Materials

The samples used in this study had ultrahigh purity (≈ 99.99 wt.% W, wt.% = mass of W in grams relative to the mass of total sample material in grams) polycrystalline W disks with 4.5 mm diameter and 1 mm thickness (Goodfellow) and a grain size of ≈ 1.25 μm. Samples were annealed at 1000 ℃ in a vacuum environment (≈1.3×10^-4 Pa, 1 Pa ≈ 7.5×10^-3 torr) for 1 h after polishing to a mirror surface with a final finishing of ≈ 0.5 μm. The estimated grain size post-annealing was ≈ 1.75 μm. 10 keV He-3 (³He, for NDP) and He-4 (⁴He) ion implantation were performed at room temperature under vacuum conditions of ≈ 10^-7torr using a 20 keV noble-gas feeding ion gun with a beam-raster scanning area of 0.2 cm². The ion gun was installed on an ORNL-UTK Joint Gas Implantation and Thermal Desorption System (GITDS) [18]. Three different fluence levels (5×10¹⁴ He atoms cm^-2, 3×10¹⁵ He atoms cm^-2, 1×10¹⁶ He atoms cm^-2) were considered with a fluence rate (aka flux) of ≈ 3×10¹² He atoms cm^-2s^-1 for both ³He and ⁴He ion implantations. Note that the units that include He atoms herein are shortened to He. Figure 1 shows the Stopping and Range of Ions in Matter (SRIM) calculation (ion distribution and quick calculation of damage) of the He depth profiles and the vacancy production rate in 10 keV ³He-and ⁴He-implanted W, respectively. Figure 1 reveals similar profiles for both ³He and ⁴He; however, ⁴He exhibits more vacancies than ³He under the same implantation energy.

Fig. 1Full-screen View

(Color online) SRIM calculation of the implanted He profile and vacancy production rate of 10 keV ³He and ⁴He in W

Thermal desorption spectroscopy

Thermal He desorption measurements were performed on ⁴He ion-implanted W using the ORNL-UTK Joint GITDS [18]. The baseline pressure of the TDS system was ≈ 1×10^-9 torr. The temperature profile used for the ⁴He-implanted samples was consistent with that for the NDP samples (³He -implanted ones), i.e., increasing sample temperature to 1000 ℃ with a heating rate of 0.5 °C s^-1 and then holding at 1000 ℃ for 1 h. The desorbed He was captured using a quadrupole mass spectrometer and calibrated by employing a VTI standard He leak. The recorded He desorption spectra provided data to validate the developed model. He retention and the thermal stability of He-defect complexes in W from room temperature to 1000 ℃ could be assessed from the He desorption spectra.

Neutron depth profiling

A 1 h vacuum annealing at 1000 ℃ was performed following the room-temperature implantation of 10 keV ³He on the samples sent to the National Institute of Standards and Technology (NIST) Material Measurement Laboratory and NIST Center for Neutron Research (NCNR) for NDP measurements. NDP [19] is a nominally nondestructive isotopic characterization technique that can be used to estimate the spatial distribution of He in W following a heat treatment [20]. This technique relies on the large thermal neutron absorption cross-section (5333 barns, 1 barn = 1×10^-28 m² [19]) of ³He. This enables the mapping of the distribution and concentration of He atoms in W by measuring the final kinetic energy of the proton (p), produced from the nuclear reaction between neutrons and ³He, after it has passed through the material. A schematic of the interior of the NDP instrument is shown in Fig. 2 (adapted from Ref. [21]).

Fig. 2Full-screen View

(Color online) Planar view of the NDP facility at NIST, as reproduced from Ref. [21]

NDP was conducted at the cold NDP (cNDP) station at the end of Neutron Guide-5 at NCNR. The sample was attached to a supported Teflon aperture (≈ 3 mm in diameter, and the results are the average values across this diameter) in the center of the vacuum chamber facing a Si-barrier detector (ORTEC). This detector, with an active area of 150 mm², is ≈ 10 cm away from the neutron beam spot on the sample and has an energy resolution of ≈ 18 keV. The ³He atoms in W absorb a cold neutron and emit ³He and p particles with initial kinetic energies according to the following nuclear reaction: ${}^3\text{He}+\text{neutron}\to \text{proton}(\text{p}\mathrm{,}572\text{ keV})+\text{triton}\left({}^3\text{H}\mathrm{,191}\text{ keV}\right)\mathrm{.}$ (1) The electronic stopping force for the p, the ion profile analyzed in this study, and ³H in W were 160 keV μm^-1 at 572 keV and 290 keV μm^-1 at 191 keV, respectively, as calculated by SRIM [22, 23]. These charged particles predominantly lost energy through inelastic Coulombic interactions with atomic electrons along the outward path from the reaction sites. The detector recorded the count rate and residual energy of the detected charged particles simultaneously (Fig. 2). The charged particles lost negligible energy after leaving the surface of the sample because the chamber was maintained at a vacuum level of < 10^-6 torr. Energy loss was an indicator of the path length traveled by the particles within the sample. The Transport Range of Ions in Materials (TRIM) code was used to estimate the path length. Theoretically, both p and ³H spectra can be used to determine the ³H profile in W. The profile from the ³H spectrum provides more detailed information than the p spectrum because the stopping power of ³H is much larger than that of p. However, the ³H energy (191 keV) was low and difficult to distinguish from low-energy noise in the spectra. Therefore, the p spectrum was used to analyze the ³He spatial distribution.

The concentration of ³He in the sample was obtained by comparing the count rate measured from the sample with that of a well-characterized in-house ¹⁰B concentration standard sample [19]. All NDP data were normalized to data from a neutron fluence rate monitor with corrected deadtime and background and, when necessary, normalized to their aperture size. The measured profiles were average values relative to the size of the aperture. Long-neutron-beam exposure times (several tens of hours) were used to minimize uncertainty in the statistical counting of the charged particles (≈ 1 %, 1σ). For the nuclear reaction shown in Eq. (1), the Q value is approximately 764 keV, whereas the energy of the incident neutron is below 5 meV. Thus, the incident neutron energy is too small to perturb ³He from its original reaction site or significantly move the center of mass in the reaction.

Laser Ablation Mass Spectrometry (LAMS)

LAMS was used to quantify the retention and depth profiles of the gaseous species in the W samples [17]. ⁴He ion-implanted W samples were first cleaned with acetone, followed by isopropyl alcohol, and then adhered by Kapton tape to a flat stainless-steel sample holder. The LAMS chamber was pumped to a vacuum of the order of 10^-8 torr before testing. A 60 mJ, 532 nm, Nd:YAG laser was used at 3% power, 1.8 mJ s^-1 (1 mJ s^-1 = 1 W), to produce a 1 Hz, 5 ns pulse. A plasma plume composed of elements ablated by the laser pulse was produced as it impinged on the W sample surface. The vacuum system guided the ablated gaseous species from the LAMS sample chamber to a quadruple mass spectrometer, where the species were identified and quantified. These experiments were uncertain due to the crater shape and volume created by the laser ablation process. The volume was calculated by microscopic observation but had similar uncertainty, as discussed in detail below.

The reliability of He depth profiling using LAMS is critically dependent on the correlation between the crater volume and the number of accumulated ablations that generate the crater. For this study, crater volume calibration was performed on a W control sample prepared with the same surface finish as the He-implanted samples. The ablated crater volumes were calculated as a function of the number of laser ablation pulses by measuring the crater depth, bottom inner width, upper outer width, and average width at the surface using a Keyence optical microscope. The He signal captured by the mass spectrometer following each ablation was converted to atomic flux using the same calibration procedure as for TDS. The integration of the He atomic flux over the He peak duration gave the total amount of He in a single ablation, which was then divided by the corresponding ablation volume to calculate the concentration. Further information on the calibration can be found in [17, 24]. Six consecutive ablations per location were performed on the He-implanted samples, resulting in a final characterization depth of approximately 900 nm and a crater width of ≈ 50 μm. The depth-dependent He concentration was measured by averaging nine different spatial locations in the sample to ensure sufficient statistical data.

Cluster dynamics modeling

A cluster dynamics model based on the diffusion-reaction rate theory was used in this study to predict the He-defect cluster evolution in W in coordination with the experimental characterization results. This model, developed by Xu and Wirth [25-27], is based on the classical rate theory for computing one-dimensional (1D) time- and space-dependent volumetric concentrations (in nm^-3) of defect clusters under various irradiation or post-irradiation annealing conditions. It can incorporate vacancies, self-interstitials, and He clusters with sizes up to tens of thousands and has flexibility in terms of the number of mobile species and transformations. reaction kinetics and constants are assumed to be isotropic in nature and are most suitable for the three-dimensional motion of defect clusters. This model and its corresponding modified versions have been applied to simulate He defect interactions in He-implanted iron [25, 26], defect evolution in 1 MeV Kr⁺ irradiation in thin Mo foils [28] and neutron-irradiated high-purity iron [29]. Details of this model are available in [26, 29]. Here, we expand the application of this model to study He–vacancy interactions in He-implanted W.

In this study, clusters of interstitials (I), vacancies (V), He, and He-V complexes, as well as the reactions that result in their transformation, are considered. Three numbers, NI, NV, and NHe, were selected to define the maximum phase space. Only reactions and clusters contained in this predefined phase space were considered. Mobile species considered in this model include single W self-interstitials atom (SIA) (I₁), di- and tri-SIA (I₂, I₃), single vacancy (V₁), interstitial He atom (He₁) and small clusters of interstitial He atoms (He₂, He₃, He₄, He₅). Other defects, including He-V clusters, V clusters, and large helium clusters (He_x, where x>5), were considered immobile. Table 1 lists the pre-factors of the diffusivities and migration energies (eV) of the mobile species used in the current model. These values are consistent with the atomistic modeling of W [11].

The source term for the radiation-induced defects is highly dependent on the implantation energy. At high implantation energies (several MeV), the effect of the collision cascade must be properly treated. However, at low implantation energies (several to a few tens of keV), spatially dependent Frenkel pair production is assumed, and the SRIM calculation results are used as the input for both radiation-induced defects and implanted He in the cluster dynamics model [28]. The reactions among the clusters included in the model involved cluster generation via small clusters capturing mobile species or the dissociation of larger clusters, annihilation by capturing mobile species leading to recombination, or dissociation by emitting a single I, V, or He. This high-pressure cluster ejects a surrounding W lattice atom to form a He-vacancy cluster if a cluster of interstitial He atoms grows by capturing other mobile interstitial He atoms and reaches a critical size. This process is known as trap mutation [30]. The maximum size of the interstitial He cluster has been fixed at He₉ in this study, although molecular dynamics (MD) simulations have indicated that in proximity to free surfaces, trap mutations can occur at much smaller sizes [30]. Any He cluster containing more than nine He atoms spontaneously transforms into He_xV. The construction of partial differential equations describing the evolution of the defined clusters is based on classical rate theory. The binding energies for small He–V clusters are based on the values from several computational and theoretical models [9, 31]. For large clusters, the binding energies are extrapolated from the existing binding energy values for smaller clusters [11]. To identify the key parameters that affect the accuracy of model predictions, parameter optimization was performed within a reasonable range for the following parameters: the migration energy of a single vacancy and the binding energies of small He-V clusters.

Thermal He desorption spectra of ⁴He implanted W

The measured He desorption spectra from the 10 keV ⁴He-implanted W with three different fluences during the 1000 ℃ 1 h heat treatment process are shown in Fig. 3. Background noise from the mass spectrometer was the main source of scatter in the raw data. ⁴He implantation occurred due to a low signal-to-noise level in the TDS and the very low amount of desorbed He from room temperature (RT, ≈ 23 ℃) to 1000 ℃. The differences in the desorption spectra of the ³He-and ⁴He-implanted W are discussed in Sect. 4.3 based on cluster dynamics modeling predictions.

Fig. 3Full-screen View

(Color online) ⁴He desorption peak during 1000 ℃ 1 h annealing process measured by TDS; the solid green line shows the temperature profile and the red, magenta, and blue circles show the He desorption flux as a function of implanted He fluence. Uncertainty is based on the equipment calibration and is less than 5% (not shown)

A general observation from Fig. 3 is that the He desorption flux increases with the He implantation fluence. The He desorption signals of W implanted at 1×10¹⁶ He cm^-2 and 3×10¹⁵ He cm^-2 are apparent, whereas the He desorption signal of the lowest fluence sample has a low level just above the background. For the sample implanted to 1×10¹⁶ He cm^-2, a small He desorption peak is evident at 200 ℃ and a shoulder develops at ≈ 620 ℃ followed by a continuous increase of the He flux up to the maximum temperature of 1000 ℃, resulting in an incompletely developed He desorption peak in the linear temperature ramping process from 700 ℃ to 1000 ℃. The measured He flux starts decreasing and finally reaches and remains at the background level when the maximum temperature is attained. Similar features were observed in the He desorption spectra of the other two samples. For 3×10¹⁵ He cm^-2 sample, a small peak around 200 ℃ was also captured along with a 2^nd small peak at ≈ 320 ℃. No He desorption shoulders were observed in the spectrum. Similarly, the He desorption flux increased in the linear temperature-ramping regime up to the maximum temperature and decreased to the background level during the high-temperature annealing process. For the lowest fluence sample, the detailed features of the spectra could not be deconvolved from the measured signals because the desorbed He was close to the system resolution.

³He depth profiling determined by NDP

Figure 4 represents the He depth profiles in W samples implanted with ³He at three different fluences following 1 h 1000 ℃ annealing, as measured by NDP. Note that the nonzero experimental data above the sample surface (depth < 0) are caused by signal broadening and do not represent the actual He content. Measurable ³He depth profiles were obtained for the samples implanted at fluences of 3×10^{15 3}He cm^-2 and 1×10^{16 3}He cm^-2. In these samples, the ³He concentration peaked at a depth of approximately 30 nm to 50 nm and extended to more than 200 nm. The profile of the ³He implant sample at the lowest fluence could not be well-resolved from the background signal. NDP results for the as-implanted W samples were not obtained because of the unavailability of the samples during the experiments. If the SRIM simulation results represent the as-implanted condition, the NDP results imply that 1000 ℃ annealing drives He diffusion to depths >150 nm while maintaining the He peak positions near the sample’s surface. However, the calculated spatial accuracies of the measured He profiles must be assessed. Notably, the leading edge of NDP data, which is the surface of W in this case, is subject to spectral broadening. This can cause the data points to appear on the negative side of the 0-depth position. The width of the leading edge is related to the resolution of the silicon barrier detector and the roughness of the sample surface, among other factors. This broadening differs from the signal broadening due to charged-particle straggling, which is discussed in this paper.

Fig. 4Full-screen View

(Color online) NDP depth profile of ³He in W implanted at 10 keV ³He to fluences of 5×10^{14 3}He cm^-2, 3×10^{15 3}He cm^-2 and 1×10^{16 3}He cm^-2, respectively, following 1 h 1000 ℃ annealing. The data has been binned to the resolution of the NDP detector (≈ 18 keV). Uncertainty bars are 1σ and are based on experimental counting statistics. The dashed black line indicates the surface of the sample and the beginning of the ³He profile. Solid lines were added for reference and do not represent a mathematical fit

The acquired NDP spectrum represents a convolution of the actual energy distribution of the charged particles and the measurement system. Each component of the system, i.e., the detector, digital multichannel analyzer (MCA), and sample, introduces uncertainties that can broaden the energy profile relative to the measured energy of the charged particle. Two main energy-broadening contributions can be identified: (1) the overall detector energy broadening (referred to as σ_det) represented by a system resolution of ≈ 18 keV, and (2) energy straggling as the charged particles travel through the sample material (σ_strag). GEANT4 Monte Carlo simulations [32] were conducted to evaluate critical parameters, such as sample geometry, detector solid angle, proton particle incident angle, nuclear-stopping power, and electronic-stopping power, to assess the energy straggling of energetic p traveling through the W sample. Table 2 lists the σ_strag resulting from the 572 keV p emission from a W depth of 50 nm to 500 nm. As the depth of the emitted proton increases, the resulting energy broadening increases from 2.7 keV (50 nm depth) to 8.7 keV (500 nm depth). Notably, the energy broadening caused by the sample material is much smaller than that caused by the detector system because the system resolution (≈ 18 keV) is much larger than the straggling-induced broadening.

The effect of energy broadening on the actual data collected from the NDP detector system can be approximated using the detector response function R(x), assuming that a Gaussian model can describe the energy-broadening effects [33]: $R_i\left(x\right)=\frac{k}{2}\left[erf\left(\frac{E_i+\text{Δ}-\overline{E}\left(x\right)}{\sqrt{2}{\sigma }_{E\left(x\right)}}\right)-erf\left(\frac{E_i-\text{Δ}-\overline{E}\left(x\right)}{\sqrt{2}{\sigma }_{E\left(x\right)}}\right)\right]\mathrm{,}$ (2) where σ_E(x) is the total standard deviation of the total energy-broadening effect (σ_det+σ_strag), Δ is one half the width of an MCA channel, $\overline{E}\left(x\right)$ is the average energy corresponding to a particle emitted from depth x, Ei is the mean energy of channel I, and k is a constant accounting for the neutron flux, neutron cross-section, and detection efficiency. Based on the detector response function and peak broadening effect computed using Eq. (2), Figure 5 shows the normalized detector response curve of the 572 keV proton simulated as if produced inside W and transmitted through a 50 nm or 100 nm depth of W. Apparently, peak broadening does not change the peak position. For the 50 nm and 100 nm cases, the peak position was centered at 50 nm and 100 nm, respectively, after considering the peak-broadening effect. This is in good agreement with the experimental NDP values. Cooling the detector to cryogenic temperatures may be a viable method to reduce this broadening.

Fig. 5Full-screen View

(Color online) Normalized detector response of 572 keV proton ions from the ³He(n,p)³H reaction after traveling through 50 nm (red) or 100 nm (blue) of W, respectively, including broadening effects due to sample material only (SRIM results only, solid line), and due to material as well as detector system (dashed line)

An ideal material (perfectly smooth and homogeneous) contributes significantly less to peak broadening in NDP data than the detector system. Considering the broadening of the sample material (i.e., perfect detection system), the width of the detector response peak (i.e., full-width half-maximum of the peak) extends only up to 50 nm for p coming from less than 100 nm within W. However, considering the detector resolution, the width of the detector response curve extends up to 200 nm, which is ≈ four times the broadening caused. Additionally, the analyzed samples are neither smooth (0.5 μm roughness) nor homogenous; both factors contribute to signal broadening. Because of these complications, deconvoluting the detector response from the measured raw NDP data is extremely difficult. Therefore, the NDP results presented in Fig. 4 are expected to overestimate the ³He depth in W, although the ³He peak positions determined in NDP measurements are considered accurate.

Calculation of the depth scale of the NDP profile is another contributing factor to the observed broadening. NDP depth profile calculations were performed by inputting the estimated values of material atomic composition and densities into TRIM, running the simulation program, and then using the output results to calculate an energy-to-depth calibration equation. In this study, W has been assumed to be pure and polycrystalline with a theoretical density of 19.25 g cm^-3. These idealized parameters may not reflect the real conditions of the measured sample (e.g., the presence of bubbles or voids owing to implantation). Therefore, the reported NDP depth scale may be inaccurate. The total He calculation is not dependent on these parameters and should provide a good estimate of the total He within the W material before and after annealing. An important question related to the extent to which the ³He spatial distribution changed following 1000℃ annealing is addressed below.

LAMS experimental results

LAMS measurements were performed on the 10 keV, 10¹⁶ He cm^{-2 4}He before and after 1 h, 1000 ℃ annealing. The purpose was to assess the change in the spatial distribution of He following annealing at 1000 ℃ and to provide additional He depth profile data. Figure 6 shows the He concentration measured by LAMS compared with the SRIM simulation of the implanted He depth dependence for the 10 keV and 10¹⁶ He cm^-2 implantation conditions. The uncertainty bars shown in Fig. 6 are calculated by averaging the measurements from multiple laser ablation positions. They are dominated by the fluctuation of the He concentration measured at different positions and are reported to be 1σ, significantly larger than those calculated for the NDP measurements (based on one-spot measurement and calculated from experimental counting statistics). In the as-implanted condition, the He concentration measured by LAMS at depths of ≈ 20 nm and ≈ 30 nm agree with the simulated He implantation profile predicted by SRIM. Beyond 100 nm, the He concentration decreases to essentially zero (background level) in both the SRIM simulation and LAMS measurement results.

Fig. 6Full-screen View

(Color online) He concentration measured by LAMS for the implanted (black stars) and annealed (at 1000 ℃ (red stars)) W samples, in comparison with SRIM (green circles) prediction of the implanted-He depth profile; the uncertainty is estimated from the crater volume created by the laser ablation (see text for details)

He was not detected beyond 100 nm as well in the sample annealed at 1000 ℃ for 1 h. However, the measured He concentration in this sample decreased at near-surface depths in comparison with the as-implanted samples. This decrease was consistent with He diffusion to the surface, desorption, and some diffusion to greater depths. However, the LAMS measurements indicated that the diffusional broadening depth was less than 100 nm, beyond which they did not indicate any significant He concentration. The center of the LAMS profile from the annealed sample was within a reasonable range, 25 nm and 45 nm, the concentration peak estimated from the NDP data for the same sample.

He desorption process: Comparison between cluster dynamics modeling and experiment

The thermal ⁴He desorption spectrum from W implanted into 1×10¹⁶ He cm^-2 during the heat treatment process was first reproduced using the model to evaluate the applicability of the default energetics and kinetic parameters. The blue line in Fig. 7 represents the simulated desorption spectra. The binding energies of the He_nV_m clusters shown in Fig. 7 have been predicted using the initial default values based on ab initio simulations and extrapolation to larger clusters. The simulated curve in Fig. 7 results from the optimization of the He_nV_m binding energies, and the resulting values are listed in Table 3.

Fig. 7Full-screen View

(Color online) He desorption spectrum of 1×10^{16 4}He cm^-2 implanted W during 1000 ℃ 1 h annealing process measured by TDS (red dots) and simulated by cluster dynamics model (blue curves). Simulation curve based on (a) He_nV_m binding energies from ab initio and extrapolation, and (b) an optimized parameter set. Uncertainty is based on the equipment calibration and is less than 5%

Figure 7a illustrates the cluster dynamics model using the initial parameterization. The model predicts several peaks in the TDS data. However, the quantitative peak heights of the predicted He release flux were approximately one order of magnitude higher than those measured experimentally. The He binding energies of the small He_nV_m clusters were optimized based on the hypothesis that the presence of impurities within the W samples could affect the binding and diffusional kinetic energetics. The revised parameters are presented in Table 3. With the same set of optimized values, the model was in good agreement for all three implantation fluences in terms of the peak number, position, and intensity.

Figure 8 shows the simulated TDS spectra compared to the experimental results for the W samples implanted with ⁴He at three different fluence levels using the same optimized parameter set. The intensities of the 1000 ℃ desorption peaks are in good agreement with the experimental results at each fluence. The 200 ℃ He desorption peaks, incompletely developed peaks in the linear temperature ramping process, and decreasing He flux in the 1000 ℃ annealing stage were also successfully captured using this model. A small desorption shoulder from 580 ℃ to 700 ℃ was predicted by the cluster dynamics model; however, this peak was only observed in the TDS measurement of the highest fluence sample.

Fig. 8Full-screen View

(Color online) ⁴He desorption spectra from W implanted at fluences of 5×10¹⁴ He cm^-2, 3×10¹⁵ He cm^-2, and 1×10¹⁶ He cm^-2 during 1000 ℃ 1 h annealing process measured by TDS (circles) and simulated by cluster dynamics model (solid line). Uncertainty is based on the equipment calibration and is less than 5%

The measured He desorption spectrum results from the thermally driven evolution of all the clusters present in the W samples. The cluster dynamics model predicts that the cluster distribution would qualify before and after the major He desorption peaks at 25 ℃, 250 ℃, and 1000 ℃. This analysis was performed to identify the primary clusters contributing to each He desorption peak. The He-vacancy cluster distributions at these three peak positions at a depth of 30 nm below the W surface are shown in Fig. 9. The model predicts a majority of He interstitial clusters containing 6 He atoms to 8 He atoms as well as He-V complexes with 1 He atom to 9 He atoms (Fig. 9a) with heating to 25 ℃ following the implantation. At 250 ℃, following the first desorption peak, the concentrations of He₆, He₇V, He₈V, and He₈V are the most significant. Following the major He desorption in the linear temperature ramping process and high-temperature annealing, He_xV₂ (3 ≤ x ≤ 15) clusters develop owing to the evolution of the mobile species. The model indicates that the dissociation of He₈ is the largest contributor to the He desorption peak at 200 ℃ when comparing the change in the He-V cluster concentration from 25 ℃ to 250 ℃ (Fig. 9a and 9b, respectively). Between 250 ℃ and 1000 ℃ (Fig. 9b and 9c, respectively) the model indicates that the dissociation of He₇V, He₈V and He₈V are responsible for the main He release peak. Notably, at this implanted He fluence, the evolution of He-vacancy clusters in W was not significant, indicating that these clusters were relatively stable. This was expected based on the large binding energies of He to the He-V complexes listed in Table 3. The thermal stability of He-V clusters strongly depends on the He/V ratio in W [10, 34]. This phenomenon has also been observed in other material systems such as Fe [35, 36] and Ni [37]. Based on the above analysis, the cluster dynamics model suggests that the major desorption peak at high temperatures is mainly caused by He desorption from the dissociation of He-V complexes, whereas the low-temperature desorption features are due to desorption from weak He sinks, such as dislocations. Transmission electron microscopy studies in other TDS experimental studies under similar implantation conditions [38] also confirm the above deduction.

Fig. 9Full-screen View

(Color online) He_nV_m distribution predicted during thermal annealing by the cluster dynamics model following 10 keV ⁴He implantation to 10¹⁶ atoms cm^-2 using optimized cluster binding energies at a depth of 30 nm below the W surface, for the peak desorption temperatures of (a) 25 ℃, (b) 250 ℃, and (c) 1000 ℃. Uncertainty values were not calculated for these models

He Depth profiling: Comparison between cluster dynamics modeling and experiments

The ³He concentration profile in W was simulated using a cluster dynamics model. The atomic mass difference between the two He isotopes influenced only the diffusivity ($\text{2}{D}_{\text{He}4}=\sqrt{3}{D}_{\text{He3}}$), whereas the binding energies in the model did not change. The other difference was the spatially dependent Frenkel pair production and ³He depth profiling calculated using SRIM (See Sect. 2.1 Fig. 1). Figure 10 compares the cluster dynamics modeling predictions with the NDP measurements. The NDP results indicate that the concentration of He for the 1×10¹⁶ He cm^-2 peaked at a depth of 42 nm (± 12 nm, 2σ, three-parameter Gaussian fit), which was statistically similar to the depth of the maximum He concentration predicted by the Monte Carlo simulations and within 3σ of the value estimated from the cluster dynamics model and LAMS experiment. However, as indicated above, an obvious discrepancy existed between modeling and NDP measurements concerning the ³He spatial distribution for depths greater than 50 nm. The tail of the measured NDP spectra extended >200 nm, which could be attributed to energy broadening, detector resolution, and the use of idealized input parameters in the depth-scale calculations (see Sect. 3.2). Alternatively, cluster dynamics modeling predicted that He did not diffuse significantly beyond 75 nm.

Fig. 10Full-screen View

(Color online) ³He depth profiles for W implanted by 10 keV ³He after annealing at 1000 ℃ for 1 h as a function of implantation fluence, measured by NDP (circles with dashed line to guide the eye, see Fig. 4 for uncertainties) and simulated by cluster dynamics simulation without peak broadening effect (green, solid lines). Notably, the total He calculated from the NDP datasets is consistent with the estimated amount of He in each measured sample

The cluster dynamics model only accounts for the physical interaction between He and defect complexes as a function of the temperature (and ion implantation) conditions but does not explicitly model the experimental measurements using a synthetic diagnostic. While the NDP (curve dashed line in Fig. 10) incorporates a convolution of cluster dynamics and peak broadening effects (based on the description in Sect. 3.2), the NDP experimental results show a similar peak width with dashed lines in Fig. 5. The latter suggests that detector resolution, rather than He diffusion or interaction with the sample material, is the major cause for the measured He content beyond 100 nm observed in the NDP experiment. The total He calculated from the NDP datasets was statistically similar to that estimated for the measured samples. Therefore, NDP is a useful tool for quantifying the total implanted He in W metal.

The comparison between the LAMS and cluster dynamics results further validates our conclusion that NDP data beyond 100 nm result predominately from detector resolution-induced broadening. Figure 11 shows the ³He distribution in W implanted with 10 keV He ions at a fluence of 1×10¹⁶ He cm^-2 before and after annealing at 1000 ℃ for 1 h, simulated by cluster dynamics model. The SRIM results for as-implanted samples and the LAMS results for as-implanted and annealed 1×10¹⁶ He cm^-2 are also shown in Fig. 11 for comparison. Apparently, for the 1×10¹⁶ He atom cm^-2 sample after annealing, LAMS detects no discernable He in the implanted W samples beyond a depth of 100 nm, which is consistent with the cluster dynamics simulation results. Furthermore, the magnitude of the He concentration measured using the LAMS is reasonably consistent with the model prediction.

Fig. 11Full-screen View

(Color online) Cluster dynamics simulated (black and red filled circles) and SRIM (green circles)He depth-dependent profile of W implanted at a fluence of 1×10¹⁶ He cm^-2. The experimentally measured LAMS results are also shown as black and red symbols, respectively, for comparison

The cluster dynamics predicts that the spatial distribution of He in the as-implanted samples has a similar distribution as the He depth distribution predicted by SRIM, which has been used as the input for the model. This is rationalized by the fact that the implantation is conducted at room temperature, at which the mobility of the species is limited. However, an obvious discrepancy between these two models for the as-implanted condition is that the deeper tail of the He distribution simulated by the cluster dynamics model shifts toward the surface, and the peak width is narrower compared with the SRIM result. This is because of the strong trapping capacity of the vacancy defects in the damaged area, which act as sinks for mobile interstitial He atoms. In the cluster dynamics simulations, the depth-dependent production rates of the He and Frenkel pairs are obtained from SRIM and used as inputs.

The cluster dynamics simulation predicted that the He concentration decreases over the entire implantation range after annealing at 1000 ℃ for 1 h. The He concentration at the peak position decreased by approximately four times during thermal annealing, although the depth of the maximum He concentration remained unchanged at ≈ 25 nm. This change agrees with the calculated amount of ³He measured for the NDP samples. The simulation results agree reasonably well with the LAMS experimental observations, both in terms of the spatial depth dependence of He and the absolute magnitude of the He concentration. Furthermore, both cluster dynamics and LAMS measurements indicate that a limited amount of He diffuses past 75 nm below the W surface. Therefore, the decrease in the He concentration within the implanted region is mainly caused by He desorption from the surface and not by He diffusion from the damaged regime deeper into bulk W.

Examination of the He-defect cluster distribution before and after annealing from the cluster dynamics simulation reveals that the dominant cluster configurations of the desorbed He are He interstitials and some relatively weaker bound He-vacancy defect clusters. During annealing, the motion of these highly mobile species is predominantly controlled by the concentration gradient of He. Because the concentration gradient is considerably steeper in the near-surface region than in the deeper bulk region, He diffuses more readily to the surface and desorbs from the sample.

Isotopic effect: Comparison of ³He and ⁴He desorption behavior by cluster dynamics modeling

Because of the strong background signal of the mass/charge of three in the TDS system, the thermal ³He desorption spectra were not measured, and TDS measurements were used instead of ⁴He with equivalent implantation and thermal annealing conditions. Here, we describe the cluster dynamics modeling results to investigate any differences in the desorption behavior. The simulated TDS curves for ⁴He and ³He implanted with W under the same implantation and heat treatment conditions are shown in Fig. 12. As evident, the difference between the two predicted desorption spectra is subtle. The relatively smaller He desorption magnitude of ³He results from the smaller damage production rate and larger backscattered fraction based on SRIM calculations. The higher mobility of ³He also leads to a slight shift in the He desorption peaks to a lower-temperature regime. Overall, the differences between the predicted thermal desorption of ³He and ⁴He are insignificant; therefore, using ³He to study the depth profiling of He in W is reasonable.

Fig. 12Full-screen View

(Color online) Cluster dynamics simulated TDS spectra for ³He (black)- and ⁴He (red)-implanted W, as a function of time and implanted He fluence. Uncertainty values were not calculated for these models