. The stopping powers of the monomer ions S_i(E, C₁) were calculated with SRIM 2013 [31]. With decreasing the C₆₀ energy from 6 MeV to 1 MeV, S_e decreases but S_n increases. S_e was greater than S_n at 2 MeV or higher, where the channeling-like effect was observed. On the contrary, S_e was comparable to S_n at 1 MeV where the track length was comparable between the 0°and 7° incidences.

The assumption of N = 60 in Equation (1) is rigorously valid only when the interaction between each C constituent is negligible. This is not the case for the C₆₀ ion, where 60 C atoms are injected simultaneously to the size of the C₆₀ molecule, i.e., a radius of 0.7 nm. A strong enhancement or reduction was expected. However, the experiments reported that the approximation of N~60 was not so bad. Recently, Kaneko et al. calculated the electronic stopping power of a C₆₀ ion in electron gas, with assuming that the shape and the size of C₆₀ did not change, and derived the value of N. While the value of N weakly depends on the energy, it is approximately reduced as N/60~0.8, i.e., N~50, between 2 MeV and 10 MeV [32]. We instead considered that the calculated factor of 0.8 was very close to unity, indicating that the approximation of N~60 was not so bad.

While the energy dependence of the track length was weaker for the 7° incidence, as shown in Figure 3a, similar weak energy dependence was also observed in crystalline silicon irradiated with 1–6 MeV C₆₀⁺ ions with an incident angle of 7° [24].

4. Discussion

4.1. Surface Damage Zone

Currently, we have no idea about the formation processes of the surface damage zones. First of all, ion fluence of 5 × 10¹¹ C₆₀/cm² was applied to the samples, which is too low to overlap the tracks to form a continuous amorphous layer.

The thickness of the damaged zones ranged from nearly zero to ~50 nm, depending on the sample. Contrarily, the range of C₆₀ ion with energy E after fragmentation could be roughly approximated by the range of monoatomic C ion with energy E/60. Following this approximation, the ranges of 4 MeV and 6 MeV C₆₀ ions were estimated from SRIM 2013 [31] as 280 nm and 400 nm, respectively, both of which were much deeper than the thickness of the damage zones. Therefore, conventional amorphization due to the accumulation of track overlaps was excluded.

Furthermore, even two TEM samples that were prepared under almost the same conditions exhibited quite different thicknesses of the damage zones. It was speculated that the thickness of the damage zone was determined not by the irradiation conditions of C₆₀ ions, but possibly by the fabrication processes or the observation processes of the TEM samples. It should be noted that quartz has a high susceptibility for amorphization. In fact, as reported in the Supplementary Materials in Ref. [23], we observed a crystalline-amorphous transition of quartz during TEM observation. Sample surfaces or deposited metal layers could be seeds for amorphization, particularly under electron or focused ion beam irradiations. The damage zones are always observed at the bottom of the Pt layers, when they do exist.

In addition, prolonged TEM observation could increase the thickness of the damage zones. We also tried observations using a scanning TEM (STEM) JEM-2100F, which irradiated the sample with a much higher electron flux, and we observed a drastic increase in damage zone thickness. Under the conventional bright field observation by JEM-2100, we did not notice changes in the thickness of the damage zone during the observations. However, slow changes cannot be excluded.

4.2. Factors Governing the Track Length

To discuss the ion penetration of C₆₀ ions in solids, the dissociation processes of C₆₀ molecules should be taken into account. When a C₆₀ molecular ion is injected into a solid, the C₆₀ molecule is no longer stable due to two effects [2]. The first one is the repulsive forces between the ionized C constituents, as each C atom forming a C₆₀ molecule is suffered by ionization once the C₆₀ ion is injected into a solid. Because of the repulsive Coulombic force between each C constituent, the C₆₀ molecule expands until it is regarded as 60 independent C ions. The second effect is the nuclear collisions between constituent atoms of the target material and carbon atoms of C₆₀ molecule. This process leads loss of carbon atoms from the C₆₀ molecule, which finally results in the fragmentation of the C₆₀ molecules. For C₆₀ ions of a few tens of MeV or lower, the latter process is reported to be dominant [2]. Because of these two processes, C₆₀ ions tend to break down to smaller fragments or monomers, unless they cease moving before the break down. In fact, the branching of ion tracks of C₆₀ ions is reported, e.g., in YIG crystals [2].

Track formation with C₆₀ ions is also a complicated process. While the diameter of a C₆₀ molecule is 0.7 nm, the track diameter of 4 MeV C₆₀ ions in quartz is ~10 nm [23]. The energy transport from the C₆₀ ion at the center of the track (0.35 nm) to the entire body of the track (~5 nm) is governed via δ-electrons emitted from the C₆₀ ion. The inside of the track is heated up with the δ-electrons and electron cascades of lower energies. The track diameter depends on the electronic energy deposition S_e (and the ion velocity). There is a S_e threshold, below which tracks are no longer formed. The S_e threshold of quartz is known as the velocity dependent, as 2 keV/nm and 4 keV/nm for 0.5 MeV/u and 7 MeV/u, respectively [13]. Because of low velocities of C₆₀ ions (in the order of 0.001 MeV/u), a threshold of 2 keV/nm was adapted for the present study.

The electronic energy loss S_e of the C₆₀ ion was estimated from Equation (1) with the help of SRIM2013. The S_e of 6 MeV C₆₀ was derived as 18.1 keV/nm in quartz, which is much higher than the track formation threshold of 2 keV/nm. Consequently, track formation was expected. However, if a C₆₀ ion with an initial energy of 6 MeV is dissociated into 60 independent carbon monomer ions, each C monomer receives the energy of 100 keV = 6 MeV/60 on average. The S_e of the C monomer ion of 100 keV amounts to 0.30 keV/nm in quartz, which is far below the threshold of 2 keV/nm. Therefore, the track formation by a single C monomer is not expected. To generate a track in quartz, seven or more C atoms (0.30 keV/nm × 7 atoms = 2.1 keV/nm > 2 keV/nm) should form a carbon cluster. An expected, but confusing, behavior is that the fragmented cluster ions, i.e., C_p and C_q (p, q < 60), could additively contribute to track formation, if both the cluster ions traverse while maintaining themselves within a certain distance.

5. Conclusions

Ion energy dependence of the ion track formation in z-cut quartz single crystals (SiO₂) with C₆₀ ions at the energies between 1 and 6 MeV were evaluated by TEM observations at two different incident angles of the channeling condition (0° from the surface normal) and the off-channeling condition (7°). A thin Pt layer was deposited for each sample after C₆₀ ion irradiation as a surface marker. The surface damage zones, which show insensitive contrast with tilting and are probably ascribed to amorphous or strongly damaged regions, were observed between the Pt layer and the track-dominant layer.

We analyzed the data under an assumption where ion tracks were formed, even inside of the damage zones, but the tracks were not visible because of the amorphous or strongly-damaged nature of the zones. Approximately twice longer ion tracks were formed at the 0° incidence than at the 7° incidence under 6 MeV C₆₀⁺ irradiation. This observation indicates that the channeling-like effect is induced in quartz with MeV C₆₀ ions, while the sizes of C₆₀ ions was larger than the pore sizes of the quartz (0001) surface.

With decreasing the energy of the incident C₆₀ ions from 6 MeV to 1 MeV, the track length at the 0° incidence decreased more steeply than that of the 7° incidence. Consequently, the length difference between the 0° and 7° incidences decreased. At 1 MeV irradiation, the track lengths of the 0° incidence and 7° incidence became comparable. Therefore, the channeling-like effect almost disappeared around 1 MeV.