Dynamic Potential Sputtering of Lunar Analog Material by Solar Wind Ions

All the sputtering experiments presented here were performed with the same ion beam setup as described earlier (Szabo et al. 2018). Sputtering yields are measured with the Quartz Crystal Microbalance (QCM) technique (Hayderer et al. 1999a), which allows in situ observation of thin-film mass changes in real time by recording the resonance frequency of the quartz's thickness oscillation. Samples are mounted on a rotatable sample holder, allowing measurements under different angles of incidence. Experiments at different temperatures are made possible by heating the sample; however, all presented experiments were done at room temperature.

He irradiations were performed using both 4 keV ⁴He and 3 keV ³He at solar wind velocities of 1 keV amu⁻¹. It was necessary to use ³He in order to guarantee a clean He²⁺ ion beam that was not contaminated with molecular ${{\rm{H}}}_{2}^{\,\,+}$ ions. Due to the great difference in sputtering yields by H and He (about one order of magnitude), small but unavoidable H contaminations of the ion source would lead to errors in the measurement. Using ³He gas allows ³He²⁺ (m/q = 3/2) to be distinguished from any H contaminations (m/q = 2 for ${{\rm{H}}}_{2}^{\,\,+}$) in the magnetic sector field for mass-over-charge separation. A small hydrogen component of the electron cyclotron resonance ion-source plasma has to be expected due to a source base pressure of 10⁻⁷ mbar. Based on spectra acquired during ³He measurements, a H particle flux component of up to 30% can occur if they are not separated. This would lead to a significant underestimation of measured He²⁺ sputtering yields.

Similar to the previous experiments (Szabo et al. 2018), thin amorphous CaSiO₃ films deposited on our quartz crystals by Pulsed Laser Deposition (PLD) were used for the sputter yield measurements. The PLD was performed in a 0.04 mbar O₂ atmosphere at a substrate temperature of ∼270°C, with the laser operating at 5 Hz and a fluence of 2 J cm⁻² pulse⁻¹ on the sample for 60 minutes.

The films were analyzed with Rutherford Backscattering Spectrometry (RBS) and Time-of-Flight Elastic Recoil Detection Analysis (ToF-ERDA), from which sample thickness and depth-dependent elemental concentrations could be obtained. RBS using a 2 MeV He beam showed that the sample thicknesses of the films varied between 250 × 10¹⁵ at cm⁻² and 5300 × 10¹⁵ at cm⁻² depending on the PLD parameters (varying number of laser pulses). Assuming a CaSiO₃ bulk density of 2.86 g cm⁻³ (Deer et al. 1997), this corresponds to an actual film thickness between about 30 and 700 nm. ToF-ERDA analysis with 36 MeV iodine ions proves that the PLD films are very similar to the stoichiometric CaSiO₃ composition. Figure 2 shows the ERDA analysis of the 700 nm film as an example. Close to the surface, slightly less Ca than Si is observed, which is consistent with the sputter-XPS results for samples of the same batch (Szabo et al. 2018). However, across the whole analyzed area, the average composition is 18.4% Ca, 19.2% Si, 59.4% O, and only 2.0% H and 1.0% C. Similar results were also found for the 30 nm film (18.3% Ca, 20.0% Si, 59.5% O, 1.2% H, and 1.0% C), showing that PLD provides good sample compositions also at low film thicknesses. Therefore, we conclude that the film composition is close to stoichiometric CaSiO₃ across the whole film.

Zoom In Zoom Out Reset image size

XPS analysis was also done for samples that were used for the present investigations. Similar to previous results (Szabo et al. 2018), the O and C contents are higher than reported from ToF-ERDA. As surface contamination effects cannot be completely excluded from influencing XPS results, the ToF-ERDA analysis was taken as a reference of the film's composition being very close to CaSiO₃.

Kinetic sputtering yields were simulated with the BCA programs SDTrimSP and SRIM. In previous investigations, it was found that SDTrimSP can reproduce the angular dependence of Ar sputtering yields when taking into account the sample composition from XPS (Szabo et al. 2018). There, we also stated that the nominal CaSiO₃ composition leads to a significant overestimation of sputtering yields. However, the ToF-ERDA results in Figure 2 indicate that small deviations from the stoichiometric composition are only present at the surface. For prolonged sputtering experiments, they should not play a significant role and an agreement with a simulation using the stoichiometric CaSiO₃ composition should also be found.

For BCA simulations, the surface binding energies of the target elements play an especially important role. According to Sigmund's sputtering theory, the sputtering yield is inversely proportional to the surface binding energy (Sigmund 1969). In general, the heat of sublimation can be used as a good approximation for mono-elemental samples (Behrisch & Eckstein 2007), which are included as tabulated values in SRIM or SDTrimSP. However, for composite samples, the surface binding energy usually represents an unknown quantity. Different theories have been developed to calculate these energies by using, for example, bond energies and electronegativity (Malherbe et al. 1986), nearest-neighbor bond strengths (Kelly 1980), or the formation enthalpy (Möller & Posselt 2001). However, no universally accepted formalism for calculating unknown surface binding energies currently exists.

Together with using the CaSiO₃ bulk density of 2.86 g cm⁻³ (Deer et al. 1997), we therefore adapted the surface binding energies to the results of 2 keV Ar⁺ measurements for simulating the sputtering of CaSiO₃. This consistently leads to good agreement with experimental results for other energies as well. The choice of input parameters is described and justified in detail in the Appendix.

The results of simulating kinetic sputtering by 2 keV Ar⁺ ions are shown in Figure 3. The experimental values (red; taken from Szabo et al. 2018) are compared to a simulation using default parameters for SDTrimSP (green), leading to an overestimation of the experimental results. The adapted input parameters (see the Appendix) show improved agreement with the experiment (blue).

Zoom In Zoom Out Reset image size

The plotted simulations were performed in the static mode of SDTrimSP. Dynamic simulations were done for selected angles using the adapted parameters, but there were only concentration changes of a few percent observed, as well as no significant changes in the mass sputtering yield. These results are in line with experimental observations, where no substantial fluence dependence of the sputtering yield could be observed for the investigated fluences in the order of 10¹⁹ ions m⁻².

Steady-state elemental sputtering yields correspond to the bulk elemental concentrations. With a well-known sample composition and good agreement with total mass sputtering yields, SDTrimSP should thus give a good quantification of the element sputtering yields. The adapted parameters are therefore also used for the simulations of the kinetic sputtering contribution of He ions in the following sections.

First, sputtering with He⁺ at approximate solar wind velocity (1 keV amu⁻¹) was investigated for 4 keV ⁴He⁺ and for 3 keV ³He⁺. In the solar wind, ⁴He is much more abundant than ³He, but using ³He was necessary for investigations with doubly charged He, as discussed in Section 2.1.

Figure 4 shows the measured sputtering yields for ³He⁺ (red squares) and ⁴He⁺ (blue circles) under different angles of incidence (taken with respect to the surface normal). For all investigated angles, the measured sputtering yields for both He isotopes at the same impact velocity coincide within their uncertainty limits. The experimental results are plotted together with simulation results from SDTrimSP (dashed lines) and SRIM (dotted lines). Taking SRIM with default parameters as a reference for kinetic sputtering yields would significantly overestimate experimental sputtering yields. SDTrimSP, on the other hand, predicts sputtering yields mostly within the experimental error bars using our adapted simulation parameters (see Section 2.3 and the Appendix), in accordance with our findings for sputtering by Ar ions. Apart from the absolute values, the simulation predicts the sputtering yields for the two He isotopes to be very similar at the same velocity, which agrees with experimental findings. As the ionization energies—and therefore the potential energies—are equal for both He isotopes, sputtering yields obtained with 3 keV ³He can be used to describe solar wind sputtering with ⁴He.

Zoom In Zoom Out Reset image size

At the beginning of He irradiations on fresh samples, small net mass increases (up to Δm = 0.3 amu ion⁻¹) were observed due to projectile implantation. For the case of normal incidence, a steady mass decrease corresponding to a constant sputtering yield could only be found after fluences of about 1 × 10¹⁷ ions cm⁻². On fresh samples, a combination of sputtering and implantation is expected, which makes the exact determination of sputtering yields difficult. After a certain fluence, the sample will, however, be He-saturated within the implantation range. There will then be an equilibrium between implanted He and resputtered He atoms (Hayderer et al. 1999a). In this steady state, the only net mass increase is caused by sputtered wollastonite atoms, and no correction for He implantation is necessary.

The experimental He⁺ sputtering yields presented in this paper were obtained after steady state was reached. Assuming constant sputtering during these irradiations until steady state, the observed implantation varied significantly. Over a predicted implantation depth of about 30 nm, the measured mass changes correspond to an implanted He concentration between 1% and 6%. For these concentrations, dynamic SDTrimSP simulations predict maximal sputtering yield reductions of 7% in the steady state, compared to a simulation without He implantation. This value is close to the experimental uncertainties of the measured sputtering yields. Furthermore, dynamic SDTrimSP simulations in general do not show any significant sputtering yield changes due to preferential sputtering by prolonged He irradiation. Therefore, we conclude that the measured steady-state yields are representative of He sputtering of CaSiO₃, regardless of any He implantation. Nevertheless, the exact interplay between He implantation and diffusion inside the sample causing the observed transient effect of the mass change is not yet fully understood.

Sputtering yields with ³He²⁺ were measured for angles of incidence between 0° and 60° to investigate the influence of potential sputtering. To separate He²⁺ sputtering from implantation effects, the He⁺ steady state under 0° was taken as a starting point (after a previously applied fluence of about 10^{17 3}He⁺ cm⁻², as described in the previous subsection) because no more He implantation should occur there.

As it is shown in the left image in Figure 5, detailed measurements of the sputtering yield at the beginning of the irradiation show a significantly increased sputter yield of about 7 amu ion⁻¹ under normal incidence. It has to be noted that recording of the sputtering yield was only possible after an already applied fluence of about 10¹⁴ ions cm⁻². Local heating of the quartz as a result of starting ion bombardment causes an additional frequency drift for a few minutes at the beginning of each measurement (red dashed line in the left image of Figure 5). During the irradiation, the sputter yield decreases until a steady state is reached after a fluence of 10¹⁶ ions cm⁻² at a value much closer to the kinetic sputtering yield. The change of the sputtering yield y over fluence ϕ can be fitted with the formula y(ϕ) = A × exp(−ϕ/ϕ₀) + y₀ (blue dashed curve in the left image of Figure 5), which describes an exponential decay plus an offset y₀. For the measurement shown in Figure 5, the derived fit parameters are: A = 4.64 amu ion⁻¹, ϕ₀ = 1.998 × 10¹⁵ ions cm⁻², and y₀ = 2.30 amu ion⁻¹. The significant decrease of the sputtering yield indicates a change of the surface composition as a result of potential sputtering. However, the small fluence until steady state suggests that composition changes are confined to a thin region close to the surface. From the total frequency change until the steady-state fluence (the value of 1.0 × 10¹⁶ ions cm⁻² was chosen, as it is five times the decay length ϕ₀ of the exponential fit), a total mass decrease of about 32 × 10¹⁵ amu cm⁻² can be calculated. For this calculation, sputtering yields were assumed to be constant for the short fluence that is affected by thermal stabilization. The CaSiO₃ bulk density of 2.86 g cm⁻³ corresponds to an atomic density of 172 × 10¹⁵ amu cm⁻² nm⁻¹; therefore, steady state is reached within the sputtering of the first few monolayers when no further He implantation is assumed. The right image in Figure 5 shows a compilation of steady-state sputtering yields at different angles of incidence compared to the ³He⁺ measurements from Figure 4. For the steady-state yields of ³He²⁺ a constant difference of about 1 amu ion⁻¹ to the SDTrimSP prediction is observed for all investigated angles of incidence.

Zoom In Zoom Out Reset image size

Similar fluence dependencies of potential sputtering were found in previous investigations of potential sputtering using SiO₂ (Varga et al. 1997), Al₂O₃ (Hayderer et al. 2001a), and MgO_x (Hayderer et al. 2001b) samples. In these studies, the decrease of the sputtering yield was attributed to multiply charged ions causing a preferential sputtering of oxygen. Following the defect-mediated theory of potential sputtering, only O anions would desorb as a result of potential sputtering of an oxide target (Sporn et al. 1997). In this theory, an approaching ion that captures an electron from the insulating targets creates a localized electronic defect, a so-called self-trapped hole and a self-trapped exciton, which subsequently leads to the desorption of neutral atoms (Hayderer et al. 1999b). Defect-mediated sputtering has been extensively investigated for alkali-halides, showing precise agreement with the theory (Neidhart et al. 1995a; Hayderer et al. 1999b; Wirtz et al. 2000; Aumayr & Winter 2004). For other materials where no formation of localized defects has been reported, no potential sputtering was observed (Aumayr & Winter 2004). In the case of an oxide sample, the self-trapped hole only affects the O anions, and for electron irradiation of SiO₂, only O anion desorption is reported (Sporn et al. 1997). Preferential O depletion by potential sputtering would then similarly cause a decrease in the surface O concentration for CaSiO₃, and therefore also a decrease of potential sputtering until a steady state is reached.

In the present work, identical initial conditions with a high potential sputtering yield could be reproduced in two ways: either by sputter cleaning the sample's surface with Ar⁺ ions, or by oxygen flooding of the sample chamber (partial pressure of 10⁻³–10⁻⁴ mbar for several hours, either at room temperature or heated to 200°C). The first method corresponds to sputter removal of the O-depleted layers, thus exposing a stoichiometric CaSiO₃ surface again, while the oxygen flooding reoxidizes a depleted surface. The success of both methods is a strong indication that the qualitative explanation proposed by Sporn et al. (1997) as well as Hayderer et al. (2001a, 2001b) is indeed correct.

Fluence-dependent sputtering yields were similarly found for Ar⁸⁺ measurements in a new, more detailed investigation presented in Figure 6. Contrary to He, no changes in sputtering yields for prolonged Ar⁺ irradiation were observed, which indicates that Ar implantation has no significant effect for CaSiO₃. This was also assumed for measurements with Ar^q+ with (q > 1), so no correction of the sputtering yield due to implantation effects had to be applied.

Zoom In Zoom Out Reset image size

The measurements in Figure 6 show the same exponential decrease of the form y(ϕ) = A × exp(−ϕ/ϕ₀) + y₀ as described in the previous subsection. The fit parameters for the measurement in the left image of Figure 6 are: A = 54.06 amu ion⁻¹, ϕ₀ = 8.52 × 10¹³ ions cm⁻², and y₀ = 57.76 amu ion⁻¹. The fluences needed for steady-state sputtering are therefore lower, by about one order of magnitude, compared to ³He. Constant increases compared to the kinetic sputtering yields are found for all angles, in this case 22 amu ion⁻¹ (see the right image in Figure 6). The mass decrease up until a fluence of 4.3 × 10¹⁴ ions cm⁻² (five times the decay length of the exponential fit) is 29 × 10¹⁵ amu cm⁻², which is very similar to the observed value for ³He irradiations. It is therefore a common scenario for both ³He and Ar that steady state is reached after sputtering the first few atomic monolayers. The similar exponential decrease also supports the assumption of O depletion and therefore smaller potential sputtering effects.

Changes in O sputtering yields were investigated by Meyer et al. (2011) for Ar sputtering of lunar regolith simulant using a quadrupole mass spectrometer approach (QMS). In this study, no significant changes were observed, but with their reported high beam fluxes of 10¹⁴–10¹⁵ ions cm⁻² s⁻¹, it might be difficult to observe the pre-steady-state phase. Hijazi et al. (2014) support constant sputtering yields with a remark about their anorthite measurements with Ar⁹⁺, but they emphasize that further investigation is needed, especially due to unknown surface roughness effects. However, their later published calculations do include decreasing sputtering yields over fluence (Hijazi et al. 2017). Even if potential sputtering only affects O atoms, a complete depletion of surface O would not be expected, because kinetic sputtering will erode Ca and Si atoms and thus expose fresh O at the receding surface. Therefore, a surface O concentration that is lower than the initial one (but still nonzero) should be present in the equilibrium, and the observed constant O sputter yields by Meyer et al. (2011) could be in agreement with this explanation.

Using both of the described in situ sample preparation methods, initial sputtering yields (i.e., sputter yields at the beginning of the irradiation) were measured, and the results are shown in Figure 7. Measurements with 8 keV Ar⁺ are not possible in the setup used, due to a limited maximum acceleration voltage of 6 kV. Therefore, an SDTrimSP simulation is used as a reference for kinetic sputtering by 8 keV Ar ions, which is included as the black dotted line in Figure 7. The difference between this value and the measured sputtering yield is attributed to potential sputtering. For Ar charge states up to 8+, the potential sputtering yield is then proportional to the ion's potential energy (see the dashed green line in Figure 7). Its slope (γ_Ar ≈ 9.2 ± 1.8 O atoms keV⁻¹ or 147.4 ± 29.5 amu keV⁻¹) gives the dependence of the potential sputtering yield on the ion's potential energy, which will later be used to calculate potential sputtering effects numerically (see Section 4, Equation (4)). Sporn et al. (1997) investigated this dependence for potential sputtering of SiO₂ using multiply charged Ar and Xe ions. They found that the sputtering yields increase with 1 SiO₂ per 500 eV potential energy. This corresponds to 120 amu keV⁻¹, and is therefore close to our findings for Ar^q+ on CaSiO₃.

Zoom In Zoom Out Reset image size

However, the initial sputtering yield of ³He²⁺ that is shown in Figure 5 does not fit the same dependence. To describe the initial value of ∼7 amu ion⁻¹, a different slope γ_He ≈ 5.1 ± 1.3 O atoms keV⁻¹ (81.3 ± 20.0 amu keV⁻¹) has to be used. This would differ from our original assumption of a uniform potential sputtering behavior independent of ion species. Hijazi et al. (2017) report such a close-to-linear uniform scaling for potential sputtering on anorthite, but find a lower slope of 3.2 O atoms keV⁻¹. This indicates a significant material dependence, which should be investigated in the future.

Figure 7 also shows the measured yields from Szabo et al. (2018) in red. As they were measured multiple times to achieve better statistics, but without any oxidization or sputter cleaning in between, they have to be interpreted as steady-state sputtering yields. These steady-state yields were reinvestigated for the present publication and found to agree with the previously published values.

The previously shown measurements open up several questions that have yet to be answered quantitatively. It is necessary to investigate whether preferential sputtering of oxygen can explain the fluence dependence of potential sputtering. Furthermore, different steady-state behaviors between He and Ar could also be explained in connection to this process, due to the different kinetic sputtering yields. While potential sputtering presumably only erodes O atoms from CaSiO₃, a higher kinetic sputtering also causes additional removal of Ca and Si. This would bring more O to the surface, leading to higher potential sputtering yields in the steady state.

To investigate if this qualitative assumption reproduces the previously shown measurements, we applied a model for the dynamic sputtering consisting of a system of coupled differential equations. A similar model has been used by Barghouty et al. (2011), Hijazi et al. (2017), and Alnussirat et al. (2018) to extrapolate changes of surface compositions of lunar soil simulants and anorthite mineral due to solar wind sputtering from measured sputtering yields.

In the scope of this model, potential sputtering only causes the removal of O atoms. Cluster sputtering has been observed for slow, highly charged ions (Schenkel et al. 1998), where a potential energy of over 100 keV is transferred to the sample. However, for solar wind–relevant sputtering, the potential energies are much lower. For these potential energies in Ar^q+ (q ≤ 9) sputtering of LiF, cluster yields were found to be at least two orders of magnitudes below atomic sputtering yields (Neidhart et al. 1995b). This supports the assumption of only O atoms being eroded, especially for the important case of He²⁺ with a potential energy of only 77 eV.

The coupled differential equations of the sputtering model are then as follows:

$$\begin{eqnarray}\,\begin{array}{rcl}\displaystyle \frac{{{dC}}_{\mathrm{Ca}}\left(\phi \right)}{d\phi } & = & \displaystyle \frac{1}{{n}_{A}}\left[-{Y}_{\mathrm{Ca}}\left(\phi \right)+{C}_{\mathrm{Ca}}^{b}\left(\sum _{i}{Y}_{i}\left(\phi \right)\right)\right]\\ \displaystyle \frac{{{dC}}_{\mathrm{Si}}\left(\phi \right)}{d\phi } & = & \displaystyle \frac{1}{{n}_{A}}\left[-{Y}_{\mathrm{Si}}\left(\phi \right)+{C}_{\mathrm{Si}}^{b}\left(\sum _{i}{Y}_{i}\left(\phi \right)\right)\right]\\ \displaystyle \frac{{{dC}}_{{\rm{O}}}\left(\phi \right)}{d\phi } & = & \displaystyle \frac{1}{{n}_{A}}\left[-{Y}_{{\rm{O}}}\left(\phi \right)+{C}_{{\rm{O}}}^{b}\left(\sum _{i}{Y}_{i}\left(\phi \right)\right)\right].\end{array}\,\end{eqnarray} \tag{ 1 }$$

The surface concentration C_i of element i represents the relative concentration of the top monolayer, with n_A being the number of atoms per monolayer of 1.763 × 10¹⁵ at cm⁻² for CaSiO₃. Its change over fluence ϕ is the result of two processes: (1) Each incoming ion sputters a mean number of Y_i atoms, which decreases the surface concentration of element i. (2) Any sputtered surface atom can be replaced by a bulk atom of element i with a probability that is equal the bulk concentration ${C}_{i}^{b}$ (as an approximation, changes to the concentration of deeper layers are neglected here). This process increases C_i and is described by the second term in brackets. There, the sum of sputtering yields with index i is taken over all target elements.

The kinetic sputtering yield ${Y}_{i}^{\mathrm{kin}}$ of element i is taken from the CaSiO₃ sputtering yield simulated with SDTrimSP ${Y}_{i}^{\mathrm{SDTrimSP}}$ and rescaled with the fluence-dependent concentration:

$$\begin{eqnarray}&&{Y}_{i}^{\mathrm{kin}}(\phi )={Y}_{i}^{\mathrm{SDTrimSP}}\displaystyle \frac{{C}_{i}(\phi )}{{C}_{i}^{b}}.\end{eqnarray} \tag{ 2 }$$

Therefore, the system of differential Equation (1) is coupled via the sputtering yields, as they are proportional to the respective element concentrations C_i(ϕ).

For Ca and Si, only kinetic sputtering is calculated, while O sputtering is assumed to be the sum of a kinetic and a potential contribution:

$$\begin{eqnarray}\,\begin{array}{rcl}{Y}_{\mathrm{Ca}}\left(\phi \right) & = & {Y}_{\mathrm{Ca}}^{\mathrm{kin}}\left(\phi \right)\\ {Y}_{\mathrm{Si}}\left(\phi \right) & = & {Y}_{\mathrm{Si}}^{\mathrm{kin}}\left(\phi \right)\\ {Y}_{{\rm{O}}}\left(\phi \right) & = & {Y}_{{\rm{O}}}^{\mathrm{kin}}\left(\phi \right)+{Y}_{{\rm{O}}}^{\mathrm{pot}}\left(\phi \right).\end{array}\,\end{eqnarray} \tag{ 3 }$$

For the potential sputtering yield, we use the following expression based on the observed linear dependence of sputtering yields on potential energy (see Figure 7):

$$\begin{eqnarray}&&{Y}_{{\rm{O}}}^{\mathrm{pot}}(\phi )=\gamma \displaystyle \frac{{C}_{{\rm{O}}}(\phi )}{{C}_{{\rm{O}}}^{b}}\left({E}_{\mathrm{pot}}-2{E}_{B}\right).\end{eqnarray} \tag{ 4 }$$

The potential sputtering yield in O atoms/ion is here proportional to the surface O concentration C_O and the ion's potential energy E_pot minus twice the material's band gap E_B, which was kept as the potential sputtering threshold from Hijazi et al. (2017) and Szabo et al. (2018). The parameter γ describes how efficiently potential energy can cause desorption of O atoms, and can be calculated from the measurement of the initial sputtering yields (see Figure 7). As mentioned in Section 3, for Ar and He, different parameters γ had to be taken (γ_Ar ≈ 9.2 [O atoms keV⁻¹] and γ_He ≈ 5.1 [O atoms keV⁻¹]).

The total sputtering yield y in amu ion⁻¹, which is the quantity measured with a QCM setup, is calculated by summing up the products of elemental sputtering yields Y_i and atomic masses m_i:

$$\begin{eqnarray}&&y(\phi )={Y}_{\mathrm{Ca}}(\phi ){m}_{\mathrm{Ca}}+{Y}_{\mathrm{Si}}(\phi ){m}_{\mathrm{Si}}+{Y}_{{\rm{O}}}(\phi ){m}_{{\rm{O}}}.\end{eqnarray} \tag{ 5 }$$

The system of differential equations was solved numerically with Wolfram Mathematica (Version 11.2) to calculate the fluence-dependent surface concentrations. With these quantities, the fluence-dependent sputtering yields and steady-state conditions can also be obtained. In the next subsections, the focus will be placed on comparing steady-state measurements with the corresponding sputtering yields $\displaystyle \mathop{\mathrm{lim}}\limits_{\phi \to \infty }y(\phi )$.

Using the model introduced in Section 4.1, the steady-state sputtering yields for He²⁺ can be reproduced well, as can be seen in Figure 8. There, the blue dashed line shows the results when the parameter γ_He of the measured initial ³He²⁺ sputtering yield is used. The shaded blue area represents an error estimate of the calculation based on errors of SDTrimSP simulations (∼30% for He) and uncertainties in determining γ_He. For He²⁺, potential sputtering plays an important role in preferentially sputtering O, and due to the O depletion (see Figure 9 in Section 4.4), the sputtering yield decreases in good agreement with the experiment.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As mentioned before, our experiments do not indicate a universal potential sputtering scaling. This behavior does not agree with the findings by Hijazi et al. (2017) or our previous assumptions. Varying values for γ_Ar and γ_He could be explained by the phenomenon of kinetically assisted potential sputtering, which was observed previously for MgO_x samples (Hayderer et al. 2001b). Here, potential sputtering was found to be proportional to the kinetic energy of the impacting ion (in addition to the potential energy), which would be in accordance with the different He and Ar energies.

Otherwise, the calculation for the steady-state yields using the Ar potential sputtering behavior as a universal scaling γ_Ar also shows a reasonable agreement. Steady-state sputtering yields are only 5% higher than for the γ_He calculation, and therefore also reproduce He²⁺ measurements. The potential energy of He⁺ (24 eV) might be high enough to cause changes in the sample surface's elemental composition. He²⁺ yields have always been recorded after sufficient He⁺ bombardment in order to avoid complications due to He implantation (see Section 3.1). If He⁺ already causes preferential O depletion, this could explain lower measured He²⁺ initial yields (i.e., an underestimation of the efficiency parameter γ). However, differences between γ_Ar calculation and the measured He⁺ yield are quite significant, and agree much better when γ_He is used.

Analysis of our calculations shows that different surface binding energy models and possible variations in the sample composition noticeably affect the outcome. Due to these uncertainties, no definitive recommendation can be given about which of the two γ parameters should be used, because the steady-state behavior of He²⁺ can be described well in both cases. Nevertheless, total agreement for γ_He is better, which is why the He calculations in the following sections show results based on γ_He potential sputtering.

The calculation is also able to reproduce very well how the initial linear dependence of the potential sputtering yield with E_pot develops into a much less pronounced dependence for the steady-state yield on the ion's potential energy, as shown in Figure 7. As a comparison with the experimental yields, the calculated steady-state yields are included in Figure 7 as the dashed blue line. The shaded area again gives an uncertainty estimate for this calculation. Even though a simple model was used, the absolute values of the calculated steady-state yields agree very well with all measured Ar charge states.

With our model, we have successfully linked different effects of potential sputtering in cases of He and Ar bombardment to the depletion of surface O. The steady-state O concentration is shown in Figure 9 for He (red, using γ_He) and Ar (blue) charge states. For He, potential sputtering is dominant at the beginning of the irradiation, causing a strong depletion of surface O (see the sputtering yield measurement shown in Figure 5). As the potential sputtering is assumed to be proportional to the O concentration, its contribution is smaller than expected in the steady state when compared to kinetic sputtering alone (see the comparison between steady-state yield and SDTrimSP simulations in Figure 5). In contrast, for Ar irradiation, kinetic sputtering plays an important role in exposing fresh bulk O atoms at the surface. Ca and Si are sputtered more efficiently than by He ion impact, which leads to a higher O concentration in the steady state compared to He with the same potential energy. Therefore, higher differences can be observed between experimental steady-state yields including potential sputtering and the kinetic sputtering yield alone (see Figure 6).

Consequently, kinetic and potential sputtering in the steady state cannot be treated independently, but their interplay is important to understand the development of the sputtering yield.

The interplay of kinetic and potential sputtering is also very important for the solar wind in general, where mainly H⁺ and He²⁺ bombard mineral surfaces of atmosphereless bodies at the same time. Figure 10 shows the results from a simulation of these effects by modeling solar wind sputtering with 96% H⁺ and 4% He²⁺ (Russell et al. 2016) under normal incidence.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Kinetic sputtering yields are taken from SDTrimSP simulations with adapted input parameters as described in the Appendix. For H sputtering, these simulations predict 0.26 amu ion⁻¹, in good agreement with previously published values (Szabo et al. 2018). The changes of the surface concentrations for Ca (orange), Si (blue), and O (green) as a result of ion sputtering are plotted over ion fluence on the left image, while the right image shows the development of the respective yields. Two calculations are compared: dashed lines represent modeling of only kinetic sputtering effects, while full lines include potential sputtering by He²⁺ ions. Furthermore, the effect of only proton sputtering was calculated, but is not shown in Figure 10. The results for all three scenarios are listed in Table 1.

With potential sputtering, a clear O depletion by 48% to a surface concentration of 0.31 is predicted as a result of potential sputtering. Compared to only proton sputtering, the steady-state O content is smaller by 40% when potential sputtering is included, similar to the 22% calculated for KREEP lunar analog material (Barghouty et al. 2011), 27% for anorthite (Hijazi et al. 2017), and 26% for JSC-1A lunar regolith simulant (Alnussirat et al. 2018). This is caused solely by the potential sputtering, as the concentrations are barely affected by just including kinetic sputtering by He ions. This has also resulted from the calculations for other analog materials (Barghouty et al. 2011; Hijazi et al. 2017; Alnussirat et al. 2018).

On the other hand, all sputtering yields are increased by including the potential sputtering effects. O atoms are sputtered by the potential energy, while Ca and Si erosion is increased because of the change in surface concentration. In the steady state, where the ratio between yields represents the bulk ratio, all sputtering yields are increased by 43% compared to kinetic sputtering only (full versus dashed lines in Figure 10). The yield increase compared to proton sputtering is 71%, which is on the same order as 52% on KREEP (Barghouty et al. 2011) and 46% on anorthite (Hijazi et al. 2017). Just including He kinetic sputtering causes a total sputtering yield increase of only 20%, similar to the 26% reported for KREEP (Barghouty et al. 2011 and 25% for anorthite (Hijazi et al. 2017).

Our results therefore underline the importance of including at least He²⁺ in solar wind modeling, in accordance with previously published work. Further minor effects are then to be expected for multiply charged heavy ions. Changes in surface composition as well as increases in sputtering yield both give a consistent picture based on a model that can reproduce experimental sputtering yields.