Surface morphology and topography evolution of soda-lime silica glass after 1.0 MeV Si ion bombardment

Surface pattern formation on soda-lime silica glass by 1 MeV Si ion irradiation impinging at an angle of 70° with respect to the surface normal has been studied. Modification of surfaces were analyzed for total ion fluences applied between 1×1017 up to 4×1017 ions/cm2. The surface morphology and topography were studied by scanning electron microscopy (SEM), and atomic force microscopy (AFM). These surface techniques enabled the determination of roughness, characteristic wavelengths, and correlation lengths. In addition, electron dispersive spectroscopy (EDS) scans were applied on the surface topography to study the variation of the Si content on the obtained surface patterns. From the measurement of these variables, linear and non-linear regimes were established. At linear regime, the surface morphology develops from an initial flat surface giving rise to ripples for fluences up to 1.4×1017 ions/cm2. As the ion bombardment continues surface evolve into wrinkles finalizing at cellular-like structures, growing under an anomalous scaling process. The EDS scans indicate the presence of shadowing effects. The morphological changes observed can be explained in terms of a combination of thermal mass diffusion and geometrical factors during ion irradiation, including shadowing and subsequent (secondary) surface erosion effects adapted to few MeV energies.


Introduction
The emergence of surface patterns by ion beam irradiation (IBI) techniques is known to occur on a variety of materials including semiconductors [1][2][3], metals [4,5], and insulators [6][7][8], under a wide range of experimental conditions.Since its discovery by Cunningham et al [9] and Návez et al [10], this nano structuring process has drawn attention due to its potential uses in the surface functionalization of materials for applications in microfluidics [11,12], orthopedic implants [13][14][15], and solar cell manufacturing [16][17][18].As a result, IBI techniques can modify the top surface layers of materials triggering the formation of patterns over large surface areas (few cm 2 ).That is, experimental surface patterns characteristics depend on irradiation parameters and in the target material.Surface changes on top of compliant solid substrates have accelerated research, specially to generate wrinkles grids on transparent dielectric glasses such as SiO 2 [6,19], soda-lime silica [18], Al 2 O 3 [19][20][21], Si 3 N 4 [20] and Muscovite (mica) [22], in order to functionalize the surface through nanograting patterns as templates for photonic and electronic applications [23][24][25].For these studies, wrinkle formations were produced by ion beams with energies of few keV.Also, among these materials the soda-lime silica is a low-cost material widely used as substrate because it is recognized by its physical properties including a high transmittance of visible light, moderate chemical stability, and its manufacturing low cost [26,27].These advantages make this glass an ideal material for applications in many industries over their surface and bulk improvement by ion irradiation methods [28].
Typically, transparent glasses are common materials for MeV ion irradiation in order to modify their optical properties by point defect generation [29] or nanoparticle synthesis by ion implantation [30,31].Other studies focus on their mechanical stability, including borosilicate-based glasses for radioactive waste disposal [32].However, there are few studies on surface morphology changes and the patterns generated after ion implantation of glasses at energies of a few MeV [7,8,33,34].
From a physical description point of view, advances in the study of surface irradiation by energetic ion beams have allowed to tailor specific patterns, as described by continuum models based on the linear Bradley-Harper (BH) [35], and non-linear extensions [36,37].Considering amorphous substrates or those that undergo amorphization, two main regimes exist throughout the evolution of an irradiated surface.For the former, structures and growth of interface height surface ripples occur exponentially with ion dose and are characterized by a wavelength l which remains constant.For the non-linear behavior, the interface width saturates with a broadening of surface structures.The transition to the non-linear regime takes place at doses or fluences higher than a critical value Φ c [36,38].
Current continuum models for surface dynamics are known to be described for ion beam conditions at low (0.1-10 keV) [3,39,40] and medium (10-200 keV) [3,41] energies.For ion irradiation these two regions, surface processes generated by ion-atom interactions are those due to the slowing down of ions in the target material by ion-atom (nuclear collisions) and ion-electron (ionization) [28,42].Further considerations at higher energies is possible, as there is evidence that similar processes occur near the surface at MeV energies [7,8,33,43,44].Thus, pattern formation at surfaces focuses primarily in low to medium energy ion beams [39].At energies beyond a couple of hundred keV, the electronic stopping power becomes become important [28,42], prevailing processes given by thermal spikes as influenced on by substrate heating, and atomic relaxation near the surface.That is, both effects on the slowing down of ions in a target material are usually considered [3,39].Thus, it is reasonable to assume that surface dynamics through ion irradiation methods at a few MeV may be applied as starting approximations on their phenomenological descriptions [39].
This work presents a study of surface pattern formation as function of the total fluence Φ on soda-lime silica glass irradiated by 1 MeV Si ions where in first instance for the impinging ions the penetration inside the material is deeper and electronic stopping power dominates over the nuclear one at the surface.Si ions were chosen to avoid the incorporation of a different atomic species during the implantation process, so as not adding another variable to the experiment.This limits changes to the main physical and chemical properties of the material.Moreover, the bombarding Si ion has a similar mass to the target atoms, allowing the generation of atomic displacements by ballistic collisions, supporting the modification on the surface morphology.

Experimental methods
Commercial soda-lime silica glass slides were employed in the preparation of the substrate samples.The typical composition of soda-lime silica glass is 73% SiO2%-15% Na 2 O-7% CaO-4% MgO-1% Al 2 O 3 [26,27,45].The samples were obtained from rectangular cut outs with dimensions of 12 mm ´10 mm ´1.0 mm, and surface dust or impurities were removed by immersion in a solution of ethyl alcohol under an ultrasonic bath.The prepared substrates were implanted with 1 MeV Si +1 ions under vacuum conditions of 10 −7 torr at room temperature using the 3MV Pelletron accelerator (NEC 9SDH-2) at the Instituto de Física, of the Universidad Nacional Autónoma de México.The ion beam impinged at 70 o angle to the surface normal with a beam current of 1 μA over a square area of 0.25 cm 2 centered on the glass rectangles, corresponding to an ion flux of 2.5 × 10 13 ions cm −2 s −1 .The samples irradiation fluences Φ ranged from of 1.1 × 10 17 ions cm −2 to of 4.0 × 10 17 ions cm −2 .
After ion irradiation, the surface morphology and topography were studied by surface analysis techniques including scanning electron microscopy (JEOL SEM-5600LV) and atomic force microscopy (JEOL SPM-4210).Acquired AFM micrographs surface areas over 25 ´25 mm 2 on the implanted substrates were analyzed by the open-source software Gwyddion [46].The roughness value w for surface profiles was extracted through the root mean square (RMS) function on the surface height h(x) at position x along vertical lines scans [47].Statistical measurements were performed over the complete surface topography data.The pattern surface wavelength λ for each implanted sample was determined from 1-dimension power spectral density functions (1D PSDFs) of the AFM images by applying the Fourier Transform.The λ values for each sample were obtained by the relation , m where the wave vector k m correspond to the center position of the broad bump for the PSD plots [48].The correlation length x (or width of the structures) [47,48] was calculated by ) as evaluated at = r 0. Also, to complement the description of surface dynamics, the exponent a for surface roughness [49] was calculated from the linear fit of the log-log plot of the height-height correlation function, Using a Schottky field emission scanning electron microscope (SEM JEOL JSM-7800F), energy dispersive x-ray spectroscopy (EDS) was performed on samples along linear scans to determine variations on the surface elemental composition.Characteristic x-rays were collected by an Oxford XMaxN50 detector located at 60°with respect to the surface normal for a fixed acquisition time of 75 seconds.

Results
Figure 1 shows SEM micrographs of the surface morphology of soda-lime glass substrates after implantation, where the arrow indicates the surface projection on the ion beam direction.Micrometer-sized structures can be observed for increasing ion fluence.Upon an examination of the achieved morphologies, three types of structures can be highlighted: ripples, wrinkles, and cellular-like structures.From figures 1(a)-(c), an initial flat surface evolves into an undulating pattern as aligned in a perpendicular mode with respect to the ion beam direction.This ripple growth mode occurs as the ion implantation doses increased from Φ = 1.1 10 17 cm −2 to 1.3 10 17 cm −2 in agreement with reported experiments for many materials irradiated by ions at low and medium energy [39].Thereafter, a morphology change occurs as illustrated by a wrinkling of the surface at Φ = 1.4 10 17 cm −2 to 1.5 10 17 cm −2 , as observed in figures 1(d)-(e).For Φ = 2.0 10 17 cm −2 , figure 1(f) shows that on some surface sectors the separation between wrinkles become larger and mass accumulation on the crests is observed.After further ion irradiation, another morphology change occurs, cellular-like structures emerge with size between 6-8 μm over Φ = 3 10 17 cm −2 , as observed in figures 1(g)- (h).This surface evolution indicates that the sample at Φ = 2.0 10 17 cm −2 , corresponds to an intermediate stage in the transition from wrinkles to cellular-like structures.
Figure 2 shows AFM micrographs for the sample substrates at the irradiated surface zone with respect to the ion fluence and where the arrow indicates the surface projection of the ion beam direction.In this case, the surface pattern orientations are in agree with those observed by SEM.To illustrate the topographic surface behavior, figure 3 shows the height amplitude profile scans along the vertical lines indicated in figure 2 for each sample.In figures 3(a) through (c), sinusoidal profiles appear, indicated by the presence of surface ripples as observed through SEM images.For these ion fluences, the ripple amplitudes grow from 50 nm to 160 nm as function of the ion dose.In subsequent ion fluences, surface profiles replace sinusoidal shapes into faceted saw tooth-like profiles as given by figures 3(d)-(f).This same morphological change has been reported in irradiations at low and medium ion energy conditions [39] indicating the crossover between the linear and non-linear regime.The critical fluence F c for this transition can be estimated around the value of 1.4 10 17 cm −2 .For the two higher doses applied another change in the topography occurs, where flattened columnar formations appear with heights up to 2 μm as shown in figures 3(g) and (h).Also, the broadening of structures is observed, which can be identified by the separation between peaks.Figure 4 shows the RMS surface roughness w with respect to the ion fluence Φ.For Φ between 1.1 × 10 17 cm −2 and 1.4 × 10 17 cm −2 the values for w follow a linear behavior in a semi-log plot corresponding to an exponential growth.Although, for Φ above 1.4 × 10 17 cm −2 the w values growth more slowly following a power law function ~Fb w [50], where the measured growth exponent b =  4.0 0.16. Figure 5 shows the surface pattern characteristic wavelengths and the correlation length ξ.It can be noted that in the linear regime the distance between the surface patterns is like their lateral size (λ ∼ ξ).Meanwhile in the non-linear regime the distance between the patterns increases faster than its correlation length (λ > ξ), where l exhibits coarsening as a power law l ~Fg , with the wavelength exponent g =  0.81 0.15.Also, at this regime ξ can be adjusted by a power law with the dynamic exponent / =  z 1 0.25 0.12.The variation of the roughness exponent a is shown in figure 6.For the linear regime, a has a highly variable behavior, while for subsequent fluences at non-linear regime, a stabilized and settle around 0.8.These slow growth of a in the non-linear regime seems to be correlated with the growth of w in figure 4.
Figure 7 shows EDS linear scan for the Si-K x-ray count ratio intensity along horizontal lines on three compared surfaces.The top micrographs correspond to SEM images, while the bottom is x-ray count ratio for the profile scan.For the non-irradiated region, figure 7(a), the x-ray count ratio registered exhibit random variations from point to point, indicating a stable glass silicon composition.Figure 7(b) shows the EDS scan for the sample irradiated at Φ = 1.2 10 17 cm −2 (corresponding to the linear regime), where the arrow indicates the ion beam direction projection on the surface, while the x-ray detector is located perpendicular to the arrow at upper of the SEM micrography.For this sample, increments on the amount of Si atoms are observed in the wavy facing the impinging ion beam, while a pronounced decrease on the back facing ripple structure.This effect is more notorious for sample with Φ = 4.0 10 17 cm −2 at the non-linear regime, as shown in figure 7(c).
Furthermore, the EDS study indicates that the mass accumulation in the crests observed in figure 1(f) for sample at Φ = 2.0 10 17 cm −2 are rich in Si than the surrounding regions.

Discussion
The experimental irradiation conditions applied on soda-lime glass generate three types of surface morphologies.The initial one by wavy pattern formation under a linear regime for Φ < F C where the height amplitude grows as function of Φ, while l remains constant.For Φ > F C saturation of the interface width is observed, and the height amplitudes increase slowly to a stabilization value of few micrometers through the presence of non-linear effects involved during the ion irradiation.Also, at the non-linear regime an enlargement in l or separation between peaks is observed, while the behavior of x indicates that the peak width reaches a few micrometers.These two effects lead to the broadening of structures especially for the higher doses, figures 3(g)-(h), where cell-like structures are observed, figures 1(g)-(h).The observed patterns dynamic behavior agrees with the linear and non-linear regimes predicted by pattern formation models in IBI at low and medium energies [39] as represented in figures 1(a)-(e) and 2(a)-(e), as generally obtained through substrates that undergo amorphization targets.
For the initial two morphologies, ripple formation to wrinkle transformation presentcommon surface behavior as those reported previously on transparent dielectrics irradiated at low-medium energies including SiO 2 [6,19,51,52], soda-lime [18,53], Al 2 O 3 [54,55], Si 3 N 4 [20,21,55], muscovite [22] and at high energies in SiO 2 [7, 8].In these cases, for q < 75 o the ripple and wrinkle wave vectors are parallel to the ion beam projection onto the surface [52,53].The main difference in these studies is the order of magnitude on the wavelength l related to the impinging ion energy instead of the material composition.However, the formation of cell-like   structures has not been previously reported at oblique angles of incidence [6-8, 18-21, 51-56], thus they can be considered as an effect of the MeV ion energy applied.
The measured l (figure 5) are in the same magnitude of a few micrometers to those reported on fused silica by MeV bombardment with Si [8] and Au ions [7], instead to the tens and hundreds of nanometers produced by Ar and Xe ions at low energies in transparent dielectrics.Also, these differences in l length by ion energy have  been observed in metals and semiconductors irradiated at low energies [3,5] where the wavelength may vary in the tens and hundreds of nanometers, instead to the few micrometers size at medium [41] and high energies [44,56].
In relation to the scaling exponents at the non-linear regime there is not enough data to make a direct correlation between different experimental irradiation conditions at room temperature, due to the variability of reported values.As an example, the measured scaling exponent g is slightly smaller than the value reported for soda-lime irradiated by 0.8 keV Ar ions at q = 35 o [53].But this g value is 5.4 times larger than the values reported for SiO 2 irradiated by 0.8 keV Ar + at q = 60 o [51] and for Al 2 O 3 by 1 keV Xe + at q = 55 o [21].For the rugosity, the measured exponent b is similarly to the observed in SiO 2 by 0.8 keV Ar + irradiation at q = 60 o [51] but half the reported for soda-lime at q = 35 o [53].Also, for muscovite bombarded with 12 keV Ar + at q = 60 o [22], the reported value of b is within that measured in this work and accounts for its uncertainty.The value of g is half from that measured here.
In silicate glasses the transition from the initial ripples morphology to wrinkles, shown in figures 1(d)-(e), can be explained as a buckling (swelling) effect on the surface as observed at low energy Ar ion modifies sodalime glass [18].Also, this swelling effect on the irradiated surface region has been reported previously in the Si ion bombardment of high purity silica with the same experimental conditions [8].
The measured mean value for the scaling exponent z is consistent only with the Mullins growth model [57].Therefore, the observed surface stabilization (slow increase of w) would be due to a relaxation process by thermal diffusion.Regarding the measured roughness exponent α, it is within the predicted values by the Kuramoto-Sivashinsky [58] growth model.Again, the large value of a > 0.5 suggests that surface evolution in the non-linear regime could be influenced by diffusion processes.The mass accumulations on the surface crests observed in figure 1(f), for the sample at the transition from wrinkles pattern to cellular-like structures, can be explained through this diffusion process in combination with the presence of shadowing effect (as discussed below).In this way, the Si rich composition at the ripple's higher parts and the mass accumulations can be related to segregation of the Si excess in the glass, as observed by EDS.In fact, these thermal diffusive processes are stimulated by the surface heating due to electronic stopping power S , e since using a SRIM simulation [42] this is an order of magnitude greater than nuclear stopping power S n by / S S 13.6 e n for the impinging 1 MeV Si ions.Also, for low energy ion irradiation, where nuclear stopping is clearly dominant, those mass accumulations on wrinkle crests are not observed on soda-lime [18,53] and SiO 2 [6,19,51,52].However, at high energy bombardment, this kind of mass accumulation has been observed by Ahmad [56] on crystalline Si irradiated by 2.5 MeV Cu ions at q = 60 o with Φ > 6.5 10 17 cm −2 , where features are produced in the higher parts of the patterns.
In the context of the roughness kinetic theory, the measured exponents do not obey the dynamic scaling condition / a b = z that should be fulfilled [49].In this way, the observed power-law for w and x at the results section would be unconventional (anomalous) [59].Also, applying a Monte Carlo simulation for the growth of mounded surfaces in thin films, Pelliccione et al [59] found that the dynamic scaling breaks when / g ¹ z 1 , which is a relationship that holds in the results of this work.According to this, the unconventional scaling in the non-linear regime can correspond to the fact that x of the surface patterns grows slower than their wavelength l.
To understand the role of non-local effects on the evolution of the topography, the EDS scans carried out for the Si-K x-rays showing Si higher content in surface peaks than in valleys (see figure 7), indicate the presence of shadowing effect during irradiation.The shadowing become significant when the undulatory pattern reach a high amplitude size enough to generate shadows for the incoming ions as is shown in figure 8(a).Under this circumstance, more Si ions are implanted on top of the hills than on the valleys where the ions do not arrive in the same amount, because many of them are blocked by the preceding peak.The same behavior is observed in Si irradiated by MeV Cu ion where a higher concentration of Cu is observed at the crests of ripples [56].Surface diffusion and shadowing effects lead to mass accumulation features at the crests.According to Carter [60] the shadowing effect become significant when the w/λ ratio exceeds a threshold value, / /  p l p q w 2 2 tan 2 .( )Figure 9 shows the measured ratios / p l w 2 2 and where the horizontal line indicates the threshold value of 0.36 for the experimental conditions applied in this work.From this figure is evident the dominance of shadowing effect on samples for Φ between -1.4 4.0 10 17 cm −2 where the measured ratios are larger than the threshold value.
The observed coarsening on the wavelength may be considered comparably as that given by the Hauffe mechanism for low-medium energy ions [61].Under this mechanism, part of the incident ions gets superficially implanted in the crests of the peaks producing the shadow effect, while some other ions can be dispersed by scattering events on the peaks.Those ions reflected by the ridges towards nearby features can continue the erosion at lower regions of the surface, as shown in the right of figure 8(a).At higher energies the ions penetrate deeper in the sample and the backward dispersion is much less likely than forward scattering, maintaining the shadow but eliminating the effects produced by the reflection of the impinging ions.However, the projected ion ranges and their straggling could be larger enough to allow some ions to break through to the peaks, emerging at the other side with low energy such that the Hauffe mechanisms appear, as shown in figure 8(b).Thus, the erosion of the valleys and low-lying regions of the surface continues for higher energies.For larger irradiation fluences both processes lead to an increase of the wavelength l l ¢ > and the pattern amplitude ¢ > h h, as shown in figure 8(c).Considering the projected range with its straggling for 1 MeV Si ions on soda-lime glass calculated by SRIM [42] and the measured x values for the experimental conditions applied, some ions can be able to trespass the peaks and emerge with an energy of few keV, as has been proposed.This mechanism agrees with the slowly increment of w observed at non-linear regime.
The combination of surface diffusion and ion trespassing the peaks are the proposed processes responsible for the formation of the cell-like structures, figures 1(g)-(h).These structures were not observed on SiO 2 by MeV Au ion irradiation at q = 60 o [7], where the Au ion range is less than a half micrometer and unable to pass through the ripples.Similar situation is observed on Si under 2.5 MeV Cu ion irradiation at q = 60 o [56].In the former case the morphology evolves under surface diffusion and the generation of a similar stage to that is shown in figure 1(f).The formation of cell-like structures is not reached, even after increasing the ion fluence.Meanwhile, for the latter situation, the Cu projected range is not large enough to trespass ripples and for this reason the structure coarsening does not continue.

Conclusions
The formation of surface patterns on soda-lime glass irradiated at 70°with 1 MeV ions has been studied.For the total ion fluences applied, the pattern formation dynamics agreed with the presence of a linear and non-linear behaviors, as it is predicted by accepted theoretical models for low-medium energy ions (eV-KeV).The obtained surfaces scale with respect to the fluence, including height, interface width and wavelength of patterns.The micrometer-sized structures correspond to experiments in the range energies of MeV.At the transition to the non-linear regime the formation of surface wrinkles as a buckling effect is observed.The analysis of the scaling exponents suggests that the dynamics of surface in the non-linear regime scale anomalously and it is determined by diffusion processes.Also, as irradiation continues, geometrical effects take on a higher importance including shadowing.Under this circumstance, the l coarsening at MeV energies is associated to a mechanism in which for the impinging ions with enough energy to break through neighboring peaks continue to erode lower surface For low and medium energy irradiation some ions are implanted on the crests producing a shadow effect, while others can be deflected towards lower regions on the surface and altering neighboring valleys.(b) At higher energies, some ions can pass through peaks emerging with low energy and erode neighboring valleys.(c) For both ion energy ranges, after large irradiation doses the lower surface features can be eroded to increase the wavelength (l l > ¢) and the amplitude of the pattern ( ¢ > h h).
regions.This mechanism can explain the slow growth of w and amplitude pattern.The final cell structure formations are a contribution of mass diffusion and geometrical effects.

Figure 1 .
Figure 1.SEM micrographs at X 2000 of soda-lime glass irradiated with 1 MeV silicon ions for increasing ion fluence.The projected ion beam direction is from top to bottom on all images (as the arrow indicates).

Figure 2 .
Figure 2. AFM micrographs on 25 μm × 25 μm areas on soda-lime silica glass implanted with silicon ions.The surface projected ion beam direction is from top to bottom on all images, as it is indicated by the arrow.

Figure 3 .
Figure 3.Typical one-dimensional surface profiles along vertical lines on the AFM images of figure 2. The ion beam direction is from left to right, as indicated by the superimposed arrow.

Figure 4 .
Figure 4. Surface RMS roughness w with respect to increasing fluence Φ.A critical ion fluence around Φc ~1.4 10 17 cm −2 indicates the transition between linear and non-linear regime.

Figure 5 .
Figure 5.The characteristic wavelength l and the correlation length x for the surface patterns with respect to the fluence Φ.The critical fluence around Φ c ~1.4 × 10 17 cm −2 indicates the transition between the linear and non-linear regime.

Figure 6 .
Figure 6.The roughness exponent a respect to the fluence Φ.The critical fluence Φ c ~1.4 × 10 17 cm −2 indicates the transition between the linear and non-linear regime.

Figure 7 .
Figure 7. EDS linear scans for the Si-K x-ray count ratio intensity along the horizontal lines on the SEM images for: (a) a nonirradiated sample surface region; (b) sample with F = 1.2 10 17 cm −2 at the linear regime; and (c) sample F = 4.0 10 17 cm −2 at the non-linear regime.The arrows indicate the ion beam direction projection on surface, while the x-ray detector is located perpendicular to the arrow at upper of the SEM micrography.

Figure 8 .
Figure 8.(a) For low and medium energy irradiation some ions are implanted on the crests producing a shadow effect, while others can be deflected towards lower regions on the surface and altering neighboring valleys.(b) At higher energies, some ions can pass through peaks emerging with low energy and erode neighboring valleys.(c) For both ion energy ranges, after large irradiation doses the lower surface features can be eroded to increase the wavelength (l l > ¢) and the amplitude of the pattern ( ¢ > h h).

Figure 9 .
Figure 9. Limiting condition for the Carter shadowing effect.The solid red line has been calculated at a value of 0.36.The shadowing effect appears for fluences above F = 1.4 10 c