Neon ion beam induced pattern formation on amorphous carbon surfaces

We investigate the ripple pattern formation on amorphous carbon surfaces at room temperature during low energy Ne ion irradiation as a function of the ion incidence angle. Monte Carlo simulations of the curvature coefficients applied to the Bradley-Harper and Cater-Vishnyakov models, including the recent extensions by Harrison-Bradley and Hofsass predict that pattern formation on amorphous carbon thin films should be possible for low energy Ne ions from 250 eV up to 1500 eV. Moreover, simulations are able to explain the absence of pattern formation in certain cases. Our experimental results are compared with prediction using current linear theoretical models and applying the crater function formalism, as well as Monte Carlo simulations to calculate curvature coefficients using the SDTrimSP program. Calculations indicate that no patterns should be generated up to 45° incidence angle if the dynamic behavior of the thickness of the ion irradiated layer introduced by Hofsass is taken into account, while patte...


INTRODUCTION
Low energy ion sputtering of solid elemental or compound surfaces at oblique ion incidence could produce a periodic self-forming nanostructure due to ion erosion and mass redistribution.Mechanisms of pattern formation by ion-beam erosion and directed mass redistribution can be described by the linear theory of Bradley-Harper (HB) 1 and the model of Carter-Vishnyakov (CV). 2 An attractive theoretical approach to describe erosion as well as mass redistribution is the so called crater function formalism (CFF), which relies on molecular dynamic simulations.4][5][6][7][8] Recently Harrison and Bradley have shown that the crater function models used up to now are incomplete and must be extended to include the surface curvature dependence of the erosion crater function. 9This curvature dependence is already accounted in the original Bradley-Harper model using Sigmund's ellipsoidal energy deposition and contributes to the stabilization of the surface under ion irradiation for most ion incidence angles.However, for large angles of incidence this curvature dependence leads to a strong destabilizing contribution.Another essential extension, which was neglected in the CV model 2 is that the height evolution of the surface of an irradiated layer is dependent of its thickness.Such a thickness dependent contribution to the equation of motion was recently introduced by Hofsäss. 10,11According to Hofsäss, for an ion irradiated film, the layer thickness d at a given position depends on the ion incidence angle, which leads to dx 2 in a case of a surface curvature and a given recoil drift velocity ν x (h) at the surface h.The external constraint between surface h and interface H generates a condition, which overrides the no-slip condition and leads to a non-zero term ν x (H) dt in the calculation of dh dt .This constraint leads to a thickness-dependent curvature coefficient D 11 defined by (eq.21 of ref. 11 with surface drift velocity v x (h) given by eq.43 of ref. 11) D 11 is always positive and thus contributes to a stabilization of the surface in x direction.Moreover, D 11 (0 The coefficient has all features required to solve the inconsistency between experimentally observed and predictions of the truncated crater function theory as described by Perkinson et al. 12 Recently, Bradley and Hofsäss introduced a theory of the effect of ion implantation on the ioninduced pattern formation and found that implantation of self-ions has a destabilizing effect along the projected ion beam direction for incidence angles exceed a critical value. 13Our group has also shown in another recent publication that incorporation of non-volatile ions leads to a curvature dependent term in the equation of motion of a surface height profile and has a stabilizing effect on the surface in the projected direction of ion beam up to a critical angle of about 45 • .For larger angles the incorporation of ions contributes to the destabilization of the surface.The implantation of ions was interpreted as a negative sputter yield, which has an opposite effect compared to the sputter erosion.For 5 keV Ne ion irradiation of amorphous carbon, ripple patterns were found for 65 • and 70 • incidence angles and fluence of about 5×10 17 ions/cm 2 , whereas the surface remains flat for 10 keV Ne ion irradiation at 65 • and 70 • incidence angles.Rutherford backscattering spectroscopy (RBS) measurements show that for both cases the loss of implanted Ne is mainly due to sputter erosion and, at larger incidence angles, back reflection, whereas loss of Ne by out-diffusion is a minor contribution. 14e can describe the height evolution of the surface along x-direction, the projected direction of the incident ion beam, with the equation where J is the incident ion flux.F S ,rad •d 3 is the coefficient for ion-induced viscous flow in the thin film approximation. 10The curvature coefficient C 11 consists of three terms The erosive and redistributive contribution themselves are obtained as the sum of two coefficients in analogy to Harrison-Bradley and Hofsäss. 9-11are the erosive and redistributive curvature coefficients as introduced in BH and CV models but expressed in the crater function formalism.T 11 is the curvature dependence of the erosion crater function introduced by Harrison-Bradley. 9D 11 is the thickness-dependent curvature coefficient defined in eq. ( 1), which arises from the dynamic variation of the layer thickness as function of ion incidence angle.C implantation 11 is the implantation curvature coefficient introduced by Hofsäss et al. 14 Our recent experimental study of pattern formation on Si produced by Argon ion beam shows that pattern formation is strongly suppressed in the ion energy between 1.3 keV and 10 keV, which could be explained by combining the BH theory, the CV model including the curvature dependence of the erosion crater function and the recent introduced thickness-dependent curvature coefficient, but not be understood only with BH theory, or CV model, or the combination of the both, without the recent extensions. 15lthough there exist numerous experimental studies used Ar ion irradiation, [16][17][18][19][20][21][22][23] very few studies were done for light Ne ions.According Vishnyakov-Carter the use of light Ne + ions and low energies can inhibit surface wave and subsequent large amplitude faceting on Si at room temperature. 24iberi et al. reported also that no ripples are observed on Si surfaces irradiated with Ne + ions for ion energies below 2000 eV, but no data were shown. 25However, Zhu et al. observed periodical ripples on diamond-like carbon (DLC) surfaces irradiated with 1500 eV Ne ions with 60 • incidence angle at 700 • C. 26 In this paper we investigate the ion-induced pattern formation on amorphous carbon surfaces at room temperature during low energy Ne ion irradiation from 250 eV up to 1500 eV taking into account the implantation of Ne ions into the film.The ripple pattern formation was investigated as a function of ion incidence angle.Our aim is to confirm the stabilizing contribution of the thickness-dependent curvature coefficient D 11 , 10,11 which solves the inconsistency between measurements and truncated crater function theory, 12 and the destabilizing effect of ion implantation introduced by Hofsäss and Bradley. 13,14We used the Monte Carlo simulation program SDTrimSP [27][28][29] to calculate the curvature coefficients derived from erosion and redistribution crater functions, including the recent extensions.The simulations were done in dynamic mode, i.e. with the assumption that Ne ions are implanted into the carbon film and for the whole angular range in 5 • steps and for 7 curvatures K between K = 0.02 nm 1 and K = +0.02nm 1 in analogy to Hofsäss et al. 14

EXPERIMENTAL
Erosion experiments were done with high purity tetrahedral amorphous carbon (ta-C) thin films of about 270 nm thickness grown on Si(100) wafers of 7.5 cm diameter from the Fraunhofer IWS institute in Dresden, Germany.The ta-C films typically have a mass density of 3 g/cm 3 and are extremely flat with rms-roughness of about 0.1 nm.For the low energy (250 eV-1.5 keV) Ne ion irradiation we used a microwave plasma ion source (Tectra Gen II) with a board beam and current density of about 50-100 µA/cm 2 .The ion flux was measured with a Faraday cup, which could be placed in front of the sample.The sample holder was cooled with water during irradiation.In order to verify the purity of the irradiated samples and to measure the residual Ne content, a number of samples were analyzed with Rutherford backscattering spectrometry (RBS) using a 900 keV He 2+ analyzing beam.Table I shows the ion implantation and the residual Ne content, which were calculated with SDTrimSP, compared to the RBS analysis of residual Ne content in ion-irradiated ta-C films.
The surface topography of the irradiated thin films was analyzed by atomic force microscopy (AFM) in contact mode using Nanosurf microscope and Si cantilever with mean tip radius of 7 nm.Topography analysis as well as statistical analysis was done using the open source software Gwyddion. 30

RESULTS
The AFM images of Fig. 1 show the surface morphology of ta-C for irradiation with 250 eV and 500 eV 20 Ne + ions with an ion fluence of 1 3×10 17 ions/cm 2 as a function of ion incidence angle.We observed ripple patterns with wave vector parallel to the projected ion beam direction,  a positive curvature coefficient for ta-C samples irradiated with 1.5 keV ions and a very small negative curvature coefficient between 75 • -80 • for 850 eV ion irradiation, i.e. no ripples should occur (Fig. 5).

DISCUSSION
We have investigated the ripple pattern formation on amorphous carbon thin film due to Ne ion irradiation for a broad range of ion energies and ion incidence angles.Similar to the model case of Ar ion irradiation of Si, 15 we find a well define regime of irradiation parameters where formation of parallel ripples occurs.In the case Ne on a-C ripples are observed for incidence angles between   5)) is taken into account we are able to correctly predict the regime where parallel ripple patterns are formed.
The different contribution of erosion, redistribution and implantation to the total curvature coefficient C total 11 can be evaluated from Fig. 4 and Fig. 5. Erosion has mainly a stabilizing contribution at larger angles, and pattern formation is mainly due to mass redistribution and ion implantation.The simulations also show that pattern formation does not occur for incidence angles up to about 50 • .The stabilization of the surface in this angular regime is due to the positive coefficient D 11 and also the stabilizing effect of implantation of Ne, i.e. the coefficient C implantation 11 .

CONCLUSION
In this work we have investigated the ripple pattern formation on amorphous carbon surfaces under low energy Ne ion irradiation.We find ripple formation for ion energies up to 5 keV and ion incidence angles between 50 • and 75 • .For other conditions, the surfaces remain flat.Using the Monte Carlo Simulation program SDTrimSP [27][28][29] we calculated the curvature coefficients C 11 , taking into account the BH theory, including the curvature dependence of the crater function introduced by Harrison and Bradley, 9 the CV model, the dynamic layer thickness dependence introduced by Hofsäss 10,11 as well as the effect of ion implantation. 13,14The C 11 coefficients become negative in the experimentally observed regime and are thus able to quantitatively predict pattern formation by irradiation with low energy Ne ions.Our calculation results are in excellent agreement with the compilation of experimental results shown in Figs. 1 and 2. Without the stabilizing curvature coefficient D 11 , the absence of patterns at 45 • cannot be explained.Furthermore, we find that the implantation curvature coefficient C implantation 11 has a destabilizing effect for angles above 45 • and contributes, especially in the case of 850 and 1500 eV ion irradiation, to the formation of ripple patterns.

FIG. 1 .
FIG. 1. AFM images of surface patterns on ta-C thin films eroded with 250 eV and 500 eV Ne ions at incidence angles of 45 • -75 • .Ripple patterns oriented parallel to the ion beam direction observed for angles above 50 • .

FIG. 4 .
FIG. 4. Calculated curvature coefficients C total 11 for 250 and 500 eV 20 Ne + ion irradiation of ta-C.C total 11 includes the effect of ion implantation.The coefficient for erosion includes the curvature dependence of the erosion crater function as introduced in Refs.9.In the lower diagram, the coefficient of redistribution includes the dynamic layer thickness dependence as introduced in Refs.10.Dynamic layer thickness dependence is neglected in the upper diagram.

FIG. 5 .
FIG. 5. Calculated curvature coefficients C total 11 for 850 and 1500 eV 20 Ne + ion irradiation of ta-C.C total 11 includes the effect of ion implantation.The coefficient for erosion includes the curvature dependence of the erosion crater function as introduced in Refs.9.In the lower diagram, the coefficient of redistribution includes the dynamic layer thickness dependence as introduced in Refs.10.Dynamic layer thickness dependence is neglected in the upper diagram.

TABLE I .
Concentration of implanted Ne ions and the residual Ne content calculated with SDTrimSP.The last column shows the measured residual Ne content using Rutherford backscattering spectroscopy.