Effects of collision cascade density on radiation defect dynamics in 3C-SiC

Effects of the collision cascade density on radiation damage in SiC remain poorly understood. Here, we study damage buildup and defect interaction dynamics in 3C-SiC bombarded at 100 °C with either continuous or pulsed beams of 500 keV Ne, Ar, Kr, or Xe ions. We find that bombardment with heavier ions, which create denser collision cascades, results in a decrease in the dynamic annealing efficiency and an increase in both the amorphization cross-section constant and the time constant of dynamic annealing. The cascade density behavior of these parameters is non-linear and appears to be uncorrelated. These results demonstrate clearly (and quantitatively) an important role of the collision cascade density in dynamic radiation defect processes in 3C-SiC.

dependence of the Φ amorph on m (for any given T), with the highest Φ amorph for electrons 11 and the lowest for 500 keV Ar ions 15 . This apparent inconsistency could be attributed to differences in F, E, and the method of defect characterization used by different groups [11][12][13][14][15] . Hence, in the present work, we study the m effect in 3C-SiC with all the other irradiation conditions kept constant or otherwise controlled.
Ion m effects on Φ amorph have also been studied for 6H-SiC and 4H-SiC polymorphs 13,[16][17][18][19][20][21] . Although an increase in the damage production efficiency with increasing m has typically been observed in most previous studies of 6H-and 4H-SiC 13,[16][17][18][19] , negligible 20 and inverse 21 (i.e., a reduction in the damage production efficiency for heavier ions) m effects have also been reported. Extrapolation of these results to the case of 3C-SiC is, however, not fully justified, given previous reports of a significant difference in the radiation response of different SiC polymorphs 19,22,23 . At elevated Ts, DA processes are expected to be different in various SiC polymorphs since such processes are controlled by the type and properties of lattice-structure-specific point and extended defects 15 .
Damage buildup studies are traditionally performed by bombardment with continuous (rather than pulsed) ion beams 3 . Such experiments provide limited insight into the dynamics of point defect interaction during irradiation. Our recent work [24][25][26][27][28][29] has demonstrated that defect interaction dynamics can be accessed in experiments with pulsed ion beams when the Φ is delivered as a train of equal square pulses with a duration of t on and an instantaneous dose rate of F on , separated by a passive portion of the beam duty cycle of t off . Such pulsed beam experiments allow us to measure the characteristic DA time constant (τ) and the defect diffusion length (L d ) by studying the dependence of stable lattice disorder on t off and t on , respectively [24][25][26][27][28][29] . We have recently measured a τ of ~3 ms and a L d of ~10 nm for 3C-SiC bombarded at 100 °C with pulsed beams of 500 keV Ar ions 28,29 .
Here, we study both the damage buildup behavior and defect interaction dynamics in 3C-SiC bombarded at 100 °C with different m ions (from 20 Ne to 129 Xe) with a fixed E of 500 keV (see Table 1). We focus on the effects of the collision cascade density on radiation dynamics at a fixed T. We have chosen 100 °C since this is an irradiation regime with pronounced DA 15 . It is also relevant for elevated-temperature implantation of SiC-based devices and for SiC performance in a nuclear reactor environment 1,2 . In this E range (0-500 keV), for all four ion species, the electronic energy loss is weakly and non-monotonically dependent on m, while the nuclear energy loss experiences a dramatic increase with increasing m 30 . Our results reveal that the amorphization cross-section constant (ξ amorph ) and τ increase and the DA efficiency (ξ DA ) decreases with increasing m. Ion m (and, hence, ρ cascade ) dependencies of different parameters are, however, non-linear and appear to be uncorrelated. This clearly demonstrates that the ρ cascade non-trivially influences not only the efficiency of damage accumulation but also defect interaction dynamics in SiC.

Results and Discussion
Damage buildup. Insight into the physics of radiation damage formation could often be gained by analyzing the damage buildup behavior: the dependence of the amount of stable post-irradiation lattice disorder on Φ . Hence, before embarking on pulsed beam experiments, we first measured the damage buildup under continuous beam irradiation (i.e., t off = 0 ms). Figure 1(a) shows normalized depth profiles of lattice vacancies ballistically generated in SiC by 500 keV Ne, Ar, Kr, or Xe ions, calculated with the TRIM code 30 . All four profiles show expected unimodal Gaussian-like shapes, with peaks at depths that we refer to as R pd s, indicated by vertical dashed lines in Fig. 1(a) (at 540, 300, 155, and 100 nm). Such R pd s decrease with increasing m, which is also expected from ion ballistics 30 .
Representative experimental depth profiles of relative disorder for bombardment with continuous ion beams for these four different ion species and selected Φ s are plotted in Fig. 1(b). A comparison of Fig. 1(a) and (b) shows that, for all four ion species, shapes of profiles of stable lattice disorder and ballistically generated vacancies closely resemble each other. The maximum bulk damage is observed at depths close to the corresponding R pd s. The difference is in relatively small surface peaks in Fig. 1(b), reflecting surface disordering and the expected surface scattering of the probing He ions in ion channeling experiments. For all four ion species, bulk damage peaks (with heights of n) are centered at depths close to their respective R pd values in Fig. 1(b). These observations are in agreement with results of our recent systematic study 15 of the T-dependence of damage buildup in 3C-SiC under 500 keV Ar ion bombardment. Figure 2 summarizes bulk damage buildup curves [i.e., n(Φ ) dependencies] for bombardment with continuous beams of the four ion species. All the damage buildup curves of Fig. 2 are sigmoidal, suggesting nucleation-limited (i.e., stimulated) defect accumulation. Shown in Fig. 2 Table 1. Irradiation conditions of this study: the instantaneous dose rate (F on ), the total ion dose (Φ), and the displacement generation rate (R gen ). Irradiation was performed at 100 °C with an ion energy of 500 keV for all ion masses. Also given are experimental values of the DA time constant (τ), the amorphization cross-section constant (ξ amorph ), and the DA efficiency (ξ DA ).
Scientific RepoRts | 7:44703 | DOI: 10.1038/srep44703 buildup curves with a phenomenological stimulated amorphization model from ref. 15. Within this model, the total damage level is given by the following expressions: Here, f amorph is the fraction of atoms in the amorphous phase, f cluster is the atomic fraction of stable point defect clusters, σ cluster is the cluster production cross-section, f cluster the maximum saturation fraction of defect clusters in the lattice, h(x) is the Heaviside step function [h(x) = 0 for x < 0 and h(x) = 1 for x ≥ 0], Φ crit is the critical dose above which amorphization proceeds, and ξ amorph is the amorphization cross-section constant. Figure 2 shows that such a stimulated amorphization model provides an excellent fit for all the cases. Ion m (and, hence, ρ cascade ) dependencies of the fitting parameters (σ cluster , ξ amorph , and Φ crit ) and the Φ amorph (taken as the Φ corresponding to n = 0.95) are shown in Fig. 3(a) and (b). It is seen that, within fitting errors, σ cluster and Φ crit are independent of m, while ξ amorph exhibits a monotonic increase with increasing m. A fast increase in ξ amorph occurs on increasing m from Ne to Ar, followed by a saturation stage (or a minor growth within error bars) with further increasing m from Ar to Xe. For example, for Φ s resulting in 0.4 DPA, the bulk damage level differs by ~1.2 times after Ne and Ar ions bombardment, while the corresponding difference in n between cases of Ar and Xe ions is only ~8%.
The difference in damage buildup revealed by Figs 2, 3(a) and (b) could be related not only to different ρ cascade s created by different ion species but also to different R gen s. Indeed, the four damage buildup curves shown by solid symbols in Fig. 2 were measured with a constant F of 1.9 × 10 13 cm −2 s −1 . Since heavier ions create more atomic displacements per ion at their R pds , they also result in larger R gen s when a constant F is maintained for different m. For example, irradiation with Xe ions results in an ~5 times larger R gen than for the case of Ar ion bombardment with the same F (see Table 1).
Hence, in order to differentiate between ρ cascade and R gen effects (i.e., between intra-cascade and inter-cascade phenomena, related to the average dose rate), we have measured damage buildup curves for Ar and Xe ion bombardment with lower Fs of 8.4 × 10 12 and 4 × 10 12 cm −2 s −1 , respectively. Such lower F Xe ion bombardment results in the same R gen (at R pd ) as that for Ar ions with a F of 1.9 × 10 13 cm −2 s −1 , while lower F Ar ion bombardment was done in order to match the R gen for Ne ion bombardment (see the R gen column of Table 1). Results are shown in Fig. 2 by open symbols, demonstrating a negligible dose-rate effect for both Ar and Xe ion bombardment for the F range studied.
We further clarify that the difference in damage buildup between Ne and the heavier ions is not related to a lower R gen of Ne ions. For Ne ion bombardment, a very large F of ~1.8 × 10 14 cm −2 s −1 would be required in order to match the R gen (at R pd ) of Xe ions with a F of 1.9 × 10 13 cm −2 s −1 (see Table 1). Such large current beams are beyond our experimental capabilities. Instead, we have measured the n(F) dependence for Ne ions, as shown in Fig. 4. It is seen that n sub-linearly increases with F and saturates for F ≳ 1.5 × 10 13 cm −2 s −1 . This suggests a negligible contribution of the effect of the average dose rate to a pronounced difference in ξ amorph between Ne and heavier ions. The difference observed in the damage buildup of Ne and heavier ions is, therefore, attributed to ρ cascade phenomena. This conclusion is further supported by open symbols in Fig. 3(a) showing the ρ cascade dependence of ξ amorph for the case of F → 0 obtained by the analysis of pulsed beam data measured with a t off ≫ τ, as discussed below.
It is interesting to compare ρ cascade effects revealed by Figs 2, 3(a) and (b) for 3C-SiC with those in other non-metallic materials. Previous experiments for different materials have revealed that the efficiency of the formation of stable damage generally increases with increasing m 6,8-10,13,16-19,31,32 . However, even the qualitative behavior is non-trivial and depends strongly on the material and irradiation conditions such as Φ , F, and T. For example, for Si at room T, an increase in the ρ cascade leads to a gradual increase in the damage formation efficiency 10 . For GaN at room T, there is a threshold-like increase in damage with increasing m, suggesting an important role of energy spikes 6,9 . For ZnO, the bulk disorder is essentially independent of the ρ cascade , while the evolution of near-surface damage exhibits strong and complex ρ cascade effects 31,32 . As already mentioned, an increase in the damage production efficiency with increasing m has also been observed in most previous studies of 6H and 4H polymorphs of SiC 13,16-19 , although we are not aware of any previous systematic studies of the m effect in 6H-and 3C-SiC at room T and above when DA processes are pronounced. The physical mechanisms behind such differences between ρ cascade effects in different materials are currently not well understood and deserve further systematic studies.
Defect interaction dynamics. Based on the above damage buildup data (Fig. 2), we have chosen Φ s for pulsed beam experiments so that, for t off = 0 (i.e., continuous beam irradiation), n is in the range of 0.6-0.8, which is in a nonlinear regime of damage buildup with pronounced DA 15 . We have measured n(t off ) dependencies for all four ion species in order to obtain τ values. Figure 1(c) shows two sets of representative depth profiles of relative disorder in 3C-SiC bombarded with Ne or Xe ions with three different t off values (given in the legend) and all the other parameters kept constant. It is seen that, for both Ne and Xe cases, n decreases with increasing t off , while the damage level at the sample surface remains unchanged, suggesting different dynamic mechanisms of bulk and surface disordering. This behavior is qualitatively similar to that previously reported in pulsed-beam studies of Si bombarded at room T with 500 keV Ne, Ar, Kr, or Xe ions, of 3C-SiC irradiated at 100 °C with 500 keV Ar ions, and of 4H-SiC bombarded with 500 keV Ar ions in the T range of 25-250 °C [26][27][28] .
We have found such a reduction in n with increasing t off for 3C-SiC for all four ion species (Fig. 5). Solid lines in Fig. 5 are fits of the data via the Marquardt-Levenberg algorithm 33 with the second order decay equation  Here, n ∞ is relative disorder for t off ≫ τ. All the n(t off ) dependencies from Fig. 5 obey the second order decay better than the first order (i.e., exponential) decay. The effect of m (and, hence, ρ cascade ) on τ is summarized in Fig. 3(c), revealing a monotonic increase in τ with increasing m. Such an increase in τ with increasing m is consistent with our recent finding for Si at room T 26 . Slower defect relaxation dynamics for irradiation with heavier ions could suggest that heavier ions result in the formation of lattice defects that act as efficient traps for migrating point defects, slowing down the defect relaxation dynamics. Alternatively, an increase in τ with increasing m could reflect a possible dependence of τ on the the instantaneous concentration of mobile (rather than stable) defects at the end of each pulse 26 . Future systematic studies of τ(t on ) dependencies should shed light on the physics behind the ρ cascade dependence of τ revealed here.
Also plotted in Fig. 3(c) is the m dependence of the DA efficiency (ξ DA ): ξ = − ∞ DA n n n (0) . As discussed in detail previously 26 , for our choice of pulsing parameters, ξ DA is the magnitude of the dose-rate effect; i.e., the difference between n for continuous beam irradiation with dose rates of F = F on and F → 0. Figure 3(c) shows that, with increasing m, ξ DA gradually decreases from ~46 to ~29%.
The above results clearly demonstrate the complexity of DA processes in 3C-SiC, revealing non-linear and uncorrelated ρ cascade dependencies of the ξ amorph and defect dynamics parameters (τ and ξ DA ). A comparison of data from Figs 2, 3(a) and (c) also reveals another unexpected result: a strong ρ cascade dependence of the dose-rate effect measured in pulsed beam experiments [ξ DA in Fig. 3(c)] and minor dose-rate (i.e., R gen ) effects studied   [Figs 2 and 3(a)]. This observation suggests that n(F) dependencies for different m ion have shapes similar to that for the case of 500 keV Ne ion bombardment shown in Fig. 4, with a pronounced saturation effect for large F values. With such non-linear n(F) dependencies, the difference between the magnitudes of the dose-rate effect measured by the pulsed beam method and traditional dose-rate dependent damage buildup is related to the difference in the range of F values over which these measurements are done. In the pulsed beam method, measurements extend to F → 0, where the dose-rate effect (i.e., the slope of the n(F) dependence) is maximum. These observations warrant future systematic dose-rate studies in 3C-SiC.
In summary, we have studied the damage buildup and defect interaction dynamics in 3C-SiC bombarded at 100 °C with 500 keV Ne, Ar, Kr, or Xe ions. We have found that, with increasing ρ cascade by increasing ion m from Ne to Xe, the ξ DA (i.e., the magnitude of the dose-rate effect) gradually decreases, accompanied by an increase in the τ from 3.1 to 5.2 ms. At the same time, the ξ amorph increase significantly only on changing ion m from 20 Ne to 40 Ar, with a weak m dependence with a further increase in ion m. These results clearly demonstrate that radiation defect dynamics in 3C-SiC is complex and strongly depends on the collision cascade density. These observations have important implications for the development of predictive modeling capabilities to describe radiation damage processes in SiC.

Methods
Depth profiles and three-dimensional distributions of ballistically-generated lattice vacancies were calculated with the TRIM code (version SRIM-2013.00, full cascade calculations) 30 with an atomic concentration of SiC of 9.64 × 10 22 atoms cm −3 (ref. 2) and threshold energies for atomic displacements of 20 and 35 eV for C and Si sublattices, respectively 34 . To convert to displacements per atom (DPA) at the R pd , Φ s in 10 14 cm −2 are multiplied by 0.036, 0.085, 0.193, and 0.342 for Ne, Ar, Kr, and Xe ions, respectively.
Cascade densities (ρ cascade s) at R pd s were calculated based on the algorithm similar to that proposed by Heinisch and Singh 5 . We define the ρ cascade as the average local density of lattice vacancies within individual cascades with an averaging radius of 10 nm. Such an averaging radius was chosen to be comparable with our recent estimates of the L d in 3C-SiC 29 . Values of ρ cascade were obtained by averaging over ≳ 600 individual cascades.
We used single-crystal epilayers of (001) 3C-SiC (on Si wafers with a diameter of 100 mm) obtained from NOVASiC. The epilayers had a thickness of ≳ 2 μm and a resistivity of 1-10 Ω cm. The crystal quality of as-received films was verified by measuring a minimum 2 MeV 4 He ion channeling yield of ~1.5%, consistent across the wafer. A transmission electron microscopy study of as-received SiC films was reported in ref. 15.
The 4 MV ion accelerator (National Electrostatics Corporation, model 4UH) at Lawrence Livermore National Laboratory was used for both ion irradiation and ion beam analysis. The ion irradiation conditions used in this study are summarized in Table 1. Ion bombardment was done with 500 keV 20 Ne + , 40 Ar + , 84 Kr + , or 129 Xe + ions at ~7° off the [100] direction to minimize channeling effects. All irradiations were performed in the broad beam (rather than raster) mode 24 . To improve thermal contact, the samples were attached to the Cu sample holder with conductive Ag paste. The target T was kept at 100 ± 1 °C. Irradiated areas were ~4 × 5 mm 2 . Total Φ s were in the range of 0.1-0.9 DPA. Ion beam pulsing was achieved by applying high voltage pulses to a pair of parallel plates to deflect the ion beam off the target so that the total Φ was split into a train of equal square pulses with a dose per pulse of Φ pulse = F on t on . The adjacent pulses were separated by time t off .
In such pulsed beam experiments, it is important to maintain a constant F on throughout the experiment and have good control of both Φ and T. In our experiments, all the data points in each n(t off ) curve were measured in the same experimental run to avoid possible slight variations in dosimetry or wafer T between different runs. Control of the dosimetry and T is crucial since we are dealing with a steep portion of the damage buildup curve (Fig. 2) and an exponential T dependence of the damage formation efficiency 15 .
Depth profiles of lattice disorder in the Si sublattice were measured ex-situ at room T with 2 MeV 4 He ions incident along the [001] direction and backscattered into a detector at 164° relative to the incident beam direction. Spectra were analyzed with one of the conventional algorithms 35 for extracting the effective number of scattering centers (referred to below as "relative disorder"). Values of averaged bulk disorder (n, with n = 1 corresponding to full amorphization) were obtained by averaging depth profiles of relative disorder over 10 channels (~25 nm) centered on the bulk damage peak maximum (i.e., R pd ). Error bars of n are standard deviations. For each ion m, τ was measured by studying the dependence of n on t off , which was varied between 1 and 50 ms, with a constant F on of (1.9 ± 0.1) × 10 13 cm −2 s −1 and a t on of 1 ms.