Microstructure of nickel nanoparticles embedded in carbon films: case study on annealing effect by micromorphology analysis

The presented study is aimed at analyzing the surface texture of amorphous hydrogenated carbon layers containing nickel nanoparticles (Ni‐NPs@a‐C:H) within their structure, which were deposited by Radio Frequency (RF) sputtering and RF‐Plasma Enhanced Chemical Vapor Deposition (RF‐PECVD) methods on glass substrates. Prepared films were then used as research material following their annealing at two different temperatures of 250 °C and 350 °C in an inert argon atmosphere. Series of height samples were taken with the help of atomic force microscopy (AFM) operating in a non‐contact mode and examined in order to determine their fractal characteristics. Raw AFM data were first plane‐fitted to remove the surface bow exhibiting the so‐called residual surface, and then numerically processed to calculate the Areal Autocorrelation Function (AACF), which was later used to compute the Structure Function (SF). The log–log plots of the latter served for calculation of fractal properties of surfaces under investigation, including fractal dimension D, and pseudo‐topothesy K. The analysis of 3‐D surface texture helps to understand their essential characteristics and their implications as well as graphical models and their implementation in computer simulation. Copyright © 2016 John Wiley & Sons, Ltd.


Introduction
Carbon films used as hosts for foreign atoms are widely recognized for their large potential in engineering applications including, nanoelectronics, field emission displays, solar cells and electrochemical devices. The properties of such nanostructures are positively correlated with their structural properties and spatial characteristics.
Over the last decades, the 3-D surface morphology has been an important topic in surface material science, advanced materials, synthesis and characterization of nanostructure materials, computational fluid dynamics, image processing and fractal/multifractal geometry, to characterize the basic microstructures at the nanometer level of the thin films [1][2][3][4] .
The 3-D surface morphology of thin films is important in nanotechnology, from the synthesis of materials and the characterization of microstructure, to the measurement of properties and can yield important insights into the functionality, part performance and service life [5][6][7][8][9] . The engineering surface design and manufacturing lead to many interdisciplinary researches, including surface topography to assure quality and functional performance requirements in a number of different, and sometimes complimentary, ways [10][11][12][13][14][15] .
Fractal approach is focused on topographical features of any engineering 3-D surface that appear identical regardless of the length scale and gives insight into statistical self-similarity, which appear only in a limited area of spatial scales [17,18,20] .
Metallic nanoparticles with a size less than 100 nm have been investigated because of pronounced optical effects and microstructure properties, including Surface Plasmon Resonance (SPR) absorption [25] and Power Spectral Density (PSD) [26] , respectively.
This work aims to synthesize the Ni NPs @ a-C: H films by RFsputtering and RF-PECVD method on the glass substrates, and to determine the 3-D surface micro texture by means of AFM data in connection with the statistical and fractal analyses.

Materials and experimental techniques for the preparation of thin film
Amorphous carbon films containing Ni nanoparticles were prepared in a capacitively-coupled RF-PECVD system operating at 13.56-MHz power supply. Reactor chamber was equipped with two electrodes of different diameters. The smaller electrode was connected with the power source and a thin Ni target on it, while the bigger one remained at zero potential and connected to the body of the stainless steel chamber. The nanostructured thin films were deposited on glass substrates at room temperature. The chamber was pumped down to a base pressure of 10 À3 Pa prior to the process, but during the process the chamber was filled with acetylene.
The first step of the process took 45 min and it was carried out using 180 W of supply RF power with 3.5 Pa of the gas pressure. Later on, the samples were annealed for 30 min at two different temperatures of 250°C and 350°C in the ambient argon atmosphere in a furnace made from a 90-cm-long quartz tube with 8 cm of inner diameter. The furnace allowed to stabilize the annealing temperature measured with a thermocouple. The schematic diagrams of the deposition system and the furnace are shown in Fig. 1 (a) and (b), respectively. Table 1 summarizes preparation details of the samples.

Properties and characterization of thin films
Obtained layers were investigated with a spectrophotometer (Stellar.net, USA) in order to measure and compare the widths and the locations of SPR peaks in UV-Vis spectra, before and after the annealing step. The instrument used a 2-mm-wide optical fiber to transfer a non-polarized light beam (400-850 nm) through the samples to a CCD detector. Ion beam scattering was excited using 2.0-MeV He + ions generated in the van de Graff accelerator in the Centro de Micro-An´alisis de Materiales (CMAM). Solid state detectors for backscattered particles were placed at 162°with resolution of 15 keV. The incident ion beam was perpendicular to the sample surface. The SIMN RA software was used to analyze the RBS data in order to determine the thickness of the films and their elemental composition.
AFM series of height samples of the 3-D surface topography were taken in a non-contact mode using Multimode instrument (Digital Instruments, Santa Barbara, CA). The scan rate was in the range from 10 to 20 nm/s, and the images were completed after acquiring 256 × 256 scan steps covering the 1 μm × 1 μm of the scan area. AFM measurements were performed at room temperature (24 ± 1°C), and the tip cantilevers were those specified in Ref. [27] .

Characterization of the thin film surface texture
Raw AFM height samples were first plane-fitted to remove the longest wavelength components prior to any other computation. Then, the images were numerically processed to calculate the Autocorrelation Function, which was used to determine the anisotropy ratio S tr (texture aspect ratio), and to compute the Structure Function (SF). The log-log plots of the latter were used to calculate fractal properties of the studied surfaces, such as fractal dimension D, and pseudo-topothesy K. Details of the computation procedure   and its comparison to other methods were published elsewhere [17,19,28] . Normalized Areal Autocorrelation Function (AACF) can be computed using the following formula [29] : where: <… >-the mean value, σ-is the root-mean-square surface roughness (normalizing term), whereas (τ x, τ y )-discrete spatial lags along scan axes. S tr is defined as the ratio of extreme autocorrelation decay lengths τ with which the normalized AACF falls down from 1.0 to 0.2 [30] : where: a1, and a2-are the axes of the fastest and the slowest AACF decay, respectively. For S tr > 0.5 the surface is said to be isotropic (the higher S tr the more isotropic surface), while for S tr < 0.3 surface is said to be strongly anisotropic. The SF can be directly derived from the AACF according to [31] : After radial averaging, the log-log plot of the SF allows deriving the main fractal parameters: fractal dimension D, pseudo-topothesy K and corner frequency f c . Fractal properties of the surface emerge from respective scaling behavior, which in turn is associated with the way the surface is formed at various scale lengths. Transition points between fractal regimes are referred to as the corner frequencies f c . For comparison, the cube-count fractal dimension D CC was determined according to the method proposed in Ref. [17] .
Functional parameters can be derived from the cumulative height distribution profile also known as the bearing curve. The curve itself can be obtained by sorting original sampled data in a row from the highest peak to the lowest valley, and plot them on the percent scale. According to DIN 4776 standard, functional measures include, among others (see Fig. 2): • kernel roughness depth S k -the height of the core material at the flattest region of the bearing curve; • reduced peak height S pk , reduced valley depth S vk -the heights of the profile above/below the core profile respectively; • upper bearing area M r1 , lower bearing area M r2 -the intersection points of horizontal lines plotted from both ends of the flattest tangent of the bearing curve with that curve that delimit peaks and valleys from the core, respectively; the percentage of the peaks and valleys; • surface bearing index S bi -the ratio of the RMS roughness over the surface height at 5% of the bearing curve; • core fluid retention index S ci -the ratio of the void volume of the unit sampling area at the core zone over the RMS roughness; • valley fluid retention index S vi -the ratio of the void volume of the unit sampling area at the valley zone over the RMS roughness.

Statistical analysis
Experimental data were analyzed statistically using GraphPad InStat version 3.20 (GraphPad, San Diego, CA, USA) package. In order to determine the significance level of a difference in average results obtained from the same and from different surface sites, analysis of variance (ANOVA) complete with a post-hoc Tukey's test were used. P values less than 0.05 were assumed to prove statistically significant difference.

The Minkowski functionals
AFM data were also processed with the help of Gwyddion 2.28 software towards computation of the Minkowski Functionals (MFs) that includes: volume V, surface S and Euler-Poincaré characteristics (or connectivity number χ), expressed as [32,33] : where: N is the total number of pixels; N white -the number of 'white' pixels, that is pixels above the threshold (pixels below the threshold are referred to as 'black'); N bound -the number of white-black pixel boundaries; C white and C black -the number of continuous sets of white and black pixels respectively. Figure 3 exhibits non-homogeneous surface topography of the samples under study scanned over square areas of 1 μm × 1 μm.

Results
Presented AFM images uncover the locations of nanostructured individuals in the a-C:H film. The contents of Ni, C and O elements inside the films were determined from RBS spectra shown in Fig. 4, recorded before and after sample annealing.
The UV-Vis absorption spectra of the samples under investigation are shown in Fig. 5.
Log-log plots of the profile SFs drawn in a relation to the separation lengths are shown in Fig. 6.
Statistical and fractal surfaces properties of prepared samples are shown in Table 2, whereas Table 3 summarizes main functional parameters describing key surface texture features. Figures 7, 8 and 9 show the MF characteristics, that is the dimensionless functions of V(z), S(z) and c(z), of the samples under study in correspondence with Fig. 3. Figure 10 shows the typical Transmission Electron Microscopy (TEM) of as deposited and annealed at 250°C samples.  Figure 4a displays RBS spectra of Ni-NPs@a-C:H films before and after annealing step. It turns out that the O atoms appear from the surface of the annealed samples. For comparison, Fig. 4b shows the spectra taken from the un-annealed sample. The steps at 580 and 980 keV correspond to O and Si nuclei of amorphous SiO 2 substrate, respectively. The step at 410 keV is because of C nuclei, while that at 1520 keV comes from Ni nuclei. The results of SIMN RA software which simulates the RBS spectra show that the ratios of Ni/C and Ni/O are 2.4 and 4, respectively.

Discussion
In Fig. 5 an absorption peak near 368 nm because of localized SPR of Ni-NPs is visible [34] . Initially the peak in sample #1 is wide, but in sample #2 becomes sharp with a small red shift, while by increasing the annealing temperature to 350°C in sample #3, a small blue shift can be seen. Note that both red and blue shifts, shown in Fig. 4, occur because of changes in the size and distribution of NPs [35] . These variations in LSPR peaks are correlated with microscopic changes in AFM images and RBS spectra (Figs 3 and  4) which are all the effect of the annealing procedures.
In general, AFM images shown in Fig. 3 exhibit bifractal structure of the studied films composed with aggregated clusters of smaller ferromagnetic nickel particles. Such a structure is confirmed by the plots of the ACF function presented in Fig. 6, where one can distinguish two corner frequencies: τ s1 in the range 20-40 nm, which corresponds to the particle diameter and is 10 times larger than the step size (about 4 nm), and τ s2 in the range 85-240 nm, which corresponds to the cluster size. Annealing is found to influence both the particle and the cluster sizes: as-deposited particles are 35 nm in diameter, and aggregate into 120-nm diameter clusters, after annealing at 250°C the particle diameter decreases to 22 nm, and the cluster size decreases to 85 nm, whereas after annealing at 350°C the particle size goes up to 40 nm, and the cluster size goes up to 240 nm.
Discussed structure is best seen in Fig. 3B, where some form of self-assembly occurs, but the mechanisms behind such a cluster formation remain unknown. On the other hand, obtained surface roughness values steadily fall down with increasing annealing   temperature, which proves that the residual surface flattens because of the thermal motion of adsorbed nanoparticles. In such a picture, annealing at 250°C possibly establishes a compromise between the Arrhenius-type thermally activated diffusion (interaction of nanoparticles with the substrate), and the dipole-dipole interaction between ferromagnetic nanoparticles. The dipole-dipole interaction is always present in systems comprised of magnetic nanoparticles and can be considered the dominating interaction provided that the agglomeration of nanoparticles is absent and that they are stabilized within an isolated matrix [36] .
Other results generally confirm presented findings. Surface anisotropy ratio approaches maximum at 0.84 for sample annealed at 250°C, which is specific of very isotropic surface. In contrary, remaining samples exhibit rather low surface anisotropy ratio (0.45-0.55) corresponding to anisotropic or even highly anisotropic surface. Also, the fractal dimensions in a bifractal model take their lowest values in the sample annealed at 250°C, with D s1 being significantly lower than D s2 . It means that the surface of the clusters is more developed than the surface of their nanoparticle components. As in previous studies, the fractal dimension estimated using the cube-count method D cc is found constant among the samples under study and very close to that describing NPs (D s1 ) [17] . Table 2 presents main functional characteristics of the surfaces. Unfortunately, no such data on similar structures were published so far; hence, any comparison between them is impossible. After all, the kernel roughness depth S k substantially decreases among the samples: from 19 nm (as-deposited surface) down to 10 nm in the sample annealed at 350°C. As a rule, S k defines the working base of the structure responsible for its general and long-term tribological behavior. Smaller S k would correspond to higher mechanical resistance and gives higher load-carrying capacity during contacting operations. Reduced peak height S pk turns out to be correlated with S k falling down from 24 nm to 17 nm after the annealing process is completed. Reduced peak height describes the region of the surface that quickly vanishes in the first contact because of abrasion, and provides useful information on the running-in properties of the surface for bearing applications. Short running-in time (which is associated with small S k ) is preferable in engineering surfaces. Obtained S k values are specific of the deposited surfaces because the amount of material exposed to  Table 2. Statistical and fractal surface properties of prepared samples that involve: S tr -surface anisotropy ratio, D s -fractal dimension (from the log-log plot of the structure function), K s -pseudo-topothesy, τ scorner frequency, D cc -fractal dimension (from the cube-count method), S q -RMS surface roughness  wileyonlinelibrary.com/journal/sia mechanical damage is significantly large. Similar conclusion can be drawn considering the upper bearing area M r1 , which actually describes the material ratio of the height data in the peak area. Observed films exhibit M r1 slightly varying between 12 and 15% confirming relatively large distribution of the peaks to the overall surface. On the other hand, the reduced valley depth S vk is found to remain almost constant during the stages of the process. As seen in Table 2, S vk is equal to 13 nm before the final annealing is performed, and decreases to 11 nm afterwards. This parameter specifies the level of the deepest valleys that should withstand the wearing process serving otherwise as lubrication channels. In general, large S vk values are suitable for obtaining good fluid retention    properties; however, results presented in the paper remain low. The same holds for the lower bearing index M r2 . Its complement to 100% actually depicts the percentage of the valleys on the surface, and steadily falls between 8 and 8.5%. In general, results presented here suggest that the as-deposited surface becomes flat during subsequent annealing processes in accordance with the roughness data in the Table 1 (S q ).
Another parameter under study is the surface bearing index S bi with the larger value indicating better bearing property. For a perfect Gaussian surface it approaches about 0.61, whereas here it only slightly varies from 0.55 to 0.58, which might be because of the randomness of the deposition process. The last two parameters, core fluid retention index S ci and valley fluid retention index S vi , take extremely small values, which is a common property of the deposited materials. They simultaneously increase within about 50% of their initial values during the annealing process. The former index, S ci , goes up from 2.24 · 10 À5 to 4.06 · 10 À5 , whereas in a gaussian surface it should approach 1.56. The latter one changes from 1.30 · 10 À6 to 2.11 · 10 À6 , while the Gaussian surface exhibits S vi close to 0.11. Obtained results clearly indicate good bearing properties in the peak zone, but extremely weak fluid retention characteristics within kernel and valley zones of the analyzed surfaces.
The functions V(z), S(z) and C(z) confirm the surface patterns concerning the size of the structural unit.
It can be seen that the Minkowski volume V(z) curve initially remains almost flat, then it rapidly decreases to zero, returning to the constant value at the end (Fig. 7). On the other hand, the Minkowski surface S(z) curve rapidly increases to a maximum value, then rapidly decreases to a local minimum and continues with a slight oscillation. Finally, it monotonically approaches zero (Fig. 8). Unlike the previous curves, the Minkowski connectivity c(z) plot fluctuates between extreme values (positive and negative for different ranges, see Fig. 9). A negative value of connectivity number χ indicates a predominance of valleys, the minimum χ represents the largest density of valleys and the maximum value of χ is equal to the largest density of peaks.
Confirming all above results Fig. 10b shows the agglomerated nickel nanoparticles after annealing.

Conclusions
This work demonstrates three-dimensional surface texture analysis of Ni nanoparticles embedded in amorphous, hydrogenated carbon thin films (Ni-NPs@a-C:H) that serve as host materials. The films were deposited by RF-sputtering and RF-PECVD methods on the glass substrates. The characterizations involved: RBS and UVVIS absorption spectra, AFM measurements and fractal analyses.
It turns out from the RBS spectra that O nuclei are detected from the surface of the annealed films. LSPR peak of the films under study is found to undergo a small red shift for sample annealed at 250°C and a small blue shift for 350°C which are related to change in the size and distribution of NPs.
The 3-D surface texture patterns of the samples were investigated by AFM. AFM in correlation with statistical and fractal surface parameters can characterize changes in the spatial arrangement of nanoscale individuals at the micro-and nano scale.
The 3-D surface texture analysis is a novel method to recognize and predict structural features of thin film surfaces, synthesized by RF-sputtering and RF-PECVD method, to micro/nano scale surface processing and measurement. Also, the 3-D surface texture of thin films determined by specific parameters can be inserted in mathematical models to characterize the 3-D pattern of local surface more accurate.