Surfactant-driven self-organized surface patterns by ion beam erosion

In this paper, we report on the self-organized pattern formation on Si surfaces driven by Fe surfactant atoms. Si substrates were irradiated with 5 keV Xe ions at normal incidence and ion fluences up to 5×1017 Xe+ cm−2 under continuous deposition of Fe surfactant atoms. In the absence of Fe deposition, uniform flat surfaces were obtained. With Fe surfactants, pronounced patterns, such as dots, combinations of dots and ripples and ripples with about 100 nm wavelength, were generated. The Fe coverage and deposition direction determine the pattern type and the pattern orientation, respectively. A critical Fe steady-state coverage for onset of dot formation and onset of ripple formation ranges between 2×1015 and 6×1015 Fe cm−2. With increasing ion fluence, the pattern contrast increases but the pattern type remains unchanged. The surface region consists of a thin amorphous FexSi layer with x≈0.2 in the ripple and dot regions and x≈0.03 in the intermediate regions. Pattern formation is explained by ion-induced diffusion and phase separation of the initially flat amorphous FexSi layer and subsequent ion beam erosion with composition-dependent sputter yield. Directed deposition of Fe causes preferential deposition and shadowing and determines the final pattern orientation and morphology.

3 latter case are ultrathin nanostructured silicide [20] and carbide films [21] formed on Si and amorphous carbon substrates. Surfactant-assisted ion beam erosion allows one to manipulate the sputtering erosion of substrate atoms in manifold ways and on length scales from the nanometer range to macroscopic dimensions. As a consequence, self-organized pattern formation processes during ion beam erosion are drastically modified not only by intentionally deposited surfactant atoms but also by unintentionally deposited contaminants.
Earlier studies of ion beam erosion under simultaneous co-deposition were devoted to cone formation or relief surface structure formation during sputter erosion of metal and silicon substrates [22]- [27] and to the investigation of the sputter yield amplification effect [28]- [32]. The most prominent example of cone formation during ion beam erosion is the unusual behavior of Mo on Si and some metal surfaces, leading to pronounced cone patterns [24], [33]- [39]. However, in these studies, the formation of a steady-state surface coverage was hardly observed. Instead the observed cone formation was described as due to Mo seeding, suggesting an initial seeding mechanism rather than a dynamic equilibrium or a steady-state situation.
In several experimental studies, unusual formation of dot patterns on compound semiconductor surfaces was observed for normal ion incidence on GaSb [40,41], InSb [42] and InP [43] as well as for near-normal ion incidence of 25 • -42 • on GaAs and InP [44]. Recently, this pattern formation was explained as self-sustained etch masking [45] due to continuous segregation of one component as a result of preferential sputtering effects. This mechanism is rather similar to surfactant sputtering or processes leading to cone formation; however, the surfactants are not deposited but are continuously enriched at the compound substrate surface due to preferential sputtering.
Reports by Frost et al [48], Ziberi et al [47], [49][50][51] and Ling et al [52] on the ion beam erosion of Si surfaces with keV noble gas ions have shown the formation of different types of dot, hole and ripple nanopatterns for a wide regime of ion incidence angles, surprisingly also for near-normal ion incidence angles between 0 • and 30 • . The type of pattern seemed to depend rather sensitively on the ion incidence angle. There have been attempts to extend continuum theories based on the nonlinear Kuramoto-Sivashinsky equation towards an anisotropically generalized non-local equation to model the observed unusual pattern formation, in particular dot pattern formation at normal ion incidence, but with limited success [5,46]. Recently, Macko et al [53] have proved that the observed diversity of patterns is due to Fe contamination of the Si surface introduced during sputter erosion. In their study, a co-deposition of Fe from a stainless steel target irradiated together with the silicon substrate was carried out using 2 keVKr + ions at an ion incidence angle of 30 • . The irradiation setup was similar to that used by our group for surfactant sputtering studies [18]. They observed a large variety of nanopatterns ranging from dot to ripple patterns, whereas no patterns were formed without Fe co-deposition (the present work and [15,16]). Qualitatively, the study clearly shows that the type of pattern generated depends on the amount of co-deposited Fe, i.e. the steady-state Fe coverage. In addition, the study provides evidence that the pattern orientation depends on the deposition direction of the incident Fe atoms, similar to observations in early studies of relief pattern formation by ion bombardment [22]. Sánchez-García et al [54] recently demonstrated the formation of nanodot and nanohole patterns on Si induced by 1 keV Ar + ion beam erosion at normal ion incidence. Here, the pattern formation was caused by the incorporation of Fe and Mo contaminants with concentrations of up to 3.5 × 10 15 cm −2 originating from sputter erosion of the ion source cathodes as well as substrate holder parts. The experiments carried out by Macko et al [53] and Sánchez-García et al [54] describe, in essence, a surfactant sputtering process. The previously 4 mentioned large variety of patterns observed by Frost et al [48], Ziberi et al [47], [49][50][51] and Ling et al [52] for sputtering of Si at near-normal ion incidence can thus be easily explained by unintentional contamination of the substrate, most likely due to the Fe atoms sputtered off the vacuum chamber wall.
In this paper, we investigate the nanopattern formation on Si surfaces by surfactant sputtering using 5 keV Xe ions at normal incidence and co-deposition of Fe surfactant atoms. A low Fe steady-state coverage is achieved by simultaneous sputtering of the Si substrate and an adjacent inclined steel target, which is simultaneously exposed to the ion beam. Steel was chosen as the sputter target because it resembles the walls of the vacuum chamber, which may be exposed to an ion beam unintentionally. The pattern morphology, wavelength, amplitude and orientation, as well as the sputter yield, are quantitatively analyzed as a function of ion fluence, Fe steady-state coverage and Fe-deposition direction. Furthermore, the microstructure and composition of the patterned surface were analyzed by transmission electron microscopy (TEM), energy dispersive x-ray spectroscopy (EDX) and Rutherford backscattering spectroscopy (RBS), revealing the formation of a thin amorphous Fe x Si surface layer.

Experimental
For the surfactant sputtering studies, we have used single-crystalline Si(100) substrates of size 7 × 10 mm 2 , with measured root mean square (rms) surface roughness < 0.1 nm. The substrates were cleaned sequentially in an ultrasonic bath with acetone and methanol. A 5 keVXe + ion beam with a low beam divergence of about 12 mm diameter was provided by a low-energy mass selected Colutron ® ion beam system using a Wien-filter mass selection and a beam sweep system [24]. The ion flux on the substrate was about 1 µA cm −2 . All substrates were kept at room temperature and irradiated under high vacuum conditions of 2 × 10 −6 Pa with the ion beam incident along the normal direction of the Si surface.
Previous studies have shown that sputtering of Si surfaces at normal ion incidence without surfactants produces rather flat and uniform surface topography without any indication of pattern formation [15,16]. To confirm this with our experimental setup and to ensure that our irradiations are free of unintentional contaminations, we have carried out irradiation of Si with 5 keV Xe + ions at normal ion incidence and incidence angle of up to 30 • for ion fluences of up to 2 × 10 18 cm −2 .
For surfactant-assisted erosion studies, the source of Fe surfactant atoms was a steel target (9SMnPb28K free cutting steel, < 0.14% C, < 0.11% P, < 0.33% S, < 0.01% N, < 1.3% Mn, 0.05% Si, < 0.35% Pb) positioned adjacent to the Si substrate at inclination angles of 20 • -60 • of its surface normal relative to the ion beam direction. One half of the ion beam irradiated the Si substrate, while the other half simultaneously irradiated the steel target. The irradiation setup is schematically shown in figure 1. Sputtered Fe atoms are deposited with a certain incidence angle distribution of 60 • -90 • with respect to the surface normal and within about ±45 • in-plane azimuthal angle. With such a geometrical arrangement, a fraction of atoms sputtered off the surfactant target were directly deposited with a low kinetic energy of a few tens of eV onto the Si substrate. The Fe-deposition flux varies across the Si substrate and allows one to study the erosion effects as a function of surfactant coverage.
The surface morphology of the irradiated Si substrates was analyzed by atomic force microscopy (AFM) in contact mode using a Nanosurf microscope over an area of 3 × 3 µm 2 . For the tip, we used AFM probe-type PPP-CONTR Si cantilevers from NanoAndMore GmBH with a mean tip radius of < 7 nm. AFM measurements were carried out using Nanosurf Easyscan software. For topography analysis as well as statistical analysis and Fourier transformation, we used the open source software Gwyddion. Rutherford backscattering spectroscopy (RBS) with 900 keV He ++ ions and a beam spot of 1 mm diameter was used to quantitatively determine the average Fe coverage on different spots of the Si samples with and without ion beam erosion of the Si substrate. The sputtering yields were measured with mechanical surface profilometry. The microstructure of iron-silicide nanopatterns was analyzed using TEM and EDX using a 200 kV Philips CM 200-UT microscope equipped with a field emission electron source and for imaging a 4 megapixel cooled CCD sensor. The scanning mode of the microscope allows the measurement of EDX line scans along a defined path. TEM sample preparation was performed using a focused ion beam (FIB) system. This preparation technique requires deposition of a Pt cover layer. In order to spatially separate the Si-Fe surface from this Pt layer in the TEM images, the samples were coated with an amorphous carbon capping layer prior to TEM sample preparation. The capping layer was deposited using 100 eV low-energy carbon ion beam deposition [55].
Simulations of sputtering yields, ion and recoil distributions and ballistic mixing were performed using the Monte Carlo codes SRIM 2003-2008 [56] and the TRIDYN [57]. The TRIDYN surface binding energy input parameters were slightly adjusted to reproduce measured sputter yields for Si and Fe erosion with Xe ions, as well as corresponding SRIM sputter yields. It should be noted that SRIM versions 2008 and 2010 give much lower sputter yields for light elements such as Si or C compared to version 2006 and earlier versions, TRIDYN and experimental values. On the other hand, the angular emission distribution of sputtered light atoms such as Si or C atoms is completely different in SRIM version 2006 and earlier versions.
The Fe-deposition flux on the Si substrate is low enough to ensure a net positive erosion rate and rapid establishment of a steady-state surfactant coverage. The saturation coverage establishes already for ion fluences as low as 1 × 10 16 cm −2 [19]. TRIDYN simulations for 6 our erosion condition show that the saturation coverage is reached after about 3 × 10 16 cm −2 . In the present study, we used ion fluences between 1 × 10 17 and 5 × 10 17 ions cm −2 and thus investigated the pattern formation under steady-state coverage conditions. The relative local deposition flux at different spots on the substrate was calculated assuming a cos y θ angular emission distribution of sputtered atoms with y ≈ 1-1.5 [58,59] and the given substrate-target geometry. It turns out that the Fe coverage across the substrate varies up to a factor of 5 with the lowest coverage at the most distant point from the sputter target. This is in agreement with the local Fe-deposition flux, measured in irradiation experiments with an aluminum shield in front of the Si substrate. In this situation, surfactant atoms are sputtered off the steel target and deposited on the Si substrate, on which no sputtering takes place.
For a steel co-sputter target inclined at 30 • to the beam direction, we measured the deposition ratio of 0.04-0.12 Fe atoms per Xe ion at different positions on the substrate and a resulting steady-state Fe coverage of 2.5-5.5 × 10 15 Fe cm −2 . This is larger compared to the saturation value of 1 × 10 15 Fe cm −2 obtained from TRIDYN simulations [57] for pure ballistic mixing of Fe and Si by the Xe ion beam. The larger saturation value may be explained by pronounced ion beam-induced diffusion of Fe into subsurface regions.
Besides Fe as the major surfactant component, there is also a low fraction of < 1% of C, P, S, Mn and Pb, as constituents of the free cutting steel used, which are expected to play a negligible role in our study. The carbon sputter yield from SRIM simulations [56] is lower than 0.05 atom ion −1 for 5 keV Xe incident on steel. From RBS analyses of the sputtered Si substrates, we can give an upper limit for a coverage with Pb of < 5 × 10 12 cm −2 , i.e. at least three orders of magnitude lower compared to the Fe coverages. However, the residual concentration of Xe in the irradiated layer is about 10 15 Xe cm −2 or about 2 at.%. Macko et al [53] also considered indirect erosion due to ions reflected or backscattered from the co-deposition sputter target. In our case, the total fraction of Xe ions backscattered from the steel surface is at most 6% according to SRIM simulations. The fraction arriving at the Si substrate is even smaller. Therefore, we can neglect the influence of indirect erosion.

Results
AFM topographic images of Si surfaces, solely sputter eroded with 5 keV Xe ions with a fluence of 5 × 10 17 cm −2 , are shown in figure 2. The ion incidence angle was varied between 0 • and 30 • . The surface remains extremely flat without any surface features even after the removal of about 200 nm of material during the sputter process. The images prove that sputter erosion of Si with noble gas ions at normal and near-normal ion incidence up to 30 • without surfactants or contaminations on the surface does not generate any surface patterns. We have repeated these experiments for even higher fluences up to 1 × 10 18 cm −2 and lower ion energies of 2 keV, with the same result.
Topographic AFM images of silicon surfaces, which were irradiated with normal incident Xe ions at a fluence of 5 × 10 17 ions cm −2 and for different Fe coverage between 1.8 × 10 15 and 1.3 × 10 16 at. cm −2 , are shown in figure 3. The inset shows the corresponding fast Fourier transform (FFT) images. The indicated Fe coverage was determined by RBS measurements. The large variation in Fe coverage was achieved by a series of erosion experiments, each with a different inclination angle of 20 • -60 • between the steel target normal and the substrate normal. In figure 3, the projected deposition direction of Fe atoms is from left to right. A clearly discernible dependence of the surface topography on the Fe steady-state coverage is observed. No patterns were formed for Fe coverage smaller than 2 × 10 15 at. cm −2 (figure 3(i)) and the surface remains flat with rms roughness below 1 nm. At an Fe coverage of 2.5 × 10 15 at. cm −2 (figure 3(h)), a dot pattern appears with dot height varying from 2 to 10 nm. The average dot diameter is 55 ± 8 nm and the dot area density is 135 dots µm −2 . The FFT images in figures 3(f)-(h) show an almost isotropic distribution of dots. The power spectral density analysis gives an average dot spacing of about 110 ± 10 nm. For Fe coverage of 3.0 and 3.2 × 10 15 at. cm −2 , we find a reduced dot area density of 95 and 88 dots µm −2 , respectively. The dot diameter and the dot height increase, reaching a diameter of 70 ± 7 and 80 ± 7 nm, and a height of 10 ± 2 and 12 ± 2 nm, respectively. The average spacing increases to about 130 ± 15 nm. As an example, the size distribution of dots extracted with Gwyddion analysis software for the sample shown in figure 3(f) is displayed in figure 4. The majority of dots have a diameter of 80 nm with a Gaussian distribution with full-width at half-maximum (FWHM) = 14 nm (i.e. 80 ± 7 nm). There are also larger dots with diameters up to 150 nm, represented by a Gaussian distribution with a mean diameter of 105 nm and FWHM = 40 nm. Few dots have diameters smaller than 50 nm. At an Fe coverage of 4.0 × 10 15 at. cm −2 (figure 3(e)), more and more dots are arranged along rows with some dots combining to form short ripples. The average spacing between short ripples or rows of dots is about 120 ± 10 nm. The orientation of the ripples and rows of dots is roughly perpendicular to the projected deposition direction of the Fe atoms. At an Fe coverage of 5.4 × 10 15 at. cm −2 (figure 3(d)), many short and clearly separated ripple fragments are formed with a length of about a few hundreds of nm. The ripples exhibit a slight curvature and the ripple orientation is slightly non-uniform but almost perpendicular to the projected deposition direction of the Fe atoms (from left to right). Dots appear at dislocations or at points where ripples are interrupted. The wavelength is 110 ± 6 nm. For even higher Fe coverage of 6 × 10 15 at. cm −2 (figures 3(c)-(a)), the dots disappear and a distorted ripple pattern with many dislocation defects is formed with a ripple wave vector oriented parallel to the projected Fe-deposition direction. The ripple wavelength is 115-125 nm. In these cases, the Fe steady-state coverage is equivalent to 0.7-1.5 nm Fe.
To investigate the role of ion fluence on the nanopattern formation at different Fe coverage, normal incident Xe-ion sputtering has been carried out on Si substrates with ion fluences varied from 1 × 10 17 to 5 × 10 17 ions cm −2 . Adjacent to the Si substrate, a steel surfactant target was mounted with its normal tilted at 30 • relative to the ion beam. Figure 5 shows typical AFM images of the Si surface after ion beam erosion with a Fe steady-state coverage of 5.0 × 10 15 at. cm −2 (figures 5(a)-(c)) and 3.0 × 10 15 at. cm −2 (figures 5(d)-(f)), respectively. In figure 5, the projected Fe-deposition direction is from left to right. For the Fe steady-state coverage of 5.0 × 10 15 at. cm −2 , weak nanopatterns of short ripples were observed in addition to dots already appearing for an ion fluence as low as 1 × 10 17 ions cm −2 ( figure 5(a)). The crests of the short ripples are oriented perpendicular to the Fe-deposition direction. The ripples increase in length and height with increasing ion fluence and arrange themselves more and more regularly (figures 5(b) and (c)). At a lower Fe coverage of 3.0 × 10 15 at. cm −2 , the surface remains flat with an rms roughness of 0.5 nm for ion fluences up to 1 × 10 17 ions cm −2 . A dot   The influence of the Fe-deposition direction on the orientation of the formed nanopatterns becomes obvious by comparing the results from two experiments with different Fe-deposition directions, as shown in figure 6. In one experiment (figure 6(a)), the steel target was positioned on the left side of the Si substrate (i.e. the Fe-deposition direction is from the left), whereas in another setup ( figure 6(b)) the steel target was mounted on the top side of the Si substrate (i.e. the Fe-deposition direction is from the top). In both cases Si substrates were irradiated with a normal incident Xe beam and adjacent steel targets with their surface normal tilted towards the Si substrate at an angle of 30 • with respect to the ion beam. The AFM images in figure 6 clearly show that the orientations of the ripple patterns, mixed patterns of short ripples plus dots and the rows of dots in dot patterns are essentially perpendicular to the Fe-deposition direction, proving that the deposition direction of the surfactant atoms determines the pattern orientation. Representative cross sections of the ripple and dot patterns are also shown in figure 6. The shape of the dots is rather symmetric but the shape of the ripples is asymmetric with the steeper slopes facing the Fe-deposition direction. Also, the regions in between ripples and dots have a weak slope that is also related to the Fe-deposition direction.
In the steady-state condition, the Fe coverage, i.e. the areal density of the deposited Fe surfactant atoms, is independent of the Xe ion fluence and only depends on the ratio between Fedeposition flux and Xe-ion flux [18]. The Fe coverage was measured with RBS for a deposition ratio up to 0.12 Fe atom per Xe ion and ion fluences between 1 × 10 17 and 5 × 10 17 ions cm −2 . The experimental results shown in figure 7 confirm that for a Xe fluence of 1 × 10 17 ions cm −2 the Fe coverage has already reached its saturation value. The results are also in good agreement with calculations of the relative deposition flux assuming a cos θ angular distribution of sputtered particles, as described in the experimental section.
The patterns formed at different Fe coverages and ion fluences show a characteristic evolution of structure height, structure density and rms roughness. Furthermore, a characteristic evolution of the overall sputter yield is observed. The analysis of the rms roughness and the sputter yield as a function of Fe coverage is shown in figure 8. The evolution of the rms roughness clearly shows a rather well-defined critical Fe coverage for the onset of dot formation (2 × 10 15 cm −2 ), the onset of merging of dots to form ripples (4 × 10 15 cm −2 ) and the onset of ripple formation (6 × 10 15 cm −2 ). In the regime where dot patterns are formed, the dot height increases roughly linear with increasing coverage. In the regimes with mixed dots and short ripples and also ripples, the rms roughness has almost a constant value. The pattern contrast significantly increases with ion fluence (figure 5).
The measured sputter yield for low Fe coverage corresponds to the sputter yield Y Si ≈ 1.7 for pure Si. With the onset of dot and ripple formation, the sputter yield increases up to about Y ≈ 3.4. The reasons for this increase may be (i) the sputter yield amplification effect described by Nender et al [30] and Berg et al [32] or (ii) an increase in the sputter yield due to the patterned surface leading to local oblique ion incidence. The sputter yield calculated from TRIDYN simulations, which only account for ballistic mixing, is slightly lower than Y Si . Thus ballistic mixing would only be compatible with the sputter yield up to 2 × 10 15 Fe cm −2 coverage, i.e. within the flat surface regime. The sputter yield amplification effect could only explain the measured maximum sputter yield of Y ≈ 3.4 for an extreme surface morphology, e.g. consisting of a 1.5 nm buried pure Fe layer and a 0.5 nm top Si layer. However, such a surface morphology is not observed. Based on the measured Fe coverage and depth distribution obtained from RBS, TEM and EDX data, a sputter yield amplification of at most 25% is reasonable. Therefore, the major contribution to the high sputter yield is caused by a local oblique ion incidence due to the patterned surface. In particular, the steeper slopes at the ripple and dot structures are subjected to enhanced sputtering. In the height profiles of the patterns shown in figure 6, the local incidence

Scenario for pattern formation
Based on our experimental results, we propose a sequence of processes to describe the mechanism of pattern formation that relies on a completely different mechanism compared to the commonly applied continuum theories.
According to figure 7, the saturation coverage with Fe is already reached at a fluence of 1 × 10 17 Xe cm −2 . According to TRIDYN calculations, saturation is already reached at 3 × 10 16 Xe cm −2 . From figures 3(i), 5(a) and (d), it is shown that for a low coverage of 1.8 × 10 15 Fe cm −2 the Si surface is flat, even for a fluence of 5 × 10 17 Xe cm −2 . For 3 × 10 15 Fe cm −2 , the surface is still flat at 1 × 10 17 Xe cm −2 . For 5 × 10 15 Fe cm −2 , a weak irregular pattern appears at 1 × 10 17 Xe cm −2 . Therefore, the saturation Fe coverage is reached before the patterns start to form. In addition, at fluences of 1 × 10 17 Xe cm −2 , the surface region is already completely amorphized up to about 15 nm depth so that crystal structure effects can be ruled out. Therefore the initial steps of pattern formation are caused by none of the following: directional effects of the Fe-deposition, directional effects of the ion beam, and the Si crystal structure. Instead, we propose a phase separation of the amorphous Fe x Si surface region into regions with higher and lower Fe content, driven by ion-induced diffusion. Preliminary cross-sectional TEM analyses support an inhomogeneous composition in the flat amorphous surface layers with saturation Fe coverage. However, evidence of an initial phase separation is expected from scanning Auger microanalysis.
Ion-induced phase separation has been observed previously as a volume effect, e.g. in binary metal alloys [60]- [62], metal nanocrystal formation at Si/SiO 2 interfaces [63], FePt nanocrystal formation in Pt/Clayered films [64], ion-irradiated Cr/Cr coatings [65] and ionirradiated sub-stoichiometric GeO x films [66], and it was modeled using kinetic Monte Carlo simulations [60,67,68]. The Fe-Si system has a tendency to form FeSi and FeSi 2 alloys upon annealing to about 600-800 • C [69]- [71] or by ion beam mixing of Fe-Si bi-layers at lower temperatures, 450-550 • C [72]. The latter study demonstrates that ion irradiation promotes Fe x Si alloy formation. For annealing of sub-nm Fe films on Si, the formation of two-dimensional (2D) FeSi 2 islands was observed [69]. Therefore, we may expect that in our experiments the 2D phase separation may be induced by low-energy Xe-ion irradiation. The ion irradiation itself would also have an opposite effect, because displacement events in the collision cascade may, to some extent, hinder the accumulation of Fe into Fe x Si clusters or islands. As a balanced ionbeam-driven effect, a phase separation in Fe x Si regions with variable Fe content may occur. Up to this stage, no pattern is formed, but only the Fe areal density becomes inhomogeneous.
For different local Fe concentrations of the amorphous Fe x Si layer, we may expect slightly different local sputter yields for Si. We do not have to take into account the Fe sputter yield because we have reached dynamic equilibrium, so that the effective loss of Fe is zero. For higher Fe content, we expect a slightly lower Si sputter yield compared to regions with lower Fe content or pure Si. As a consequence, regions with higher Fe content are sputtered with a lower rate. Therefore, dot-like patterns will develop with increasing ion fluence. These initial dot patterns should be rather isotropic with no long-range order. This is confirmed by the FFT images of figures 3(f)-(h) and 5(a). In figure 5, it is observed that the pattern contrast increases with ion fluence, reaching eventually dot and ripple heights of about h ≈ 10 nm at a fluence of = 5 × 10 17 Xe cm −2 . If such a pattern height results from the composition-dependent sputter yield, we can calculate the difference in sputter yield between Fe-rich dot and ripple regions Y dot and Fe-poor intermediate regions with fluence range and atomic density n. For = 5 × 10 17 Xe cm −2 and n ≈ 5 × 10 17 cm −3 , we obtain a value of Y ≈ 0.1, only about 6% of the Si sputter yield, which would be sufficient to generate the observed pattern height. From TRIDYN (or SRIM) simulations of the sputter yield of Fe x Si for initial composition x = 0.2 and x = 0.03, we obtain Y ≈ 0.06 ± 0.03. Therefore, TRIDYN results support the idea that the composition-dependent sputter yield is sufficiently large to explain the observed pattern evolution.
When a pattern with a certain dot height is established, the directed deposition of atoms comes into play. Deposition occurs preferentially onto one side of the dots and also shadowing effects lead to a reduced deposition on the dot or ripple region opposite to the deposition direction. Therefore, we get preferential deposition in the dot and ripple regions and thus an additional local increase in the Fe concentration. When the Fe coverage is sufficiently large, dots may merge into short ripples and eventually a complete ripple pattern is generated. Due to the angular spread of the deposition directions, the ripples may develop a curvature, as can be seen in figures 3(d), 6(a) and (b). This curvature of the ripples may be responsible for the high defect density of the measured ripple patterns.
For oblique ion incidence, a ripple pattern already forms in the low fluence regime (∼ 10 16 ions cm −2 ) driven by a Bradley-Harper-type mechanism. For example, for 5 keV Xe + irradiation of Si at 70 • -75 • ion incidence angle, a ripple pattern with 30 nm wavelength and wave vector parallel to the projected ion direction appears already at a fluence of 3 × 10 15 Xe cm −2 [15]. For surfactant sputtering under such conditions, a ripple pattern exists before the steady-state coverage reaches its equilibrium value. The initial ripple pattern is then generated by the ion beam and the surfactants may modify this pattern, i.e. leading to relief-like structures or smooth surfaces, as observed for Ag, Pt or Au surfactants on Si [18].
The question arises as to whether keV heavy ions such as Xe are able to induce significant diffusion processes. For 5 keV Xe in Si, we find from SRIM about 150 displacements per ion. The overall shape of the collision cascade is roughly cylindrical around the ion path. About 60% of the ion's energy is released into phonon excitation, i.e. local vibrational excitations of Si atoms. Using the cylindrical thermal spike model [73], we can predict the number n S of atoms within the collision cascade volume and also the number of rearrangements n T due to phonon excitation within the cascade volume. For keV heavy ions in e.g. amorphous carbon [73], the ratio n T /n s reaches a value of about n T /n S ≈ 3 and n S is of the order of 10 3 atoms (figure 16 and equation (57) in [73]). With these numbers, we can estimate the amount of ion-induced diffusion. Each incident Xe ion will rearrange about n T ≈ 3 × 10 3 atoms, which is much more than the 150 displaced atoms due to collisions. Therefore, the phonon excitationinduced thermal spike dominates over displacement collisions. Within a 15 nm thick amorphous Fe x Si layer, we have about σ = 7.5 × 10 16 atoms cm −2 with average atomic spacing a ≈ 0.3 nm. An ion fluence of = 1 × 10 17 Xe cm −2 rearranges about · n T = 3 × 10 20 atoms cm −2 within this layer, or each atom of the layer undergoes about N = · n T /σ ≈ 4000 rearrangements. For a 3D random walk, the mean square distance is given by R 2 N = 3N a 2 ; with step distance a ≈ 0.3 nm and N ≈ 4000, we obtain R 2 N ≈ 33 nm. This estimate shows that ion-induced diffusion of Fe and Si atoms over distances sufficiently large to account for pronounced phase separation should be possible.

Discussion
In the absence of simultaneous deposition of surfactant atoms or in the absence of Fe as contamination of the Si surface, absolutely no nanopatterns are formed during normal ion incidence sputter erosion with 5 keV Xe ions and only flat surfaces are obtained. A pronounced self-organized pattern formation is triggered and driven by continuous Fe co-deposition from an adjacent steel sputter target irradiated with the same ion beam. Already for a fluence below 10 17 Xe cm −2 a steady-state Fe coverage is established, which varied between 10 15 and 10 16 Fe cm −2 depending on the local Fe-deposition flux. The measured local Fe-deposition flux is in good agreement with a calculation of the flux of sputtered Fe atoms assuming a cos y θ angular distribution of sputtered atoms, a quadratic distance dependence and taking into account the local Fe atom incidence angle.
The AFM images in figures 3 and 5 emphasize the fact that the amount of Fe steadystate coverage is a key parameter for the formation of nanopatterns on the Si surface during normal incident ion beam sputtering. The Fe coverage determines the type of pattern, such as dot patterns, mixed dot and ripple patterns and ripple patterns. With increasing ion fluence, the pattern contrast increases, i.e. the dot and ripple height increases, but the type of pattern remains unchanged. We find a critical Fe steady-state coverage for onset of dot formation (2 × 10 15 Fe cm −2 ), merging of dots to short ripples (4 × 10 15 Fe cm −2 ) and onset of ripple formation (6 × 10 15 Fe cm −2 ). The orientation of the ripples and chains of dots is perpendicular to the overall deposition direction of Fe atoms.
When dot patterns start forming at 2 × 10 15 Fe cm −2 coverage, with increasing coverage the dot density decreases and the pattern contrast (dot height) increases. This continues until dots merge into short ripples. The rms roughness in this regime remains rather constant. At the onset of complete ripple pattern formation at 6 × 10 15 Fe cm −2 , the roughness increases further and reaches a larger saturation value.
The ripple patterns are highly distorted, showing a large number of dislocations and also a slight curvature of ripples. This is probably caused by the distribution of Fe surfactant deposition directions with an azimuthal angle of about ±45 • around the average deposition direction and grazing incidence angles between 75 • and 90 • with respect to the surface normal.
Compared to the sputter yield Y Si ≈ 1.7 of pure Si, the overall sputter yield of patterned Si with Fe steady-state coverage is larger and may reach values of up to Y ≈ 3.4. The main reason for this increase is the roughness of the patterns itself, leading to locally varying ion incidence angles and corresponding sputter yield. A sputter yield amplification effect plays a minor role.
AFM height profiles and also TEM images reveal a highly asymmetric shape of the ripples that is related to the Fe surfactant deposition direction. TEM and EDX analyses show that an amorphous Fe x Si phase with a thickness of 15-25 nm is formed, which can be explained by ion beam damage. The Fe concentration is inhomogeneous and reaches values of x ≈ 0.20 (5) in the ripple and dot regions and x ≈ 0.03(1) in the flat intermediate regions.
The inhomogeneous Fe distribution is, in our opinion, initially caused by ion-induced diffusion and phase separation processes and eventually enhanced due to the directed deposition of Fe. Moreover, the slight inclination of the flat regions in between ripples and dots with inclination angles of up to 8 • with respect to the global surface normal may be due to sputtering of the steep slopes of the patterns and re-deposition into the intermediate regions. Ion-induced diffusion is also seen as a major contribution for the decrease in the dot area density and the merging of dots to ripples at nearly constant rms roughness. The increase in pattern contrast with increasing ion fluence can be explained by a composition-dependent sputtering yield.
Preliminary cross-sectional TEM analyses support an inhomogeneous composition in the initial flat amorphous surface layers with saturation Fe coverage. However, clear evidence of an initial phase separation may be provided e.g. with scanning Auger microanalysis, which should show a lateral non-uniform Fe concentration. Analyses of some samples are currently under way. To support the assumption that directed deposition of surfactant atoms has no influence on the initial pattern formation, one could perform analogous experiments using surfactant atoms, which do not tend to phase separate when forming an amorphous compound layer with Si. In particular, we expect that the same experiment with a silicon target as the source of surfactants should yield a flat and pattern-free surface after erosion. On the other hand, systems with a strong tendency to phase separate or with strong surface diffusion of surfactants should produce rather distinct patterns. Candidates for that are Ag and Mo surfactants. Experiments outlined here are currently under way.
An open question is whether the patterns are static or dynamic. For sputtering of pure Si at oblique ion incidence, it was observed that the ripple patterns move with a certain velocity [74] in agreement with theoretical predictions [3]. In the case of normal ion incidence, we would not expect such a dynamic behavior. However, it may be induced by the directed asymmetric Fe deposition, leading to the local asymmetric patterns and thus asymmetric local sputter rates.
A further challenge is to reduce the pattern defect density and to create more uniform dot and ripple patterns, which may then be of interest for e.g. optical or sensor applications requiring large-area nanopatterned surfaces. This may be achieved by a more precisely directed surfactant deposition using a more distant sputter target.

Conclusion
We have shown that directed deposition of Fe surfactant atoms triggers and drives the selforganized formation of nanopatterns during ion beam sputter erosion of Si substrates at normal ion incidence. Without these surfactants or contaminations, no patterns were formed and the surfaces remained flat. The Fe surfactant coverage rapidly reached a steady-state value. We have observed the critical values of this coverage for the onset of dot formation, merging of dots and onset of ripple formation between 2 × 10 15 and 6 × 10 16 Fe cm −2 . Thus, the Fe coverage determines the pattern type, whereas the ion fluence determines the pattern contrast. The pattern orientation is determined by the Fe-deposition direction. Continuous Fe surfactant deposition in combination with ion irradiation gives rise to ballistic mixing, damage formation and most probably strong ion-induced diffusion. In particular, ion-induced diffusion, ion-induced phase separation and a composition-dependent sputter yield are seen as major processes leading to dot and ripple pattern formation. Therefore, our results support a novel mechanism for pattern formation by ion beam erosion, which is different from the commonly applied mechanisms based on curvature-dependent sputter yields and surface diffusion. Recently, at the IBMM 2010 conference, Zhou and Lu [75] presented a continuum model to describe the surface evolution of Si during normal incidence ion sputtering with Fe incorporation. Their model includes surface-stress-induced instability and preferential sputtering as additional mechanisms for pattern formation. At the same conference Castro and Cuerno [76] introduced ion irradiationinduced viscous flow as a novel contribution to surface pattern formation. This underlines that ion-induced effects on the volume of the amorphized layer generated by the ion beam on top of the substrate may have relevant contributions to pattern formation.
Surfactant sputtering turns out to be a versatile method for creating novel surface nanopatterns with manifold possible applications. Our results provide the relevant parameters to achieve well-controlled pattern formation. They open the door to quantitatively reveal the mechanisms of pattern formation and provide valuable input to develop new theoretical models based on ion-induced diffusion and phase separation for surfactant-driven pattern formation.