Transition from ripples to faceted structures under low-energy argon ion bombardment of silicon: understanding the role of shadowing and sputtering
© Basu et al.; licensee Springer. 2013
Received: 5 April 2013
Accepted: 7 June 2013
Published: 19 June 2013
In this study, we have investigated temporal evolution of silicon surface topography under 500-eV argon ion bombardment for two angles of incidence, namely 70° and 72.5°. For both angles, parallel-mode ripples are observed at low fluences (up to 2 × 1017 ions cm-2) which undergo a transition to faceted structures at a higher fluence of 5 × 1017 ions cm-2. Facet coarsening takes place at further higher fluences. This transition from ripples to faceted structures is attributed to the shadowing effect due to a height difference between peaks and valleys of the ripples. The observed facet coarsening is attributed to a mechanism based on reflection of primary ions from the facets. In addition, the role of sputtering is investigated (for both the angles) by computing the fractional change in sputtering yield and the evolution of surface roughness.
81.05.Cy, 81.16.Rf, 61.80.Jh, 87.64.Dz
KeywordsSilicon Ion beam patterning Atomic force microscopy
Low-energy ion beam sputtering (IBS) is considered to be a very promising and cost-effective technique to fabricate self-organized nanoscale periodic patterns on a large-area (up to 2- to 3-in. diameter) solid surface in a single step . Such nanoscale periodic structures (mostly ripples) are considered to be useful as templates for growth of nanofunctional thin films having potential applications in plasmonics, nanoscale magnetism, and other technological applications. For instance, Ag films deposited on rippled silicon substrate show strong optical anisotropy [2, 3] and Fe films on rippled substrates demonstrate magnetic anisotropy which are driven by morphological anisotropy [4, 5]. Direct nanoscale ripple patterning can also induce in-plane uniaxial magnetic anisotropy in epitaxial  and polycrystalline ferromagnetic Fe or Ni films . In another study, it has been shown that rippled Au films show anisotropy in electrical transport property .
It is well established that ripple characteristics depend on beam and target parameters, namely ion species, ion energy, ion flux, ion fluence, ion incident angle, composition, and sample temperature [9–17]. In addition, experimental studies have shown that evolution of ion beam-induced ripple morphology is related to continuous change in sputtering yield even at any given angle [18–20]. For instance, Stevie et al. reported that in the case of ripple formation at 52° (for 6 keV O2+ ions), the sputtering yield got enhanced by nearly 70% as compared to the initial value . However, an accurate prediction of change in sputtering yield is still not well developed due to a complex nature of the problem (i.e. complex mechanisms leading to a surface morphology and the existing interplay between these mechanisms and change in sputtering yield).
In addition to the experimental studies, there exist substantial amount of theoretical studies to explain IBS-induced ripple formation. Bradley-Harper (B-H) theory and its extensions were invoked to explain ion erosion-induced ripple formation due to off-normal ion bombardment and its coarsening [22, 23]. Following these theories, there are reports which show that although ripples are more or less periodic in nature in the linear regime, with increasing time, it may change to a sawtooth-like morphology [9, 12, 13]. This type of transition from ripples to sawtooth or faceted structures was mentioned by Makeev and Barabasi for small surface gradients [24, 25] which was later generalized by Carter at intermediate ion energies (few tens of kiloelectron volts) for all surface gradients . In his work, Carter showed (based on geometrical argument) that with the growth of ripple amplitude-to-wavelength ratio, the shadowing of the incident ion beam by surface features can lead to formation of sawtooth-like facets. In a later work, this model was applied to explain morphological transition observed under bombardment of silicon by 30 keV argon ions . However, applicability of this very approach is yet to be explored for low-energy (hundreds of electron volts) ion-induced transition from ripples to faceted structures under continuous ion bombardment. A major reason for this is the lack of available experimental data on the formation of faceted structures using low-energy ions.
For instance, Keller and Facsko reviewed the temporal evolution of ripple formation on Si by low-energy Ar ion bombardment . They compared the predictions of various continuum models with experimentally observed ripple morphologies. In a previous work, Ziberi et al. reported well-ordered ripple formation on Si surface by 1,200 eV argon ion bombardment at 15° . This contradicts the results of Keller and Facsko where the surface remained stable at near-normal incidence of Ar ions. In another work, Frost et al. reported on various pattern formations (ripples, dots, and their combination) and smoothening of silicon surface by low-energy ion beam erosion . The effect of elevated target temperature during ion beam sputtering was addressed by Brown et al. . Evolution of surface morphology during 500 eV Ar ion-induced erosion of Si(111) at an oblique incidence of 60° was demonstrated over a temperature range of 773 to 1,003 K. Formation of dots with rectangular symmetry was reported at temperatures above 963 K, whereas perpendicular-mode ripples were observed below this temperature. Thus, there is a room to look for controlled synthesis of self-organized faceted structures on silicon surface using similar ion energies.
In this study, we report on the transition from ripples to faceted structures on silicon surface beyond a threshold ion fluence and their coarsening at even higher fluences. As a novelty, we study this transition in the unexplored low ion energy regime which is roughly two orders of magnitude lower than those studied in the aforementioned works [9, 12, 13, 26, 27]. In this energy regime, smaller ion penetration depth, ion-mediated amorphization, and sputtering yields may lead to different pattern formation and dynamics. We have selected two different oblique incident angles, namely 70° and 72.5°.
In addressing the mechanism of the observed transition, variation in the erosion rate of a sinusoidal surface is calculated using the theoretical model of Carter . It is seen that for critical values of the amplitude-to-wavelength ratio, inter-peak shadowing of incident ion flux can lead to a transition from ripples to faceted structures. The coarsening behaviour of faceted structures with increasing fluence is explained in light of Hauffe’s mechanism based on reflection of primary ions . Carter’s theory is also used to calculate fractional change in sputtering yield for ripples and faceted structures (where we have replaced the amplitude-to-wavelength ratio by amplitude-to-base width ratio for the latter ones) which is observed to follow a nearly similar trend as that of surface roughness as the evolution of the observed patterns takes place.
where Y(θ) is the sputtering yield, and the coefficients a(θ), b(θ), and c(θ) are functions of cosθ, sinθ, and sputtering yield Y(θ) and its derivatives. Thus, fractional change in sputtering yield becomes a polynomial function of even powers of h0/λ.
According to this condition, if the ratio (h0/λ) exceeds a threshold value, troughs of a sinusoid will not be eroded further but instead erosion will take place at the crests. This in turn may give rise to a sawtooth-like waveform.
Following Ar ion exposure, the samples were imaged by ex situ atomic force microscopy (AFM). Silicon probes were used having a diameter of approximately 10 nm. Root mean square (rms) surface roughness, w, and two-dimensional (2D) autocorrelation function were calculated for all AFM images using the WSxM software . Wavelength of ripple patterns was calculated from the respective autocorrelation functions. As far as faceted structures are concerned, instead of wavelength, we considered the average base width value which was calculated from a large number of line profiles drawn on the respective AFM images. In addition, Rutherford backscattering spectrometric and X-ray photoelectron spectroscopic measurements were performed on Ar ion-bombarded Si samples which did not show the presence of any impurity above their respective detection limits.
Results and discussion
Calculated values of ripple wavelength ( λ ), feature height ( h ), and base width of mounds/facets
Angle of incidence
Fluence (ions cm-2)
Average feature height (nm)
Average base width (nm)
1 × 1017
2 × 1017
5 × 1017
10 × 1017
15 × 1017
20 × 1017
1 × 1017
2 × 1017
5 × 1017
10 × 1017
15 × 1017
20 × 1017
To explain the transition from a rippled surface to faceted structures, we invoke the shadowing condition stated in Equation 2. Let us first consider the case of 70° and the fluence of 1 × 1017 ions cm-2 where the calculated value of 2πh0/λ turns out to be 0.369, whereas tan(π/2 - θ) is 0.364. Thus, 2πh0/λ is slightly above the limiting condition which indicates the shadowing effect to start playing a role at this fluence itself. In the case of 2 × 1017 ions cm-2, the shadowing effect becomes more prominent since 2πh0/λ turns out to be 0.551. As a result, crests of the ripples should undergo more erosion compared to troughs, and hence, there is a likelihood of mounds/facets to evolve. This explains the observation of mounds at this fluence. Similar behaviour is observed in the case of 72.5°. For instance, in the case of 1 × 1017 ions cm-2, 2πh0/λ equals to 0.242, while tan(π/2 - θ) turns out to be 0.315. Thus, the condition for no shadowing, i.e. tan(π/2 - θ) ≥ 2πh0/λ gets satisfied here, and ripples are expected to be seen. The observation of sinusoidal ripples in Figure 4a supports this theoretical prediction. On the other hand, shadowing sets in at the fluence of 2 × 1017 ions cm-2 since in this case tan(π/2 - θ) becomes smaller than 2πh0/λ (=0.465). This leads to the formation of small mound-like entities (in the form of broken ripples) appearing on the corrugated surface.
We now go on to explain the coarsening behaviour of faceted structures (as is evident from Table 1) at higher fluences (>5 × 1017 ions cm-2) using the mechanism proposed by Hauffe . In this framework, the intensity of reflected ions impinging on an arbitrary area on a facet depends on the dimensions of the reflecting adjoining facets. According to V n ~ jY, where j is the ion density on the surface element (which also contains the reflected ions), Y is the sputtering yield, and V n is the displacement velocity of a surface element in the direction of its normal, it is clear that the displacement velocity will be higher for the larger facet. This does not require a particular form of spatial distribution of reflected ions albeit it is necessary that the reflected ions should fall on the neighbouring facets. Accordingly, a smaller facet will disappear into the next bigger one and form an even bigger facet. This corroborates well with the cross-sectional line profiles corresponding to faceted structures shown in Figures 5d,e,f and 6d,e,f which reveal clear enhancements in lateral dimension and height of the faceted structures with increasing ion fluence.
In summary, temporal evolution of surface topography has been systematically studied for silicon under 500 eV Ar ion bombardment for two angles of incidence, namely 70° and 72.5°. For both angles of incidence, parallel-mode ripples are formed at lower fluences which subsequently undergo a transition from parallel-mode ripples to mound/faceted structures. This transition from ripples to mounds and/or faceted structures is explained geometrically which takes into account the inter-peak shadowing effect. Thus, it can be concluded that Carter’s model (mostly used to explain experimental data at intermediate ion energies), applied for the first time in the low ion energy regime, successfully explains the pattern transition observed in the present case. With increasing ion fluence, faceted structures undergo coarsening, i.e. they grow bigger in both lateral dimension and height. The coarsening behaviour is explained by invoking Hauffe’s mechanism which is based on reflection of primary ions on facets. In addition, to check the role of sputtering, fractional change in sputtering yield (with respect to the flat surface) was calculated based on Carter’s theory. It is seen that both fractional change in sputtering yield and surface roughness increase almost in a similar way with fluence-dependent increase in lateral dimension of ripples/facets. Looking into this similar behaviour, it may be concluded that the role of sputtering-induced roughening process cannot be ignored for evolution of ion-induced self-organized patterns.
The authors would like to acknowledge Sandeep Kumar Garg for fruitful discussion on calculation of fractional change in sputtering yield.
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