3. Sputtering from plasma-material interactions

#### 3.1. Solid-phase sputtering of fusion-relevant materials

dimension of the surface is known [8] and the agreement is very good. Figure 2b shows the sputtering yield of 100 eV C on C as a function of the fractal dimension for a variety of incident angles. Initially, adding roughness increases the yield. This is due to the ability of the incident ions to knock off target atoms, which may protrude from the surface. Therefore, as expected, higher angles of incidence show an even greater rise in sputtering. The sputtering goes down for a very high roughness because the sputtered atoms are recaptured by overhanging features. Planar TRIM results are also shown. Note that the effective surface roughness for planar TRIM is only 2.00 at the normal incidence. The algorithm described earlier picks the location of the initial collision partner. If that partner would be above the surface, it is not used. The set of initial collision partner locations has a nonuniform depth distribution if the incident angle is not perpendicular to the surface. An equivalent roughness to the fractal surfaces can then be assigned. FTRIM predicts less sputtering than TRIM at higher angles of incidence and more sputtering at normal incidence. This result is significant, in that the realistic surfaces that evolve due to plasma-induced erosion and re-deposition in a fusion device with enhanced roughness will likely impact the amount of net erosion and reflected energy of fuel particles

Figure 1. (a) Rn and Re, particle and energy reflection coefficients, versus fractal dimension D for normal incidence (α = 0) and grazing incidence (α = 75) for three different surfaces. H is incident on Ni at 50 eV. The error bars are the size of the data points. Note the large drop-off of R at the grazing incidence when D is greater than 2.00. (b) Reflection coefficients for 10, 50, and 100 eV H on Ni as a function of the incident angle (with respect to normal, w.R.T.) for a fractal Ni surface with dimension 2.30. Planar TRIM results and a molecular dynamics calculation using the embedded atom method (EAM) are also shown. Note that planar TRIM predicts reflection at the grazing incidence to be two to three times more likely than the fractal TRIM results. Statistical errors in the fractal and planar TRIM reflection coefficients are

that can influence the operational regimes in these devices.

52 Plasma Science and Technology - Basic Fundamentals and Modern Applications

generally less than 5%.

One of the fundamental interactions between plasmas and material surfaces is physical sputtering or ion-induced desorption. The plasma edge magnetic field lines in a magnetic fusion device such as a tokamak directs energetic charged particles to gyro-orbit and bombards surfaces at both incident angle distributions and energy distributions that are linked with the operational regime of the fusion device. Therefore, the average incident angle will be close to 45 with respect to the normal and low-incident-particle energies. Fusion device PMI can be divided between two overall types of solid-state materials: low-Z materials and high-Z materials. There is a trade-off in the selection of materials for the first wall in fusion devices. The cooling of the plasma due to eroded particles from the device wall material goes as ~Z2 . Therefore, low-Z materials are attractive; however, these materials tend to have low surface binding energies, which result in high-sputter yields. The sputtering yield is defined as the ratio of flux of sputtered particles over the flux of incident energetic particles. High-Z materials can sputter orders of magnitude lower than low-Z materials; however, this must be balanced against plasma cooling losses. As stated earlier in fusion devices, the material surface will evolve where roughness can become significant [9–11].

#### 3.1.1. Low-Z material sputtering by light incident particles

Low-Z material sputtering is relevant to plasma-surface interaction physics in fusion devices from the standpoint of minimizing fractional impurity levels in fusion plasmas [12]. Figure 3a shows experimental measurements and VFTRIM-3D simulations of sputtering yields for Li, He, and D bombardment at 45 incidence on deuterium-treated solid-phase lithium [13].

VFTRIM-3D simulation results for deuterium bombardment are shown in Figure 3a with open triangles (pointing toward right), while closed triangles represent IIAX data. The solid line serves to guide the eye. The experimental and simulated yields versus incident-particle energy diverge with a decreasing energy primarily in the low 10–100 eV range, although the error bars are relatively large. At these lower energies, the range of incoming deuterium ions extends only to a few monolayers. Over the period of the dose, the surface may be enriched with more deuterium, leading to a lower amount of lithium sputtered than predicted. In addition, at these lower energies, the influence of surface roughness on the sputtering yield is enhanced. This occurs due to D atoms segregating to protruding regions of the surface where the net attractive force to the bulk/surface goes as r�<sup>3</sup> (where r is the distance from the surface) [16] and thus the effective binding energy to the surface for these atoms drops. Studies have shown that hydrogen atoms will tend to segregate to interstitial sites in a metal lattice [17–19]. In addition, the diffusion of hydrogen atoms has been measured in lithium experiments investigated by Sugai [15]. Such diffusion is not modeled by TRIM-SP, only that a continuous distribution of D atoms exists in the lithium bcc lattice. Thus, the ability for diffusion and segregation of deuterium atoms around the protruding regions of the lithium surface adds to the probability that less amount of lithium is sputtered since a larger amount of deuterium is preferentially sputtered. The yield reaches a maximum around 200–300 eV. At an incident-particle energy of 200 eV, where the yield is a maximum, the mean sputtered energy of lithium atoms is 9.0 eV as

Fundamentals of Plasma-Material Interactions in Magnetic Fusion Devices

http://dx.doi.org/10.5772/intechopen.77157

55

Figure 3a also shows the experimental and computational results for He+ bombardment of Dtreated lithium at 45� incidence. The line with open circles represents the TRIM-SP simulation data. The solid circles represent IIAX data. The prediction made by the computational model falls within the experimental error. The functional behavior shows a maximum of the sputtering yield of lithium at 500 eV. The decrease of lithium sputtering due to deuteration of lithium is stronger for helium bombardment than for deuterium. This is due to the effective transfer of energy from the incident hydrogen isotopes to the implanted deuterium atoms,

Beryllium sputtering has been studied quite extensively ranging from ion-beam experiments to experiments from magnetized linear plasma devices, such as PISCES-B [20–29]. Figure 3b shows both experimental data and simulation data for deuterium bombardment of beryllium. Experimental data are shown in x's and half-filled squares for IIAX data by Ruzic et al. [24], filled squares for Roth et al. [20], which are adjusted to 45� incidence by an empirical formula given by Yamamura et al. [30]. The empirical relation is shown as Eq. (1) and the fitting parameters used are obtained from the quoted reference for the factors f and αopt where αopt is the nominal incidence angle at maximum yield [31]. Simulated data for TRIM-SP are shown in open circles and triangles [23]. TRIM-SP simulation is shown with open diamonds for 45� incidence [32]

leading to a relatively larger net momentum imparted to lithium surface atoms.

Y Eð Þ <sup>o</sup>; α

Y Eð Þ <sup>o</sup>; <sup>α</sup> <sup>¼</sup> <sup>0</sup> <sup>¼</sup> exp <sup>f</sup> <sup>1</sup> � <sup>1</sup>

TRIM-SP simulations were done for a fixed surface binding energy of 3.38 eV, which is the heat of sublimation for beryllium. Since in the IIAX experiment, beryllium was saturated with

cos α cos αopt

cos <sup>f</sup> <sup>α</sup> (1)

predicted by TRIM-SP.

Figure 3. (a) Experimental and VFTRIM-3D simulation data for li, D, and he bombardment of solid-phase D-treated lithium at 45 incidence. (b) Experimental and simulation results for D<sup>+</sup> bombardment of D-treated beryllium at 45 incidence. Normal incidence data are adjusted to 45 using Yamamura's formula for oblique incidence.

Experimental data were taken at the Ion-surface Interaction Experiment (IIAX) facility, which is an ion beam experimental device able to measure, among other things, physical sputtering yields for low-energy, light-particle interaction. The data is done at 45 incidence, based roughly on the average angle of incidence a sheath-accelerated, gyrating particle makes where the magnetic field lines cross the divertor plates at oblique incident angles [14].

Computational runs were modeled using a surface, which consisted of 50 a/o Li and 50 a/o D, consistent with deuterium concentration measurements [15]. The model used a surface binding energy of 1.68 eV based on the heat of sublimation for solid lithium. The value of 1.68 eV for the surface binding energy of Li has been measured in plasma-surface interaction experiments in PISCES-B [16]. The bond energy (BE)—the energy to break a bond in the bulk—was taken as BE = 0.1 SBE. Deuteration of the solid lithium surface is done with a deuterium plasma from a hollow cathode source with a flux of 1016 ions/cm<sup>2</sup> /s for 20 min. This flux is sufficient to saturate the surface and have enough atomic percentage of deuterium to assume a 50/50 composition at the surface over a range at least the depth of origin of sputtered species.

The sputtering yield behavior shown in Figure 3a is as expected. Due to the ineffective transfer of energy between hydrogen isotopes and lithium compared to helium or lithium itself, lithium sputtering due to hydrogen isotopes is relatively low. For the same incident energy, hydrogen atoms will penetrate farther into the lithium bcc lattice. Therefore, hydrogen isotope bombardment of lithium will reach a maximum sputtering yield at a lower incident energy than for helium or lithium bombardment. At greater energies, the penetration depth is deep enough that the net backward momentum distributed to surface atoms is not sufficient to overcome the surface binding energy, and thus the lithium-sputtering yield begins to decrease. Self-sputtering of lithium will be discussed in Section 4.2, following which we discuss lithium sputtering from deuterium and helium bombardment.

VFTRIM-3D simulation results for deuterium bombardment are shown in Figure 3a with open triangles (pointing toward right), while closed triangles represent IIAX data. The solid line serves to guide the eye. The experimental and simulated yields versus incident-particle energy diverge with a decreasing energy primarily in the low 10–100 eV range, although the error bars are relatively large. At these lower energies, the range of incoming deuterium ions extends only to a few monolayers. Over the period of the dose, the surface may be enriched with more deuterium, leading to a lower amount of lithium sputtered than predicted. In addition, at these lower energies, the influence of surface roughness on the sputtering yield is enhanced. This occurs due to D atoms segregating to protruding regions of the surface where the net attractive force to the bulk/surface goes as r�<sup>3</sup> (where r is the distance from the surface) [16] and thus the effective binding energy to the surface for these atoms drops. Studies have shown that hydrogen atoms will tend to segregate to interstitial sites in a metal lattice [17–19]. In addition, the diffusion of hydrogen atoms has been measured in lithium experiments investigated by Sugai [15]. Such diffusion is not modeled by TRIM-SP, only that a continuous distribution of D atoms exists in the lithium bcc lattice. Thus, the ability for diffusion and segregation of deuterium atoms around the protruding regions of the lithium surface adds to the probability that less amount of lithium is sputtered since a larger amount of deuterium is preferentially sputtered. The yield reaches a maximum around 200–300 eV. At an incident-particle energy of 200 eV, where the yield is a maximum, the mean sputtered energy of lithium atoms is 9.0 eV as predicted by TRIM-SP.

Figure 3a also shows the experimental and computational results for He+ bombardment of Dtreated lithium at 45� incidence. The line with open circles represents the TRIM-SP simulation data. The solid circles represent IIAX data. The prediction made by the computational model falls within the experimental error. The functional behavior shows a maximum of the sputtering yield of lithium at 500 eV. The decrease of lithium sputtering due to deuteration of lithium is stronger for helium bombardment than for deuterium. This is due to the effective transfer of energy from the incident hydrogen isotopes to the implanted deuterium atoms, leading to a relatively larger net momentum imparted to lithium surface atoms.

Experimental data were taken at the Ion-surface Interaction Experiment (IIAX) facility, which is an ion beam experimental device able to measure, among other things, physical sputtering yields for low-energy, light-particle interaction. The data is done at 45 incidence, based roughly on the average angle of incidence a sheath-accelerated, gyrating particle makes where

Figure 3. (a) Experimental and VFTRIM-3D simulation data for li, D, and he bombardment of solid-phase D-treated lithium at 45 incidence. (b) Experimental and simulation results for D<sup>+</sup> bombardment of D-treated beryllium at 45

Computational runs were modeled using a surface, which consisted of 50 a/o Li and 50 a/o D, consistent with deuterium concentration measurements [15]. The model used a surface binding energy of 1.68 eV based on the heat of sublimation for solid lithium. The value of 1.68 eV for the surface binding energy of Li has been measured in plasma-surface interaction experiments in PISCES-B [16]. The bond energy (BE)—the energy to break a bond in the bulk—was taken as BE = 0.1 SBE. Deuteration of the solid lithium surface is done with a deuterium

sufficient to saturate the surface and have enough atomic percentage of deuterium to assume a 50/50 composition at the surface over a range at least the depth of origin of sputtered species. The sputtering yield behavior shown in Figure 3a is as expected. Due to the ineffective transfer of energy between hydrogen isotopes and lithium compared to helium or lithium itself, lithium sputtering due to hydrogen isotopes is relatively low. For the same incident energy, hydrogen atoms will penetrate farther into the lithium bcc lattice. Therefore, hydrogen isotope bombardment of lithium will reach a maximum sputtering yield at a lower incident energy than for helium or lithium bombardment. At greater energies, the penetration depth is deep enough that the net backward momentum distributed to surface atoms is not sufficient to overcome the surface binding energy, and thus the lithium-sputtering yield begins to decrease. Self-sputtering of lithium will be discussed in Section 4.2, following which we discuss lithium

/s for 20 min. This flux is

the magnetic field lines cross the divertor plates at oblique incident angles [14].

incidence. Normal incidence data are adjusted to 45 using Yamamura's formula for oblique incidence.

54 Plasma Science and Technology - Basic Fundamentals and Modern Applications

plasma from a hollow cathode source with a flux of 1016 ions/cm<sup>2</sup>

sputtering from deuterium and helium bombardment.

Beryllium sputtering has been studied quite extensively ranging from ion-beam experiments to experiments from magnetized linear plasma devices, such as PISCES-B [20–29]. Figure 3b shows both experimental data and simulation data for deuterium bombardment of beryllium. Experimental data are shown in x's and half-filled squares for IIAX data by Ruzic et al. [24], filled squares for Roth et al. [20], which are adjusted to 45� incidence by an empirical formula given by Yamamura et al. [30]. The empirical relation is shown as Eq. (1) and the fitting parameters used are obtained from the quoted reference for the factors f and αopt where αopt is the nominal incidence angle at maximum yield [31]. Simulated data for TRIM-SP are shown in open circles and triangles [23]. TRIM-SP simulation is shown with open diamonds for 45� incidence [32]

$$\frac{Y(E\_o, a)}{Y(E\_o, a = 0)} = \frac{\exp\left(f\left[1 - \frac{1}{\cos a}\right] \cos \alpha\_{opt}\right)}{\cos f a} \tag{1}$$

TRIM-SP simulations were done for a fixed surface binding energy of 3.38 eV, which is the heat of sublimation for beryllium. Since in the IIAX experiment, beryllium was saturated with deuterium at room temperature, a surface composed of a D/Be ratio of 0.33 was used based on saturation experiments [33]. VFTRIM-3D simulations use a vectorized version of TRIM-SP known as TRVMC, which uses a binding energy of 1 eV for hydrogen isotopes [32] and beryllium's heat of sublimation. This binding energy was also utilized by TRIM-SP for consistency.

The data shown in Figure 3b show a maximum between 300 and 500 eV, closely resembling BeO data taken by Roth et al. [20]. Beryllium has a high affinity for oxygen at room temperature, thus the surface binding energy is effectively increased, reducing the sputtering yield. In addition, deuterium-treated surfaces effectively decrease beryllium sputtering due to preferential sputtering of embedded deuterium atoms. As a consequence, the beryllium sputtering yield from deuterium-treated surfaces measured in IIAX is predicted well by VFTRIM-3D simulations. TRIM-SP simulations do not account for deuterium treatment, and thus their yields are higher than anticipated, coincidently matching VFTRIM-3D results. If deuterium saturation was used by TRIM-SP modeling, beryllium sputtering would be effectively decreased, thus not predicting the experimental data in IIAX. The ability for VFTRIM-3D to effectively model surface roughness also leads to the high predictability of experimental data both in IIAX and from Roth et al. [20].
