The shape and ordering of self-organized nanostructures by ion sputtering

Nuclear Instruments and Methods in Physics Research B 216 (2004) 9–19 www.elsevier.com/locate/nimb

The shape and ordering of self-organized nanostructures by ion sputtering €che, B. Rauschenbach F. Frost *, B. Ziberi, T. Ho Leibniz-Institut f€ur Oberfl€achenmodifizierung e.V., Permoserstrasse 15, 04318 Leipzig, Germany

Abstract The formation of periodic ripple structures on surfaces bombarded with ions at oblique (off-normal) incidence is a well-known and intensely studied phenomenon. In contrast to these long standing investigations, a new self-organization phenomenon can be observed for ion sputtering at oblique ion incidence with simultaneous sample rotation, where the formation of nanometer-sized islands (dimension < 100 nm) can be observed. For prolonged sputtering, these island or dot structures are characterized by relatively uniform size distribution and a remarkable large degree of spatial ordering. This contribution focuses on the specific role of both ion incidence angle and temperature on the dimension, geometrical shape and the spatial arrangement of the arising nanostructures during low-energy ion sputtering. Scanning force microscopy (AFM) and high-resolution transmission electron microscopy (HRTEM) are used to investigate the evolution of the surface topography and morphology of these self-organized crystalline nanostructures. Depending on the ion incidence and temperature, these nanostructures show hexagonal or square ordering with conical or sinusoidal shape. New experimental results for dot formation on InP, GaSb, InSb and InAs surfaces will be presented.
2003 Elsevier B.V. All rights reserved. PACS: 81.16.Dn; 81.16.Rf; 61.82.Fk Keywords: Ion beam; Sputtering; III–V semiconductors; Self-organization; Nanostructuring

1. Introduction The surface topography evolution during lowenergy ion beam sputtering is a rather complex matter. Due to different roughening and smoothing mechanisms a multitude of topographies can result from surface erosion. Besides the actual removal of material, this surface erosion process often give raise to a pronounced topography evo*

Corresponding author. Tel.: +49-341-235-2652; fax: +49341-235-2595. E-mail address: [email protected] (F. Frost).

lution, generally accomplished by a kinetic roughening of the surface. For many technological applications (e.g. depth profiling, etching) this roughness evolution is detrimental. However, with the fast-growing interest in nanotechnology, ion beam sputtering is frequently regarded as an alternative process for the generation of various nanostructured surfaces or interfaces via selforganization. Regarding self-organization effects and spontaneous pattern formation during ion sputtering, the phenomenon of ripple formation was intensely studied in the last four decades. Ripple formation describes the fact that, generally,

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2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2003.11.014

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for off-normal ion incidence a quasi-periodic height modulation in a ripple or wavelike structure develops. Since the first detection of ripple structures on glass surfaces by Navez et al. [1], ripple formation has been also observed for a number of different materials [2–26]. In a first linear theory, based on SigmundÕs linear cascade theory of sputtering of amorphous targets [27,28], Bradley and Harper (BH) describe ripple formation as a consequence of a surface instability caused by the competition between roughening (curvature dependent sputtering) and smoothing (surface diffusion) processes [29]. More generalized theories include further high order linear as well as nonlinear effects with different physical origins [30–36]. Recently, other surface relaxation mechanisms were proposed in order to allow for non-thermal surface smoothing [19,35]. In contrast, arrays of zero- or two-dimensional nanostructures can be formed by ion sputtering under normal ion incidence or, alternatively, under oblique ion incidence with simultaneous sample rotation. For semiconductor surfaces, this new phenomenon was explored nearly simultaneous for normal incidence low-energy Arþ ion sputtering of GaSb [37] and oblique ion incidence sputtering of InP with sample rotation [38]. Both experiments have shown that the abolishment of the anisotropy in the evolution of the surface topography, naturally given by the direction of the ion incidence, causes the formation of nanostructures with a cone-like shape and diameters < 100 nm. For continuously, sputtering these dot structures are characterized by a relatively uniform size distribution and a very large degree of spatial ordering showing a hexagonal symmetry. Similar pattern formation was reported for Arþ sputtering of silicon [39], but with a different shape of the nanodots. In contrast to advanced lithographic methods and subsequent etching procedures for pattern production with structure sizes <200 nm, which are complex technological processes, self-organized spontaneous pattern formation on the nanometer scale, as observed in erosion of surfaces by ion bombardment, is a cost-efficient Ôbottom upÕ approach for the fabrication of nanostructures. With suitable broad beam ion sources, large-area

surface processing is possible. Such a special ion beam facility has been developed in the Leibniz Institute for Surface Modification, within a R&D contract, enabling the nanostructuring of wafer surfaces up to 150 mm diameter via self-organization by ion beam erosion. However, the approach of nanostructuring by self-organization has often the disadvantage of less control on structure, size, shape and ordering of the nanostructures compared to different lithographic techniques. Nevertheless, in this work it will be shown that the size, shape and ordering of the nanostructures can be controlled to some degree by appropriate variation of the ion energy, ion incidence angle and temperature during ion beam erosion.

2. Experiment Ion beam etching was performed in a custom built ion beam etching system (base pressure 1 · 106 mbar). Within the experiments, the ion energy Eion and ion fluence were varied from 300 to 2000 eV and from 1 · 1016 to 2 · 1019 cm2 , respectively. The given ion beam current densities were measured for normal ion incidence. The Kaufman-type ion source used in the experiments was home-built and equipped with a two-grid ion optic system (beam diameter 200 mm). The total voltage applied between the two grids is the sum of the absolute values of beam (screen grid, determining the ion energy) and accelerator voltage (accelerator grid). This total voltage, together with the geometrical dimensions (spacing between grids, thickness of grids, hole diameter), including the shape of the plasma sheath boundary at the screen grid, defines the ion optical parameters of the source. Both grids are manufactured from high purity graphite. The operating conditions of the ion source were optimized with respect to welldefined ion energy distributions and ion beam divergences [40,41]. The samples used in this work were commercially available epi-polished (1 0 0) InP, (1 0 0) GaSb, (1 0 0) InAs and (1 0 0) InSb substrates characterized by a root-mean-square roughness between 0.2 and 0.3 nm, respectively. All samples

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were mounted on a water cooled aluminium substrate stage (temperature adjustable from 265 to 370 K). The sample stage rotates around the surface normal with 15 rpm. The angle of ion beam incidence aion can be chosen in the range from 0 to 90 with respect to the surface normal. The surface topography was investigated by atomic force microscopy (AFM) using a dimension 3000 system with NanoScope IIIa controller from digital instruments operating in tapping mode. All measurements were conducted in air using silicon tips with a nominal tip radius of <10 nm. Because a careful tip evaluation and calibration is important for a reliable roughness evaluation, a recently proposed special procedure was used to maintain a constant quality of the Si tips during the measurements [42,43]. All AFM measurements were performed for different scan sizes with a resolution of 512 · 512 pixels. The rms surface roughness w was calculated using the rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D E 2 relation w ¼ ½hð~ r; tÞ  hhð~ r; tÞi , where h i denotes the spatial average. The two-dimensional auto-correlation function was calculated using the relation Cð~ r; tÞ ¼ hhð~ r; tÞhð0; tÞi. The power spectral density function (PSD) is obtained from the auto-correlation function by Fourier transformation. In the case of isotropic surface, the power spectral density function is reduced to a onedimensional quantity by angular averaging. From the first order peak in the PSD, the periodicity of surface structures can be deduced. The full-width at half-maximum of the first order peak is a

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quantitative measure of fluctuation of the structure separations or periodicity [44]. High-resolution transmission electron microscopy (HRTEM) was performed in a 400 keV microscope possessing a point resolution of 0.155 nm. Cross-sectional samples were prepared by gluing samples face to face, embedding resulting sandwiches in alumina tubes, wire-saw cutting, plan-parallel grinding, one-sided polishing, othersided dimpling followed by polishing to a residual thickness of about 15 lm and Arþ -ion beam etching at 2.8 keV.

3. Results and discussion 3.1. Pattern formation with simultaneous sample rotation It is now well established that sample rotation often leads to reduced surface roughening during ion sputtering of surfaces. This benefit of sample rotation was first explored by Zalar for depth profiling in auger electron spectroscopy [45]. However, sample rotation does not always suppress surface roughening. In contrast to the case of off-normal bombardment and no rotation no preferred orientation of the emerging surface structures are expected for rotation. A clear example demonstrating the difference in surface evolution is shown in Fig. 1. Under identical experimental conditions InSb surfaces were bombarded for 10 min with Arþ ions at room

Fig. 1. AFM images of InSb surfaces (3 lm · 3 lm) bombarded with Arþ ions at room temperature (Eion ¼ 500 eV, aion ¼ 80, jion ¼ 400 lA cm2 , sputter time of 10 min): (a) no sample rotation and (b) sample rotation. Please note the different z-scale.

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temperature (ion energy Eion ¼ 500 eV, ion incidence angle aion ¼ 80, ion flux or ion beam current density jion ¼ 400 lA cm2 ). For the non-rotating sample, ripple structures are formed running along the direction of the incident ion beam with a ripple wavelength of 80 nm and a ripple amplitude of

13 nm. For the rotating sample small isotropic distributed dots with a mean separation of 110 nm and a lateral size between 40 and 60 nm have evolved. The mean height of the dots is 12–14 nm and the rms roughness is reduced to 3.4 nm compared to 7.0 nm for the rippled surface. Furthermore, the dots show no lateral ordering as observed for the ripple structures. The formation of ordered dots is demonstrated in Fig. 2, where a self-organized dot pattern was produced by ion sputtering with Eion ¼ 500 eV, aion ¼ 30, jion ¼ 400 lA cm2 and erosion time of 90 min. The AFM scan (3 lm · 3 lm, Fig. 2(a)) displays domains with hexagonally close-packed dot arrays. The hexagonal arrangement of the dots is clarified in Fig. 2(b), which shows the autocorrelation image for a representative sector of the surface. The maximal size of the individual domains is 1 lm. Due to the random azimuthal orientation of these domains, a ring-like Fourier spectrum (FFT, Fig. 2(c)) is observed. The high

degree of self-organization is clearly seen by the high order satellite peaks in the Fourier spectrum (up to four orders are visible). From the first peak of the angular averaged PSD function, a mean dot diameter of 71 ± 8 nm was obtained. Because of the close-packed ordering, the separation between the dots is identical to their lateral size. The size fluctuation of the dots (8 nm) was calculated from the full-width of half-maximum (FWHM) of the first order PSD peak. As shown in earlier work by Facsko et al. [46] and Frost et al. [38,47] the lateral size of the dots can be controlled by the sputter time (in the initial stage of sputtering) and ion energy. However, for prolonged sputtering, the induced dot pattern is stable. Therefore, for most experiments presented here, sputter times between 60 and 90 min were chosen in order to reach the steady state of the pattern formation. Facsko et al. [48] have also shown that the pattern formation is independent of the respective surface orientation, i.e. for identical ion beam processing the same pattern evolves on (1 0 0), (1 1 1) and amorphous GaSb surfaces. The reason is the amorphization of the surface by the incoming ions, which reaches a steady state after an ion fluence of 1 · 1016 cm2 , long before an ordered dot arrangement is reached.

Fig. 2. Self-organized InP dot pattern produced by ion sputtering with Eion ¼ 500 eV, aion ¼ 30, jion ¼ 400 lA cm2 , sputter time of 90 min: (a) 3 lm · 3 lm AFM image, (b) auto-correlation function image (1 lm · 1 lm) of a representative sector of the surface and (c) Fourier spectrum of image (a) showing the higher order satellite peaks (up to four orders are visible, image range from )85.3 to 85.3 lm1 ).

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3.2. The shape and ordering of nanodots on InP and GaSb In this section we review some results on the influence of the ion incidence angle and sample temperature on the resulting dot pattern for ion beam sputtering with sample rotation. Fig. 3 shows the topography of Arþ sputtered GaSb surfaces (Eion ¼ 500 eV, T ¼ 313 K, jion ¼ 300 lA cm2 , sputter time 90 min) at different ion incidence angles. The corresponding twodimensional auto-correlation functions for surface areas of 500 nm · 500 nm emphasize the local symmetry of dot arrangement. Starting with aion ¼ 0, a hexagonal arrangement of the dots becomes visible. This holds also for aion ¼ 15 [Figs. 3(a) and (e)]. Increasing the ion incidence angle to 30, the hexagonal dot array shifts to a square pattern [Fig. 3(b) and (f)]. By further increasing aion to 60, the hexagonal arrangement emerges again. At aion ¼ 70, dots continue to exist but without a clear local pattern [Fig. 3(c) and (g)]. Last, for more oblique ion incidence [aion ¼ 75, Fig. 3(d) and (g)], a hexagonal pattern is observed again. The scenario of transition from hexagonal

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to square pattern and vice versa is only observed at elevated temperatures. For lower temperatures (e.g. room temperature), a successive transition from hexagonal to no pattern and back to a hexagonal pattern with increasing ion incidence angle was found. From Fig. 3, it is also realized that the dot diameter and height vary as a function of aion . However, there is an additional important difference in the shape of nanodots formed at normal (or near-normal) and glancing ion incidence, respectively. An inspection of the geometrical shape of the different dots using cross-sectional high-resolution TEM (Fig. 4) reveals that the nanostructures produced at normal incidence show conical shape with a rounded apex and sidewall angles from 60 to 70 (Fig. 4(a), Eion ¼ 500 eV, T ¼ 285 K, jion ¼ 300 lA cm2 , sputter time 90 min). The width as well as the height of these dots are in the range of 50 nm. In contrast, the dots formed at ion incidence of aion ¼ 75 (Eion ¼ 1200 eV, T ¼ 285 K, jion ¼ 300 lA cm2 , sputter time 90 min) show a sinusoidal shape, with a diameter of 20 nm and a dot height of 10 nm (Fig. 4(b)). Both kinds of dots are covered by a thin amorphous layer (a-GaSb + oxide with a

Fig. 3. Topography (upper row) and corresponding auto-correlation function images (lower row) of Arþ sputtered GaSb surfaces (Eion ¼ 500 eV, T ¼ 313 K, jion ¼ 300 lA cm2 , sputter time 90 min) at different ion incidence angles: (a), (e) aion ¼ 15; (b), (f) aion ¼ 30; (c), (g) aion ¼ 70; (d), (h) aion ¼ 75. Images sizes are (a)–(c) 3 lm · 3 lm, (d) 1 m · 1 lm, (e)–(g) 500 nm · 500 nm and (h) 250 nm · 250 nm.

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Fig. 4. Cross-sectional high-resolution TEM images of the dot patterns produced at normal and grazing ion incidence, respectively. (a) aion ¼ 0, Eion ¼ 500 eV, T ¼ 285 K, jion ¼ 300 lA cm2 , sputter time 90 min; (b) aion ¼ 75, Eion ¼ 1200 eV, T ¼ 285 K, jion ¼ 300 lA cm2 , sputter time 90 min. The thin amorphous layer (a-GaSb + oxide) has a thickness of 4 nm.

thickness of 4 nm) and the crystallinity and orientation of dots and bulk are identical. With increasing ion energy, the different shape at normal and grazing ion incidence persists, but the lateral as well as the vertical size of the dot structures increases. The surface height profiles and, therefore, the shape of these nanostructures are in agreement with those obtained by AFM, if tip convolution effects are taken into account. Similar results are also obtained for InP, but with a less ordered dot pattern at grazing ion incidence (70–85).

In order to give a more quantified description of the dot pattern change with increasing ion incidence, several characteristics are deduced from the AFM images. These are summarized in Fig. 5(a)– (c), which show four PSD functions for characteristic ion incidence angles, the rms roughness w versus aion , the mean dot size k and the dot size fluctuation Dk=k versus aion . From Fig. 5(a) and corresponding to the AFM images Fig. 4(a,b), it is evident that k changes with aion and the ordering is maximal at near-normal (15) and grazing ion incidence (75), as seen from the high order peaks in the PSDÕs. Fig. 5(b) shows that the vertical surface roughness is maximal at aion ¼ 25, i.e. the dot height is greatest at aion ¼ 25. For ion incidence angles >25, the dot height continuously decreases. This trend is different from the relation between k and aion (Fig. 5(c)), where the lateral dot size have a maximum at aion ¼ 60. In Fig. 5(c), we have also plotted the ratio between the lateral fluctuations, Dk, and the lateral size, k, of the dots. This ratio serves as a measure for the ordering of the dot structures and confirms the conclusion that the degree of ordering is maximal at normal/nearnormal and grazing ion incidence. In a second set of experiments, the influence of the sample temperature during sputtering was

Fig. 5. (a) Angular averaged PSDÕs obtained from AFM images in Fig. 3(a)–(d), (b) rms surface roughness versus ion incidence angle and (c) lateral dot size k and normalized dot size fluctuation Dk=k as a function of ion incidence angle. Ion beam processing parameters were the same as in Fig. 3.

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studied. Unfortunately, the temperature can be varied only in a small range conditional on the ion beam etching system employed. Fig. 6 illustrates AFM images of Arþ sputtered InP surfaces (Eion ¼ 500 eV, aion ¼ 30, jion ¼ 300 lA cm2 , sputter time 90 min), when the temperature of the substrate stage increases from 268 K [Fig. 6(a)] to 335 K [Fig. 6(d)]. The corresponding two-dimensional auto-correlation functions derived for surface areas of 750 nm · 750 nm highlight the symmetry of the local dot arrangement. The changing of the symmetry from a hexagonal to a square pattern is evident. Further, the mean separation between the individual dots as well as height of the dots increases with temperature. From Fig. 6(c) and (d), it is also evident that the surface profile measured by AFM is definitively affected by the limited resolution of the AFM probe used, i.e. the sidewall angles of the nanostructures are significantly steeper than the sidewall angles of the AFM probe. The results of the AFM image analysis are summarized in Fig. 7. The PSDÕs confirm the results of the visual inspection of the AFM images. Thus, the ordering decreases (also emphasized by the two Fourier spectra) and the mean dot separation increases

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with temperature (Fig. 7(b)). This behaviour is in contrast to the experiment for GaSb (not shown), where the dot size/separation k and the ordering Dk are nearly constant in the investigated range of temperature, although a transition from hexagonal to square ordering of the dots is clearly evident at elevated temperatures (see also Fig. 3(b) and (f)). Preliminary HRTEM investigations reveal that the InP and GaSb dots produced at 30 ion incidence and at elevated temperature show a truncated conical shape with side wall angles >80. This means that the shape of the cone-like dots can be modified by appropriate sputter conditions. Summarizing these results, it has been shown that the ion incidence angle and sample temperature during surface sputtering are two crucial factors that determine the shape of the dots, their lateral arrangement, as well as the lateral size and dot separation. Against the background of these complex interrelationships between pattern formation and ion beam or sample parameters, it is clear that many of the experimental findings cannot be understood within the context of current models. In a former work [47], we discussed the dot formation qualitatively using a stochastic partial

Fig. 6. Topography (upper row) and corresponding auto-correlation function images (lower row) of Arþ sputtered InP surfaces (Eion ¼ 500 eV, aion ¼ 30, jion ¼ 300 lA cm2 , sputter time 90 min) at different temperature of the substrate stage. (a), (e) T ¼ 268 K; (b), (f) T ¼ 286 K; (c), (g) T ¼ 313 K; (d), (h) T ¼ 335 K. Images sizes are (a)–(d) 3 lm · 3 lm, (e)–(h) 750 nm · 750 nm.

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Fig. 7. (a) Angular averaged PSDÕs obtained from AFM images in Fig. 6(a)–(d). The two Fourier spectra (image range from )85.3 to 85.3 lm1 , the rings in the Fourier spectra are marked by white circles) illustrate the decreasing ordering of the dot pattern with temperature and (b) lateral dot size k and normalized dot size fluctuation Dk=k as a function of ion incidence angle. Ion beam processing parameters were the same as in Fig. 6.

differential equation, which was proposed intentionally to describe this pattern formation. For this purpose, different surface relaxation mechanisms were included and the theory was extended to the case of simultaneous sample rotation. Provided that surface erosion smoothing is the dominant relaxation process, this theory predicts quantitatively the formation of dot pattern and the magnitude of its spatial period at nearly glancing ion incidence angles of 75–80. However, the current status of this theory does not allow for predicting the formation of ordered dot arrays at (near) normal and grazing ion incidence, simultaneously. Furthermore, the observed transformation from hexagonal to square patterns at elevated temperatures cannot be predicted. The conical shape of the dots formed at (near) normal incidence provide evidence of the importance of sputter effects related to the local surface gradient. However, the formation of truncated cones at oblique ion incidence and at elevated temperatures is still unexplained. For more detailed discussion, the reader is referred to a former work [47].

3.3. Pattern formation on InAs and InSb In addition to the extensive investigations for pattern formation on InP and GaSb, some experiments were carried out for the low-energy ion bombardment of InAs and InSb surfaces. Initial results are shown in Fig. 8, where self-organized dot structures are generated on InAs surfaces by ion beam sputtering. The ion beam processing parameters were Eion ¼ 1000 eV, aion ¼ 30, jion ¼ 270 lA cm2 , sputter time 60 min, T ¼ 285 K. The high degree of self-organization is seen by the higher order satellite peaks in the Fourier spectrum again. The mean dot diameter was 60 ± 7 nm. The dot height is 50 nm and a HRTEM inspection reveals the cone-like shape of the nanostructures and their single crystalline nature, except for a thin amorphous layer at the surface of the dots. Two facts are remarkable compared to the experiments on InP and GaSb. The regular dot patterns appear only in a very limited range of ion incidence angles ( 30) and for definite settings of the accelerator grid voltage. The accelerator

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Fig. 8. Self-organized dot structures generated on a InAs surface by ion beam sputtering. The ion beam processing parameters were Eion ¼ 1000 eV, aion ¼ 30, jion ¼ 270 lA cm2 , sputter time 60 min, T ¼ 285 K. (a) 2 lm · 2 lm AFM image (inset: Fourier spectrum from )51.2 to 51.2 lm1 with high order satellite peaks demonstrating the high degree of self-organization, the rings in the Fourier spectrum are marked by white circles). (b) From the first peak of the angular averaged PSD function an mean dot diameter of 60 ± 7 nm was determined.

Fig. 9. Self-organized dot pattern with bimodal size distribution on a InSb surface produced by ion sputtering at grazing ion incidence (Eion ¼ 1200 eV, aion ¼ 85, jion ¼ 320 lA cm2 , sputter time 90 min, T ¼ 285 K). (a) 3 lm · 3 lm AFM image, inset: Fourier spectrum (the rings in the Fourier spectrum are marked by white circles), (b) 500 nm · 500 nm AFM image and (c) angular averaged PSD functions of image (a) and (b). The three peaks are attributed to the mean lateral separation of the large dots, their lateral size and the size/separation of the small dots, respectively.

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voltage is very crucial for the ion optical properties of the ion source and jointly responsible for the divergence within the broad ion beam. Therefore this is possibly the first direct indication of the importance of the ion beam divergence on the selforganized pattern formation using broad beam ion sources. More detailed investigations of the relation between dot formation and the influence of ion source settings are currently in progress. It is worthwhile to mention that a similar complex interplay between pattern production and ion optical properties of the ion source was found for the ion erosion of silicon surfaces. Finally, we will address a special feature observed for the dot formation on InSb surfaces. Similar to GaSb, dots with a small size distribution can be induced on InSb surfaces at normal or near-normal ion incidence (not shown), but with a less ordered dot patterns than observed for GaSb and InP. However, at grazing ion incidence (Eion ¼ 1200 eV, aion ¼ 85, jion ¼ 320 lA cm2 , sputter time 90 min, T ¼ 285 K) nanodots with different lateral sizes develop (Fig. 9). In AFM images with two different magnifications (Fig. 9(a) and (b)), two kinds of dots are clearly resolved. The dots are characterized by a bimodal distribution. From the rings in the Fourier spectrum (inset in Fig. 9(a), the rings are marked by white circles) or the peaks in the corresponding PSD function (Fig. 9(c)), the lateral separation of large dots and their lateral size are given by 100 and 55 nm, respectively. The peak splitting results from the difference between dot separation and diameter. The small dots have a mean lateral size of 20 nm. Due to the finite resolution of the AFM probe, it is not possible to distinguish between the separation of the small dots and their lateral size. The height of the large dots is 10 nm, whereas the height of the small dot was measured as 2 nm. It should be noted that this behaviour resembles the self-organized growth of InSb during molecular beam epitaxy [49]. This might be an indication that, for a thorough understanding of these complex pattern formation processes during ion erosion, mechanisms affecting epitaxial growth as, e.g., stressinduced self-organization, have to be considered [50].

4. Conclusions In this article, the specific role of the angle of ion incidence and temperature on the formation of self-organized nanostructures arising during lowenergy ion sputtering of semiconductor surfaces have been reviewed. Scanning force microscopy and high-resolution transmission electron microscopy were used to investigate the evolution of the surface topography and morphology of these selforganized crystalline nanostructures. It was demonstrated that the lateral size, shape and ordering of the nanostructures can be controlled to some degree by appropriate variation of the ion energy, ion incidence angle and temperature during ion beam erosion. Depending on the ion incidence and temperature, these nanostructures show hexagonal or square lateral ordering with a (truncated) conical or sinusoidal shape. Furthermore, initial results on pattern formation on InAs surfaces by ion sputtering were presented pointing to the importance of ion beam divergence effects on the pattern formation. Finally, the complex nanostructure formation on InSb surfaces with a bimodal size distribution has been reported. We are well aware that the understanding of this fascinating and complex self-organized pattern formation is vitally important to establish the process for a broad range of applications. However, this requires a more detailed modelling of the underlying physics beyond the current status.

Acknowledgements The authors would like to thank Prof. U. G€ osele (Max Planck Insititute for Microstructure Physics Halle, Germany) for enabling the TEM investigation. This work is supported by Deutsche Forschungsgemeinschaft.

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