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Study of the mechanical properties of tetrahedral amorphous carbon films by nanoindentation and nanowear measurements
Diamond and Related Materials 10 Ž2001. 145᎐152
Study of the mechanical properties of tetrahedral amorphous carbon films by nanoindentation and nanowear measurements E. Martınez ´ a , J.L. Andujar ´ a,U , M.C. Polo a , J. Esteve a , J. Robertsonb, W.I. Milne b a
` Uni¨ ersitat de Barcelona, Departament de Fısica A¨ . Diagonal 647, Barcelona E-08028, Spain ´ Aplicada i Optica, b Engineering Department, Uni¨ ersity of Cambridge, Trumptington Street, Cambridge CB2 1PZ, UK
Abstract Nanoindentation and nanowear measurements, along with the associated analysis suitable for the mechanical characterization of tetrahedral amorphous carbon Žta-C. films are discussed in this paper. Films of approximately 100-nm thick were deposited on silicon substrates at room temperature in a filtered cathodic vacuum arc evaporation system with an improved S-bend filter that yields films with high values of mass density Ž3.2 grcm3 . and sp 3 content Ž84᎐88%. when operating in a broad bias voltage range Žy20 V to y350 V.. Nanoindentation measurements were carried out on the films with a Berkovich diamond indenter applying loads in the 100 N᎐2 mN range, leading to maximum penetration depths between 10 and 60 nm. In this measurement range, the ta-C thin-films present a basically elastic behavior with high hardness Ž45 GPa. and high Young’s modulus Ž340 GPa. values. Due to the low thickness of the films and the shallow penetration depths involved in the measurement, the substrate influence must be taken into account and the area function of the indenter should be accurately calibrated for determination of both hardness and Young’s modulus. Moreover, nanowear measurements were performed on the films with a sharp diamond tip using multiple scans over an area of 3 m2 , producing a progressive wear crater with well-defined depth which shows an increasing linear dependence with the number of scans. The wear resistance at nanometric scale is found to be a function of the film hardness. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Hardness; Mechanical properties; Tetrahedral amorphous carbon; Wear
1. Introduction Over the last few years the preparation of tetrahedral amorphous carbon Žta-C. thin-films by several energetic vapour deposition methods w1,2x, from which films with sp 3 content higher than 80% can be grown, has become an increasingly important research area. One of the most attractive applications of ta-C films lies in their use as thin protective coatings on magnetic
U
Corresponding author. Tel.: q349-3-402-1146; fax: q349-3-4021138. E-mail address: [email protected] ŽJ.L. Andujar ´ ..
storage devices. However, in spite of the work done on the study and characterization of the ta-C film structural properties as a function of deposition conditions, few reports deal with the characterization of the mechanical properties w3x. The low thicknesses of the films Žtypically less than 100 nm. require the use of nanoindentation techniques with careful interpretation of the measurement results. The published studies often report the measured values of hardness and elastic modulus without mentioning the tip shape of the diamond indenter used and the details of the measurement, which makes the comparison between the results from different studies and their correlation with other film properties very difficult to make.
0925-9635r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 0 . 0 0 4 6 1 - 1
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E. Martınez ´ et al. r Diamond and Related Materials 10 (2001) 145᎐152
Recently, we reported the preparation of ta-C films in a filtered cathodic vacuum arc ŽFCVA. system with an improved S-bend filter that yields high values of mass density Ž3.2 grcm3 . and sp 3 content Ž84᎐88%. over a broad bias voltage range Žy20 V to y350 V. w4x. In this paper, we report upon the mechanical characterization of these dense ta-C films, where the hardness, Young’s modulus and nanowear behavior are discussed and related to the film structural properties. The nanoindentation load vs. penetration curves obtained for the thin film-substrate system are analyzed together with AFM images of the residual indentation impressions. Much attention has been paid to the influence of the substrate and the indenter area on the hardness and Young’s modulus values obtained from nanoindentation measurements. The wear behavior of the ta-C thin-films has also been characterized at a nanometric scale and correlations between hardness and nanowear have been established.
ness of the ta-C films Žapprox. 100 nm. the normal loads applied to the diamond indenter were kept in the 100 N᎐2 mN range. These loads led to maximum penetration depths of 10᎐60 nm, lower than the film thickness. AFM images of the sample surface were recorded before and after indentation process. At least 20 indentations under different maximum loads were performed at different locations for each sample to check the consistency of the results. Nanowear tests were conducted using a scanning probe microscope ŽSPM. w7x by dry sliding of a 300-nm radius diamond tip on the sample surface in multiple scans. During the diamond sliding, the tip scanning frequency was 1 Hz and the scan area was 3 = 3 m. The constant normal load applied to the indenter was varied from 10 to 380 N, which is a relatively high value for such a sharp indenter. AFM images of the resulting wear craters were obtained for an increasing number of wear cycles.
2. Experimental
3. Results and discussion
The ta-C films for this study were prepared at room temperature on silicon substrates in a FCVA system that incorporates an off-plane, double bend ŽS-bend. magnetic filter. Films in the thickness range 70᎐120 nm were grown using an arc current of 75 A at a deposition rate of 0.6 nmrs. The base pressure was below 10y5 Pa, which increased to approximately 10y4 Pa during deposition. The energy of incident ions was varied by applying a negative d.c. bias voltage to the substrates in the range from y20 to y350 V. The film mass density and sp 3 fraction were determined by X-ray reflectivity and electron energy loss spectroscopy, respectively w4x. The hardness and Young’s modulus of the ta-C thin-films were measured with a commercially available nanoindenter ŽHysitron Inc.. interfaced with an atomic force microscope software ŽNanoscope, Digital Instruments. w5x. This system allows us to obtain the load vs. penetration curves for a loading᎐unloading cycle and also to image the residual indentation impression. The system load and depth resolutions were 0.1 N and 0.2 nm, respectively. Nanoindentation measurements were carried out using a Berkovich diamond indenter with a tip radius of approximately 150 nm. The hardness and Young’s modulus values were obtained from the analysis of the unloading curve by applying the analysis method proposed by Oliver and Pharr w6x. In order to get an accurate area function, the tip area calibration was performed by indenting a standard fused quartz bulk sample in the range of 5᎐75 nm contact depth penetrations. The area function was determined assuming a constant reduced modulus of 69.64 GPa for the quartz reference sample and by fitting the resulting areas by a polynomial function. Due to the low thick-
3.1. Hardness and Young’s modulus measurements For each ta-C thin-film, multiple indentations were performed at different locations with increasing loads and penetration depths. This allows us to plot the hardness and reduced elastic modulus values as a function of the contact penetration depth, which means the depth at which the sample and the diamond indenter are in contact when the maximum load is applied. The reduced elastic modulus is the elastic parameter that can be directly calculated from the nanoindentation experimental data through the Sneddon’s equation w8x and it includes the indenter elastic effects and the sample Poisson’s coefficient. Fig. 1 shows one of these curves for an 80-nm thick sample deposited at y60 V substrate bias voltage. For all the samples, the curves showed the same typical behavior which can be split up into three distinct regions, starting from their values at high contact depths, hardness and reduced modulus increased with decreasing contact depths and applied loads Žzone 1.. They then reach a maximum value that remains constant for a limited contact depth range Žzone 2. and finally, they decrease at lower contact depths Žzone 3.. An accurate study of these three zones allows us to establish a procedure to determine the hardness and elastic modulus of the thin-films, which is explained in the following paragraph. Firstly, in order to identify the contact depth range influenced by an inaccurate area function calibration, we study the hardness and reduced modulus values as a function of the contact depth obtained for the standard fused quartz sample ŽFig. 2.. The values shown are those calculated using the corrected area function. The
E. Martınez ´ et al. r Diamond and Related Materials 10 (2001) 145᎐152
Fig. 1. Hardness and reduced modulus as a function of the contact depth measured in a 80-nm thick ta-C film.
calibration procedure used was the same as that described by Oliver and Pharr w6x. It should be noticed that even after the calibration, both the hardness and the reduced modulus values decreased for contact depths lower than 10᎐11 nm and 7᎐8 nm, respectively. The slight difference in the hardness and reduced modulus behavior is related to the different dependences that the two quantities show with the projected contact area Ž H A Ay1 while Er A Ay1r2 .. By superimposing these results onto the experimental curves shown in Fig. 1, the hardness and reduced modulus diminution for small values of the contact depth can be explained. Therefore, the data obtained for the lowest contact depth values were not taken into account to evaluate the hardness and elastic modulus of the ta-C thin-films. Secondly, with the aim of investigating the substrate influence on the hardness and elastic modulus values
Fig. 2. Hardness and reduced modulus obtained for the standard bulk fused quartz sample after the calibration procedure.
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obtained for the ta-C films ŽFig. 1., the shape of the indentation curves and the AFM residual indentation images were studied. Fig. 3a shows the load-penetration experimental curves obtained at four different maximum loads: 200; 700; 1000; and 2000 N for the same sample studied in Fig. 1. It can be seen that the indentations performed at maximum loads of 2000 and 1000 N showed large hysteresis effects due to the substrate influence that appears as a pop-in in the loading curve ŽFig. 3b.. The indentation curve corresponding to a 700-N maximum load showed slight hysteresis behavior that could be associated with the plastic deformation of the film itself or to the plastic deformation of the substrate induced through the thin-film while it maintains elastic behavior. For indentation curves obtained by applying loads below 700 N, the load᎐penetration curves showed no hysteresis effects and no residual depth, showing a virtual elastic behavior ŽFig. 3c.. The AFM images corresponding to the residual impressions of the indentations performed at 200, 700, 1000 and 2000 N maximum load on the same sample of Fig. 1 are shown in Fig. 4. In the case of the indentations performed at 2000 and 1000 N maximum load ŽFig. 4a,b., the AFM images show triangular-shaped marks on the sample surface of welldefined residual depth, as would be expected from the indentation curves. For the indentation at 700 N load, the AFM image revealed a slight mark on the sample surface. This impression is not triangular but circularshaped because the real diamond indenter has a blunt tip at these penetration depths. No residual mark could be detected in the AFM measurements for the 200 N indentation, corroborating the absence of residual depth indicated by the indentation curve of Fig. 3c. The correlation between the load-penetration curves shape and the hardness and elastic modulus values referred to in Fig. 1, indicates some interesting results about the contact depth range where substrate effects must be taken into account. Once the calibration effects have been eliminated, the points that form a constant hardness and reduced modulus values region correspond to indentation curves of virtually pure elastic behavior. The first point where hardness decreases Žat approx. 17 nm contact depth. corresponds to the indentation at 700 N load. For higher contact depths values, the reduction in hardness and elastic modulus values is due to the substrate effects. Hardness values decrease as a consequence of substrate effects at maximum indenter penetration depths of about the 20% of film thickness. This is consistent with the usually accepted rule that by indenting less than 10᎐20% of film thickness, the true film hardness values are obtained w9x. By combining the results for the area function calibration effects and the substrate effects, it seems that the most correct hardness and reduced modulus values
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Fig. 3. Load vs. penetration curves obtained for the 80-nm thick ta-C film at different maximum indentation loads: Ža. 200 N; 700 N; 1000 N; and 2000 N; Žb. Plastic effects due to the substrate in a 2000-N curve; and Žc. Virtual elastic behavior in a 200-N indentation curve.
for the ta-C thin-films are those belonging to the ‘constant zone’ Žlabeled as ‘zone 2’ in Fig. 1.. Therefore, the mechanical properties of the ta-C films have been evaluated by plotting the hardness and elastic modulus vs. contact depth curves for each sample and by averaging the values obtained in this measurement zone. 3.2. Hardness and Young’s modulus ¨ alues related to the deposition parameter and film properties Fig. 5 plots the hardness and Young’s modulus values Žassuming a Poisson’s coefficient s 0.2. as a function of the substrate bias for the ta-C samples. The hardness values are in the range between 43 and 47 GPa while the Young’s modulus lies in the range between 310 and 340 GPa. These values compare well with those found in the literature. However, we have found a great scattering in the hardness and Young’s modulus values reported. This scattering of values can be due to some important factors that should be considered. The first factor is the area function calibration that requires high accuracy for the low penetration depth range involved in ta-C thin-films. The second factor is the difference in hardness values measured in highly elastic materials when using indenters of Berkovich or cube corner geometries. As predicted by
the Hertz theory w10x and corroborated for Sneddon in the case of rigid conical indenters w8x, the hardness of elastic materials is dramatically increased when the angle of the conical indenter decreases. The third factor deals with the Young’s modulus calculation from the experimental reduced modulus obtained. This calculation needs to assume a Poisson’s coefficient that is usually taken as 0.25 w3,11x or in most of cases not specified w12᎐14x. Recently, a Poisson’s coefficient value for ta-C thin-films of 0.12, measured by surface Brillouin scattering has been reported by Ferrari et al. w15x. It should be noted that the use of higher Poisson’s coefficient values lead to higher Young’s modulus values. These three points may be the cause of the differences in the hardness and Youngs’s modulus values found in the literature for various ta-C thin-films. Thus, some authors reported hardness and modulus values in the range of 24᎐59 GPa and 200᎐400 GPa, respectively, for measurements performed with Berkovich indenters w3,13,16,17x. Our values obtained for the ta-C thin-films are consistent with these references. Other authors that used a cube corner to perform the measurements have obtained hardness and modulus values of 60᎐70 and 470 GPa w11x. Nevertheless, other references we have found, ignore these important factors and do not specify the shape of the indenter, the range of tip calibration and the Poisson’s coefficient value used w12,14x. It seems to be of crucial importance to specify these factors in order to compare the hardness and Young’s modulus results. Although only slight differences have been found in the mechanical properties of the films by changing the substrate bias voltage over a wide range, some other properties such as the residual stress of the films were found to be strongly dependent on this deposition parameter w4x. The monotonous hardness and elastic modulus behavior of the ta-C films could be related to the small differences found in the constitutive properties of the films. The sp 3 content measured for all the films was approximately of 88%, which is a very high values and did not change significantly when varying the substrate bias voltage w4x. Only for the films deposited at extreme substrate bias voltage values, i.e. y20 and y350 V did the sp 3 content decrease to values of 84᎐86%. This decrease corresponds well with the hardness and Young’s modulus reduction observed at the extreme substrate bias voltage values in Fig. 5. With regards to density, a clear correlation between the previously measured density values w4x and the hardness and Young’s modulus of the films seems to exist ŽFig. 6.. The denser samples, which also correspond to those of higher sp 3 content and substrate bias voltage between y40 and y250 V, present the highest hardness and Young’s modulus values.
E. Martınez ´ et al. r Diamond and Related Materials 10 (2001) 145᎐152
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Fig. 4. AFM images corresponding to the residual impressions for indentations performed on the 80-nm thick ta-C films at loads: Ža. 2000 N; Žb. 1000 N; Žc. 700 N; and Žd. 200 N.
These results seem to indicate that substrate bias voltage, the sole deposition parameter varied in this set of ta-C samples, has little influence over the constitutive and the mechanical properties of the studied films. 3.3. Nanowear measurements The wear behavior on a nanometric scale for the ta-C thin-films was also studied by multiple dry sliding of a diamond tip on the sample surface. Nanowear measurements were performed by applying a constant normal load to the diamond tip. The depths of the resulting wear craters were measured from the AFM images taken for an increasing number of wear cycles.
Fig. 7 shows the wear depth vs. the number of wear cycles curves obtained by applying different normal loads for an 80-nm thick sample deposited at y60 V substrate bias voltage. It can be seen that the wear depth increases linearly with the number of wear cycles Žup to 100 cycles. for measurements performed with 10 and 40 N. Nevertheless, due to the high hardness of the ta-C films, the residual depths of the wear craters produced were extremely shallow, sometimes below 1 nm, which is the system resolution. For the same test conditions and a 40 N applied load, wear depths of 27 nm for bare silicon have been reported w18x. The comparison with this reference value provides an idea of the extremely high wear resistance of the ta-C thin-
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Fig. 5. Hardness and Young’s modulus values measured for a set of ta-C films deposited with different substrate bias.
films. In order to minimize the error in the measurement of crater depths at 10 and 40 N, the maximum load allowed by the experimental system Ž380 N. was chosen to perform the wear measurements in all the samples. For this maximum load of 380 N, a linear relationship was also found between the wear depth and the number of wear cycles ŽFig. 7.. Moreover, a slight deviation from this linear behavior can be observed for more than 70 wear cycles. This change in the wear depth vs. wear cycle number curve can be attributed to different wear regimes: an initial mild wear regime; and a more severe wear regime at a higher number of wear cycles. A similar behavior was obtained for all the ta-C films tested. These two different wear behaviors can be observed in the AFM wear crater images ob-
Fig. 7. Wear depth as a function of the number of wear cycles for measurements performed at Ža. 380 N; Žb. 40 N; and Žc. 10 N of constant normal load on the 80-nm thick ta-C film.
tained for 10 and 80 wear cycles ŽFig. 8. applying a normal load of 380 N. The wear craters obtained at 10 wear cycles showed smooth erosion at the surface deep inside the crater ŽFig. 8a. while the AFM image corresponding to 80 wear cycles ŽFig. 8b. shows some material ploughed by the indenter. The two wear regimes could not be distinguished for the measurements performed applying lower load values. It has been reported that a critical load value exists at which wear changes from a low wear regime to a high wear regime w19x. From our results, it seems that our low wear rate regime is associated with a wear mode that produces smooth worn surfaces and the high wear rate is associated with a ploughing wear mode that produces irregular worn surfaces. This latter wear mode starts after the accumulation of enough defects on the smooth worn surface. 3.4. Nanowear measurements related to the deposition parameter and film properties
Fig. 6. Hardness and Young’s modulus values as a function of density for ta-C coatings deposited with different substrate bias.
By defining the wear rate as the slope of the linear part of the wear depth vs. wear cycle number curve, the wear rates at 380 N load were calculated for all the ta-C thin-films. The inverse of the obtained wear rates, which give an idea of the film wear resistance, are plotted against the substrate bias voltage in Fig. 9. From this figure, it can be noticed that the wear resistance of the coatings behaves in a similar way, will respect to the substrate bias voltage, as does the hardness. Thus, the relationship between nanowear and consituent film properties such as sp 3 content and density is analagous to that already studied in the case of hardness and Young’s modulus. That is, the densest
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Fig. 9. Wear resistance Žinverse of wear rate. calculated at 380 N of normal load as a function of the substrate bias for the ta-C films.
properties have been measured on tetrahedral amorphous carbon thin-films prepared by the filtered cathodic vacuum arc technique over a wide range of substrate bias voltage Žbetween y350 and y20 V.. Due to the low thickness of the films, the measurement of hardness and Young’s modulus by the nanoindentation technique require careful analysis of the data in order to take into account both the area function calibration and the substrate effects. Wear behavior of the ta-C thin-films at a nanometric scale appears to be closely related to the film hardness, which is usually not the determining factor in the macroscopic scale wear behavior. Fig. 8. AFM images of the residual wear craters produced applying 380 N of normal load after Ža. 10 wear cycles and Žb. 80 wear cycles.
coatings with 88% sp 3 content have high wear resistance values which remain almost constant for coatings deposited with substrate bias voltage values in the range of y40 to y250 V. Fig. 10 shows the relationship between hardness and wear and the nanometric scale, as has been previously reported by Bhushan w3x. This is not necessarily true for the wear measurements performed at a macroscopic scale, in which it is commonly accepted that low friction coefficient and good adhesion of the films to the substrate are the determining factors to achieve good wear resistance w20x.
4. Conclusions Excellent mechanical properties and nanowear
Fig. 10. Wear rate calculated at 380 N of normal load as a function of the hardness of the ta-C films.
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Acknowledgements This research has been supported in part by the SpanishrBritish Acciones Integrades Programme Žproject HB1998-0013. and by the Commission for Cultural, Educational and Scientific Exchange between the United States of America and Spain. E. Martınez ac´ knowledges the financial support of the DGR of the Generalitat de Catalunya and the collaboration and assistance of Prof. David Bogy and Dr R.Y. Lo from the Computer Mechanics Laboratory of the University of California in Berkeley ŽUS.. References w1x w2x w3x w4x
Y. Lifshitz, Diam. Relat. Mater. 8 Ž1999. 1659. A. Grill, Diam. Relat. Mater. 8 Ž1999. 428. B. Bhushan, Diam. Relat. Mater. 8 Ž1999. 1985. M.C. Polo, J.L. Andujar, A. Hart, J. Robertson, W.I. Milne, ´ Diam. Relat. Mater. 9 Ž2000. 663. w5x B. Bhushan, A.V. Kulkarni, W. Bonin, J.T. Wyrobek, Phil. Mag. A 74 Ž1996. 1117. w6x W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 Ž1992. 1564.
w7x Z.G. Jiang, C.J. Lu, D.B. Bogy, T. Miyamoto, J. Tribol. Trans. ASME 117 Ž1995. 328. w8x I.N. Sneddon, Int. J. Engng. Sci. 3 Ž1965. 47. w9x S. Bec, A. Tonck, J.M. Georges, E. Georges, J.L. Loubet, Phil. Mag. A 74 Ž1996. 1061. w10x H. Hertz, J. reine angewandte Matthematik 92 Ž1882. 156. w11x R.Y. Lo, D.B. Bogy, J. Mater. Res. 14 Ž1999. 2276. w12x S. Xu, B.K. Tay, H.S. Tan, L. Zhong, Y.Q. Tu, S.R.P. Silva, W.I. Milne, J. Appl. Phys. 79 Ž1996. 7234. w13x G.M. Pharr, D.L. Callahan, S.D. McAdams, T.Y. Tsui, S. Anders, A. Anders, J.W. Ager III, I.G. Brown, C.S. Bathia, S.R.P. Silva, J. Robertson, Appl. Phys. Lett. 68 Ž1996. 779. w14x T.A. Friedmann, J.P. Sullivan, J. Knapp, D.R. Tallant, D.M. Follstaedt, D.L. Medlin, P.B. Mirkarimi, App. Phys. Lett. 71 Ž1997. 3820. w15x A.C. Ferrari, J. Robertson, M.G. Beghi, C.E. Bottani, R. Ferulano, R. Pastorelli, App. Phys. Lett. 75 Ž1999. 1893. w16x S. Anders, A. Anders, I.G. Brown, B. Wei, K. Komvopoulos, J.W. Ager, K.M. Yu, III, Surf. Coat. Technol. 68᎐69 Ž1994. 388. w17x X. Li, B. Bhushan, Thin Solid Films 315 Ž1998. 214. w18x B. Bhushan, V.N. Koinkar, J. Appl. Phy. 75 Ž1994. 5741. w19x S. Umemura, Y. Andoh, S. Hirono, T. Miyamoto, R. Kaneko, Phil. Mag. A 74 Ž1996. 1143. w20x K. Holmberg, A. Matthews, in: D. Downson ŽEd.., Coatings Tribology, Elsevier, 1994.
Study of the mechanical properties of tetrahedral amorphous carbon films by nanoindentation and nanowear measurements E. Martınez ´ a , J.L. Andujar ´ a,U , M.C. Polo a , J. Esteve a , J. Robertsonb, W.I. Milne b a
` Uni¨ ersitat de Barcelona, Departament de Fısica A¨ . Diagonal 647, Barcelona E-08028, Spain ´ Aplicada i Optica, b Engineering Department, Uni¨ ersity of Cambridge, Trumptington Street, Cambridge CB2 1PZ, UK
Abstract Nanoindentation and nanowear measurements, along with the associated analysis suitable for the mechanical characterization of tetrahedral amorphous carbon Žta-C. films are discussed in this paper. Films of approximately 100-nm thick were deposited on silicon substrates at room temperature in a filtered cathodic vacuum arc evaporation system with an improved S-bend filter that yields films with high values of mass density Ž3.2 grcm3 . and sp 3 content Ž84᎐88%. when operating in a broad bias voltage range Žy20 V to y350 V.. Nanoindentation measurements were carried out on the films with a Berkovich diamond indenter applying loads in the 100 N᎐2 mN range, leading to maximum penetration depths between 10 and 60 nm. In this measurement range, the ta-C thin-films present a basically elastic behavior with high hardness Ž45 GPa. and high Young’s modulus Ž340 GPa. values. Due to the low thickness of the films and the shallow penetration depths involved in the measurement, the substrate influence must be taken into account and the area function of the indenter should be accurately calibrated for determination of both hardness and Young’s modulus. Moreover, nanowear measurements were performed on the films with a sharp diamond tip using multiple scans over an area of 3 m2 , producing a progressive wear crater with well-defined depth which shows an increasing linear dependence with the number of scans. The wear resistance at nanometric scale is found to be a function of the film hardness. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Hardness; Mechanical properties; Tetrahedral amorphous carbon; Wear
1. Introduction Over the last few years the preparation of tetrahedral amorphous carbon Žta-C. thin-films by several energetic vapour deposition methods w1,2x, from which films with sp 3 content higher than 80% can be grown, has become an increasingly important research area. One of the most attractive applications of ta-C films lies in their use as thin protective coatings on magnetic
U
Corresponding author. Tel.: q349-3-402-1146; fax: q349-3-4021138. E-mail address: [email protected] ŽJ.L. Andujar ´ ..
storage devices. However, in spite of the work done on the study and characterization of the ta-C film structural properties as a function of deposition conditions, few reports deal with the characterization of the mechanical properties w3x. The low thicknesses of the films Žtypically less than 100 nm. require the use of nanoindentation techniques with careful interpretation of the measurement results. The published studies often report the measured values of hardness and elastic modulus without mentioning the tip shape of the diamond indenter used and the details of the measurement, which makes the comparison between the results from different studies and their correlation with other film properties very difficult to make.
0925-9635r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 0 . 0 0 4 6 1 - 1
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E. Martınez ´ et al. r Diamond and Related Materials 10 (2001) 145᎐152
Recently, we reported the preparation of ta-C films in a filtered cathodic vacuum arc ŽFCVA. system with an improved S-bend filter that yields high values of mass density Ž3.2 grcm3 . and sp 3 content Ž84᎐88%. over a broad bias voltage range Žy20 V to y350 V. w4x. In this paper, we report upon the mechanical characterization of these dense ta-C films, where the hardness, Young’s modulus and nanowear behavior are discussed and related to the film structural properties. The nanoindentation load vs. penetration curves obtained for the thin film-substrate system are analyzed together with AFM images of the residual indentation impressions. Much attention has been paid to the influence of the substrate and the indenter area on the hardness and Young’s modulus values obtained from nanoindentation measurements. The wear behavior of the ta-C thin-films has also been characterized at a nanometric scale and correlations between hardness and nanowear have been established.
ness of the ta-C films Žapprox. 100 nm. the normal loads applied to the diamond indenter were kept in the 100 N᎐2 mN range. These loads led to maximum penetration depths of 10᎐60 nm, lower than the film thickness. AFM images of the sample surface were recorded before and after indentation process. At least 20 indentations under different maximum loads were performed at different locations for each sample to check the consistency of the results. Nanowear tests were conducted using a scanning probe microscope ŽSPM. w7x by dry sliding of a 300-nm radius diamond tip on the sample surface in multiple scans. During the diamond sliding, the tip scanning frequency was 1 Hz and the scan area was 3 = 3 m. The constant normal load applied to the indenter was varied from 10 to 380 N, which is a relatively high value for such a sharp indenter. AFM images of the resulting wear craters were obtained for an increasing number of wear cycles.
2. Experimental
3. Results and discussion
The ta-C films for this study were prepared at room temperature on silicon substrates in a FCVA system that incorporates an off-plane, double bend ŽS-bend. magnetic filter. Films in the thickness range 70᎐120 nm were grown using an arc current of 75 A at a deposition rate of 0.6 nmrs. The base pressure was below 10y5 Pa, which increased to approximately 10y4 Pa during deposition. The energy of incident ions was varied by applying a negative d.c. bias voltage to the substrates in the range from y20 to y350 V. The film mass density and sp 3 fraction were determined by X-ray reflectivity and electron energy loss spectroscopy, respectively w4x. The hardness and Young’s modulus of the ta-C thin-films were measured with a commercially available nanoindenter ŽHysitron Inc.. interfaced with an atomic force microscope software ŽNanoscope, Digital Instruments. w5x. This system allows us to obtain the load vs. penetration curves for a loading᎐unloading cycle and also to image the residual indentation impression. The system load and depth resolutions were 0.1 N and 0.2 nm, respectively. Nanoindentation measurements were carried out using a Berkovich diamond indenter with a tip radius of approximately 150 nm. The hardness and Young’s modulus values were obtained from the analysis of the unloading curve by applying the analysis method proposed by Oliver and Pharr w6x. In order to get an accurate area function, the tip area calibration was performed by indenting a standard fused quartz bulk sample in the range of 5᎐75 nm contact depth penetrations. The area function was determined assuming a constant reduced modulus of 69.64 GPa for the quartz reference sample and by fitting the resulting areas by a polynomial function. Due to the low thick-
3.1. Hardness and Young’s modulus measurements For each ta-C thin-film, multiple indentations were performed at different locations with increasing loads and penetration depths. This allows us to plot the hardness and reduced elastic modulus values as a function of the contact penetration depth, which means the depth at which the sample and the diamond indenter are in contact when the maximum load is applied. The reduced elastic modulus is the elastic parameter that can be directly calculated from the nanoindentation experimental data through the Sneddon’s equation w8x and it includes the indenter elastic effects and the sample Poisson’s coefficient. Fig. 1 shows one of these curves for an 80-nm thick sample deposited at y60 V substrate bias voltage. For all the samples, the curves showed the same typical behavior which can be split up into three distinct regions, starting from their values at high contact depths, hardness and reduced modulus increased with decreasing contact depths and applied loads Žzone 1.. They then reach a maximum value that remains constant for a limited contact depth range Žzone 2. and finally, they decrease at lower contact depths Žzone 3.. An accurate study of these three zones allows us to establish a procedure to determine the hardness and elastic modulus of the thin-films, which is explained in the following paragraph. Firstly, in order to identify the contact depth range influenced by an inaccurate area function calibration, we study the hardness and reduced modulus values as a function of the contact depth obtained for the standard fused quartz sample ŽFig. 2.. The values shown are those calculated using the corrected area function. The
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Fig. 1. Hardness and reduced modulus as a function of the contact depth measured in a 80-nm thick ta-C film.
calibration procedure used was the same as that described by Oliver and Pharr w6x. It should be noticed that even after the calibration, both the hardness and the reduced modulus values decreased for contact depths lower than 10᎐11 nm and 7᎐8 nm, respectively. The slight difference in the hardness and reduced modulus behavior is related to the different dependences that the two quantities show with the projected contact area Ž H A Ay1 while Er A Ay1r2 .. By superimposing these results onto the experimental curves shown in Fig. 1, the hardness and reduced modulus diminution for small values of the contact depth can be explained. Therefore, the data obtained for the lowest contact depth values were not taken into account to evaluate the hardness and elastic modulus of the ta-C thin-films. Secondly, with the aim of investigating the substrate influence on the hardness and elastic modulus values
Fig. 2. Hardness and reduced modulus obtained for the standard bulk fused quartz sample after the calibration procedure.
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obtained for the ta-C films ŽFig. 1., the shape of the indentation curves and the AFM residual indentation images were studied. Fig. 3a shows the load-penetration experimental curves obtained at four different maximum loads: 200; 700; 1000; and 2000 N for the same sample studied in Fig. 1. It can be seen that the indentations performed at maximum loads of 2000 and 1000 N showed large hysteresis effects due to the substrate influence that appears as a pop-in in the loading curve ŽFig. 3b.. The indentation curve corresponding to a 700-N maximum load showed slight hysteresis behavior that could be associated with the plastic deformation of the film itself or to the plastic deformation of the substrate induced through the thin-film while it maintains elastic behavior. For indentation curves obtained by applying loads below 700 N, the load᎐penetration curves showed no hysteresis effects and no residual depth, showing a virtual elastic behavior ŽFig. 3c.. The AFM images corresponding to the residual impressions of the indentations performed at 200, 700, 1000 and 2000 N maximum load on the same sample of Fig. 1 are shown in Fig. 4. In the case of the indentations performed at 2000 and 1000 N maximum load ŽFig. 4a,b., the AFM images show triangular-shaped marks on the sample surface of welldefined residual depth, as would be expected from the indentation curves. For the indentation at 700 N load, the AFM image revealed a slight mark on the sample surface. This impression is not triangular but circularshaped because the real diamond indenter has a blunt tip at these penetration depths. No residual mark could be detected in the AFM measurements for the 200 N indentation, corroborating the absence of residual depth indicated by the indentation curve of Fig. 3c. The correlation between the load-penetration curves shape and the hardness and elastic modulus values referred to in Fig. 1, indicates some interesting results about the contact depth range where substrate effects must be taken into account. Once the calibration effects have been eliminated, the points that form a constant hardness and reduced modulus values region correspond to indentation curves of virtually pure elastic behavior. The first point where hardness decreases Žat approx. 17 nm contact depth. corresponds to the indentation at 700 N load. For higher contact depths values, the reduction in hardness and elastic modulus values is due to the substrate effects. Hardness values decrease as a consequence of substrate effects at maximum indenter penetration depths of about the 20% of film thickness. This is consistent with the usually accepted rule that by indenting less than 10᎐20% of film thickness, the true film hardness values are obtained w9x. By combining the results for the area function calibration effects and the substrate effects, it seems that the most correct hardness and reduced modulus values
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Fig. 3. Load vs. penetration curves obtained for the 80-nm thick ta-C film at different maximum indentation loads: Ža. 200 N; 700 N; 1000 N; and 2000 N; Žb. Plastic effects due to the substrate in a 2000-N curve; and Žc. Virtual elastic behavior in a 200-N indentation curve.
for the ta-C thin-films are those belonging to the ‘constant zone’ Žlabeled as ‘zone 2’ in Fig. 1.. Therefore, the mechanical properties of the ta-C films have been evaluated by plotting the hardness and elastic modulus vs. contact depth curves for each sample and by averaging the values obtained in this measurement zone. 3.2. Hardness and Young’s modulus ¨ alues related to the deposition parameter and film properties Fig. 5 plots the hardness and Young’s modulus values Žassuming a Poisson’s coefficient s 0.2. as a function of the substrate bias for the ta-C samples. The hardness values are in the range between 43 and 47 GPa while the Young’s modulus lies in the range between 310 and 340 GPa. These values compare well with those found in the literature. However, we have found a great scattering in the hardness and Young’s modulus values reported. This scattering of values can be due to some important factors that should be considered. The first factor is the area function calibration that requires high accuracy for the low penetration depth range involved in ta-C thin-films. The second factor is the difference in hardness values measured in highly elastic materials when using indenters of Berkovich or cube corner geometries. As predicted by
the Hertz theory w10x and corroborated for Sneddon in the case of rigid conical indenters w8x, the hardness of elastic materials is dramatically increased when the angle of the conical indenter decreases. The third factor deals with the Young’s modulus calculation from the experimental reduced modulus obtained. This calculation needs to assume a Poisson’s coefficient that is usually taken as 0.25 w3,11x or in most of cases not specified w12᎐14x. Recently, a Poisson’s coefficient value for ta-C thin-films of 0.12, measured by surface Brillouin scattering has been reported by Ferrari et al. w15x. It should be noted that the use of higher Poisson’s coefficient values lead to higher Young’s modulus values. These three points may be the cause of the differences in the hardness and Youngs’s modulus values found in the literature for various ta-C thin-films. Thus, some authors reported hardness and modulus values in the range of 24᎐59 GPa and 200᎐400 GPa, respectively, for measurements performed with Berkovich indenters w3,13,16,17x. Our values obtained for the ta-C thin-films are consistent with these references. Other authors that used a cube corner to perform the measurements have obtained hardness and modulus values of 60᎐70 and 470 GPa w11x. Nevertheless, other references we have found, ignore these important factors and do not specify the shape of the indenter, the range of tip calibration and the Poisson’s coefficient value used w12,14x. It seems to be of crucial importance to specify these factors in order to compare the hardness and Young’s modulus results. Although only slight differences have been found in the mechanical properties of the films by changing the substrate bias voltage over a wide range, some other properties such as the residual stress of the films were found to be strongly dependent on this deposition parameter w4x. The monotonous hardness and elastic modulus behavior of the ta-C films could be related to the small differences found in the constitutive properties of the films. The sp 3 content measured for all the films was approximately of 88%, which is a very high values and did not change significantly when varying the substrate bias voltage w4x. Only for the films deposited at extreme substrate bias voltage values, i.e. y20 and y350 V did the sp 3 content decrease to values of 84᎐86%. This decrease corresponds well with the hardness and Young’s modulus reduction observed at the extreme substrate bias voltage values in Fig. 5. With regards to density, a clear correlation between the previously measured density values w4x and the hardness and Young’s modulus of the films seems to exist ŽFig. 6.. The denser samples, which also correspond to those of higher sp 3 content and substrate bias voltage between y40 and y250 V, present the highest hardness and Young’s modulus values.
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Fig. 4. AFM images corresponding to the residual impressions for indentations performed on the 80-nm thick ta-C films at loads: Ža. 2000 N; Žb. 1000 N; Žc. 700 N; and Žd. 200 N.
These results seem to indicate that substrate bias voltage, the sole deposition parameter varied in this set of ta-C samples, has little influence over the constitutive and the mechanical properties of the studied films. 3.3. Nanowear measurements The wear behavior on a nanometric scale for the ta-C thin-films was also studied by multiple dry sliding of a diamond tip on the sample surface. Nanowear measurements were performed by applying a constant normal load to the diamond tip. The depths of the resulting wear craters were measured from the AFM images taken for an increasing number of wear cycles.
Fig. 7 shows the wear depth vs. the number of wear cycles curves obtained by applying different normal loads for an 80-nm thick sample deposited at y60 V substrate bias voltage. It can be seen that the wear depth increases linearly with the number of wear cycles Žup to 100 cycles. for measurements performed with 10 and 40 N. Nevertheless, due to the high hardness of the ta-C films, the residual depths of the wear craters produced were extremely shallow, sometimes below 1 nm, which is the system resolution. For the same test conditions and a 40 N applied load, wear depths of 27 nm for bare silicon have been reported w18x. The comparison with this reference value provides an idea of the extremely high wear resistance of the ta-C thin-
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Fig. 5. Hardness and Young’s modulus values measured for a set of ta-C films deposited with different substrate bias.
films. In order to minimize the error in the measurement of crater depths at 10 and 40 N, the maximum load allowed by the experimental system Ž380 N. was chosen to perform the wear measurements in all the samples. For this maximum load of 380 N, a linear relationship was also found between the wear depth and the number of wear cycles ŽFig. 7.. Moreover, a slight deviation from this linear behavior can be observed for more than 70 wear cycles. This change in the wear depth vs. wear cycle number curve can be attributed to different wear regimes: an initial mild wear regime; and a more severe wear regime at a higher number of wear cycles. A similar behavior was obtained for all the ta-C films tested. These two different wear behaviors can be observed in the AFM wear crater images ob-
Fig. 7. Wear depth as a function of the number of wear cycles for measurements performed at Ža. 380 N; Žb. 40 N; and Žc. 10 N of constant normal load on the 80-nm thick ta-C film.
tained for 10 and 80 wear cycles ŽFig. 8. applying a normal load of 380 N. The wear craters obtained at 10 wear cycles showed smooth erosion at the surface deep inside the crater ŽFig. 8a. while the AFM image corresponding to 80 wear cycles ŽFig. 8b. shows some material ploughed by the indenter. The two wear regimes could not be distinguished for the measurements performed applying lower load values. It has been reported that a critical load value exists at which wear changes from a low wear regime to a high wear regime w19x. From our results, it seems that our low wear rate regime is associated with a wear mode that produces smooth worn surfaces and the high wear rate is associated with a ploughing wear mode that produces irregular worn surfaces. This latter wear mode starts after the accumulation of enough defects on the smooth worn surface. 3.4. Nanowear measurements related to the deposition parameter and film properties
Fig. 6. Hardness and Young’s modulus values as a function of density for ta-C coatings deposited with different substrate bias.
By defining the wear rate as the slope of the linear part of the wear depth vs. wear cycle number curve, the wear rates at 380 N load were calculated for all the ta-C thin-films. The inverse of the obtained wear rates, which give an idea of the film wear resistance, are plotted against the substrate bias voltage in Fig. 9. From this figure, it can be noticed that the wear resistance of the coatings behaves in a similar way, will respect to the substrate bias voltage, as does the hardness. Thus, the relationship between nanowear and consituent film properties such as sp 3 content and density is analagous to that already studied in the case of hardness and Young’s modulus. That is, the densest
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Fig. 9. Wear resistance Žinverse of wear rate. calculated at 380 N of normal load as a function of the substrate bias for the ta-C films.
properties have been measured on tetrahedral amorphous carbon thin-films prepared by the filtered cathodic vacuum arc technique over a wide range of substrate bias voltage Žbetween y350 and y20 V.. Due to the low thickness of the films, the measurement of hardness and Young’s modulus by the nanoindentation technique require careful analysis of the data in order to take into account both the area function calibration and the substrate effects. Wear behavior of the ta-C thin-films at a nanometric scale appears to be closely related to the film hardness, which is usually not the determining factor in the macroscopic scale wear behavior. Fig. 8. AFM images of the residual wear craters produced applying 380 N of normal load after Ža. 10 wear cycles and Žb. 80 wear cycles.
coatings with 88% sp 3 content have high wear resistance values which remain almost constant for coatings deposited with substrate bias voltage values in the range of y40 to y250 V. Fig. 10 shows the relationship between hardness and wear and the nanometric scale, as has been previously reported by Bhushan w3x. This is not necessarily true for the wear measurements performed at a macroscopic scale, in which it is commonly accepted that low friction coefficient and good adhesion of the films to the substrate are the determining factors to achieve good wear resistance w20x.
4. Conclusions Excellent mechanical properties and nanowear
Fig. 10. Wear rate calculated at 380 N of normal load as a function of the hardness of the ta-C films.
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Acknowledgements This research has been supported in part by the SpanishrBritish Acciones Integrades Programme Žproject HB1998-0013. and by the Commission for Cultural, Educational and Scientific Exchange between the United States of America and Spain. E. Martınez ac´ knowledges the financial support of the DGR of the Generalitat de Catalunya and the collaboration and assistance of Prof. David Bogy and Dr R.Y. Lo from the Computer Mechanics Laboratory of the University of California in Berkeley ŽUS.. References w1x w2x w3x w4x
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