Figs. 7.6(a) and (b) compare STM topographs after 0.25 MLE 5 keV Ar+ incident at
ϑ = 81◦ and at 550 K in the absence and in the presence of PO = 5 × 10−6mbar,
respectively. Figs. 7.6(c) and (d) compare STM topographs after 1.5 MLE 5 keV Ar+ incident at ϑ = 87◦ and at 550 K in the absence and in the presence of P
O = 5 ×
10−6mbar, respectively. As expected, in both cases the presence of the background pressure increases ΘS. To quantify the effect of the oxygen background pressure the
ratio ∆Θ of the amount of material removed ΘS(PO = 5 × 10−6mbar) from the oxygen
covered surface to the amount of material removed from the clean surface ΘS(PO= 0)
is plotted against the angle of incidence ϑ in fig. 7.4.
It increases from a factor of 2 at 81◦ and 83◦ to about a factor of 40 at ϑ = 87◦.
The question arises, why the enhancement of surface damage by adsorbates increases so strongly with the ϑ. The answer is conceptually simple. While the contribution of adsorbed oxygen to sputtering is only moderately dependent on ϑ and never ceases, sputtering on a clean surface ceases with increasing ϑ [compare Fig. 7.6(a) and Fig.
7.6(c)], thus bringing the denominator in the ratio of ∆Θ to zero and ∆Θ to infinity. As pointed out already in Section7.1the kinetic energy of motion along the surface normal E⊥ [compare (7.1)] becomes smaller and smaller with increasing ϑ. The variation of
ϑ from 81◦ to 87◦ changes E⊥ from 122 eV to 14 eV in the case of 5 keV Ar+ ions.
With increasing ϑ the transferred E⊥ thus first drops below the sputtering threshold
(The displacement energy equals to 34 eV for Pt [119]) and then below the threshold for adatom production. In the molecular dynamics simulations sputtering ceases for ϑ > 82◦ and adatom production for ϑ > 83◦if 5 keV Ar+is used on Pt(111) (see section
7.3). Although experimentally we find indeed a drastic decrease of sputtering from 81◦ and 87◦ [compare Fig. 7.6(a) and Fig. 7.6(c)] it is not absent entirely at ϑ = 87◦ thus
keeping ∆Θ finite. Similar to the CO case at ϑ = 87◦ the reason for sputtering is likely unavoidable adsorption of trace amounts of gas species from the background and the ensuing adsorption induced sputtering.
(a)
(b)
(c)
(d)
Figure 7.6: STM topographs after 0.25 MLE 5 keV Ar+ at ϑ = 81◦ [(a),(b)] and 1.5 MLE 5 keV Ar+ ions at ϑ = 87◦ [(c),(d)]. In fig. (a), (c) the sample was exposed
to the ion beam in the absence of an oxygen partial pressure, in (b),(d) PO = 5 ×
10−6mbar. The direction of the ion beam is indicated by an arrow. The image size is 1750˚A × 1750˚A.
7.5
Discussion
A number of issues not yet discussed in the previous sections will be addressed here. Ion-induced adsorbate desorption may be simply calculated using classical-trajectory (or Monte Carlo) simulations, in which only binary collisions are taken into account, and
7. TERRACE DAMAGE AND THE EFFECT OF ADSORBATES ON ITS FORMATION 81 82 83 84 85 86 87 0 10 20 30 40 50 angle of incidence (°)
Figure 7.7: Ratio ∆Θ of the removed material from the oxygen covered to the clean surface as a function of ϑ.
even the Pt substrate may be considered fixed during the simulation. Such a procedure is of course not possible for determining the sputtering of the substrate, and for this reason we started MD simulations of the entire process. A simple binary-collision description was developed by Winters and Sigmund [49] as introduced in section2.2.4. For grazing incidence ion erosion where the reflection coefficient is close to unity, the calculation of the three contributions of the cross section (direct knock-off, reflected ion contribution and the sputtered atom contribution) is reduced to the calculation of the direct knock-off contribution σ1 since the scattered ions do not enter into the crystal on
the flat terrace. This contribution to the desorption cross section is calculated by using a power potential for the interaction between the collision partners [ion ≡ (1), surface atom ≡ (2) and adsorbate ≡ (3)]. The direct knock-off contribution can be calculated by using formula 7.12. σ1 = C13 cos ϑ · m(EU3) −m 1 − X−m (7.12) The coefficient C13depends on the mass ratio between the colliding particles and the
nuclear charge and is specified in [48]. For a universal potential of the Lenz-Jensen type a value m = 0.25 results [138]. The kinetic energy of the impinging particles is denoted with E, U3 is the binding energy of the oxygen adsorbate (U3= 5.18 eV, and the factor
et al. were able to reproduce their experimental findings for nitrogen desorption on tungsten through keV ions with an accuracy better than a factor of two. Using (7.12) for our situation results in σO = 36 ˚A2. This value is in reasonable agreement with our
experimental (σO = 20 ˚A2) and molecular dynamics (σO= 32.6 ˚A2) results.
The next issue we need to address is the reliability of the experimental and the- oretical cross sections. The overall agreement for the desorption cross section σO is
satisfactory with 20 ˚A2 and 32.6 ˚A2 for experiment and simulation, respectively. Also the overall agreement for the sputtering cross section σS in the presence of oxygen is
rather good with 10.7 ˚A2 and 11.3 ˚A2 for experiment and simulation, respectively. As apparent from (7.8) the removed amount ΘS depends on the product of σS and ΘO.
The latter quantity is exponentially dependent on σOas apparent from (7.6). Therefore
the rise of ΘS in our fit is rather sensitive to σO. We are therefore confident that the
experimental value for σO is a reasonable estimate.
In simulation and experiment several possible sources of error must be discussed. As known Chapter 5, MD simulation has a tendency to overestimate sputter and adatom yields for grazing incidence. We discuss in the following several issues connected with the reliability of our MD simulations.
1. A prime source of systematic error in every simulation is the implementation of the interatomic potentials. In this case, the O-Pt potential appears particularly difficult to implement: it is known to be of many-body nature; its bond strength decreases strongly from the value of 3.81 eV in a Pt-O dimer bond [139] to 1.73 eV, as it is used here to describe the interaction with a Pt surface [140]. However, during the ion-surface interaction, the O atom may be dynamically exposed to different bonding environments, ranging from implantation (12 Pt neighbours) to desorption (0 Pt neighbours). We checked the influence of the bonding part of the Pt-O potential by performing a reference simulation (for a restricted number of events), in which bonding was entirely switched off. No statistically significant deviations from our result with the full (repulsive and attractive) potential were found. We conclude that it is mainly the repulsive part of the Pt-O interaction which is relevant for the fate of the adsorbate and the induced sputtering. 2. In the simulation, the fate of the adsorbate under irradiation can be easily fol-
lowed. The cross section for implantation (43.9 ˚A2) is even larger than that for
desorption (32.6 ˚A2). Experiment measures essentially the removal of O from the surface; hence the experimental desorption cross section of 20 ˚A2 not only includes O desorption, but also O incorporation into the target. However, from an inspection of the depth distribution of implanted O atoms we find that 77% are ‘implanted’ into the first layer, 9 % into the 2nd layer, and the remainder form a highly skewed distribution extending deep into the Pt crystal. We feel that our
7. TERRACE DAMAGE AND THE EFFECT OF ADSORBATES ON ITS FORMATION
potential cannot safely predict the fate of the shallow implanted O atoms; many of them may actually return to the surface in the course of time and will thus not be removed from the surface.
3. In experiment, only the effects of a finite adsorbate coverage can be determined, while for simulation it is most convenient – and also of fundamental interest – to study the effect of a single adsorbate atom. These two views can be combined as long as the linear relations (7.2) and (7.9) hold. From our previous work with isolated Pt adatoms on a Pt (111) surface we could derive a criterion for the maximum coverage Θlinfor which the single adatom results could be extrapolated
linearly to finite coverages,
Θlin∼=
Ω Ainfl
. (7.13)
Here Ainfl denotes the zone of influence around the adatom, into which the pro-
jectile must hit in order to collide with the adsorbate atom; depending on the process of interest (e.g., sputtering or adsorbate desorption), this zone of influ- ence may assume slightly different values. The idea behind Eq. (7.13) is that linearity holds as long as the zones of influence of the individual adsorbate atoms do not overlap. In our case, we measure a value of Ainfl = 19 ˚A2 for sputtering
and Ainfl= 48.5 ˚A2 for desorption. Thus we may trust our results up to coverages
of Θlin ∼= 0.35 for sputtering; this includes the O saturation coverage of 0.25. For
oxygen desorption, it is Θlin ∼= 0.14 and our linear extrapolation, Eq. (7.11), to
the saturation coverage is subject to a larger error.
4. In (7.8) σS is just a multiplier determining the magnitude of ΘS. As pointed
out already in Section 7.2, our experimental σS not only includes the additional
sputtering at the locations of the adsorbed oxygen adatoms. The damage created by the presence of oxygen (adatoms, adatom clusters surface vacancy clusters) itself enhances ΘS, as the damage is illuminated by the ion beam and allows for
large angle scattering events. This positive feedback mechanism is not included in our MD simulation. In the simulation always a single oxygen atom on a perfect surface is investigated. Thus σS as derived in experiment significantly
overestimates the true σS and thus should also overestimate the value obtained
in the MD simulations. This is not the case, most likely due to the general overestimation of sputter yields on Pt(111) through MD simulations.
A third issue to be addressed is how realistic experimental values for ΘS,clean are
in the light of our results on adsorbate enhanced sputtering. Indeed for ϑ > 83◦ the MD simulations predict the absence of any surface damage (see chapter5). Even when considering the MD simulations with proper skepticism, it appears unlikely that for
ϑ = 87◦ 5 keV Ar+ions are able to induce surface damage. Let us consider for instance the case of CO adsorption described in Section 7.1. Using the data of Poelsema et al. [132] and a rough estimate for the sputtering cross section of adsorbed CO based on our data shown in Section 7.1we find a partial pressure of PCO≈ 3 · 10−10mbar to be
sufficient to induce the observed ΘS,clean = 0.04 ML after 1 MLE at 400 K. Although
the CO partial pressure in the absence of the ion beam is in low 10−11mbar range, turning on the ion beam results in a considerable increase of the CO background of about 1·10−10mbar. It is thus nothing but plausible that the removed material Θ
S,clean
at very large angles ϑ is largely due to adsorbate induced sputtering resulting from the adsorption prior to the onset of ion exposure and the adsorption induced by the pressure rise of the ion beam itself. The adsorbate enhanced erosion is relevant in a number of situations. Among them is pattern formation under grazing incidence conditions, which might be accelerated under poor vacuum conditions. Also ion scattering experiments under grazing incidence conditions are always endangered to be obscured by effects of unwanted adsorption.
In the present context, it is particularly interesting to compare the effect of a single adsorbate on the surface with that of a single adatom; these latter simulations have been performed for the same Pt(111) surface as investigated here, but for another incidence angle (83◦) azimuth ([¯1¯12]); hence a comparison with those results can only be performed qualitatively. As Table 7.1 shows, the desorption cross sections for the adsorbate and the adatom are of similar magnitude. However, the Pt adatom gives rise to an order of magnitude larger sputter and adatom-creation effect, while the O adsorbate is implanted with an order of magnitude larger efficiency. The first feature can be understood by the small O/Pt mass ratio: even though the O adsorbate can receive quite large energies from the Ar projectile, its sputter efficiency is small. The larger implantation cross section of O can be traced back to the small atomic radius of O which lets it fit easier into the Pt crystal than a Pt atom.
7.6
Conclusion
Scanning tunneling microscopy experiments demonstrate that sputtering on terraces in grazing incidence ion erosion is dominated by adsorbed particles. Molecular dynam- ics simulations reveal that the physical mechanism responsible for adparticle induced sputtering is direct knock-off impacts of the impinging ions on the adsorbates. The energized adsorbates in turn transfer energy to substrate atoms which eventually be- come sputtered. At extremely grazing incidence we found an enhancement of the initial erosion rate by a factor of 40 through adsorbed oxygen atoms. A similar enhancement of the initial erosion rate is found for adsorbed carbon monoxide. This is particularly important since CO adsorbs with high sticking probability at room temperature on
7. TERRACE DAMAGE AND THE EFFECT OF ADSORBATES ON ITS FORMATION
many metal surfaces and it is at the same time a major component of the background gas in UHV systems. The desorption cross section and the related and adsorbate in- duced sputtering cross section for oxygen are extracted from experiment and molecular dynamics. Both numbers agree within the experimental uncertainties. The obtained desorption cross section also agrees reasonably with the one derived for knock-off des- orption calculated within the Winters and Sigmund theory. Our results show that a reliable measurement of the sputtering yield of perfect crystalline terraces at grazing incidence is very difficult due to hardly avoidable minute amounts of adsorbed particles. However, as soon as a significant number of vacancy and adatom clusters are present on the substrate, the presence of adsorbates will be less important for the erosion rate.
Rapid coarsening of ion beam
ripple patterns by defect
annihilation
8.1
Introduction
In this chapter coarsening of ion beam ripple patterns is described. The fluence dependent measurements presented here can also be found in [32]. The data have been used to develop a simple model, which explains athermal coarsening of ion induced ripple patterns.
Coarsening, i.e. the increase of the characteristic feature size with time, is a well known and ubiquitous phenomenon in the physics of structure formation. Ostwald ripening [141], grain growth [142] or grain boundary grooving [143] are examples for coarsening phenomena driven by the minimization of surface or interface energy in a system. Coarsening also takes place in systems far from equilibrium with nonconserved particle numbers, e.g. in molecular beam epitaxy (MBE) or ion beam erosion.
Siegert [144] and Moldovan and Golubovi´c [145] first realized that coarsening in MBE and ion beam erosion under conditions where kinetically preferred facets are established is enabled by defects in the evolving pattern. The demand for reduction of effective system energy stored in the facet edges drives the reduction of edge length and gives rise to the motion of defects and their subsequent annihilation reactions. The facet edge mobility itself requires thermally activated surface diffusion and is thus dependent on the characteristic feature size λ of the pattern and on temperature T . The feature size is found to develop with time t according to a power law λ ∝ tn with coarsening exponents n ranging from 1/3 to 1/4 depending on the symmetry of the crystalline substrate [145;146], in partial accordance with experiments [67;147;148].
8. RAPID COARSENING OF ION BEAM RIPPLE PATTERNS BY DEFECT ANNIHILATION
However, there are also situations where coarsening is not an energy minimizing process. Using scanning tunneling microscopy (STM), here we show that under grazing incidence ion erosion of a crystalline surface rapid, athermal coarsening of the ripple pattern takes place through the annihilation of mobile defects, which are driven by the ion beam along the ripple direction. The mechanism is similar to that described by Werner and Kocurek [149] for coarsening in transverse aeolian sand dunes, where defects are driven by the wind perpendicular to the crest lines. This establishes a connection between coarsening of ion beam ripples (λ ≈ 10−8m) and dunes (λ ≈ 103m),
complementing existing theoretical attempts to use models of aeolian ripple formation for the description of ion beam ripples [150;151].
Ripple patterns form under ion erosion of solid surfaces through a variety of different mechanisms [9], and in all cases such patterns contain a certain density of defects that reflect the random fluctuations during the initial stages of the evolution. Defect density has been used as a measure for the degree of order in ion-induced ripple patterns [152; 153], but the dynamical evolution of defects and their relation to coarsening behavior has so far been studied only on a qualitative level [13; 154]. In the specific case of grazing incidence erosion of crystalline surfaces considered here, the topography evolution can be largely reduced to the ion-induced propagation of surface steps.
This basic simplicity of the dynamics allows to quantitatively relate the coarsening behavior to the fundamental time constant of the process, the propagation velocity of individual steps.
8.2
Results
Coarsening during 5 keV Ar+grazing incidence ion exposure of Pt(111) is visualized in Figs. 1(a)-1(f) after fluences from 1 MLE up to 300 MLE. As visible in Fig. 1(a) after exposure to 1 MLE, the formation of a ripple pattern is rapid. The pattern is aligned along the projection of the ion beam direction on the surface. In the initial stage steps of monoatomic height can still be distinguished in the STM topography. Details of the pattern formation mechanism can be found in section 2.5.3 or in [10; 32]. Important for the following investigation is the ion beam induced motion of illuminated ascending step edges, i.e. the step edge velocity. In the case of the [¯1¯12] azimuthal direction and at an angle of incidence of 83◦ a step edge sputtering yield of Ystep = 7.7 ± 0.9 has been measured [see table 5.1]. The step edge velocity can be calculated with equation
5.2 and equals to v = 28 ± 3 nm/MLE.
As visible in Figs. 1(b)-1(f) λ strongly increases with F . Figure 2 represents the dependence of λ on F quantitatively. After a rapid initial increase of λ up to 20 MLE it becomes a linear function of F . Within the limits of error the wavelength increase is identical for 350 K and 450 K evidencing the athermal nature of the coarsening. Above
Figure 8.1: (a)-(f) STM topographs of Pt(111) after exposure to 5 keV Ar+ incident at an angle ϑ = 83◦ at 450 K. The scan size is always 2450 ˚A × 2450 ˚A. The ion fluences
are (a) 1 MLE, (b) 5 MLE, (c) 20 MLE, (d) 70 MLE, (e) 160 MLE and (f) 300 MLE. The projection of the ion beam direction onto the surface is indicated by an arrow in (a). The four types of defects in the ripple pattern are circled in (c). They are start (S), end (E), bifurcation (B) and merger (M) defects. (g) displays a height profile along the coordinate X of the line indicated in (f). (h) A hexagonal vacancy island formed after sputtering and equilibration at 750 K [87] (indicated by the white hexagon) is elongated through the motion of the illuminated steps in beam direction during grazing incidence ion exposure at 550 K.
8. RAPID COARSENING OF ION BEAM RIPPLE PATTERNS BY DEFECT ANNIHILATION 0 50 100 150 200 250 300 0 10 20 30 40 ( n m ) F (MLE) 350K 450K 550K 1 10 100 1 10 ( M L ) F(MLE)
Figure 8.2: Pattern wavelength λ and roughness σ (inset) as a function of ion fluence F for 350 K (full dots), 450 K (full squares) and 550 K (full up triangles). Lines to guide the eye.
450 K step edge diffusion sets in causing a significant increase of the initial wavelength [10]. Besides an apparent upward shift, the functional dependence of λ on F in the thermal regime at 550 K is still similar to the lower temperature cases.
The inset of Fig. 2 displays the evolution of the surface roughness σ with F . A power law behavior with σ ∝ Fβis found over a fluence range of more than two decades. The exponents β are 0.50, 0.48 and 0.59 for 350 K, 450 K and 550 K, respectively. An exponent β = 1/2 results for a Poisson model, i.e. for a situation where material transport between different atomic layers is suppressed (large step edge barrier for surface vacancies) [155]. The observed preferential nucleation of surface vacancies at the bottom of grooves is consistent with this scenario.
The formation of stable kinetically preferred facets in the pattern (slope selection) would require the identity of the exponents n and β, which is not observed here. Indeed, the height profile of Fig. 1(g) taken through the ripples of Fig. 1(f) does not display a single set of preferred facets but rather a parabolic ridge profile.
It is well visible in Fig. 1 that defects originating from the initial randomness of nucleation and coalescence of monolayer vacancy islands are present in all stages of pattern evolution. Four types of topological pattern defects are circled and labeled in