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Sizes and distances of metal clusters in Au-, Pt-, W- and Fe-containing diamond-like carbon hard coatings: a comparative study by small angle X-ray scattering, wide angle X-ray diffraction, transmission electron microscopy and scanning tunnelling microscopy
Thin Solid Films 347 (1999) 60±71
Sizes and distances of metal clusters in Au-, Pt-, W- and Fe-containing diamond-like carbon hard coatings: a comparative study by small angle X-ray scattering, wide angle X-ray diffraction, transmission electron microscopy and scanning tunnelling microscopy Kirsten I. Schiffmann a,*, Matthias Fryda a, GuÈnther Goerigk b, Rolf Lauer c, Peter Hinze c, Andreas Bulack d a
Fraunhofer Institut fuÈr Schicht- und Ober¯aÈchentechnik (FhG-IST), Bienroder Weg 54E, D-38108 Braunschweig Germany b Forschungszentrum JuÈlich, Postfach 1913, D-52425 JuÈlich, Germany c Physikalisch-Technische Bundesanstalt (PTB), D-38023 Braunschweig, Germany d Institut fuÈr Ober¯aÈchentechnik und plasmatechnische Werkstoffentwicklung (IOPW), D-38108 Braunschweig, Germany Received 6 June 1998; received in revised form 22 October 1998; accepted 10 November 1998
Abstract Metal-containing diamond-like carbon hard coatings (Me-DLC) consist of nanometre size metallic particles, embedded into an amorphous hydrocarbon matrix. Their mechanical, tribological and electrical properties are strongly in¯uenced by the size and density of metallic clusters in the ®lm. In this paper a systematic investigation of mean sizes and mean centre-of-mass distances of metal clusters in Me-DLC ®lms is presented. Films with four different kinds of metal (gold, platinum, tungsten and iron) and metal contents ranging from 0 to 50 at.% are analysed, each by four complementary analytical techniques: small angle X-ray scattering, wide angle X-ray diffraction, transmission electron microscopy and scanning tunnelling microscopy. Increasing particle radii and particle distances in the range of 1 to 5 nm and 2 to 10 nm respectively are found with increasing metal content of the ®lm. Cluster sizes and distances correlate to the melting-point and the carbide forming behaviour of the metal. The results of different materials are compared and the suitability of analytical techniques for this particular application is discussed. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Metal clusters; Diamond-like carbon
1. Introduction Amorphous hydrocarbon coatings (a-C:H), often called diamond-like carbon (DLC), can be modi®ed by introducing a metallic component into the ®lm during the deposition process. This leads to a new class of materials called metalcontaining hydrocarbon ®lms (Me-C:H, Me-DLC). First works on these materials performed at the Philips Research Laboratory Hamburg were published in 1983 by Dimigen et al. [1,2], indicating interesting tribological properties for the metal-containing ®lms. Structural investigations by Grischke and others [3,4] in 1989 showed that the metallic component is not distributed homogeneously within the DLC matrix, but forms small clusters of nanometre size, which are carbidic in the case of carbide-forming metals. KoÈberle [5,6] studied the electrical properties of noble metal and carbide * Corresponding author. Tel.: 1 49-531-2155-577; fax.: 1 49-5312155-903. E-mail address: [email protected] (K.I. Schiffmann)
forming Me-C:H systems. He found that electrical conductivity of Me-C:H ®lms may be varied by up to 12 orders of magnitude by adjusting the metal content of the ®lm between 0 and 100 at.%. He also found that particle percolation and the degree of three-dimensional cross-linking of the hydrocarbon matrix strongly in¯uence electrical conductivity. Taube [7] and Wang et al. [8] showed that mechanical properties of various Me-C:H ®lms likewise depend on the metal concentration and the type of metal in the ®lm. Hardness values of 5 to 20 GPa and Young's moduli of 50 to 200 GPa have been reported [9±11]. Tribological data have been determined by several authors [4,9,10,12±15]. Typically friction coef®cients of 0.1 to 0.2 and wear rates slightly above those of metal-free DLC have been found. Often an optimum of tribological properties is detected for metal concentrations between 10 and 30 vol.% of metal or metal carbide respectively. Electrical, mechanical, tribological or other macroscopic properties should strongly be in¯uenced by the size and density of metallic nanoparticles which in turn depend on
0040-6090/99/$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S00 40- 6090(98)0160 7-1
K.I. Schiffmann et al. / Thin Solid Films 347 (1999) 60±71
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Table 1 Preparation conditions for Me-C:H ®lms Material
Au-C:H
Pt-C:H
Fe-C:H
W-C:H
Reactor Target to substrate distance (cm) Target material Rf power (kW) Target self bias (kV) Substrate bias voltage (V) Substrate temperature (8C) Residual pressure (Pa) Working pressure (Pa) Ar ¯ow (sccm) Ethine ¯ow (sccm) Typical growth rate (nm/min)
parallel plate geometry 3±8 Au 0.6±0.85 22 0 ,200 typ. 10 24 2 322 5±100 17±600
parallel plate geometry 3±8 Pt 0.6±0.85 22 0 ,200 typ. 10 24 2 32 4±7 17±60
parallel plate geometry 5.5 Fe 0.6 21.8 2650 ,200 typ. 10 24 1.2±1.6 100 1±2.5 7±28
2 targets, sample rotation variable (,30 cm) W 6 not measured 2120 ,200 typ. 10 24 4.5±5.5 390 50±350 18±54
the metal concentration inside the ®lm. Apart from some qualitative investigations the Philips group [10,13,16] was the ®rst to start systematic investigation of these structural properties. By means of small angle X-ray scattering experiments they estimated particle centre-of-mass distances of various Me-C:H systems and found increasing particle distances (a) with increasing metal content and (b) with decreasing melting point of the metal, ranging from 1.5 to 5 nm. Also some ®rst estimations of the size of particles were given in the range of 2±4 nm for niobium-containing Me-C:H ®lms. In the following a systematic investigation of mean radii and centre-of-mass distances of metal clusters in Me-C:H ®lms will be presented. Me-C:H ®lms with four different types of metal and metal contents ranging from 0 to 50 at.% have been analysed, each by four different methods. Two direct imaging techniques, transmission electron microscopy (TEM) and scanning tunnelling microscopy (STM), have been used in conjunction with two diffraction techniques, small angle X-ray scattering (SAXS) and wide angle X-ray diffraction (XRD). Each of these techniques has speci®c advantages and restrictions for the analysis of small particles which will be discussed in this paper. The combination of methods should give a high degree of significance for the results.
2. Experimental 2.1. Preparation of coatings The preparation of samples has been performed in a combined physical and chemical vapour deposition process. A capacitively coupled radio frequency is used to excite an argon plasma which sputters atoms off a metallic target. The addition of a small ¯ow of ethine gas (C2H2) 1 leads to a 1 Similar Me-DLC ®lms (including metal cluster formation) can be achieved by using methane (CH4) [10] or ethene (C2H4) [5] as a reactive hydrocarbon component.
simultaneous deposition of metal and hydrocarbon species. By adjusting the argon-to-C2H2 ratio the metal content in the ®lms has been varied between nearly zero and about 50 at.%. As metallic components gold (Au), platinum (Pt), tungsten (W) and iron (Fe) have been chosen to observe possible differences between noble and carbide forming metals. Films have been deposited onto silicon substrates and the ®lms thickness was in the range of 1±2 mm. Deposition parameters are summarized in Table 1. More detailed information about the deposition process can be found elsewhere [4,3,11,17]. 2.2. Small angle X-ray scattering (SAXS) SAXS experiments have been performed at the JUSIFA SAXS facility in the HASYLAB/DESY at Hamburg. It uses the synchrotron radiation of the DORIS electron storage ring, resulting in high synchrotron light intensities and a widely usable range of energies. The SAXS apparatus consists of a double-crystal monochromator for selecting X-ray energies in a range of 4.5±35 keV (dE=E 2 £ 1024 ), a system of aperture slits, two sample holders and the two-dimensional position-sensitive X-ray detector, which is a multiwire proportional counter, overspreading scattering angles of 0.1±58. For a more detailed description of the experimental set-up see [18]. In order to measure only the scattering contribution of the metallic particles a contrast variation procedure [19,20] has been performed. Therefore experiments have been carried out (1) at X-ray energies of the Au-, Pt-, W-La and Fe-Ka absorption edges (anomalous scattering) and (2) far below these absorption edges (normal scattering). Both measurements were subtracted, resulting exclusively in the scattering portion of the metallic phase. To minimize absorption losses the silicon substrates of the ®lms (thickness 550 mm) were etched down to about 50 mm by a mixture of 90% HF and 10% HNO3. 2.3. Wide angle X-ray scattering (XRD) Wide angle X-ray diffraction measurements have been
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K.I. Schiffmann et al. / Thin Solid Films 347 (1999) 60±71
accomplished on a Siemens instrument with copper anode and Bragg±Brentano geometry. XRD can only be used for particle size determination. No information about particle distances is available. 2.4. Transmission electron microscopy (TEM) TEM has been performed using Philips CM200FEG equipment, with 200 kV beam energy, stabilized ®eld emission cathode and super twin lens. Samples have been prepared for top-view and for cross-sectional imaging of the ®lms by ®rst mechanically drilling, cutting and grinding the silicon substrate down to some micrometres and then by ion beam etching under small angle of incidence until perforation of the ®lm to obtain an electron transparent area of the sample. 2.5. Scanning tunnelling microscopy (STM) STM measurements have been performed using the Universal-SPM of Park Scienti®c Instruments operating in air. For all STM experiments mechanically cut PtIr wires have been used as tunnelling tips. STM images were taken at bias voltages of 0.3±1.2 V and tunnel currents of 0.06± 0.6 nA. For lateral calibration a calibration standard with inverted pyramids of 100 nm edge-length and 200 nm periodicity has been applied and the dependence of the scanner sensitivity on different scan sizes has been carefully corrected. Vertical calibration has been accomplished by a step standard of 390 nm step height. Barrier height images (BHI) have been used successfully for the identi®cation of the metallic and the hydrocarbon phase of Me-C:H coatings, using a modulation technique and lock-in detection of the (dI/dz) signal. A more detailed description and the results of BHI investigation can be found in [21]. Me-C:H ®lms often show a thin coverage with amorphous hydrocarbon residues (resulting from the shut down of the deposition process), disturbing STM imaging. To remove these residues a careful cleaning of the surfaces by a short and weak plasma etching has been found useful in some cases. Au-C:H ®lms could be imaged without any pre-treatment. Imaging of Pt-C:H ®lms was enhanced by a reactive oxygen or hydrogen plasma, while STM of W-C:H could be improved by a non-reactive argon plasma treatment. Fe-C:H imaging could not be improved by either of these different procedures or other wet-chemical treatments. It could be imaged by STM but image quality was not suf®cient for quantitative evaluation. Details about optimum conditions of plasma pre-treatment can be found elsewhere [22]. 3. Results and discussion 3.1. Small angle X-ray scattering For the evaluation of SAXS data the two-dimensional
scattering distributions were averaged radially resulting in a one-dimensional scattering curve, representing the scattering intensity I(q) as a function of the magnitude of the scattering vector q~ 4p=lsin u=2 where l is the X-ray wavelength, u is the scattering angle. If the metallic particles in the ®lm are all of the same kind and the electron densities of particles and hydrocarbon matrix are homogeneous, then the scattering intensity can be factorized in the following way [23]: 2 ÿ ÿ ÿ N P re 2 rM VP2 F q~ 2 S q~ 1 I q~ e V where N/V is the number of particles per unit volume, (r eP 2 r eM) is the difference in electron densities of the particles and the matrix (scattering contrast), VP is the mean volume of the particles. F(q) is called form-factor since it only depends on the shape of the particles. Independently of this shape, for small q-values (qr , 2) the form-factor can be approximated according to Guinier [24] by: 2 2 ÿ 2 F q < exp q RG 3
! 2
while for large q-values (qr . 5) according to Porod [25]: ÿ 2 2p AP F q < VP2 q4
3
is valid. Here RG is the radius of gyration, which in thepcase of spherical particles with radius R0 reduces to RG 3=5 R0, and Ap is the mean surface area of the particles. For spherical particles Porod also gave a closed expression for F(q) [26]: ÿ ÿ ÿ sin qR0 2 qR0 cos qR0 F q 3 ÿ qR0 3
4
The function S(q) in Eq. (1) is called the structural factor since it contains the information about the geometrical distribution of particles inside the sample. It may be represented by a correlation function developed by Sharma and Sharma [27]. The model assumes hard sphere particles and describes the probability of ®nding a particle in a distance interval [r,r 1 dr] around another particle. Especially when particles are very densely packed, strong correlations in particle distances appear and correlation peaks may be seen in the scattering curves. Often the order of magnitude of particle distances or structure sizes d is estimated by [23] d 2p=qc
5
where qc is the scattering vector of the corresponding structure in the scattering curve.
K.I. Schiffmann et al. / Thin Solid Films 347 (1999) 60±71
63
Fig. 1. Radially averaged small angle scattering distributions for (a) Au-C:H, (b) Pt-C:H, (c) W-C:H and (d) Fe-C:H with different metal concentrations. Scattering intensity I(q) is given in units of the Thomson cross-section for the scattering of X-ray photons by one electron, which are called electron units [e.u.].
Fig. 1 shows the experimental scattering curves of Au-, Pt-, W- and Fe-containing ®lms with different metal contents. In all cases for high q-values a decrease of the scattering intensity proportional to q 2n, n 4, is found according to Porods Law (Eq. (3)). This is the expected behaviour for X-ray scattering by nanometre size particles. From the exponent n 4 it can be concluded that the particles do not have fractal (n , 4) or diffuse (n . 4) surfaces, but a sharp interface to the matrix with a well de®ned surface area. Since no intensity oscillations are visible in
the Porod range there should be a wide distribution of particle radii. In the middle q-range in most cases a shoulder or local maximum is found which shifts to smaller q-values as the metal content increases. According to Eq. (5) this indicates an increase of particle distances with increasing metal concentration and consequently particle radii should increase also to solve the higher volume fraction of metal. The local maxima are especially pronounced in Au-C:H and W-C:H, indicating strong correlations in particle distances.
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The distance correlations are typically found at metal concentrations below the percolation threshold 2, i.e. where the ratio of particle diameter to particle distance is between 0.5 and 1, corresponding to relatively densely packed particles. For small q-values (q , 2p=d) in most Me-C:H samples another increase of the scattering intensity toward small q is found which does not follow Porod's law, but is proportional to q 2n, n 1...2,8. Exceptions are the samples of Pt-C:H with 5, 14 and 22 at.% Pt where no increase is found. The increase of scattering intensity at low q cannot be explained in terms of individual particles of only 1 to 5 nm radius even if a certain distribution of radii is allowed. According to Eq. (5) the existence of larger structures of more then 60 nm in diameter has to be assumed. Due to the contrast variation it can be excluded that these larger structures are simply long-range variations in electron density of the matrix. Likewise the hypothesis of a fractal aggregation of individual particles to large, strongly branched structures [29], which often are found in colloidal systems [30], can be rejected, because it should only occur near or above the percolation threshold. Since the increase at low q-values was also found for Au-C:H and Pt-C:H ®lms with less than 1 at.% Au or Pt respectively, volume fractals can certainly be excluded. The observed effect probably results from very few large particles with a wide distribution of radii in the range of tens of nanometres perhaps up to micrometres. Since scattering intensity scales with Vp2, i.e. I q t R60 , a very small number of large particles is suf®cient to explain the increase in intensity 3. Consequently it is very improbable that these large particles are found in STM or TEM images since only 50 to 300 particles can typically be resolved within one STM or TEM image. The origin of these small numbers of large particles probably can be found in a break-off of larger clusters or even small grains from the polycrystalline target falling onto the substrate during the deposition process. This hypothesis is supported by the fact that the sputter target has a rough and grainy surface after use and on the ®lm surface partially overgrown particles or grains were sometimes observed in scanning electron microscopy. Up to now no explanation has been found why some Pt-C:H samples do not show these large particles. For the quantitative evaluation of scattering curves the model of homogeneous hard spheres in a homogenous matrix was used (Eq. (1)). The form-factor of spherical particles was selected according to Porod (Eq. (4)) and for
2
The percolation threshold is the metal concentration where the metallic particles begin to touch each other and conducting paths through the samples are formed. Electrical conductivity has not been determined in this study, but from other authors the percolation threshold for Au-C:H can be found to be at about 50 at.% [5] and for W-C:H at about 15 at.% [28], respectively. 3 E.g. 1 particle of 30 nm radius generates the same scattering intensity as 1 000 000 particles of 3 nm radius!
the structural-factor the correlation function of Sharma and Sharma [27] has been applied. Theoretical scattering curves were computed and ®tted to the experimental data by variation of radii- and distance-parameters. Since particles are not monodisperse, a bimodal distribution of radii has been considered. It consists of the peaked main distribution for the small particles, and a ¯at background distribution representing the small amount of large particles. Both distributions were represented by log±normal distribution functions, the ®rst one sharply peaked while the second one has a maximum near zero and a strongly asymmetric shape resulting in a slowly, monotone decreasing shape. Other distributions may also be appropriate for the background but since it contributes only with a weight factor of less than 10 24 the exact shape of the curve is not important. For the characterization of particle distances the correlation length resulting from the Sharma-expression was used. Since the experimental correlation peaks of Me-C:H ®lms were smooth, while Sharma's expression yields relatively sharp maxima, a certain variation of the parameter was allowed by introducing a gaussian distribution also for the correlation length. The physical reason for this smearing-out of correlations probably is the fact that ®lms were not completely uniform over their ®lm thickness. Due to a gradual coverage of the metallic target by hydrocarbon species during the deposition process, gradients in the metal concentration were created leading to variations of particle distances and radii inside the sample which are averaged in SAXS experiments. The convergence of the ®ts was rather good (see Fig. 1) but in some cases the ®t results in non-physical distance values; e.g. for W-C:H between 7 and 12 at.% W distance values are smaller than particle diameters which should be physically impossible. It probably results from the fact that the Porod-range (q 24-decrease), which is rather important for the success of the ®t, is largely cut off due to the limited detector geometry and the small dimension of the particles. Using Eq. (5) instead, only evaluating the position of the correlation peak, results in meaningful values: At high metal contents (20, 25 at.% W) it coincides with the results of the ®t procedure, while it continues almost linearly towards small metal concentrations, leading to more realistic volume fractions of metal inside the ®lm. For Fe-C:H a similar behaviour was found although the deviations were not so strong. In both cases the results of Eq. (5) have been used instead of the ®t values. Additionally, for the valuation of results the following points have to be considered: 1. The model of Sharma and Sharma has been developed for monodisperse particles (atoms in a liquid) while particles in Me-C:H ®lms are strongly polydisperse. Therefore a bimodal distribution of cluster sizes has been introduced. The parametrization of this distribution by log±normal functions is somewhat arbitrary and is not determined by the ®lm growth process.
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65
Fig. 2. Wide angle X-ray diffraction patterns of Au-C:H, Pt-C:H, W-C:H with different metal concentrations and Fe-C:H containing 45 at.% Fe. Spectra are shifted vertically against each other. Numbers in brackets indicate corresponding crystallographic planes. Please notice logarithmic or linear intensity scales.
2. At high metal contents above the percolation threshold the applicability of the model will be restricted because scattering centres are no longer spherical and the size of scattering structures is no longer well de®ned. 3. Me-C:H samples in general are not homogeneous: (a) gradients in metal content exist due to target coverage during the deposition process, (b) metal enrichment or metal depletion has been observed at the sample surface due to the not well de®ned shut-down of the deposition process or due to catalytic dissociation of the amorphous C:H-matrix, e.g. for Au- or Pt-C:H ®lms, (c) metallic interlayers were sometimes used at the ®lm±substrate interface for better adhesion of the ®lm to the substrate. SAXS averages over the whole ®lm volume, thus leading to a smearing out of cluster distances and radii, while in TEM or STM only small and homogeneous sections of the sample are evaluated. 4. Another difference between SAXS and direct imaging methods is that in principle SAXS is able to resolve the contribution of smallest particles down to single atoms while with TEM and STM resolution is limited as will be discussed below.
A direct comparison of particle radii and distances determined by SAXS and the other analytical techniques will be given at the end of this section. 3.2. Wide angle X-ray scattering (XRD) The wide angle X-ray diffraction patterns of Au-, Pt-, Wand Fe-containing hydrocarbon ®lms (Fig. 2) show that particles in Me-C:H systems are always crystalline. In the case of noble metals the patterns of pure gold and platinum, respectively, were found. For W-C:H, on the other hand, the X-ray pattern corresponds to tungsten carbide (WC12x, x 0:5... 0.625). For Fe-C:H a phase identi®cation was not possible because there are several different iron carbides (Fe3C, Fe5C2, Fe2C, FeC,...) which all have a large number of very close peaks which could not be resolved even at high metal contents. While pure iron could most probably be excluded, the best correspondence in position of groups of peaks was found for Fe5C2. Considering a series of samples with decreasing metal content, always a decrease in peak intensity and an increase in peak width is found. At a certain threshold which depends
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Fig. 3. Transmission electron microscope image of an Au-C:H ®lm containing 19 at.% gold. Spherical particles and crystallographic planes are clearly visible. Image size 38 £ 38 nm 2.
on the type of metal, the samples become amorphous with respect to X-ray diffraction. The change of peak width W can mainly be attributed to a change in particle size D. Using the equation of Scherrer: D l= Wcosu
6
where l is the X-ray wavelength and u is the scattering angle, the particle diameter could easily be determined for Au-, Pt- and W-C:H ®lms. For Fe-C:H, particle size determination was not possible. The main uncertainty in XRD grain size determination is a possible in¯uence of lattice deformations due to internal stress which also results in a peak broadening according to: W 4 Dd=dtanu
7
where Dd/d is the relative lattice distortion. Lattice distortion and grain size effect can be distinguished by their different dependence on the scattering angle u . In the case of exclusively grain size widening the quantity Wcosu should be independent of u , while it should increase if there are contributions of lattice distortion. The examination of the u dependence shows no in¯uence of distortion for Au-C:H, Pt-C:H and W-C:H with 55 at.% W. For W-C:H with lower metal contents (41, 25 at.%) there were not enough peaks for evaluation, so a clear statement was not possible. 3.3. Transmission electron microscopy Fig. 3 shows a TEM image of an Au-C:H ®lm containing 19 at.% Au. It proves that particles are in fact of nearly spherical shape, con®rming the assumption made in SAXS evaluation, and in most cases consist of one single crystal
domain. Fig. 4 shows cross-sectional images of Fe-C:H with different metal contents. Fig. 4a corresponds to a metal concentration of 8.6 at.% where particles are well separated. At the substrate interface a metallic interlayer for improvement of adhesion is visible. Fig. 4b corresponds to an iron concentration of 42 at.% which obviously is already above the percolation threshold for Fe-C:H. The ®lm structure has now inverted to a nanocrystalline iron-carbide matrix with small inclusions of hydrocarbon between the metallic grains. For the evaluation 50±200 individual particles have typically been taken into account. The particle centre-of-mass distances have been determined between each particle and its 3±5 nearest neighbour particles, considering only those in a small stripe along the sample perforation where sample thickness is low and therefore projection effects are minimized. For metal contents above the percolation threshold particle radii are identi®ed with half the mean grain diameter and particle (centre-of-mass) distances are set equal to the grain diameter (closed package). The major problems of the TEM evaluation are as follows. 1. Due to the incoherent scattering of the electron beam by the amorphous matrix a granular diffraction pattern is always visible between the particles (see Fig. 3). Smallest particles cannot be distinguished from these irregular diffraction patterns and are omitted in evaluation. Consequently, (a) the experimental distribution of particle Ê . Likewise, diameters has a lower cut-off at about 2±6 A (b) in particle distance determination small particles lying between two larger ones may not be recognized as a particle, so instead of nearest neighbour distances the next-to-nearest neighbour distances are considered, shifting the distance distribution to higher values. Both effects should become more pronounced as the mean particle size decreases, i.e. for low metal concentrations and for carbide forming systems. 2. Due to the ®nite thickness of the imaged sample area the particles never lie perfectly in one plane. Consequently the measured projected interparticle distances are always smaller or equal to the true three-dimensional distances, shifting the whole distance distribution to lower values. The effects (1b) and (2) may compensate each other in parts but systematic errors will probably not vanish completely. 3.4. Scanning tunnelling microscopy Fig. 5 shows examples of STM images of a Pt-C:H surface (14 at.% Pt) and a W-C:H sample (20 at.% W). In both cases the three-dimensional arrangement of particles is clearly visible and the metallic nature of particles has been proven by barrier height imaging. For the determination of the apparent particle radii r 0 central cross-sections of particles have been taken and least-square ®ts of a circle function
K.I. Schiffmann et al. / Thin Solid Films 347 (1999) 60±71
67
Fig. 5. Scanning tunnelling microscopy images of metal clusters of (a) PtC:H with 14 at.% Pt and (b) W-C:H with 20 at.% W. Image size in both cases is 50 £ 50 nm 2, vertical scales are 10 and 6 nm respectively.
Fig. 4. Transmission electron microscope images of Fe-C:H ®lms with (a) 8.6 at.% Fe and (b) 42 at.% Fe. Image size in both cases is 145 £ 145 nm 2.
r 02 s2 1 z2 , s x2 1 y2 1=2 have been performed. It was found that particles are not always of perfect spherical shape, but in most cases the ®t-method led to a good approximation for the mean size D 2r 0 of the particles. The main problem in quantitative evaluation of STM images is the ®nite tip radius of curvature, leading to a geometrical convolution of the surface topography and the tip shape. Assuming a tip with a radius of curvature Rt, the true particle radius r is given by r r 0 2 Rt 0
8
where r is the apparent particle radius of curvature, i.e. for the determination of particle radii the tip radius of curvature has to be known.
Several authors have already shown that it is possible to reconstruct the tip radius of curvature from the STM image itself by using special deconvolution methods [31±35]. In the case of Me-C:H ®lms a specially adapted method has been developed, which makes use of the spherical shape of the particles. The method has been described in detail in [36] and it has been applied to the determination of tip radii of each individual tip used for STM imaging of MeC:H surfaces. Tip radii typically were in the range of 10 to Ê and have been determined with an accuracy of 40 A Ê . Using these tip radii and Eq. approximately ^3 to ^5 A (8), particle radii could be determined easily and it was found that the careful tip radius determination was very important since tip radii and particle radii are of the same order of magnitude, leading to severe errors if not considered. The particle distance determination, too, is affected by the ®nite size of the tip because small particles or particles lying deep between other ones are partly or completely hidden
68
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Fig. 6. Radii r and centre-of-mass distances d of metal clusters of Au-C:H, Pt-C:H, W-C:H and Fe-C:H as a function of metal content in the ®lm, determined by SAXS, XRD, TEM and STM.
due to the tip-surface convolution. Hence nearest neighbour distances are replaced by the next to nearest neighbour distances, leading to a shift of the distance distribution to higher values just as in TEM imaging, although the physical origin of the effect is completely different. Even if the tip radius of curvature is known and image deconvolution can
be performed, reconstruction of hidden particles and their corresponding distances is impossible since the STM image does not contain enough information about them. Nevertheless, to get useful distance values out of the STM images, simulations of the tip surface convolution by Monte-Carlo methods have been performed to compute
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69
Fig. 8. Radii and centre-of-mass distances of Au-, Pt-, W- and Fe-C:H ®lms containing 20 vol.% of metal or metal carbide respectively, plotted against the melting-point of corresponding metal.
The following facts can be extracted.
Fig. 7. Direct comparison of (a) radii and (b) centre-of-mass distances of metal clusters in Au-, Pt-, W- and Fe-C:H ®lms as a function of metal content of the ®lms. Values correspond to the best approximation extracted from results of all analytical methods.
the fraction of visible and invisible particles and their respective distances as a function of the tip radius of curvature, the particle radius distribution and the apparent particle distance-distribution of the sample. As a result of this selfconsistent, iterative procedure a correction factor has been calculated and applied to the experimental mean distance values, taking the concealment of particles into consideration. It was found that, depending on tip radii and metal content of the samples, apparent particle distances are about 15% to 35% too high due to hidden particles and a distinct effort can be achieved using the corrected values. A detailed description of the Monte-Carlo model and the respective results can be found in [36]. 3.5. Radii and distances of metal clusters Fig. 6 summarizes the results of particle radii and distances of Au-, Pt-, W- and Fe-C:H ®lms determined by SAXS, XRD, TEM and STM.
1. Both particle radii and particle distances increase monotonically with increasing metal content. As long as there are inclusions of hydrocarbon matrix between the grains the enlargement is relatively moderate, while approaching pure polycrystalline material, e.g. WC, particle size may increase more than proportionally. 2. At lowest metal concentrations (,5 at.%) particle radii Ê corresponding to clusters of only amount to only 5±10 A 10±100 atoms. The minimum cluster size seems to be largely independent of the type of metal inside the ®lm, while cluster sizes spread at higher metal contents (Fig. 7a). A similar behaviour is found for the cluster centreof-mass distances (Fig. 7b). The largest particle radii of Ê have been found for Au-C:H with 45 at.% up to 50 A 4 Au . Largest particle distances are approximately twice the largest radii, since this fact corresponds to an almost closed package of metallic grains inside the ®lm. 3. For comparable and not too small metal contents, MeC:H systems with a carbide forming metallic component (e.g. W, Fe) have been found to form smaller particles than those containing noble metals (Au, Pt). This may be an indication that not only single metal atoms but also a fraction of carbide molecules contribute to the deposition process in carbidic Me-C:H systems, forming smaller particles due to their lower mobility. 4. In general a decrease of mean particle size and centre-ofmass distance is found with increasing melting point of the metal (see Fig. 8). This re¯ects the fact that the diffusion coef®cient, or the mobility of metallic adatoms 4 Ê for metal contents of For Cu-C:H Fryda [13] has found radii up to 90 A 65 at.% Cu.
70
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respectively strongly increase with increasing ratio of deposition temperature to melting point (Td/Tm) of the metal. Consequently, higher melting points yield lower mobilities which result in higher densities and smaller sizes of particles. 5. An anisotropic shape of particles (elongation along ®lm growth direction) up to aspect ratios of 4:1 as supposed by Benndorf et al. [16] could not be con®rmed. TEM cross-sections do clearly verify a more or less spherical shape without any preferential orientation. The anisotropy found in two-dimensional SAXS images of tilted samples possibly results from a concatenation of particles at high metal contents (Nb-C:H, 45 at.% Nb). Indications for the validity of this explanation have been found in some TEM images. The relatively high mobility of metallic atoms to form clusters even at deposition temperatures of only 2008C probably results from signi®cantly higher effective temperatures within the growth zone of the ®lm. These higher temperatures may be due to (a) surface bombardment by electrons and neutral metal atoms from the target, (b) the heat of formation during the particle formation process and especially in the case of carbidic particles the heat of carbide formation, (c) an additional bombardment by metal ions in the case when a substrate bias is used. The in¯uence of the substrate bias on the particle size was not investigated in this study. It is known that substrate bias increases the cross-linking and density of the amorphous matrix and therefore increases hardness and wear resistance but also intrinsic stress of the ®lms [12,37]. Since substrate bias will increase surface temperature it may increase the particle size but on the other hand also defect density will increase which may yield an opposite effect. 3.6. Comparison of analytical methods Comparing the results of the four analytical techniques, in some cases a very high correspondence between the methods has been found (e.g. particle radii of Au-C:H and PtC:H). On the other hand remarkable deviations have also to be noticed, especially in particle distance determination. The sources of these deviations are mostly inherent to the combination of method and material investigated and will be summarized below. 1. SAXS results, of course, depend on the kind of model used for curve ®tting which still has to be optimized to give an adequate description of the structure of Me-C:H. In general SAXS works especially well at low densities of particles, i.e. low metal contents, while problems may occur near or above the percolation threshold. Some of the ®tting problems described above are not yet well understood and have to be investigated further. Especially the deviation of particle radii for Pt-C:H (22 at.%) from data of the other methods has not been explained up to now. Since SAXS averages over the
whole ®lm volume, results may differ from those of local, direct imaging techniques. 2. XRD only yields results on particle sizes. The main restrictions of this method with respect to the investigation of Me-C:H ®lms are: (a) lattice distortions due to internal stress, which may shift experimental particle radii toward lower values, (b) peak interferences especially for carbide forming metals, and (c) the increase of spectrum noise and transition to the X-ray amorphous state when approaching small metal contents. If a certain amount of particles are not single crystals but contain grain boundaries, deviations between X-ray size and geometrical size may appear. However, from TEM images the fraction of polycrystalline particles is estimated to be less then 3%. 3. In most Me-C:H systems TEM investigation chie¯y yields larger mean radii and distances then e.g. SAXS or XRD. As discussed above, this results from the fact that proper recognition of smallest particles is impeded due to the incoherent scattering of the electron beam by the amorphous matrix in which particles are embedded, missing those particles in the statistical evaluation. Obviously this effect completely exceeds a possible shortening of apparent distances due to the projection of 3D particle arrangement into the image plane. Additionally, since TEM is a local method, results of TEM may vary due to real differences of radii and distances inside the sample, caused e.g. by gradients in the metal content. 4. The STM results only give information about the very ®rst layer of the sample which must not be representative for the bulk material. As mentioned above, catalytic dissociation of the hydrocarbon matrix may increase particle density, while different resting times of the ethine gas and metal atoms after process ®nishing may enhance or reduce particle density in the topmost layer. This probably is the reason why distance data e.g. for AuC:H and Pt-C:H in parts deviate from the results of other methods, while respective particle radii determined by STM perfectly match the reference data. An additional source of errors in particle distance determination by STM may be the fact that the Monte Carlo procedure for correcting tip convolution effects is based on several assumptions about the shape of radii and distance distributions and the three-dimensional arrangement and mean number of nearest neighbour particles which may differ from those of real Me-C:H samples. 4. Conclusion For gold-, platinum-, tungsten- and iron-C:H-®lms the variation of size and centre-of-mass distance of metallic clusters has been quantitatively determined for metal concentrations between 0 and 50 at.%. An increase of cluster sizes and distances could be con®rmed as a general
K.I. Schiffmann et al. / Thin Solid Films 347 (1999) 60±71
behaviour of strongly different types of metal. From the quantitative differences in particle size of various types of metal investigated it can be concluded that the mobility of metallic species diffusing on the growing C:H-surface is the dominant factor in¯uencing cluster sizes. This mobility is affected by the melting-point of the metal and whether the metal forms carbides or not. Since smallest particles Ê in diameter the critical detected are in the range of 8±10 A size of nuclei during deposition must be in the range of only 10±30 atoms. The comparison of different analytical methods has shown that particle size and distance determination in MeC:H systems is not a trivial problem. The dif®culties arise from the combination of very small cluster sizes, high particle densities, a three-dimensional embedding of clusters into the matrix and the speci®c restrictions of the respective method. It is obvious that usage of only one single method may lead to signi®cant errors. Consequently the combination of two or more complementary analytical techniques is strongly recommended for quantitative investigations of the Me-C:H structure. Acknowledgements We gratefully acknowledge H. HuÈbsch and R. Thyen for the preparation of coatings. This work was ®nanced by the Volkswagen Stiftung, Hannover. References [1] H. Dimigen, H. HuÈbsch, Philips Tech. Rev. 41 (1983) 186. [2] H. Dimigen, H. HuÈbsch, R. Memming, Appl. Phys. Lett. 50 (1987) 1056. [3] M. Grischke, Fortschrittberichte VDI, Vol. 5, no. 179, 1989. [4] C.P. Klages, R. Memming, Mater. Sci. Forum 52±53 (1989) 609. [5] H. KoÈberle, Thesis, Department of Physis, University of Hamburg, 1989. [6] C.-P. Klages, H. KoÈberle, M. Bauer, R. Memming, in: J.P. Dismukes (Ed.), Proc. Int. Symp. on Diamond and Diamond-like Films, Elec. Chem. Soc. Proc., Vol. 89-12, Pennington, NJ.
71
[7] K. Taube, Fortschrittberichte VDI, Vol. 18, no. 102, 1991. [8] M. Wang, K. Schmidt, K. Reichelt, H. Dimigen, H. HuÈbsch, J. Mater. Res. 7 (1992) 667. [9] H. Dimigen, C.-P. Klages, Surf. Coat. Technol. 49 (1991) 543. [10] M. Fryda, C. Benndorf, C.-P. Klages, K. Taube, Diamond Relat. Mater. 1 (1992) 558. [11] K. Bewilogua, H. Dimigen, Surf. Coat. Technol. 61 (1993) 144. [12] M. Grischke, K. Bewilogua, H. Dimigen, Mater. Manufact. Processes 8 (1993) 407. [13] M. Fryda, Fortschrittberichte VDI, Vol. 5, no. 303, 1993. [14] D. Klaffke, Diamond Films Technol. 3 (1994) 149. [15] W. van Duyn, B. van Lochem, Thin Solid Films 181 (1989) 497. [16] C. Benndorf, M. Fryda, C.P. Klages, K. Taube, H.G. Haubold, Mater. Sci. Eng. A 140 (1991) 795. [17] J.T. Harnack, Thesis, Department of Physics, University of Hamburg, 1993. [18] H.G. Haubold, et al., Rev. Sci. Instrum. 60 (1989) 1943. [19] L.A. Feigin, D.I. Svergun, in: W. Taylor (Ed.), Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum, New York, 1987. [20] G. Goerigk, H.G. Haubold, C. Klingshirn, A. Uhrig, J. Appl. Crystallogr. 27 (1994) 907. [21] K.I. Schiffmann, M. Fryda, G. Goerigk, Mikrochim. Acta 125 (1997) 107. [22] K.I. Schiffmann, Mikrostruktur und Mikrotribologie von amorphen metallhaltigen Kohlenwassertoffschichten, Fraunhofer IRB-Verlag, Stuttgart, 1997. [23] C.G. Windsor, J. Appl. Crystallogr. 21 (1988) 582. [24] A. Guinier, Ann. Phys. 12 (1939) 161. [25] G. Porod, Kolloidzeitschrift 124 (1951) 83. [26] G. Porod, Kolloidzeitschrift 125 (1952) 51. [27] R.V. Sharma, K.C. Sharma, Physica 89A (1977) 213. [28] M. Wang, Berichte Forschungszentrum JuÈlich, No. 2595, 1991, p. 45. [29] D.F.R. Mildner, P.L. Hall, J. Phys. D: Appl. Phys. 19 (1986) 1535. [30] D.W. Schaefer, J.E. Martin, P. Wiltzius, D.S. Cannell, Phys. Rev. Lett. 52 (1984) 2371. [31] J.S. Villarrubia, J. Vac. Sci. Technol. B 14 (1996) 1518. [32] P.M. Williams, K.M. Shakesheff, M.C. Davies, D.E. Jackson, C.J. Roberts, S.J.B. Tendler, J. Vac. Sci. Technol. B 14 (1996) 1557. [33] M. Sumetskii, A.A. Kornyshev, U. Stimming, Appl. Phys. Lett. 68 (1996) 2436. [34] S. Dongmo, M. Troyon, P. Vautrot, E. Delain, N. Bonnet, J. Vac. Sci. Technol. B 14 (1996) 1552. [35] D.J. Keller, F.S. Franke, Surf. Sci. 294 (1993) 409. [36] K.I. Schiffmann, M. Fryda, G. Goerigk, R. Lauer, P. Hinze, Ultramicroscopy 66 (1996) 183. [37] K. Taube, Surf. Coat. Technol. 98 (1998) 976.
Sizes and distances of metal clusters in Au-, Pt-, W- and Fe-containing diamond-like carbon hard coatings: a comparative study by small angle X-ray scattering, wide angle X-ray diffraction, transmission electron microscopy and scanning tunnelling microscopy Kirsten I. Schiffmann a,*, Matthias Fryda a, GuÈnther Goerigk b, Rolf Lauer c, Peter Hinze c, Andreas Bulack d a
Fraunhofer Institut fuÈr Schicht- und Ober¯aÈchentechnik (FhG-IST), Bienroder Weg 54E, D-38108 Braunschweig Germany b Forschungszentrum JuÈlich, Postfach 1913, D-52425 JuÈlich, Germany c Physikalisch-Technische Bundesanstalt (PTB), D-38023 Braunschweig, Germany d Institut fuÈr Ober¯aÈchentechnik und plasmatechnische Werkstoffentwicklung (IOPW), D-38108 Braunschweig, Germany Received 6 June 1998; received in revised form 22 October 1998; accepted 10 November 1998
Abstract Metal-containing diamond-like carbon hard coatings (Me-DLC) consist of nanometre size metallic particles, embedded into an amorphous hydrocarbon matrix. Their mechanical, tribological and electrical properties are strongly in¯uenced by the size and density of metallic clusters in the ®lm. In this paper a systematic investigation of mean sizes and mean centre-of-mass distances of metal clusters in Me-DLC ®lms is presented. Films with four different kinds of metal (gold, platinum, tungsten and iron) and metal contents ranging from 0 to 50 at.% are analysed, each by four complementary analytical techniques: small angle X-ray scattering, wide angle X-ray diffraction, transmission electron microscopy and scanning tunnelling microscopy. Increasing particle radii and particle distances in the range of 1 to 5 nm and 2 to 10 nm respectively are found with increasing metal content of the ®lm. Cluster sizes and distances correlate to the melting-point and the carbide forming behaviour of the metal. The results of different materials are compared and the suitability of analytical techniques for this particular application is discussed. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Metal clusters; Diamond-like carbon
1. Introduction Amorphous hydrocarbon coatings (a-C:H), often called diamond-like carbon (DLC), can be modi®ed by introducing a metallic component into the ®lm during the deposition process. This leads to a new class of materials called metalcontaining hydrocarbon ®lms (Me-C:H, Me-DLC). First works on these materials performed at the Philips Research Laboratory Hamburg were published in 1983 by Dimigen et al. [1,2], indicating interesting tribological properties for the metal-containing ®lms. Structural investigations by Grischke and others [3,4] in 1989 showed that the metallic component is not distributed homogeneously within the DLC matrix, but forms small clusters of nanometre size, which are carbidic in the case of carbide-forming metals. KoÈberle [5,6] studied the electrical properties of noble metal and carbide * Corresponding author. Tel.: 1 49-531-2155-577; fax.: 1 49-5312155-903. E-mail address: [email protected] (K.I. Schiffmann)
forming Me-C:H systems. He found that electrical conductivity of Me-C:H ®lms may be varied by up to 12 orders of magnitude by adjusting the metal content of the ®lm between 0 and 100 at.%. He also found that particle percolation and the degree of three-dimensional cross-linking of the hydrocarbon matrix strongly in¯uence electrical conductivity. Taube [7] and Wang et al. [8] showed that mechanical properties of various Me-C:H ®lms likewise depend on the metal concentration and the type of metal in the ®lm. Hardness values of 5 to 20 GPa and Young's moduli of 50 to 200 GPa have been reported [9±11]. Tribological data have been determined by several authors [4,9,10,12±15]. Typically friction coef®cients of 0.1 to 0.2 and wear rates slightly above those of metal-free DLC have been found. Often an optimum of tribological properties is detected for metal concentrations between 10 and 30 vol.% of metal or metal carbide respectively. Electrical, mechanical, tribological or other macroscopic properties should strongly be in¯uenced by the size and density of metallic nanoparticles which in turn depend on
0040-6090/99/$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S00 40- 6090(98)0160 7-1
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61
Table 1 Preparation conditions for Me-C:H ®lms Material
Au-C:H
Pt-C:H
Fe-C:H
W-C:H
Reactor Target to substrate distance (cm) Target material Rf power (kW) Target self bias (kV) Substrate bias voltage (V) Substrate temperature (8C) Residual pressure (Pa) Working pressure (Pa) Ar ¯ow (sccm) Ethine ¯ow (sccm) Typical growth rate (nm/min)
parallel plate geometry 3±8 Au 0.6±0.85 22 0 ,200 typ. 10 24 2 322 5±100 17±600
parallel plate geometry 3±8 Pt 0.6±0.85 22 0 ,200 typ. 10 24 2 32 4±7 17±60
parallel plate geometry 5.5 Fe 0.6 21.8 2650 ,200 typ. 10 24 1.2±1.6 100 1±2.5 7±28
2 targets, sample rotation variable (,30 cm) W 6 not measured 2120 ,200 typ. 10 24 4.5±5.5 390 50±350 18±54
the metal concentration inside the ®lm. Apart from some qualitative investigations the Philips group [10,13,16] was the ®rst to start systematic investigation of these structural properties. By means of small angle X-ray scattering experiments they estimated particle centre-of-mass distances of various Me-C:H systems and found increasing particle distances (a) with increasing metal content and (b) with decreasing melting point of the metal, ranging from 1.5 to 5 nm. Also some ®rst estimations of the size of particles were given in the range of 2±4 nm for niobium-containing Me-C:H ®lms. In the following a systematic investigation of mean radii and centre-of-mass distances of metal clusters in Me-C:H ®lms will be presented. Me-C:H ®lms with four different types of metal and metal contents ranging from 0 to 50 at.% have been analysed, each by four different methods. Two direct imaging techniques, transmission electron microscopy (TEM) and scanning tunnelling microscopy (STM), have been used in conjunction with two diffraction techniques, small angle X-ray scattering (SAXS) and wide angle X-ray diffraction (XRD). Each of these techniques has speci®c advantages and restrictions for the analysis of small particles which will be discussed in this paper. The combination of methods should give a high degree of significance for the results.
2. Experimental 2.1. Preparation of coatings The preparation of samples has been performed in a combined physical and chemical vapour deposition process. A capacitively coupled radio frequency is used to excite an argon plasma which sputters atoms off a metallic target. The addition of a small ¯ow of ethine gas (C2H2) 1 leads to a 1 Similar Me-DLC ®lms (including metal cluster formation) can be achieved by using methane (CH4) [10] or ethene (C2H4) [5] as a reactive hydrocarbon component.
simultaneous deposition of metal and hydrocarbon species. By adjusting the argon-to-C2H2 ratio the metal content in the ®lms has been varied between nearly zero and about 50 at.%. As metallic components gold (Au), platinum (Pt), tungsten (W) and iron (Fe) have been chosen to observe possible differences between noble and carbide forming metals. Films have been deposited onto silicon substrates and the ®lms thickness was in the range of 1±2 mm. Deposition parameters are summarized in Table 1. More detailed information about the deposition process can be found elsewhere [4,3,11,17]. 2.2. Small angle X-ray scattering (SAXS) SAXS experiments have been performed at the JUSIFA SAXS facility in the HASYLAB/DESY at Hamburg. It uses the synchrotron radiation of the DORIS electron storage ring, resulting in high synchrotron light intensities and a widely usable range of energies. The SAXS apparatus consists of a double-crystal monochromator for selecting X-ray energies in a range of 4.5±35 keV (dE=E 2 £ 1024 ), a system of aperture slits, two sample holders and the two-dimensional position-sensitive X-ray detector, which is a multiwire proportional counter, overspreading scattering angles of 0.1±58. For a more detailed description of the experimental set-up see [18]. In order to measure only the scattering contribution of the metallic particles a contrast variation procedure [19,20] has been performed. Therefore experiments have been carried out (1) at X-ray energies of the Au-, Pt-, W-La and Fe-Ka absorption edges (anomalous scattering) and (2) far below these absorption edges (normal scattering). Both measurements were subtracted, resulting exclusively in the scattering portion of the metallic phase. To minimize absorption losses the silicon substrates of the ®lms (thickness 550 mm) were etched down to about 50 mm by a mixture of 90% HF and 10% HNO3. 2.3. Wide angle X-ray scattering (XRD) Wide angle X-ray diffraction measurements have been
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K.I. Schiffmann et al. / Thin Solid Films 347 (1999) 60±71
accomplished on a Siemens instrument with copper anode and Bragg±Brentano geometry. XRD can only be used for particle size determination. No information about particle distances is available. 2.4. Transmission electron microscopy (TEM) TEM has been performed using Philips CM200FEG equipment, with 200 kV beam energy, stabilized ®eld emission cathode and super twin lens. Samples have been prepared for top-view and for cross-sectional imaging of the ®lms by ®rst mechanically drilling, cutting and grinding the silicon substrate down to some micrometres and then by ion beam etching under small angle of incidence until perforation of the ®lm to obtain an electron transparent area of the sample. 2.5. Scanning tunnelling microscopy (STM) STM measurements have been performed using the Universal-SPM of Park Scienti®c Instruments operating in air. For all STM experiments mechanically cut PtIr wires have been used as tunnelling tips. STM images were taken at bias voltages of 0.3±1.2 V and tunnel currents of 0.06± 0.6 nA. For lateral calibration a calibration standard with inverted pyramids of 100 nm edge-length and 200 nm periodicity has been applied and the dependence of the scanner sensitivity on different scan sizes has been carefully corrected. Vertical calibration has been accomplished by a step standard of 390 nm step height. Barrier height images (BHI) have been used successfully for the identi®cation of the metallic and the hydrocarbon phase of Me-C:H coatings, using a modulation technique and lock-in detection of the (dI/dz) signal. A more detailed description and the results of BHI investigation can be found in [21]. Me-C:H ®lms often show a thin coverage with amorphous hydrocarbon residues (resulting from the shut down of the deposition process), disturbing STM imaging. To remove these residues a careful cleaning of the surfaces by a short and weak plasma etching has been found useful in some cases. Au-C:H ®lms could be imaged without any pre-treatment. Imaging of Pt-C:H ®lms was enhanced by a reactive oxygen or hydrogen plasma, while STM of W-C:H could be improved by a non-reactive argon plasma treatment. Fe-C:H imaging could not be improved by either of these different procedures or other wet-chemical treatments. It could be imaged by STM but image quality was not suf®cient for quantitative evaluation. Details about optimum conditions of plasma pre-treatment can be found elsewhere [22]. 3. Results and discussion 3.1. Small angle X-ray scattering For the evaluation of SAXS data the two-dimensional
scattering distributions were averaged radially resulting in a one-dimensional scattering curve, representing the scattering intensity I(q) as a function of the magnitude of the scattering vector q~ 4p=lsin u=2 where l is the X-ray wavelength, u is the scattering angle. If the metallic particles in the ®lm are all of the same kind and the electron densities of particles and hydrocarbon matrix are homogeneous, then the scattering intensity can be factorized in the following way [23]: 2 ÿ ÿ ÿ N P re 2 rM VP2 F q~ 2 S q~ 1 I q~ e V where N/V is the number of particles per unit volume, (r eP 2 r eM) is the difference in electron densities of the particles and the matrix (scattering contrast), VP is the mean volume of the particles. F(q) is called form-factor since it only depends on the shape of the particles. Independently of this shape, for small q-values (qr , 2) the form-factor can be approximated according to Guinier [24] by: 2 2 ÿ 2 F q < exp q RG 3
! 2
while for large q-values (qr . 5) according to Porod [25]: ÿ 2 2p AP F q < VP2 q4
3
is valid. Here RG is the radius of gyration, which in thepcase of spherical particles with radius R0 reduces to RG 3=5 R0, and Ap is the mean surface area of the particles. For spherical particles Porod also gave a closed expression for F(q) [26]: ÿ ÿ ÿ sin qR0 2 qR0 cos qR0 F q 3 ÿ qR0 3
4
The function S(q) in Eq. (1) is called the structural factor since it contains the information about the geometrical distribution of particles inside the sample. It may be represented by a correlation function developed by Sharma and Sharma [27]. The model assumes hard sphere particles and describes the probability of ®nding a particle in a distance interval [r,r 1 dr] around another particle. Especially when particles are very densely packed, strong correlations in particle distances appear and correlation peaks may be seen in the scattering curves. Often the order of magnitude of particle distances or structure sizes d is estimated by [23] d 2p=qc
5
where qc is the scattering vector of the corresponding structure in the scattering curve.
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63
Fig. 1. Radially averaged small angle scattering distributions for (a) Au-C:H, (b) Pt-C:H, (c) W-C:H and (d) Fe-C:H with different metal concentrations. Scattering intensity I(q) is given in units of the Thomson cross-section for the scattering of X-ray photons by one electron, which are called electron units [e.u.].
Fig. 1 shows the experimental scattering curves of Au-, Pt-, W- and Fe-containing ®lms with different metal contents. In all cases for high q-values a decrease of the scattering intensity proportional to q 2n, n 4, is found according to Porods Law (Eq. (3)). This is the expected behaviour for X-ray scattering by nanometre size particles. From the exponent n 4 it can be concluded that the particles do not have fractal (n , 4) or diffuse (n . 4) surfaces, but a sharp interface to the matrix with a well de®ned surface area. Since no intensity oscillations are visible in
the Porod range there should be a wide distribution of particle radii. In the middle q-range in most cases a shoulder or local maximum is found which shifts to smaller q-values as the metal content increases. According to Eq. (5) this indicates an increase of particle distances with increasing metal concentration and consequently particle radii should increase also to solve the higher volume fraction of metal. The local maxima are especially pronounced in Au-C:H and W-C:H, indicating strong correlations in particle distances.
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The distance correlations are typically found at metal concentrations below the percolation threshold 2, i.e. where the ratio of particle diameter to particle distance is between 0.5 and 1, corresponding to relatively densely packed particles. For small q-values (q , 2p=d) in most Me-C:H samples another increase of the scattering intensity toward small q is found which does not follow Porod's law, but is proportional to q 2n, n 1...2,8. Exceptions are the samples of Pt-C:H with 5, 14 and 22 at.% Pt where no increase is found. The increase of scattering intensity at low q cannot be explained in terms of individual particles of only 1 to 5 nm radius even if a certain distribution of radii is allowed. According to Eq. (5) the existence of larger structures of more then 60 nm in diameter has to be assumed. Due to the contrast variation it can be excluded that these larger structures are simply long-range variations in electron density of the matrix. Likewise the hypothesis of a fractal aggregation of individual particles to large, strongly branched structures [29], which often are found in colloidal systems [30], can be rejected, because it should only occur near or above the percolation threshold. Since the increase at low q-values was also found for Au-C:H and Pt-C:H ®lms with less than 1 at.% Au or Pt respectively, volume fractals can certainly be excluded. The observed effect probably results from very few large particles with a wide distribution of radii in the range of tens of nanometres perhaps up to micrometres. Since scattering intensity scales with Vp2, i.e. I q t R60 , a very small number of large particles is suf®cient to explain the increase in intensity 3. Consequently it is very improbable that these large particles are found in STM or TEM images since only 50 to 300 particles can typically be resolved within one STM or TEM image. The origin of these small numbers of large particles probably can be found in a break-off of larger clusters or even small grains from the polycrystalline target falling onto the substrate during the deposition process. This hypothesis is supported by the fact that the sputter target has a rough and grainy surface after use and on the ®lm surface partially overgrown particles or grains were sometimes observed in scanning electron microscopy. Up to now no explanation has been found why some Pt-C:H samples do not show these large particles. For the quantitative evaluation of scattering curves the model of homogeneous hard spheres in a homogenous matrix was used (Eq. (1)). The form-factor of spherical particles was selected according to Porod (Eq. (4)) and for
2
The percolation threshold is the metal concentration where the metallic particles begin to touch each other and conducting paths through the samples are formed. Electrical conductivity has not been determined in this study, but from other authors the percolation threshold for Au-C:H can be found to be at about 50 at.% [5] and for W-C:H at about 15 at.% [28], respectively. 3 E.g. 1 particle of 30 nm radius generates the same scattering intensity as 1 000 000 particles of 3 nm radius!
the structural-factor the correlation function of Sharma and Sharma [27] has been applied. Theoretical scattering curves were computed and ®tted to the experimental data by variation of radii- and distance-parameters. Since particles are not monodisperse, a bimodal distribution of radii has been considered. It consists of the peaked main distribution for the small particles, and a ¯at background distribution representing the small amount of large particles. Both distributions were represented by log±normal distribution functions, the ®rst one sharply peaked while the second one has a maximum near zero and a strongly asymmetric shape resulting in a slowly, monotone decreasing shape. Other distributions may also be appropriate for the background but since it contributes only with a weight factor of less than 10 24 the exact shape of the curve is not important. For the characterization of particle distances the correlation length resulting from the Sharma-expression was used. Since the experimental correlation peaks of Me-C:H ®lms were smooth, while Sharma's expression yields relatively sharp maxima, a certain variation of the parameter was allowed by introducing a gaussian distribution also for the correlation length. The physical reason for this smearing-out of correlations probably is the fact that ®lms were not completely uniform over their ®lm thickness. Due to a gradual coverage of the metallic target by hydrocarbon species during the deposition process, gradients in the metal concentration were created leading to variations of particle distances and radii inside the sample which are averaged in SAXS experiments. The convergence of the ®ts was rather good (see Fig. 1) but in some cases the ®t results in non-physical distance values; e.g. for W-C:H between 7 and 12 at.% W distance values are smaller than particle diameters which should be physically impossible. It probably results from the fact that the Porod-range (q 24-decrease), which is rather important for the success of the ®t, is largely cut off due to the limited detector geometry and the small dimension of the particles. Using Eq. (5) instead, only evaluating the position of the correlation peak, results in meaningful values: At high metal contents (20, 25 at.% W) it coincides with the results of the ®t procedure, while it continues almost linearly towards small metal concentrations, leading to more realistic volume fractions of metal inside the ®lm. For Fe-C:H a similar behaviour was found although the deviations were not so strong. In both cases the results of Eq. (5) have been used instead of the ®t values. Additionally, for the valuation of results the following points have to be considered: 1. The model of Sharma and Sharma has been developed for monodisperse particles (atoms in a liquid) while particles in Me-C:H ®lms are strongly polydisperse. Therefore a bimodal distribution of cluster sizes has been introduced. The parametrization of this distribution by log±normal functions is somewhat arbitrary and is not determined by the ®lm growth process.
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65
Fig. 2. Wide angle X-ray diffraction patterns of Au-C:H, Pt-C:H, W-C:H with different metal concentrations and Fe-C:H containing 45 at.% Fe. Spectra are shifted vertically against each other. Numbers in brackets indicate corresponding crystallographic planes. Please notice logarithmic or linear intensity scales.
2. At high metal contents above the percolation threshold the applicability of the model will be restricted because scattering centres are no longer spherical and the size of scattering structures is no longer well de®ned. 3. Me-C:H samples in general are not homogeneous: (a) gradients in metal content exist due to target coverage during the deposition process, (b) metal enrichment or metal depletion has been observed at the sample surface due to the not well de®ned shut-down of the deposition process or due to catalytic dissociation of the amorphous C:H-matrix, e.g. for Au- or Pt-C:H ®lms, (c) metallic interlayers were sometimes used at the ®lm±substrate interface for better adhesion of the ®lm to the substrate. SAXS averages over the whole ®lm volume, thus leading to a smearing out of cluster distances and radii, while in TEM or STM only small and homogeneous sections of the sample are evaluated. 4. Another difference between SAXS and direct imaging methods is that in principle SAXS is able to resolve the contribution of smallest particles down to single atoms while with TEM and STM resolution is limited as will be discussed below.
A direct comparison of particle radii and distances determined by SAXS and the other analytical techniques will be given at the end of this section. 3.2. Wide angle X-ray scattering (XRD) The wide angle X-ray diffraction patterns of Au-, Pt-, Wand Fe-containing hydrocarbon ®lms (Fig. 2) show that particles in Me-C:H systems are always crystalline. In the case of noble metals the patterns of pure gold and platinum, respectively, were found. For W-C:H, on the other hand, the X-ray pattern corresponds to tungsten carbide (WC12x, x 0:5... 0.625). For Fe-C:H a phase identi®cation was not possible because there are several different iron carbides (Fe3C, Fe5C2, Fe2C, FeC,...) which all have a large number of very close peaks which could not be resolved even at high metal contents. While pure iron could most probably be excluded, the best correspondence in position of groups of peaks was found for Fe5C2. Considering a series of samples with decreasing metal content, always a decrease in peak intensity and an increase in peak width is found. At a certain threshold which depends
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Fig. 3. Transmission electron microscope image of an Au-C:H ®lm containing 19 at.% gold. Spherical particles and crystallographic planes are clearly visible. Image size 38 £ 38 nm 2.
on the type of metal, the samples become amorphous with respect to X-ray diffraction. The change of peak width W can mainly be attributed to a change in particle size D. Using the equation of Scherrer: D l= Wcosu
6
where l is the X-ray wavelength and u is the scattering angle, the particle diameter could easily be determined for Au-, Pt- and W-C:H ®lms. For Fe-C:H, particle size determination was not possible. The main uncertainty in XRD grain size determination is a possible in¯uence of lattice deformations due to internal stress which also results in a peak broadening according to: W 4 Dd=dtanu
7
where Dd/d is the relative lattice distortion. Lattice distortion and grain size effect can be distinguished by their different dependence on the scattering angle u . In the case of exclusively grain size widening the quantity Wcosu should be independent of u , while it should increase if there are contributions of lattice distortion. The examination of the u dependence shows no in¯uence of distortion for Au-C:H, Pt-C:H and W-C:H with 55 at.% W. For W-C:H with lower metal contents (41, 25 at.%) there were not enough peaks for evaluation, so a clear statement was not possible. 3.3. Transmission electron microscopy Fig. 3 shows a TEM image of an Au-C:H ®lm containing 19 at.% Au. It proves that particles are in fact of nearly spherical shape, con®rming the assumption made in SAXS evaluation, and in most cases consist of one single crystal
domain. Fig. 4 shows cross-sectional images of Fe-C:H with different metal contents. Fig. 4a corresponds to a metal concentration of 8.6 at.% where particles are well separated. At the substrate interface a metallic interlayer for improvement of adhesion is visible. Fig. 4b corresponds to an iron concentration of 42 at.% which obviously is already above the percolation threshold for Fe-C:H. The ®lm structure has now inverted to a nanocrystalline iron-carbide matrix with small inclusions of hydrocarbon between the metallic grains. For the evaluation 50±200 individual particles have typically been taken into account. The particle centre-of-mass distances have been determined between each particle and its 3±5 nearest neighbour particles, considering only those in a small stripe along the sample perforation where sample thickness is low and therefore projection effects are minimized. For metal contents above the percolation threshold particle radii are identi®ed with half the mean grain diameter and particle (centre-of-mass) distances are set equal to the grain diameter (closed package). The major problems of the TEM evaluation are as follows. 1. Due to the incoherent scattering of the electron beam by the amorphous matrix a granular diffraction pattern is always visible between the particles (see Fig. 3). Smallest particles cannot be distinguished from these irregular diffraction patterns and are omitted in evaluation. Consequently, (a) the experimental distribution of particle Ê . Likewise, diameters has a lower cut-off at about 2±6 A (b) in particle distance determination small particles lying between two larger ones may not be recognized as a particle, so instead of nearest neighbour distances the next-to-nearest neighbour distances are considered, shifting the distance distribution to higher values. Both effects should become more pronounced as the mean particle size decreases, i.e. for low metal concentrations and for carbide forming systems. 2. Due to the ®nite thickness of the imaged sample area the particles never lie perfectly in one plane. Consequently the measured projected interparticle distances are always smaller or equal to the true three-dimensional distances, shifting the whole distance distribution to lower values. The effects (1b) and (2) may compensate each other in parts but systematic errors will probably not vanish completely. 3.4. Scanning tunnelling microscopy Fig. 5 shows examples of STM images of a Pt-C:H surface (14 at.% Pt) and a W-C:H sample (20 at.% W). In both cases the three-dimensional arrangement of particles is clearly visible and the metallic nature of particles has been proven by barrier height imaging. For the determination of the apparent particle radii r 0 central cross-sections of particles have been taken and least-square ®ts of a circle function
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67
Fig. 5. Scanning tunnelling microscopy images of metal clusters of (a) PtC:H with 14 at.% Pt and (b) W-C:H with 20 at.% W. Image size in both cases is 50 £ 50 nm 2, vertical scales are 10 and 6 nm respectively.
Fig. 4. Transmission electron microscope images of Fe-C:H ®lms with (a) 8.6 at.% Fe and (b) 42 at.% Fe. Image size in both cases is 145 £ 145 nm 2.
r 02 s2 1 z2 , s x2 1 y2 1=2 have been performed. It was found that particles are not always of perfect spherical shape, but in most cases the ®t-method led to a good approximation for the mean size D 2r 0 of the particles. The main problem in quantitative evaluation of STM images is the ®nite tip radius of curvature, leading to a geometrical convolution of the surface topography and the tip shape. Assuming a tip with a radius of curvature Rt, the true particle radius r is given by r r 0 2 Rt 0
8
where r is the apparent particle radius of curvature, i.e. for the determination of particle radii the tip radius of curvature has to be known.
Several authors have already shown that it is possible to reconstruct the tip radius of curvature from the STM image itself by using special deconvolution methods [31±35]. In the case of Me-C:H ®lms a specially adapted method has been developed, which makes use of the spherical shape of the particles. The method has been described in detail in [36] and it has been applied to the determination of tip radii of each individual tip used for STM imaging of MeC:H surfaces. Tip radii typically were in the range of 10 to Ê and have been determined with an accuracy of 40 A Ê . Using these tip radii and Eq. approximately ^3 to ^5 A (8), particle radii could be determined easily and it was found that the careful tip radius determination was very important since tip radii and particle radii are of the same order of magnitude, leading to severe errors if not considered. The particle distance determination, too, is affected by the ®nite size of the tip because small particles or particles lying deep between other ones are partly or completely hidden
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Fig. 6. Radii r and centre-of-mass distances d of metal clusters of Au-C:H, Pt-C:H, W-C:H and Fe-C:H as a function of metal content in the ®lm, determined by SAXS, XRD, TEM and STM.
due to the tip-surface convolution. Hence nearest neighbour distances are replaced by the next to nearest neighbour distances, leading to a shift of the distance distribution to higher values just as in TEM imaging, although the physical origin of the effect is completely different. Even if the tip radius of curvature is known and image deconvolution can
be performed, reconstruction of hidden particles and their corresponding distances is impossible since the STM image does not contain enough information about them. Nevertheless, to get useful distance values out of the STM images, simulations of the tip surface convolution by Monte-Carlo methods have been performed to compute
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69
Fig. 8. Radii and centre-of-mass distances of Au-, Pt-, W- and Fe-C:H ®lms containing 20 vol.% of metal or metal carbide respectively, plotted against the melting-point of corresponding metal.
The following facts can be extracted.
Fig. 7. Direct comparison of (a) radii and (b) centre-of-mass distances of metal clusters in Au-, Pt-, W- and Fe-C:H ®lms as a function of metal content of the ®lms. Values correspond to the best approximation extracted from results of all analytical methods.
the fraction of visible and invisible particles and their respective distances as a function of the tip radius of curvature, the particle radius distribution and the apparent particle distance-distribution of the sample. As a result of this selfconsistent, iterative procedure a correction factor has been calculated and applied to the experimental mean distance values, taking the concealment of particles into consideration. It was found that, depending on tip radii and metal content of the samples, apparent particle distances are about 15% to 35% too high due to hidden particles and a distinct effort can be achieved using the corrected values. A detailed description of the Monte-Carlo model and the respective results can be found in [36]. 3.5. Radii and distances of metal clusters Fig. 6 summarizes the results of particle radii and distances of Au-, Pt-, W- and Fe-C:H ®lms determined by SAXS, XRD, TEM and STM.
1. Both particle radii and particle distances increase monotonically with increasing metal content. As long as there are inclusions of hydrocarbon matrix between the grains the enlargement is relatively moderate, while approaching pure polycrystalline material, e.g. WC, particle size may increase more than proportionally. 2. At lowest metal concentrations (,5 at.%) particle radii Ê corresponding to clusters of only amount to only 5±10 A 10±100 atoms. The minimum cluster size seems to be largely independent of the type of metal inside the ®lm, while cluster sizes spread at higher metal contents (Fig. 7a). A similar behaviour is found for the cluster centreof-mass distances (Fig. 7b). The largest particle radii of Ê have been found for Au-C:H with 45 at.% up to 50 A 4 Au . Largest particle distances are approximately twice the largest radii, since this fact corresponds to an almost closed package of metallic grains inside the ®lm. 3. For comparable and not too small metal contents, MeC:H systems with a carbide forming metallic component (e.g. W, Fe) have been found to form smaller particles than those containing noble metals (Au, Pt). This may be an indication that not only single metal atoms but also a fraction of carbide molecules contribute to the deposition process in carbidic Me-C:H systems, forming smaller particles due to their lower mobility. 4. In general a decrease of mean particle size and centre-ofmass distance is found with increasing melting point of the metal (see Fig. 8). This re¯ects the fact that the diffusion coef®cient, or the mobility of metallic adatoms 4 Ê for metal contents of For Cu-C:H Fryda [13] has found radii up to 90 A 65 at.% Cu.
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respectively strongly increase with increasing ratio of deposition temperature to melting point (Td/Tm) of the metal. Consequently, higher melting points yield lower mobilities which result in higher densities and smaller sizes of particles. 5. An anisotropic shape of particles (elongation along ®lm growth direction) up to aspect ratios of 4:1 as supposed by Benndorf et al. [16] could not be con®rmed. TEM cross-sections do clearly verify a more or less spherical shape without any preferential orientation. The anisotropy found in two-dimensional SAXS images of tilted samples possibly results from a concatenation of particles at high metal contents (Nb-C:H, 45 at.% Nb). Indications for the validity of this explanation have been found in some TEM images. The relatively high mobility of metallic atoms to form clusters even at deposition temperatures of only 2008C probably results from signi®cantly higher effective temperatures within the growth zone of the ®lm. These higher temperatures may be due to (a) surface bombardment by electrons and neutral metal atoms from the target, (b) the heat of formation during the particle formation process and especially in the case of carbidic particles the heat of carbide formation, (c) an additional bombardment by metal ions in the case when a substrate bias is used. The in¯uence of the substrate bias on the particle size was not investigated in this study. It is known that substrate bias increases the cross-linking and density of the amorphous matrix and therefore increases hardness and wear resistance but also intrinsic stress of the ®lms [12,37]. Since substrate bias will increase surface temperature it may increase the particle size but on the other hand also defect density will increase which may yield an opposite effect. 3.6. Comparison of analytical methods Comparing the results of the four analytical techniques, in some cases a very high correspondence between the methods has been found (e.g. particle radii of Au-C:H and PtC:H). On the other hand remarkable deviations have also to be noticed, especially in particle distance determination. The sources of these deviations are mostly inherent to the combination of method and material investigated and will be summarized below. 1. SAXS results, of course, depend on the kind of model used for curve ®tting which still has to be optimized to give an adequate description of the structure of Me-C:H. In general SAXS works especially well at low densities of particles, i.e. low metal contents, while problems may occur near or above the percolation threshold. Some of the ®tting problems described above are not yet well understood and have to be investigated further. Especially the deviation of particle radii for Pt-C:H (22 at.%) from data of the other methods has not been explained up to now. Since SAXS averages over the
whole ®lm volume, results may differ from those of local, direct imaging techniques. 2. XRD only yields results on particle sizes. The main restrictions of this method with respect to the investigation of Me-C:H ®lms are: (a) lattice distortions due to internal stress, which may shift experimental particle radii toward lower values, (b) peak interferences especially for carbide forming metals, and (c) the increase of spectrum noise and transition to the X-ray amorphous state when approaching small metal contents. If a certain amount of particles are not single crystals but contain grain boundaries, deviations between X-ray size and geometrical size may appear. However, from TEM images the fraction of polycrystalline particles is estimated to be less then 3%. 3. In most Me-C:H systems TEM investigation chie¯y yields larger mean radii and distances then e.g. SAXS or XRD. As discussed above, this results from the fact that proper recognition of smallest particles is impeded due to the incoherent scattering of the electron beam by the amorphous matrix in which particles are embedded, missing those particles in the statistical evaluation. Obviously this effect completely exceeds a possible shortening of apparent distances due to the projection of 3D particle arrangement into the image plane. Additionally, since TEM is a local method, results of TEM may vary due to real differences of radii and distances inside the sample, caused e.g. by gradients in the metal content. 4. The STM results only give information about the very ®rst layer of the sample which must not be representative for the bulk material. As mentioned above, catalytic dissociation of the hydrocarbon matrix may increase particle density, while different resting times of the ethine gas and metal atoms after process ®nishing may enhance or reduce particle density in the topmost layer. This probably is the reason why distance data e.g. for AuC:H and Pt-C:H in parts deviate from the results of other methods, while respective particle radii determined by STM perfectly match the reference data. An additional source of errors in particle distance determination by STM may be the fact that the Monte Carlo procedure for correcting tip convolution effects is based on several assumptions about the shape of radii and distance distributions and the three-dimensional arrangement and mean number of nearest neighbour particles which may differ from those of real Me-C:H samples. 4. Conclusion For gold-, platinum-, tungsten- and iron-C:H-®lms the variation of size and centre-of-mass distance of metallic clusters has been quantitatively determined for metal concentrations between 0 and 50 at.%. An increase of cluster sizes and distances could be con®rmed as a general
K.I. Schiffmann et al. / Thin Solid Films 347 (1999) 60±71
behaviour of strongly different types of metal. From the quantitative differences in particle size of various types of metal investigated it can be concluded that the mobility of metallic species diffusing on the growing C:H-surface is the dominant factor in¯uencing cluster sizes. This mobility is affected by the melting-point of the metal and whether the metal forms carbides or not. Since smallest particles Ê in diameter the critical detected are in the range of 8±10 A size of nuclei during deposition must be in the range of only 10±30 atoms. The comparison of different analytical methods has shown that particle size and distance determination in MeC:H systems is not a trivial problem. The dif®culties arise from the combination of very small cluster sizes, high particle densities, a three-dimensional embedding of clusters into the matrix and the speci®c restrictions of the respective method. It is obvious that usage of only one single method may lead to signi®cant errors. Consequently the combination of two or more complementary analytical techniques is strongly recommended for quantitative investigations of the Me-C:H structure. Acknowledgements We gratefully acknowledge H. HuÈbsch and R. Thyen for the preparation of coatings. This work was ®nanced by the Volkswagen Stiftung, Hannover. References [1] H. Dimigen, H. HuÈbsch, Philips Tech. Rev. 41 (1983) 186. [2] H. Dimigen, H. HuÈbsch, R. Memming, Appl. Phys. Lett. 50 (1987) 1056. [3] M. Grischke, Fortschrittberichte VDI, Vol. 5, no. 179, 1989. [4] C.P. Klages, R. Memming, Mater. Sci. Forum 52±53 (1989) 609. [5] H. KoÈberle, Thesis, Department of Physis, University of Hamburg, 1989. [6] C.-P. Klages, H. KoÈberle, M. Bauer, R. Memming, in: J.P. Dismukes (Ed.), Proc. Int. Symp. on Diamond and Diamond-like Films, Elec. Chem. Soc. Proc., Vol. 89-12, Pennington, NJ.
71
[7] K. Taube, Fortschrittberichte VDI, Vol. 18, no. 102, 1991. [8] M. Wang, K. Schmidt, K. Reichelt, H. Dimigen, H. HuÈbsch, J. Mater. Res. 7 (1992) 667. [9] H. Dimigen, C.-P. Klages, Surf. Coat. Technol. 49 (1991) 543. [10] M. Fryda, C. Benndorf, C.-P. Klages, K. Taube, Diamond Relat. Mater. 1 (1992) 558. [11] K. Bewilogua, H. Dimigen, Surf. Coat. Technol. 61 (1993) 144. [12] M. Grischke, K. Bewilogua, H. Dimigen, Mater. Manufact. Processes 8 (1993) 407. [13] M. Fryda, Fortschrittberichte VDI, Vol. 5, no. 303, 1993. [14] D. Klaffke, Diamond Films Technol. 3 (1994) 149. [15] W. van Duyn, B. van Lochem, Thin Solid Films 181 (1989) 497. [16] C. Benndorf, M. Fryda, C.P. Klages, K. Taube, H.G. Haubold, Mater. Sci. Eng. A 140 (1991) 795. [17] J.T. Harnack, Thesis, Department of Physics, University of Hamburg, 1993. [18] H.G. Haubold, et al., Rev. Sci. Instrum. 60 (1989) 1943. [19] L.A. Feigin, D.I. Svergun, in: W. Taylor (Ed.), Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum, New York, 1987. [20] G. Goerigk, H.G. Haubold, C. Klingshirn, A. Uhrig, J. Appl. Crystallogr. 27 (1994) 907. [21] K.I. Schiffmann, M. Fryda, G. Goerigk, Mikrochim. Acta 125 (1997) 107. [22] K.I. Schiffmann, Mikrostruktur und Mikrotribologie von amorphen metallhaltigen Kohlenwassertoffschichten, Fraunhofer IRB-Verlag, Stuttgart, 1997. [23] C.G. Windsor, J. Appl. Crystallogr. 21 (1988) 582. [24] A. Guinier, Ann. Phys. 12 (1939) 161. [25] G. Porod, Kolloidzeitschrift 124 (1951) 83. [26] G. Porod, Kolloidzeitschrift 125 (1952) 51. [27] R.V. Sharma, K.C. Sharma, Physica 89A (1977) 213. [28] M. Wang, Berichte Forschungszentrum JuÈlich, No. 2595, 1991, p. 45. [29] D.F.R. Mildner, P.L. Hall, J. Phys. D: Appl. Phys. 19 (1986) 1535. [30] D.W. Schaefer, J.E. Martin, P. Wiltzius, D.S. Cannell, Phys. Rev. Lett. 52 (1984) 2371. [31] J.S. Villarrubia, J. Vac. Sci. Technol. B 14 (1996) 1518. [32] P.M. Williams, K.M. Shakesheff, M.C. Davies, D.E. Jackson, C.J. Roberts, S.J.B. Tendler, J. Vac. Sci. Technol. B 14 (1996) 1557. [33] M. Sumetskii, A.A. Kornyshev, U. Stimming, Appl. Phys. Lett. 68 (1996) 2436. [34] S. Dongmo, M. Troyon, P. Vautrot, E. Delain, N. Bonnet, J. Vac. Sci. Technol. B 14 (1996) 1552. [35] D.J. Keller, F.S. Franke, Surf. Sci. 294 (1993) 409. [36] K.I. Schiffmann, M. Fryda, G. Goerigk, R. Lauer, P. Hinze, Ultramicroscopy 66 (1996) 183. [37] K. Taube, Surf. Coat. Technol. 98 (1998) 976.