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

Abstract

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.

Introduction

The understanding of radiation damage phenomena in SiC is desirable for the development of radiation tolerant SiC-based nuclear ceramics and for the control of lattice disorder associated with ion-beam processing of electronic devices^1,2. Despite decades of research, however, our understanding of radiation damage processes in SiC remains limited, particularly in regimes with pronounced dynamic annealing (DA). Such DA refers to the migration and interaction of point defects (during irradiation) after the thermalization of ballistically generated collision cascades for time scales ≳1 ps³. (See, for example, a review by Kinchin, G. W. and Pease, R. S. The displacement of atoms in solids by radiation. Rep. Prog. Phys. 18, 1–51 (1955)).

Damage buildup under pronounced DA is strongly influenced by irradiation conditions³. For a fixed ion dose (Φ), the type and concentration of radiation-produced stable lattice defects depend on sample temperature (T) during irradiation, the dose rate (F), ion mass (m), and energy (E). Here, we focus on the influence of the displacement generation rate (R_gen) that is controlled by m and F. The F determines the average frequency of ion impacts onto any given area on the sample surface and, hence, the depth-dependent average rate of the ballistic generation of atomic displacements.

The R_gen depends not only on F but also on m. Generally, m determines the following three aspects of ballistic displacement generation: (i) the shape of the displacement generation depth profile, (ii) the partition between the energy deposited by ions in electronic and nuclear energy loss processes, and (iii) the effective volumetric density of displacements in collision cascades. For relatively low E ions used in the present work (with an electronic energy loss ≲1 keV nm⁻¹), electronic excitation effects (although poorly understood and requiring further studies) are typically negligible for metals and predominantly covalent ceramics such as SiC^3,4. In this case, the m effect is related to the difference in the density of collision (sub)cascades (ρ_cascade) generated by different ion species. Lighter ions create relatively dilute cascades characterized by large average distances between adjacent displacements within cascades. Heavier ions create denser cascades. Several algorithms have been developed to calculate average (sub)cascade densities^5,6,7. For most materials, experiments have revealed an increase in the efficiency of the formation of stable lattice disorder with increasing m^6,7,8 (See, for example, a review by Davies, J. A. In: Ion Implantation and Beam Processing, edited by Williams, J. S. and Poate, J. M. (Academic, New York, 1984)). This has generally been attributed to either nonlinear energy spike phenomena or more efficient intra-cascade defect clustering^6,7,8,9,10.

Here, we focus on the R_gen effects on damage buildup and DA in 3C-SiC, which is the cubic polymorph of SiC (also often referred to as β-SiC). The importance of m in damage buildup in 3C-SiC could be inferred from the analysis of previous measurements of the T dependence of the amorphization dose (Φ_amorph)^{11,12,13,14,15}. The existing Φ_amorph(T) data for 3C-SiC for 2 MeV electrons¹¹ and 1.5 MeV Xe¹², 360 keV Ar¹³, 1 MeV Kr¹⁴, and 500 keV Ar ions¹⁵ was recently summarized in ref. 15. Its analysis, however, reveals an almost random pattern of the dependence of the Φ_amorph on m (for any given T), with the highest Φ_amorph for electrons¹¹ and the lowest for 500 keV Ar ions¹⁵. 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}, negligible²⁰ and inverse²¹ (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 defects¹⁵.

Damage buildup studies are traditionally performed by bombardment with continuous (rather than pulsed) ion beams³. 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 ²⁰Ne to ¹²⁹Xe) 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 DA¹⁵. 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 m³⁰. 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.

Table 1

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 code³⁰. All four profiles show expected unimodal Gaussian-like shapes, with peaks at depths that we refer to as R_pds, indicated by vertical dashed lines in Fig. 1(a) (at 540, 300, 155, and 100 nm). Such R_pds decrease with increasing m, which is also expected from ion ballistics³⁰.

Figure 1

(a) Normalized depth profiles of the concentration of lattice vacancies ballistically generated in SiC by irradiation with 500 keV Ne, Ar, Kr, or Xe ions. Positions of the vacancy distribution maxima are indicated by vertical dashed lines. (b) Selected depth profiles of relative disorder in 3C-SiC irradiated at 100 °C with continuous beams of Ne, Ar, Kr, or Xe ions with a F of 1.9 × 10¹³ cm⁻² s⁻¹ to Φs of 0.4, 0.31, 0.33, and 0.32 DPA, respectively. The profile for Ar ions is taken from ref. 15. (c) Selected depth profiles of relative disorder in 3C-SiC bombarded with pulsed Ne (open symbols) or Xe (closed symbols) ion beams to Φs of 0.4 and 0.32 DPA, respectively, with different values of t_off (indicated in the legend in ms), t_on = 1 ms, and F_on = 1.9 × 10¹³ cm⁻² s⁻¹. For clarity, only every 5th experimental point is depicted in (b) and (c).

Representative experimental depth profiles of relative disorder for bombardment with continuous ion beams for these four different ion species and selected Φs 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_pds. 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 study¹⁵ 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 by dashed lines are results of the fitting of the damage buildup curves with a phenomenological stimulated amorphization model from ref. 15. Within this model, the total damage level is given by the following expressions:

Figure 2

Dose dependencies of relative disorder at the maximum of the bulk defect peak for 3C-SiC bombarded at 100 °C with continuous beams of 500 keV Ne, Ar, Kr, or Xe ions (closed symbols) with a F of 1.9 × 10¹³ cm⁻² s⁻¹ and (open symbols) with lower Fs of 4 × 10¹² cm⁻² s⁻¹ for Xe ions and 8.4 × 10¹² cm⁻² s⁻¹ for Ar ions. Dashed lines are results of fitting with a stimulated amorphization model from ref. 15.

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, (with %, based on results from ref. 15) is 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 Φs 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%.

Figure 3

Cascade density (ρ_cascade) dependencies of (a) the cross-section for the formation of point defect clusters (σ_cluster) and the amorphization cross-section constant (ξ_amorph); (b) the amorphization dose (Φ_amorph) and the critical dose for the onset of amorphization (Φ_crit); and (c) the effective time constant of DA (τ) and the DA efficiency (ξ_DA) for 3C-SiC bombarded at 100 °C with 500 keV Ne, Ar, Kr, or Xe ions. Open symbols in (a) show ξ_amorph for the case of F → 0 obtained by the analysis of pulsed beam data measured with t_off ≫ τ.

The difference in damage buildup revealed by Figs 2, 3(a) and (b) could be related not only to different ρ_cascades created by different ion species but also to different R_gens. Indeed, the four damage buildup curves shown by solid symbols in Fig. 2 were measured with a constant F of 1.9 × 10¹³ cm⁻² s⁻¹. Since heavier ions create more atomic displacements per ion at their R_pds, they also result in larger R_gens 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 × 10¹² and 4 × 10¹² 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 × 10¹³ 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 × 10¹⁴ 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 × 10¹³ 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 × 10¹³ 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.

Figure 4

Dose-rate dependence of relative disorder at the maximum of the bulk defect peak for 3C-SiC bombarded at 100 °C with a continuous beam of 500 keV Ne ions to a Φ of 1 × 10¹⁵ cm⁻², corresponding to 0.38 DPA. The data point for F → 0 was obtained for irradiation with a pulsed beam with a t_off of 50 ms.

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^{6,8,9,10,13,16,17,18,19,31,32}. 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 efficiency¹⁰. 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^{13,16,17,18,19}, 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 Φs 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 DA¹⁵. 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 algorithm³³ 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.

Figure 5

Level of relative bulk disorder in 3C-SiC bombarded at 100 °C with pulsed beams of 500 keV Ne, Ar, Kr, and Xe ions with t_on = 1 ms and F_on = 1.9 × 10¹³ cm⁻² s⁻¹ as a function of t_off to Φs of 0.4, 0.31, 0.33, and 0.32 DPA, respectively. Data for Ar ions is from ref. 28. Fitting curves of the data with the second order decay equation are shown by solid lines.

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 T²⁶. 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 pulse²⁶. 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): . As discussed in detail previously²⁶, 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 directly by measuring damage buildup for different ion species and F values [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 ²⁰Ne to ⁴⁰Ar, 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 × 10²² atoms cm⁻³ (ref. 2) and threshold energies for atomic displacements of 20 and 35 eV for C and Si sublattices, respectively³⁴. To convert to displacements per atom (DPA) at the R_pd, Φs in 10¹⁴ 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_cascades) at R_pds were calculated based on the algorithm similar to that proposed by Heinisch and Singh⁵. 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-SiC²⁹. 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 ⁴He 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 ²⁰Ne⁺, ⁴⁰Ar⁺, ⁸⁴Kr⁺, or ¹²⁹Xe⁺ ions at ~7° off the [100] direction to minimize channeling effects. All irradiations were performed in the broad beam (rather than raster) mode²⁴. 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 mm². Total Φs 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_ont_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 efficiency¹⁵.

Depth profiles of lattice disorder in the Si sublattice were measured ex-situ at room T with 2 MeV ⁴He 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 algorithms³⁵ 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) × 10¹³ cm⁻² s⁻¹ and a t_on of 1 ms.