Ripple coarsening on ion beam-eroded surfaces
© Teichmann et al.; licensee Springer. 2014
Received: 21 May 2014
Accepted: 18 August 2014
Published: 27 August 2014
The temporal evolution of ripple pattern on Ge, Si, Al2O3, and SiO2 by low-energy ion beam erosion with Xe + ions is studied. The experiments focus on the ripple dynamics in a fluence range from 1.1 × 1017 cm-2 to 1.3 × 1019 cm-2 at ion incidence angles of 65° and 75° and ion energies of 600 and 1,200 eV. At low fluences a short-wavelength ripple structure emerges on the surface that is superimposed and later on dominated by long wavelength structures for increasing fluences. The coarsening of short wavelength ripples depends on the material system and angle of incidence. These observations are associated with the influence of reflected primary ions and gradient-dependent sputtering. The investigations reveal that coarsening of the pattern is a universal behavior for all investigated materials, just at the earliest accessible stage of surface evolution.
Topography engineering by ion beam erosion has attracted much interest for patterning [1–8] and surface smoothening [9, 10] for several years. In the last decade, many investigations have focused on Si as a model material in order to explore the origin of ion beam patterning [7, 11–15]. The first model that was able to describe formation of self-organized nanostructures is the erosion-based theory of Bradley and Harper (BH) . The model explains the ripple formation process and orientation of ripples with respect to the ion beam direction by means of surface-curvature-dependent sputtering and temperature-dependent diffusion. Nevertheless, the model cannot explain several experimental findings. Especially a transition between a smooth and rippled surface at a certain angle of incidence is not explained. In addition to the BH model, Carter and Vishnyakov (CV)  suggested ballistic drift due to momentum transfer during ion bombardment as smoothening mechanism. In consequence, the ripple formation occurs if curvature-dependent sputtering can compensate the ballistic drift. Madi et al.  combined both approaches and modified them with a correction factor for high incidence angles. This model predicts a critical angle as starting point for patterning and explains smoothening for normal and near-normal incidence angles. Similar results have also been shown by the crater function theory of Norris et al. [19, 20]. The moments of the crater function also consist of an erosive and a dominating redistributive part.
A key factor to address the applicability of different models is the dynamic behavior of pattern formation. In generally accepted models, two regimes are distinguished . The first regime is the linear time regime of pattern formation where the wavelength of the pattern is constant. The crossover into the nonlinear regime begins if the wavelength grows with irradiation time. Alternatively, the regimes can be separated by the temporal evolution of the surface roughness which grows exponentially in the linear regime and has a power-law behavior in the nonlinear regime. Furthermore, the total ion fluence is a critical parameter that controls the structure size and regularity of the ripple pattern.
Former work revealed that coarsening by reflected ions played a crucial role for surface evolution. The mechanism has been introduced by Hauffe  and is considered to account for the ripple coarsening that was observed on SiO2 and Ge . The aim of this work is to present a comprehensive study of low-energy ion beam erosion, especially of the role of reflection of primary ions for different technical important substrate materials with Xe gas ions. In particular Si is used as reference material that is well investigated in the last decade. As direct counterpart to Si, Ge is used, which has a similar sputter yield as Si but a higher fraction of reflected ions due to its higher target mass. The oxidic pendant SiO2 (fused silica) of Si is analyzed as well as Al2O3 (sapphire), which have comparable reflection coefficients. However, Al2O3 has a lower sputter yield than SiO2 because of its higher surface-binding energy. As sputtering gas, Xe was used for which distinct pattern formation takes place on all target materials. As incidence angles, 65° and 75° were chosen, where ripple formation takes place and the sputter yield is close by its maximum.
The samples used were commercially available polished Ge(100) (initial root mean square (RMS) roughness ), Si(100) , Al2O3 and amorphous SiO2 substrate pieces. These samples were mounted on a water-cooled substrate holder in a high vacuum chamber with a base pressure of 10-6 mbar, which can be tilted from 0° (corresponding to normal ion incidence) up to 90° with respect to the axis of the ion beam source. The cooling ensures a substrate temperature below 80°C. Furthermore, the sample holder is equipped with a silicon shielding in order to prevent metallic contaminations that affect the evolving structures on Si [14, 25] as well as on Ge [24, 26]. This non co-deposition setup also prevents secondary collisions of scattered gas ions and redeposition of sputtered silicon atoms . For the experiments, a homebuilt Kaufman-type ion source is used. Furthermore, the source is equipped with two 190-mm grids with a reduced aperture of 100 mm. Hence, no metallic contaminations could be detected with Rutherford backscattering spectrometry (RBS) as well as with X-ray photoelectron spectroscopy (XPS) measurements. The Xe + ion current density was kept constant at 300 μ A/cm2 during the experiments which results in an ion flux of J = 1.87 × 1015 cm-2 s-1 in a plane perpendicular to the ion beam. The samples were irradiated for durations from 1 up to 120 min corresponding to a fluence range from 1.12 × 1017 cm-2 to 1.35 × 1019 cm-2. An ion energy of 600 and 1,200 eV was used. The surface topography was analyzed by scanning atomic force microscopy (AFM) operating in TappingMode™ or ScanAsyst™ mode . The measurements were performed in air using silicon nitride cantilever with Si tips with a nominal tip radius smaller than 5 nm (TappingMode™; Bruker Corporation, Billerica, MA, USA) or silicon nitride cantilevers with nominal tip radius of 2 nm (ScanAsyst™; Bruker Corporation). Routinely, each sample was analyzed with a scan size of 2 or 4 μ m and 10 μ m and a resolution of at least 1,024 × 1,024 pixels. The AFM data were analyzed with SPIP™  software and a custom-programmed MATLAB®; (Mathworks Inc., Natick, MA, USA) routine for calculation of the power spectral density (PSD) functions following an approach of Duparré et al. . The wavelengths of the ripple structures are determined from the corresponding PSD curve. For a given sample (sample size typically 10 mm × 10 mm), the wavelength determined at different positions across the sample is extremely small. Also, the fluctuation of the corresponding RMS surface roughness is negligible small. Therefore, no error bars are indicated in the graphs as they are typically smaller than the symbol size. However, it must be noted that the experimental reproducibility between different etching series is in the range ≤5%. For surface gradient angle calculation, SPIP™ was used again and the gradient angles are calculated in ion beam projection direction. The gradient histograms have been computed from the x-gradient images.
Another observable tendency in the evolution of the structures is the formation of faceted structures with a distinct angle towards the global surface normal. Such a process is potentially explained by gradient-dependent sputtering. In accord with Nobes et al.  and Johnson , stable facets evolve on the surface with local angle of incidence of 0°, 90° and the angle of incidence where the erosion rate is maximal. However, these angles are not exactly found in the evaluation of the surface gradients because the process is superimposed by smoothening mechanisms and the influence of reflected ions. Moreover, depending on the slope of the erosion velocity curve (Figure 8a), one can make a point to the dynamic of the system: a greater slope of the curve causes a faster evolution of the surface.
In the linear stability regime, a constant wavelength is predicted with increasing fluence. This is usually described by linear differential equations until a critical value is reached. For higher fluences the system has to be described in a nonlinear regime as the approximations for a linear stability are not admissible anymore. This raises the question if for shorter erosion times linear behavior can be observed. Castro et al.  have defined an intrinsic time scale ensuing from their experiments which describes the transition from linear to nonlinear regime. If the given calculation rule is applied to our experimental conditions, this leads to very small fluences. This fluence range is not accessible in our experimental setup. Nevertheless, the emerging ripple patterns in this fluence range have very small amplitude and regularity, which are of little relevance for technical applications. Finally, the resulting material removal is extremely low. Hence, the technological fluence range is inevitable in the nonlinear regime, and reflected ions as well as gradient-dependent sputtering have to be considered. However, the reflection of primary ions as a nonlocal process is beyond the current theoretical models. The only nonlocal process that is considered in current theoretical models is redeposition [40, 41].
Ripple dynamic is investigated on Ge, Si, Al2O3, and SiO2 by low-energy ion beam erosion for ion energies of 600 and 1,200 eV and ion incidence angles of 65° and 75°. The ion fluence was varied from 1.1 × 1017 cm-2 to 1.3 × 1019cm-2 for both angles of incidence. Coarsening of the emerging ripple pattern is observed independent of the material already for the smallest ion fluences. This coarsening behavior has been attributed to reflection of primary ions. The coarsening rate depends on the fraction of reflected primary ions and therefore depends on the specific material as well as on the angle of incidence. The so-called Hauffe mechanism necessitates that experiments and theories have to be considered in the nonlinear regime.
a AFM images of other materials can be made available on request.
This research was conducted at the Leibniz Institute of Surface Modification (IOM) in Leipzig, Germany. The team is part of a collaborative research unit funded by the German Research Foundation (DFG) which is focused on the formation of self-organized nanostructures through low-energy ion beams (FOR 845). MT and JL are PhD students in two subprojects of research unit FOR 845. Dr. FF is the head of the group ‘Ion beam assisted technologies’ at the IOM and the project leader of two subprojects in research unit FOR 845. Prof. Dr. Dr. BR is the director of the IOM Leipzig as well as spokesperson of research unit FOR 845. He is also member of the curatorship for ‘Innovation and Science,’ member of the coordination board ‘Plasma Surface Technologies,’ member of ‘Leipziger Forschungsforum’ at the University Leipzig, member of the advisory board of the International Conference on Plasma Surface Engineering, member of the editorial board of Journal of Materials, member of the advisory board of the International Conference on Ion, Electron and Laser Physics, member of the Internal advisory committee of the Translational Centre for Regenerative Medicine, member of the scientific committee of the International Conference of Surface Modification of Materials, member of the editorial board ‘Dataset of Material Science,’ member of the editorial board of Condensed Matter Physics and member of the scientific committee ‘Nanomaterials: Applications and Properties.’
The authors are grateful for financial supports from the Deutsche Forschungsgemeinschaft through research unit FOR 845.
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