High-resolution emission spectroscopy of W I lines: Comparing near-threshold sputtering of mono- and polycrystalline tungsten by Ar ions

Physical sputtering is one of the most fundamental processes in plasma surface interaction. Ions that bombard a surface may knock target atoms out of their equilibrium positions within the solid. Further interaction of the projectile and recoil atom with the crystal can create a significantly larger collisional cascade. Additionally, assuming an amorphous structure and not too high kinetic energies creates an isotropic flux within the solid. As this flux moves through the surface, it naturally has a cosine angular distribution function (ADF) and has to overcome the surface binding energy. This simple physical picture describes qualitatively why physical sputtering often creates the well-known Knudsen cosine law.¹ 

The experimental proof of such collisional cascades being the mechanism underlying physical sputtering was provided by Wehner.² He exposed low-index crystalline planes of silver to low-energy Hg ions at normal incidence and collected the deposition. The measured spot-like deposition patterns depended upon the orientation of the monocrystal surface. Furthermore, the dependence on the polar angle was non-cosine-like and non-isotropic in the azimuthal direction. These results illustrate how the collisional cascade in the near-threshold regime of physical sputtering depends on the surface orientation.

This fundamental information on the angular distribution function of sputtered atoms is vital for modeling the plasma–wall interaction in thermonuclear fusion reactors.³ For example, the currently being built International Thermonuclear Experimental Reactor (ITER) will have a tungsten wall, and its erosion via plasma particle bombardment creates impurities that can drastically change the physics of the discharge.⁴ One issue is that the high-Z element tungsten will have bound electrons even within the high-temperature region of the plasma and can rapidly cool it down.⁵ Fusing a deuteron and triton at sufficient rates for energy production depends strongly on the temperature. Thus, cooling the plasma via high-Z elements⁶ will be a lynchpin of fusion power plants, and correctly predicting the erosion and trajectory of sputtered tungsten is of the essence.

The sources of the physical erosion in a fusion reactor are the fast charge exchange (CX) neutrals for the main wall⁷ and ions in plasma-wetted areas, such as the divertor.³ Erosion due to the CX neutrals is well understood due to their kinetic energy on the order of keV since this produces the linear cascade regime for the physical sputtering, which the binary collision approximation captures accurately.^8,9 The plasma ions, however, have significantly less kinetic energy, so their collisional processes usually occur within the first few atomic layers of the plasma-facing component. The assumption of using binary collisions can also break,¹⁰ which is why the computationally more expensive molecular dynamics (MD) simulations may have to be used to capture the erosion correctly.¹¹ 

Another critical aspect of the plasma-facing components is their retention of hydrogen isotopes.¹² For example, regulatory standards strictly limit the amount of the radioactive isotope tritium stored within the wall. This issue is one of the reasons why in situ laser-based methods for monitoring retention are a highly active area of research.^13–15 Complementary to fusion reactors, specifically designed material interaction facilities enable testing the properties of the plasma-facing components within a laboratory setting.¹⁶ For instance, linear plasma devices provide fluxes of the ions onto samples similar to those expected in the divertor region of fusion reactors.

Not only isotopes of hydrogen but also seeding gas impurities bombard the divertor of fusion reactors.¹⁷ These elements, such as argon, dominate the erosion of the tungsten divertor during the so-called inter edge localized mode phases.³ Experimental data and molecular dynamics simulation suggest in the case of near-threshold sputtering of polycrystalline tungsten by Ar⁺ a butterfly-like ADF.^18,19 However, modeling by Stepanova and Dew²⁰ suggests an almost pure cosine angular distribution function at projectile energies as low as 100 eV. The current literature lacks experimental data on the angular distribution of particles sputtered via low-energy ions from monocrystalline tungsten targets.

Linear plasma devices, like PSI-2, are well suited to address this problem in the near-threshold energy regime. The diagnostic of choice is the high-resolution spectroscopy of the emission by the sputtered atoms themselves. Indeed, the line shape of sputtered atoms provides through the Doppler broadening information on the ADF and velocity distribution function (VDF). Essentially, the discharge fulfills two purposes: First, it creates the flux of ions onto a to-be-investigated sample, and second, it excites the sputtered atoms into energetically higher electronic states. Their radiative relaxation results in spontaneous emission of photons, which the spectrometer measures.

The pilot study at PSI-2 was limited to the one line of sight (LOS) that passes through the plasma source.²¹ This LOS was anti-parallel to the normal of the tungsten target (0° LOS). Adding the LOS in the direction perpendicular to the symmetry axis (90° LOS) proved that modeling both line shapes with consistent ADF and VDF is impossible within the standard model. This standard model explicitly assumes an infinite size of the target. The model proposed and benchmarked in Ref. 22 presents a method to include the geometric losses and excitation/ionization processes. The fitting of the ADF via cosine power-law scaling suggested a pronounced under-cosine distribution during near-threshold sputtering of polycrystalline tungsten by Ar⁺ bombardment.

Furthermore, improving the modeling requires accounting for the correct Zeeman hyperfine splitting of the odd isotope ¹⁸³W, as benchmarked in Ref. 23 using Kr I and Xe I transitions. The results presented in this study continue the development of the line shape emission spectroscopy of sputtered atoms. The main goal is to validate the approach of monitoring the ADF during plasma exposure since this could provide additional information on the changes in surface structure. So, for instance, the method may allow for operando monitoring of the distribution functions of atoms sputtered from strongly reformed surfaces, such as during the growth/erosion of tungsten fuzz.²⁴ 

Before attempting such time-resolved measurements, where the interpretation of the data may be difficult, it is essential to continue benchmarking the approach under well-definable conditions. This goal is the rationale for exposing low-index crystallographic planes of tungsten—(100) (111)—and a polycrystalline sample to the plasma at PSI-2 since one expects a pronounced influence on the ADF for near-threshold sputtering.¹⁹ At the same time, this is the first experimental study investigating the low-energy regime (<100 eV) for sputtering monocrystalline tungsten targets via Ar⁺ projectiles.

Observing significant changes in the line shape that depend on the surface structure of the target and align with the expectation from modeling the line shape then validates the use of line shape emission spectroscopy for monitoring changes in the ADF during plasma exposure. The data presented in this study are for biases of −60 V, −80 V, and −100 V applied to the target and represents the first measurements of such line shapes by atoms sputtered from monocrystalline samples.

A steady-state arc discharge driven between a heated LaB₆ cathode and a grounded Mo anode generates a plasma that an axial magnetic field confines, as Fig. 1 illustrates. This plasma exhibits an axisymmetric hollow electron density and temperature profile due to the geometry of the source, and the plasma propagates into an exposure area with a homogeneous magnetic field to study plasma–wall interaction. A radially movable Langmuir probe monitors the plasma parameters, and the overview paper of this linear plasma device (PSI-2) provides additional information on its characteristics.²⁵ 

One distinct advantage of this linear plasma device for spectroscopy compared to other linear machines^26–28 is the geometry of the source: The hollow and ring-shaped electrodes enable measuring optical emission spectra along the line of sight (LOS) that moves through the plasma source. In this study, we refer to this LOS as 0°. The reasoning is simply that the symmetry axis of our experiment is in this direction. Naturally, the LOS perpendicular to this direction is 90°. Figure 1 indicates these lines of sight via the two green beams that exit the vacuum vessel, and their diameters are about 2 mm to 3 mm. The LOS along 0° terminates at the surface of the target exposed to the plasma, whereas the LOS at 90° collects light from the region having an axial distance of 2 mm from the target.

The topology of the magnetic field within the exposure area created by the six Cu solenoids ensures the bombardment of the samples at normal incidence.¹⁶ In this region, the field strength of 90 mT provides the normal Zeeman splitting between a π (⁠ $Δm=0$⁠) to σ (⁠ $Δm=±1$⁠) component on the order of 1 GHz. A polarizing beam splitter (CCM1-PBS251, Thorlabs, 420–680 nm) mounted on the optical bench at the 90° LOS isolates the π components (cf. Fig. 13 of Ref. 29). Optical isolation due to a quarter waveplate (⁠ $λ/4$⁠, B. Halle, 460–680 nm) and linear polarizer (Glan–Thompson Prism, B. Halle) distinguishes between the $σ+$ and $σ−$ transitions at 0°.³⁰ Both lines of sight image simultaneously onto the slit of a high-resolution Echelle spectrometer. A bandpass filter with a width of 10 nm centered around 500 nm suppresses the superposition of different spectral orders. In this study, the 1024 horizontal pixels of the charge-coupled device (CCD) camera cover a wavelength range of 0.7 nm (⁠ $λ/Δλ≈7·105$⁠).

Two hollow cathode lamps (Ni, W) provide the calibration data needed for unambiguously deriving the wavelength dispersion of the spectrometer. The line targeted in this study is the resonant 498.4 nm transition of neutral tungsten.

As stated in the introduction, this study aims to verify that the line shape by transitions emitted by sputtered atoms does not only provide information on the energy³⁰ but also about the angular distribution function. Therefore, monocrystalline (100) (111), and a polycrystalline tungsten target are exposed to Ar ion bombardment under the same plasma conditions to create sputtered atoms. In particular, in the case of monocrystalline targets, one expects a very non-cosine-like angular distribution function.¹⁹ Several approximations can describe this effect.

For instance, adding two-cosine power-law scaling terms (⁠ $a cosb(θ)+c cosd(θ)$⁠) and optimizing their parameters (⁠ $a, b, c, d$⁠) can capture such distributions.^33,34 However, applying a fitting procedure for the measured line shape using a four-parameter ADF may run into a regime with a non-unique solution as the instrumental profile is still considerable, see Sec. III C. This issue is the rationale for optimizing a one-parameter angular distribution function.

Figure 2(c) clearly shows that this function allows for describing the emission at high average off-normal angles.

The distribution functions of Eqs. (1) and (3) feed into the recently developed space-resolved emission model for sputtered atoms.²² The main idea behind the model is to transform the distribution functions into a more natural coordinate system of the problem and then integrate the contributions by the target to the whole line of sight. The first step is to project the velocity into the LOS direction, but the remaining details depend on the particular application. In this study, one transforms $dΩ$ into $dxdy$ as the cartesian coordinates are ideal for integrating across the surface of quadratic targets. The critical advantage of this model is that it includes apriori the geometric losses of particles out of the LOS that contribute significantly to the line shape of sputtered atoms at the linear plasma device PSI-2.²² 

Here, we choose the step-profile approximation of the plasma—SRM2 of Ref. 22—due to the hollow electron density and temperature profile within PSI-2. This assumption corresponds to constant excitation and ionization rates for the 0° line of sight. In the case of the orthogonal angle of observation (90°), excitation and ionization rates are constant in front of the target and zero next to it. Section 4.1 of Ref. 22 provides a detailed description of the step-profile approximation and its validity.

Another aspect to consider is the potential confinement of the tungsten ions within the plasma column due to the magnetic field. For sputtered tungsten, one expects a most probable velocity of about 2100 ms⁻¹ (Ref. 37) giving a Larmor radius for a 90 mT magnetic field of 40 mm. Therefore, comparing this to the size of the target (13 mm × 13 mm), the FWHM of the plasma (60 mm), and the spot size of our spectroscopy system (2 mm to 3 mm) shows that we have unconfined tungsten ions. In this case, we can neglect the recombination in the line shape analysis.

Additionally to the aforementioned broadening mechanisms, the spectral shape of the W I 498.4 nm transition depends on line splitting, as discussed below.

Naturally occurring tungsten consists of five stable isotopes, with abundancies as tabulated in Refs. 38 and 39. Their difference in isotopic weight and nuclear charge distribution shifts the center of gravity energies of the atomic levels.⁴⁰  Table I presents these shifts for the 498.4 nm line.

The situation regarding the 498.4 nm line of neutral ¹⁸³W in a magnetic field of 90 mT is very similar to that of the Xe I lines studied with laser absorption at PSI-2. That is, Zeeman and hyperfine terms are of comparable size. We use the same code for addressing the hyperfine and Zeeman mixing, as reported in Ref. 23. The main idea is to evaluate the Hamiltonian within the basis of $|I,mI,J,mJ>$ wavefunctions because those remain good quantum numbers in both the weak and strong field limits. The wavefunction mixing coefficients obtained for the field of 90 mT enable the calculation of relative intensities via Eq. (A.6) of Ref. 22. Solving the Hamiltonian (5) for even isotopes of tungsten is trivial because the nuclear spin I is zero, and applying the Wigner–Eckart theorem gives relative intensities as per Eq. (17.24) of Ref. 47.

Figure 3 shows the Zeeman pattern for a field of 90 mT of the $Δm=0$ (π) and $Δm=±1$ (⁠ $σ±$⁠) transitions of the W I 498.4 nm line. The wavelength shift is defined (cf. Table I) relative to the heaviest naturally occurring tungsten isotope—¹⁸⁶W. The natural abundance of the latter is 28.4%. It has only one π unshifted component and two σ components at ±1.8 pm for the 498.4 nm line (J = 1 — J = 0 transition) within the magnetic field of 90 mT. The other highly abundant ¹⁸⁴W (30.6%) and ¹⁸²W (26.5%) isotopes create the remaining two dominant lines in the π spectrum. The isotope ¹⁸⁰W has a tiny abundance of 0.12%, responsible for an imperceptible component at about −3.8 pm. There is also a weak component at −3.4 pm due to the ¹⁸³W isotope (14.3% abundance). This isotope creates four π components, two of which are dominant at the central position of the ¹⁸³W 498.4 nm line. Thus, the intensity distribution resembles an almost pure Paschen–Back spectrum of the hyperfine structure—complete decoupling of I and J.

The spectrometer simultaneously detects emission for the two lines of sight, as indicated in Fig. 1. One can position two lamps in front of the collecting optics of the 90° and 0° directions to obtain the pixel range covered by either LOS. Figure 4(a) presents the results of this procedure: In both cases, the vertical pixel range is about 50, and they are sufficiently separated to ensure that they do not influence each other.

The high resolution of the spectrometer makes it necessary to pay special attention to the calibration. Several hollow cathode lamps (HCLs) that sputter metal and create the line emission of said metals are available to derive the reciprocal linear dispersion.⁴⁸ As it turns out, two Ni I lines of detectable strength are sufficiently close to the target line of W I 498.4 nm. For calibrating the 0° LOS of the spectrometer, we focused the emission by the Ni and W HCLs on the same vertical pixels as those covered by the 0° LOS of Fig. 4(a). Figure 4(b) shows the vertically binned spectra of the HCLs. The Ni spectrum has an additional constant offset to distinguish it from the W spectrum. Lowercase Latin letters from a to g designate each noticeable spectral line, and Table II presents the unambiguous line identification. This identification provides the data for deriving the linear wavelength dispersion of the spectrometer. Of note is that the tungsten lamp (Heraeus, 37 mm HCL, element W) contains a bit of nickel, which explains the small line intensities at positions b and c.

The next step is to extract the instrumental profile from the calibration spectrum of the tungsten lamp. Here, it is of the essence to include the isotope and hyperfine splitting. Figure 4(c) shows the spectrum of the W HCL at 498.4 nm and the contribution by each isotope. The hyperfine interaction within ¹⁸³W splits the transition into two lines. This splitting occurs due to the coupling of I = 1/2 and J = 1 for the upper level (⁠ $7F1°$⁠), resulting in the coupled quantum number of $Fu=1/2$ and $Fu=3/2$⁠. These states have slightly different energy eigenvalues and have allowed E1 transitions into the ground state with F = 1/2. For a detailed description of calculating the line positions and intensities for odd isotopes like ¹⁸³W, see Ref. 23 

The manuscript Ref. 22 which introduced the space-resolved model, showed a distinctly different dependency of the lines of sight at 0 and 90 degrees on the angular distribution function. For example, increasing the average off-normal angles creates more Doppler shift in the 90° direction and reduces the Doppler shift for the 0° angle of observation. As opposed to that, changing the VDF affects both lines of sight the same.

For visualizing this behavior, it is possible to calculate a large set of synthetic line shapes by varying the parameters s in Eq. (1) and b of Eq. (3), as Fig. 5(a) illustrates. Calculating the spectra's full width at quarter maxima (FWQM) is an excellent measure of their general line shape. Figures 5(b) and 5(c) show the FWQM depending on the parameters s and b via a 2D contour plot.

Superimposing the isolines provides a situation like those found in line-ratio methods.⁵⁰ For example, Fig. 3 of Ref. 51 represents such a case, showing temperature and density-sensitive helium line ratios. However, it is important to note that the one-parameter ADF and VDF are approximate solutions and cannot fully capture the intricate details of the distribution functions. Still, fitting these to experimental data should at least provide qualitative information about the average off-normal angle.

Simulations of the outgoing angle distribution of the sputtered particles were carried out with the PARCAS Molecular Dynamics code^52,53 using an adaptive time step.⁵⁴ The interatomic potential by Mason et al.⁵⁵ was used for the W-W interactions and the ZBL⁵⁶ universal repulsive potential for Ar-Ar and Ar-W interactions. The argon atoms were given an energy of 100 eV at normal incidence to the surfaces. We focused on the (100) and (111) low-index surfaces, which can be studied during cumulative impacts. 10 000 impacts were carried out on the surfaces, and five runs were carried out for statistics. The cells were initially perfect, but could evolve during the continuous irradiation. The calculated outgoing angular distributions are the values over the whole run and for all the five identical starting positions. Single-impact simulations were carried out on the same (100) and (111) surfaces in addition to random surfaces, following the technique in Ref. 19. For single-impact simulations, five different relaxations of the same low-index surfaces were irradiated by 10 000 impacts each, and for the random surfaces, 30 random surface orientations were studied and 5 000 impacts for each surface.

The simulation cells for the cumulative impact simulations were about $6×6×12nm3$⁠, containing around 30 000 atoms, and had a two-layer structure. At the bottom, a few layers of atoms were fixed, and the rest of the atoms were mobile. The simulation was carried out in two steps, similar to previous studies on cumulative impacts,⁵⁷ showing good agreement with experiments. First, an impact simulation, where the argon atom was given energy, was conducted for 5 ps. During this, no thermostat was applied, and any atom that was sputtered or reflected during the simulation was deleted after the simulation was done. An atom was considered sputtered/reflected if it was higher above the surface than the cutoff of the potential. After the impact simulation, a relaxation simulation was carried out to keep the temperature at 300 K without building up during the series. During this 5 ps simulation, a Berendsen thermostat⁵⁸ was applied to all mobile atoms to extract the extra heat.

The simulation cells for the single-impact simulations were half-spheres with a radius of 5 nm, containing about 17 000 atoms. The cells had a shell-like structure, where the outermost atoms were fixed, and between the fixed atoms and the mobile atoms in the center, a few layers of atoms were thermally controlled. The same setup has been previously used for low-index and random surface orientation sputtering simulations, see Ref. 19 for details. The impacting Ar atoms always hit a square on the center of the pristine cell, with a side length of 2 nm. The simulation lasted for 5 ps, and an atom was considered sputtered/reflected if it was higher above the surface than the cutoff of the potential.

The line shapes of optical transitions by sputtered atoms measured in the linear plasma device PSI-2 generally exhibit asymmetries to the central transition wavelength. For instance, Fig. 6 presents an asymmetric spectrum of the W I 498.4 nm line measured along the 0° LOS while applying a bias of −80 V to the target. The actual kinetic energy of Ar⁺ bombarding the tungsten sample at normal incidence depends on the potential difference between the plasma and the metallic target. In the case of argon discharges, the plasma potential at the radial locations covered by the sample is around −9 V. A local negative plasma potential develops due to the strongly magnetized electrons with a typical Larmor radius of 0.05 mm. The Ar ions, however, have a Larmor radius of roughly 10 mm, demonstrating much larger cross field transport for the ions, such that a negative plasma potential is required to ensure the quasineutrality of the plasma.

The most dominant spectral feature as shown in Fig. 6 is the direct emission: This emission by the sputtered atoms moving toward the observer shifts toward lower wavelengths—blue-shifted component. However, the tungsten atoms radiate isotropically, meaning they emit with the same probability into the direction of the target red-shifted light. The reflectance of the surface then decreases the signal of the red-shifted emission. In the case of mirror-like polished tungsten, one expects a reflectance of approximately 53%,⁵⁹ which agrees very nicely with the value of 54% as extracted from fitting the line shape of the data presented in Fig. 6.

A similar example is exposing a mirror-like polished Al target to an argon plasma at PSI-2. Those measurements verify that accounting for light reflection at the target is crucial for modeling the line shape along the 0° LOS: the bombardment with argon ions for one hour significantly roughens the surface, resulting in a shift from specular to diffusive reflectance. Therefore, the intensity of the red-shifted component decreases substantially compared to the blue-shifted one, as Fig. 4 of Ref. 30 shows for the case of the Al I 396.15 nm line. The additional experimental proof is the H_α emission by backscattered hydrogen atoms at PSI-2. Ref. 60 shows that the reflectance plays a crucial role in the line shape, and the intensity ratio of red to blue-shifted components depends on the reflectance of the target material, as expected.

Other significant contributions to the line shape of emission by sputtered atoms, such as tungsten, are isotopic, hyperfine, and Zeeman splitting, convolved with instrumental broadening, as discussed in Sec. III.

The data plotted in Fig. 6 directly provides information on the velocity distribution function in the 0° LOS direction. That is, the typical shift from the center wavelength to the peak of the blue-shifted emission is around 3.3 pm, corresponding to a velocity of 2000 ms⁻¹. This velocity allows for an estimation of the typical ionization length. The ionization rates from Vainshtein et al.⁶¹ and Schlummer et al.⁶² for an electron temperature of 3 eV give the ionization length, assuming a density of $2.5×1018 m−3$⁠, of approximately 40 mm. This length is significantly larger than the dimensions of the target (13 mm × 13 mm). Thus, the influence of ionization is negligible compared to geometric losses. Figures 6(a) and 6(b) of Ref. 22 show precisely this behavior based on the line shape simulation via SRM1. Furthermore, the tungsten ions are practically unmagnetized, as discussed in Sec. III.

The LOS at 90° does not intersect the target, so reflectance is irrelevant. Further assuming an azimuthal isotropy of the ADF and a plasma with homogeneous temperature and density, one would naturally expect a symmetric line shape centered around the unshifted wavelength. In this study, the target is positioned in one maximum of the hollow profile of the plasma (cf. Fig. 1). This geometry may produce a slight asymmetry: Some particles moving toward the observer (blue-shifted emission) move through the two plasma maxima. In contrast, particles moving away from the observer (red-shifted emission) pass through only one plasma maximum. Of course, the geometric losses of the particles out of the 90° LOS before reaching the second plasma maximum impose a limit to the asymmetry.

We implicitly assume azimuthal isotropy when analyzing the experimental data, and the model used in this study (SRM2 of Ref. 22) assumes excitation and ionization occur solely in the region in front of the target, producing strictly symmetric line shapes for the 90° angle of observation.

Figures 7(a) and 7(b) depict the spectra measured at 0° and 90° while applying a bias of −60 V to the target. The potential difference to the plasma provides the argon ions with a kinetic energy of 51 eV, and the magnetic field topology in the exposure area of PSI-2 ensures bombardment at normal incidence. The spectra measured along the 0° LOS have two essential differences: First, the surface structure of the three targets investigated was different—polycrystalline target, (100) and (111) planes. Second, the Zeeman pattern in the case of the W poly and W (111) targets was $σ+$⁠, whereas that of W (100) was $σ−$⁠. This fact explains the slight difference in line position and resulted from the measurement procedure. We started by exposing the polycrystalline target, varied the bias, and rotated the quarter waveplate by 90° (Fig. 1) to prove that optical isolation worked as intended (cf. Ref. 30) For the next target, we kept this alignment, exposed the W (100) sample to the plasma, and repeated the same procedure for W (111).

Comparing the spectrum due to sputtering from the poly and (111) target shows that the distribution functions must differ substantially. However, the difference in linewidth could result from changes in the VDF and ADF, as Fig. 5(b) illustrates via the isolines. Given the significant instrumental profile, it is impossible to deduce the cause for this variation by analyzing solely the 0° LOS. Therefore, we included measurements at the 90° LOS, and the variation in line shape is considerably more pronounced [cf. Fig. 7(b)]. The poly target produces a spectrum having a singular peak shape, (100) creates a flat-top-like structure with a width of a few pico meters, and (111) results in a two-peak structure owing to a considerable dip in the center of the line. This additional data are sufficient to make at least qualitative claims about the distribution functions because the width at 0° and 90° depends opposite on the ADF [cf. Figs. 5(b) and 5(c)].

Repeating these measurements at −80 V and −100 V bias provided the data needed to extract information on the VDF and ADF by fitting the one-parameter distribution functions of Eqs. (1) and (3). Again, the model underlying the analysis is SRM2,²² and we used a parameter tolerance of 0.01, resulting in decent fits to the data. Figures 8(a)–8(f) show these experimental data and the fits represented by solid lines. Tables III and IV give the optimized parameters s and b, respectively. The parameter s of the Thompson VDF is significantly different for the several targets investigated in this study. Those of the polycrystalline target are the closest to the standard value of s = 3. Quite a few mechanisms could result in this difference: The surface binding energy is not identical for all crystalline planes, and the azimuthal isotropy assumed in the modeling is only strictly fulfilled by the poly target. Furthermore, the exponentially modified cosine ADF may not capture all cases equally well.

Therefore, we compare through Figs. 9(a)–9(c) the extracted ADFs to MD simulations performed as discussed in Sec. IV. The single-impact MD and fitted ADF are fairly similar in the case of the poly target. Higher kinetic energies of the impinging argon ions create, on average, lower off-normal angles, so the distribution function slowly tends toward a cosine one. We did not conduct cumulative impact simulations for the polycrystalline target because our setup cannot handle such simulations on random surfaces. However, single-impact simulations of random surfaces are arguably sufficient for modeling the erosion of polycrystalline surfaces due to their inherently rough and variable nature.

The sputtering of tungsten atoms from the (111) plane in the near-threshold regime leads to the most probable emission angle at the highest θ found in this study. The results of single and cumulative impact MD simulations at 100 eV, plotted in Fig. 9(b), suggest an even more peaked emission profile. There is a slightly better agreement between the cumulative impact simulations and the fitted ADFs, which makes sense because one expects some modification of the surface structure due to continuous plasma exposure. The chief contributor to the discrepancy between MD simulation and fitted ADFs is most likely the one-parameter approximation of the ADF, which cannot produce such a well-defined peak. However, the at least qualitative agreement in the case of the mono targets (111) and (100) verifies the line shape emission spectroscopy for monitoring the ADF of sputtered particles in plasma exposure experiments.

This study reports on the line shape of the resonant W I 498.4 nm transition by atoms sputtered in the linear plasma device PSI-2. The main goal was to verify that our approach of using two observation angles can capture variation in the angular distribution function (ADF). Work by Jussila et al. suggested pronounced differences in the ADF of low-index crystalline tungsten mono to poly targets when bombarding them with low-energy argon ions.¹⁹ 

Hence, we exposed (111) (100), and polycrystalline tungsten targets to an argon plasma at the linear plasma device PSI-2. The argon ions bombarded the samples at normal incidence with kinetic energies below 100 eV, providing near-threshold sputtering. These sputtered particles transversed through the plasma and were excited via electron collisions. Measuring the resulting line-integrated electric dipole radiation via the 0° and 90° observation angles provided the experimental data analyzed in this work. Most critical is the comparison of the line shape that Figs. 7(a) and 7(b) show. Indeed, the line shape of the W I 498.4 nm transition differs depending on the target we exposed to the plasma. These results represent the first measurements using the line shape emission spectroscopy that show such distinct differences solely due to the surface structure.

This variation in line shape is consistent with the expectation, as given by the model benchmarked in Ref. 22 and the information on the ADF.¹⁹ The (111) target creates the broadest spectra along the 90° direction and the narrowest ones in the 0° direction. Fitting the experimental data with the recently developed SRM2²² while using a parameterized Thompson VDF and an exponentially modified cosine ADF provided consistent fits to the line profiles. The main idea was to optimize the spectra for 0° and 90° iteratively due to their opposite dependency on the ADF, as Figs. 5(a)–5(c) illustrate.

Comparing the deduced ADFs to the ones simulated using the PARCAS MD code for 100 eV Ar⁺ bombarding tungsten surfaces at normal incidence gives a decent agreement for the polycrystalline target. In the case of the monocrystalline targets, we performed single and cumulative impact MD simulations. The cumulative results agree slightly better with the ADFs, as derived from fitting the emission spectra at 0° and 90°. However, the one-parameter ADF used in this study seems less effective at accurately representing the highly peaked emission of sputtered atoms within a narrow angular interval from low-index monocrystalline planes. Although a two-cosine power-law scaling can capture these distributions, the considerable instrumental broadening due to the spectrometer would cause ambiguity in the solutions. Nonetheless, the qualitative comparison is still reasonable: the (111) target creates a peaked emission profile at large off-normal angles, as illustrated by the dip in the profile at the unshifted wavelengths [cf. Fig. 7(b)].

Additionally, we did not monitor the modification of the surface morphology in this campaign. The continuous plasma exposure of the targets shifts their mirror-like specular reflectance to the diffusive one. We will address this problem soon and investigate the time evolution of the angular distribution as for instance, was proposed for Al in Ref. 30. This method can distinguish the sputtering of re-deposited and bulk tungsten.

This study demonstrates the ability of high-resolution emission spectroscopy to detect the difference in the internal structure of plasma-contacting surfaces by analyzing the spectral line shape of atomic transitions. More specifically, our work confirms its reliability in deducing information on the ADF during the sputtering of plasma-facing components. This technique's capability for capturing time-resolved changes in the line shape could be critical for studying samples where the ADF is expected to change during plasma exposure. A prerequisite for this approach is that one needs at least two observation angles to distinguish between spectral line broadening due to the VDF and ADF. Particularly, advantageous are those angles parallel and perpendicular to the normal, as contour plots of the simulated linewidth show [cf. Figures 5(b) and 5(c)].

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200—EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

Computer time granted by the IT Center for Science—CSC—Finland is gratefully acknowledged.

The authors have no conflicts to disclose.

M. Sackers: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). O. Marchuk: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). S. Ertmer: Investigation (equal); Validation (equal); Writing – review & editing (equal). S. Brezinsek: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). F. Granberg: Data curation (equal); Formal analysis (equal); Software (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). A. Kreter: Resources (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.