Surface and Coatings Technology 122 (1999) 150â160 www.elsevier.nl/locate/surfcoat Experimental design and modelling in the investigation of process parameter eVects on the tribological and mechanical properties of r.f.-plasma-deposited a-C:H films H. Ronkainen *, J. Koskinen, S. Varjus, K. Holmberg VTT Manufacturing technology, P.O. Box 1702, 02044 VTT Espoo, Finland Received 26 October 1998; accepted in revised form 3 July 1999 Abstract Hydrogenated amorphous carbon (a-C:H ) films were deposited by the r.f. plasma technique in order to study the eVect of deposition parameters on the mechanical and tribological properties of the films. An experimental design method was used for planning the experiments, and statistical analysis and modelling to analyse the results. The high hardness of the film was found to have the highest correlation with the good wear resistance of the film. By using response surface modelling, some direct trends from the process parameters to tribological properties were found. The best wear resistance for the a-C:H films was found for low pressure (0.7â2.5 Pa) and intermediate bias voltage (â550 V ) values. By using the experimental design, the number of deposition runs could be reduced, and the statistical analysis and modelling provided useful and precise information showing also the significance of the trends observed. © 1999 Elsevier Science S.A. All rights reserved. Keywords: a-C:H; Coating optimization; Experimental design; Mechanical properties; Tribology 1. Introduction properties for both methane [15] and acetylene [16 ] source gases with a similar deposition system used in The first diamond-like carbon (DLC) films reported this study. A direct correlation of the deposition parame- in the 70s were deposited by ion-beam deposition tech- ters to tribological properties of the film has seldom niques [1â3]. R.f.-plasma-deposited hydrogenated been investigated. Enke et al. have been among the few amorphous carbon (a-C:H) films were first introduced authors who have described the friction behaviour of in the beginning of the 80s, Enke et al. [4] being among the a-C:H films by process parameters [17,18]. the first authors. Since then r.f.-plasma-deposited a-C:H Generally the eVect of process parameters has been films have been studied intensively by several authors studied by changing one separate parameter (factor) at [5]. The hydrocarbon discharge [6 ], dissociation of the a time whilst keeping other parameters constant. This source gas [7] and atomic arrangement [8] characterizing approach, however, does not necessarily lead to a real the growth process have been studied in order to explain optimum, and in some cases can even have diVerent the diVerent physical properties of a-C:H films. The implications with diVerent sets of parameters. It provides influence of diVerent deposition parameters on the no information about what happens when the factors mechanical properties of the films have been systemati- are varied simultaneously, i.e. it ignores the interactions cally explored. Typically, the deposition rate, hardness between factors and leads to isolated, unconnected and density of the films have been reviewed [9â12]. experiments. The method also requires an unnecessarily Additionally, the eVect of deposition parameters on high number of runs. Experimental design provides an internal intrinsic stresses has been investigated [13,14]. organized approach for coating optimization. It oVers For example, Zou et al. have studied the influence on a means to study systems influenced by more than one bias voltage and pressure in a wide range of film parameter and gives better estimation of the variability and noise of the system and thus increases the reliability* Corresponding author. Tel.: +358-9-456-4485; of the results. Experimental design is also a good wayfax: +358-9-460-627. E-mail address:
[email protected] (H. Ronkainen) to minimize the number of depositions and tests required 0257-8972/99/$ â see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S0257-8972 ( 99 ) 00380-1 151H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 [19]. Combined with a thorough statistical analysis and modelling, it connects experimental results and thus yields more useful and precise information of the pro- cess, and helps to determine the diVerent relationships between the process parameters and the properties in a more comprehensive manor. In this work, the experi- mental design, statistical analysis and modelling were used to study the influence of process parameters on the mechanical and tribological properties of the r.f.-plasma- deposited a-C:H films. 2. Experimental For the experimental design, the central composite design was used. Central composite design consists of a two-level factorial design with replicated centre points and symmetrically located star points [20]. The number of deposition runs was 13 with five centre points, as Fig. 2. Schematic diagram of the deposition apparatus used in the illustrated in Fig. 1. The central composite design was study. chosen, because it allows the use of three-dimensional response surface modelling of the results. The depos- itions were carried out in a random order to minimize with constant flow rate of 25 sccm of CH4 for the low pressures. For the high pressures the pumping speedthe systematic error. The a-C:H films were deposited with a capacitively was kept constant and the pressure was adjusted by changing the flow rate of the methane. The r.f. powercoupled r.f. plasma (13.56 MHz) method. A schematic diagram of the deposition apparatus is presented in was adjusted in order to obtain the desired self-bias voltage. The intention was to deposit about 0.5 mm thickFig. 2. The substrates were placed directly on the pow- ered, water-cooled cathode and the deposition temper- coatings and the deposition time was estimated accord- ingly. The deposition times varied in the range 44âature was measured with a thermometer from the back of the sample immediately after the deposition. The 135 min, which produced the final a-C:H film thicknesses in the range 0.4â0.7 mm, according to the depositioncooling power of the cathode was the same in diVerent deposition runs and therefore the deposition temper- parameters used in the deposition runs. The a-C:H films were deposited on silicon (Si) wafers with a hardness ofature varied according to the bias voltage used. Methane (CH4) was used as the source gas and the deposition 1200 HV. The thickness of the films was measured with aparameters were varied in the diVerent deposition runs according to the experimental design (Fig. 1). The pres- surface profilometer and the density was assessed according to the weight measurements of the coatedsure was varied in the range 0.7â10.7 Pa and the bias voltage in the range from â100 to â1000 V. The substrates. The hardness was determined by using Knoop hardness measurement with a load of 5 gf. Thepressure was varied by adjusting the pumping speed intrinsic stresses were evaluated with a bending beam method by determining the curvature change of the Si wafer after deposition. The hydrogen content was deter- mined with forward recoil spectroscopy (FRES). The tribological performance of the films was assessed with the pin-on-disc tests using 10 mm diameter steel balls (100Cr6) and alumina (a-Al2O3) balls sliding against the coated Si samples. The sliding velocity was 0.6 m sâ1, 10 N normal force was used for the steel balls and 5 N formal force for the alumina balls, which created the initial Herzian contact pressures of 0.8 and 0.7 GPa, respectively. The friction coeYcient was recorded during the tests. The wear of the balls was assessed by microscopic detection and the wear of the coated discs was measured using surface profilometryFig. 1. The central composite design showing the bias voltage and deposition pressure combinations applied in the study. after the test. The tribological tests were performed 152 H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 twice and the values represented are the mean values of film, higher bias voltage producing lower stresses. The deposition temperature, on the other hand, correlatedthe tests. The test results were analysed by means of the with growth rate, film density and the intrinsic stresses of the film, higher temperature producing lower filmcomputer programs, StatisticaA and ModdeA. density and intrinsic stresses, and higher growth rate. Further, the density correlated with hardness and intrin- sic stresses, higher density being related to higher hard-3. Results and discussion ness and higher intrinsic stresses. The hardness correlated with intrinsic stresses showing high hardnessThe deposition parameters, the film properties and the tribological test results are represented in Table 1. for higher stresses. When combining these correlations together, it can be concluded according to correlationWhen the deposition with the highest bias voltage (â1000 V ) was carried out, no coating was grown on analysis that the increase in bias voltage led to higher deposition temperature, lower intrinsic stress, lowerthe substrate. This particular deposition run was removed from the data before the analysis and thus this density and lower measured hardness of the film. This is in line with the results of Zou et al., since theyinformation was lost in the analysis. The analyses were carried out starting from a simple experienced a decrease in hardness with an increase in bias voltage [14]. They also reported a decrease incorrelation analysis, continuing to regression analysis and further to more complicated response surface density, intrinsic stresses and hydrogen content as the bias was increased, which is in agreement with the resultsmodels. This approach was chosen in order to determine the capabilities of diVerent methods to give relevant of this study. Zou et al. also reviewed the correlation between hardness and intrinsic stresses.information on the eVect of process parameters on the basic properties as well as the tribological properties of The deposition pressure had a correlation with the growth rate of the film, higher pressure producing highera-C:H films. growth rate. This suggests that the deposition pressure is a controlling factor for the eYciency of deposition3.1. Correlation analysis process. When the correlations of the above-mentioned basicIn the beginning, a correlation analysis was carried out for the data. In addition, the interactions between film properties were compared with the tribological properties of the films, the only general trend found wasdiVerent variables were studied, but no significant inter- action could be detected with correlation analysis. the correlation between coating wear and film hardness against both steel and alumina. The higher film hardnessIn Table 2, the correlation values of the test data are represented. The correlation was considered significant, was related to lower wear, which is in accordance with the classical Archarts wear law and the general trendif the value exceeds 0.6. This value was chosen because it gave realistic correlations and had relevance with the reviewed in the published data. For the steel pin wear, correlation with deposition temperature of the film wassignificance values (2-tailed) shown in the lower part of Table 2. The significance in this case should be less than observed, low temperature being related to lower wear of the pin. For the alumina pins, no relevant correlations0.05 in order to reach 95% or better reliability for the results. were found. When considering the friction coeYcient values, no correlation with the basic properties of theAccording to the correlation analysis, the process parameters had no direct correlation with the tribologi- films was observed. This behaviour is quite expected, since friction is generally considered as a process param-cal properties of the films. The process parameters typically correlated with the basic properties of the films, eter, not a material parameter. When the diVerent tribological properties were com-namely hardness, intrinsic stresses, density and hydrogen content of the film. pared, the low coating wear against steel correlated with low coating wear against alumina, which was inThe bias voltage had strong correlation with depos- ition temperature, higher bias increasing the temper- agreement with the earlier mentioned correlation of the coating wear and film hardness in both cases. The lowerature. The deposition temperature varied between diVerent deposition runs, because the cooling eVect of coating wear against steel was also related to lower steel pin wear. The pin wear correlated with the frictionthe water-cooled cathode was not suYcient to keep the temperature constant, when higher bias voltage values coeYcient, which can be related to the tribofilm forma- tion in the case of a steel pin sliding against a-C:H films,were used. The deposition temperature followed the bias voltage used and thus at the same time influenced the as reported earlier [21,22]. The correlation diagrams in Fig. 3 show the normal-film properties. The direct eVect of bias voltage on the film properties was thus diYcult to diVerentiate, because ised values of the basic properties â density, hardness, stress and hydrogen content plotted against each other.the bias voltage and temperature eVects were combined. The bias voltage correlated with intrinsic stresses of the The figure clearly shows the scatter of these results. It 153H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 T ab le 1 T he de po si ti on pa ra m et er s, fil m pr op er ti es an d th e tr ib ol og ic al te st re su lt s of th e de po si ti on ru ns D ep os it io n pa ra m et er s B as ic pr op er ti es of fil m s T ri bo lo gi ca l pr op er ti es of fil m s P re ss ur P re ss ur e B ia s D ep os it io n G ro w th T hi ck ne ss D en si ty H ar dn es s In tr in si c H yd ro ge n C oa ti ng w ea r 10 0C r6 F ri ct io n C oa ti ng w ea r A l 2 O 3 pi n C oe Y ci en t (P a) (m T or r) (n eg . te m pe ra tu re ra te (m m ) (g cm â3) (k g m m â2) st re ss co nt en t ag ai ns t 10 0C r6 pi n w ea r co eY ci en t ag ai ns t A l 2 O 3 w ea r (m m 3) of fr ic ti on V ) (° C ) (n m m in â1) (M P a) (% ) (m m 3) (m m 3) ag ai ns t (m m 3) ag ai ns t 10 0C r6 A l 2 O 3 1. 7 13 24 1 25 5. 20 0. 52 1. 87 18 90 21 30 24 1. 00 E + 06 8. 24 E + 03 0. 27 3 8. 15 E + 05 1. 07 E + 03 0. 15 2 1. 7 13 80 0 11 7 10 .0 0 0. 70 1. 80 18 50 12 30 23 7. 95 E + 05 1. 98 E + 04 0. 26 1 1. 08 E + 06 9. 19 E + 01 0. 06 6 9. 2 69 23 2 42 8. 73 0. 48 1. 73 16 30 16 70 29 1. 03 E + 06 2. 06 E + 03 0. 20 1 1. 02 E + 06 1. 49 E + 03 0. 17 2 9. 2 69 80 0 18 8 10 .3 6 0. 57 1. 29 10 00 33 0 27 2. 04 E + 06 1. 17 E + 05 0. 36 5 1. 39 E + 06 6. 68 E + 02 0. 15 4 5. 5 41 55 0 70 7. 80 0. 39 1. 42 11 90 77 0 29 1. 19 E + 06 5. 87 E + 03 0. 20 5 1. 19 E + 06 1. 21 E + 03 0. 15 6 5. 5 41 55 0 82 7. 06 0. 35 1. 53 14 00 91 0 24 9. 46 E + 05 8. 03 E + 03 0. 15 4 6. 54 E + 05 1. 56 E + 03 0. 07 2 5. 5 41 55 0 89 8. 00 0. 40 1. 51 13 30 77 0 28 1. 05 E + 06 7. 77 E + 03 0. 20 0 1. 05 E + 06 4. 40 E + 02 0. 17 0 5. 5 41 55 0 82 8. 60 0. 43 1. 53 16 30 94 0 30 1. 32 E + 06 7. 48 E + 03 0. 23 0 9. 42 E + 05 1. 68 E + 02 0. 23 1 5. 5 41 55 0 82 7. 30 0. 37 1. 48 12 80 90 0 22 1. 39 E + 06 5. 80 E + 03 0. 13 2 1. 44 E + 06 1. 07 E + 03 0. 11 2 5. 5 41 10 1 17 3. 85 0. 52 1. 72 12 80 13 00 35 2. 04 E + 06 9. 25 E + 03 0. 26 6 1. 17 E + 06 8. 20 E + 02 0. 15 4 5. 5 41 10 00 23 5 0. 00 0. 00 0. 00 0 0 0 0. 00 E + 01 0. 00 E + 01 0. 00 0 0. 00 E + 01 0. 00 E + 01 0. 00 0 0. 7 5 55 0 52 5. 71 0. 40 1. 78 23 70 16 30 26 8. 93 E + 05 5. 98 E + 03 0. 33 0 8. 56 E + 05 4. 60 E + 02 0. 12 2 10 .6 80 55 0 11 2 14 .7 7 0. 65 1. 62 19 70 12 60 27 1. 17 E + 06 6. 42 E + 03 0. 22 2 8. 33 E + 05 1. 82 E + 03 0. 21 0 154 H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 T ab le 2 T he co rr el at io n an d si gn ifi ca nc e va lu es of th e da ta . H _c on t = hy dr og en co nt en t, C oa t_ st = fil m w ea r ag ai ns t st ee l, P in _s t = w ea r of th e st ee l pi n, C of _s t = fr ic ti on co eY ci en t fo r st ee l ag ai ns t a- C :H , C oa t_ al u = fil m w ea r ag ai ns t al um in a, P in _a lu = w ea r of th e al um in a pi n, C of _a lu = fr ic ti on co eY ci en t fo r al um in a ag ai ns t a- C :H P re ss ur e B ia s T em pe ra tu re G ro w th T hi ck ne ss D en si ty H ar dn es s St re ss H _c on t C oa t_ St P in -S t C of _S t C oa t_ A lu P in _A lu C of _A lu ra te P ea rs on P re ss ur e 1. 00 0 0. 00 2 0. 39 9 0. 62 9 0. 16 4 â 0. 53 4 â 0. 43 6 â 0. 40 7 0. 26 1 0. 43 2 0. 31 1 â 0. 17 7 0. 21 5 0. 55 6 0. 50 9 co rr el at io n B ia s 0. 00 2 1. 00 0 0. 86 7 0. 55 4 0. 18 2 â 0. 49 5 â 0. 06 8 â 0. 63 1 â 0. 51 9 â 0. 13 6 0. 49 3 0. 16 0. 20 4 â 0. 35 3 â 0. 26 9 T em pe ra tu re 0. 39 9 0. 86 7 1. 00 0 0. 69 5 0. 35 5 â 0. 64 5 â 0. 30 8 â 0. 72 3 â 0. 33 0. 22 4 0. 76 6 0. 25 7 0. 34 3 â 0. 16 5 â 0. 04 5 G ro w th ra te 0. 62 9 0. 55 4 0. 69 5 1. 00 0 0. 53 8 â 0. 3 0. 07 6 â 0. 31 4 â 0. 21 3 â 0. 09 8 0. 25 6 â 0. 02 8 â 0. 00 1 0. 23 7 0. 3 T hi ck ne ss 0. 16 4 0. 18 2 0. 35 5 0. 53 8 1. 00 0 0. 32 0. 24 3 0. 16 9 0. 01 5 0. 09 7 0. 31 9 0. 45 4 0. 04 7 â 0. 09 0. 04 5 D en si ty â 0. 53 4 â 0. 49 5 â 0. 64 5 â 0. 3 0. 32 1. 00 0 0. 75 8 0. 92 6 â 0. 02 1 â 0. 47 2 â 0. 52 9 0. 14 â 0. 49 7 â 0. 06 3 â 0. 17 3 H ar dn es s â 0. 43 6 â 0. 06 8 â 0. 30 8 0. 07 6 0. 24 3 0. 75 8 1. 00 0 0. 73 3 â 0. 23 1 â 0. 63 5 â 0. 43 8 0. 23 2 â 0. 63 1 â 0. 07 â 0. 00 4 St re ss â 0. 40 7 â 0. 63 1 â 0. 72 3 â 0. 31 4 0. 16 9 0. 92 6 0. 73 3 1. 00 0 â 0. 04 1 â 0. 44 3 â 0. 53 2 0. 09 7 â 0. 51 3 0. 16 4 â 0. 00 3 H _C on t 0. 26 1 â 0. 51 9 â 0. 33 â 0. 21 3 0. 01 5 â 0. 02 1 â 0. 23 1 â 0. 04 1 1. 00 0 0. 54 5 â 0. 05 9 0. 20 2 0. 09 3 â 0. 08 2 0. 56 8 C oa t_ St 0. 43 2 â 0. 13 6 0. 22 4 â 0. 09 8 0. 09 7 â 0. 47 2 â 0. 63 5 â 0. 44 3 0. 54 5 1. 00 0 0. 59 1 0. 32 7 0. 61 6 â 0. 04 8 0. 28 8 P in _S t 0. 31 1 0. 49 3 0. 76 6 0. 25 6 0. 31 9 â 0. 52 9 â 0. 43 8 â 0. 53 2 â 0. 05 9 0. 59 1 1. 00 0 0. 62 5 0. 47 2 â 0. 20 6 â 0. 02 6 C of _S t â 0. 17 7 0. 16 0. 25 7 â 0. 02 8 0. 45 4 0. 14 0. 23 2 0. 09 7 0. 20 2 0. 32 7 0. 62 5 1. 00 0 0. 07 9 â 0. 44 0. 09 2 C oa t_ A lu 0. 21 5 0. 20 4 0. 34 3 â 0. 00 1 0. 04 7 â 0. 49 7 â 0. 63 1 â 0. 51 3 0. 09 3 0. 61 6 0. 47 2 0. 07 9 1. 00 0 â 0. 23 6 â 0. 02 5 P in _A lu 0. 55 6 â 0. 35 3 â 0. 16 5 0. 23 7 â 0. 09 â 0. 06 3 â 0. 07 0. 16 4 â 0. 08 2 â 0. 04 8 â 0. 20 6 â 0. 44 â 0. 23 6 1. 00 0 0. 07 7 Si g. P re ss ur e 1. 00 0 0. 99 5 0. 19 8 0. 02 8 0. 61 1 0. 07 4 0. 15 6 0. 18 9 0. 41 2 0. 16 1 0. 32 6 0. 58 3 0. 50 2 0. 06 0. 09 1 (2 -t ai le d ) B ia s 0. 99 5 1. 00 0 0. 00 0 0. 06 2 0. 57 1 0. 10 2 0. 83 4 0. 02 8 0. 08 4 0. 67 4 0. 10 3 0. 62 0. 52 6 0. 26 0. 39 7 T em pe ra tu re 0. 19 8 0. 00 0 1. 00 0 0. 01 2 0. 25 7 0. 02 4 0. 32 9 0. 00 8 0. 29 5 0. 48 3 0. 00 4 0. 41 9 0. 27 5 0. 60 8 0. 88 9 G ro w th ra te 0. 02 8 0. 06 2 0. 01 2 1. 00 0 0. 07 1 0. 34 3 0. 81 4 0. 32 1 0. 50 7 0. 76 2 0. 42 2 0. 93 2 0. 99 7 0. 45 9 0. 34 4 T hi ck ne ss 0. 61 1 0. 57 1 0. 25 7 0. 07 1 1. 00 0 0. 31 1 0. 44 7 0. 59 9 0. 96 3 0. 76 4 0. 31 2 0. 13 8 0. 88 5 0. 78 1 0. 89 D en si ty 0. 07 4 0. 10 2 0. 02 4 0. 34 3 0. 31 1 1. 00 0 0. 00 4 0. 00 0 0. 94 7 0. 12 1 0. 07 7 0. 66 4 0. 10 1 0. 84 6 0. 59 1 H ar dn es s 0. 15 6 0. 83 4 0. 32 9 0. 81 4 0. 44 7 0. 00 4 1. 00 0 0. 00 7 0. 47 1 0. 02 7 0. 15 4 0. 46 8 0. 02 8 0. 82 8 0. 99 St re ss 0. 18 9 0. 02 8 0. 00 8 0. 32 1 0. 59 9 0. 00 0 0. 00 7 1. 00 0 0. 90 0 0. 14 9 0. 07 5 0. 76 4 0. 08 8 0. 61 1 0. 99 2 H _C on t 0. 41 2 0. 08 4 0. 29 5 0. 50 7 0. 96 3 0. 94 7 0. 47 1 0. 90 0 1. 00 0 0. 06 7 0. 85 6 0. 53 0. 77 4 0. 79 9 0. 05 4 C oa t_ St 0. 16 1 0. 67 4 0. 48 3 0. 76 2 0. 76 4 0. 12 1 0. 02 7 0. 14 9 0. 06 7 1. 00 0 0. 04 3 0. 29 9 0. 03 3 0. 88 2 0. 36 4 P in _S t 0. 32 6 0. 10 3 0. 00 4 0. 42 2 0. 31 2 0. 07 7 0. 15 4 0. 07 5 0. 85 6 0. 04 3 1. 00 0 0. 03 0. 12 1 0. 52 1 0. 93 6 C of _S t 0. 58 3 0. 62 0. 41 9 0. 93 2 0. 13 8 0. 66 4 0. 46 8 0. 76 4 0. 53 0. 29 9 0. 03 1. 00 0 0. 80 7 0. 15 3 0. 77 5 C oa t_ A lu 0. 50 2 0. 52 6 0. 27 5 0. 99 7 0. 88 5 0. 10 1 0. 02 8 0. 08 8 0. 77 4 0. 03 3 0. 12 1 0. 80 7 1. 00 0 0. 46 0. 94 0 P in _A lu 0. 06 0 0. 26 0 0. 60 8 0. 45 9 0. 78 1 0. 84 6 0. 82 8 0. 61 1 0. 79 9 0. 88 2 0. 52 1 0. 15 3 0. 46 1. 00 0 0. 81 3 155H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 Fig. 3. The correlation diagrams showing normalised values for the density, hardness, stress and hydrogen content of the a-C:H films. The histograms show the frequency distribution of the results. also shows the linear correlations for density, hardness exponential and power models were applied to describe the tribological properties of the films. When the depos-and intrinsic stresses. As can be observed, the hardness and intrinsic stresses of the film are increased when the ition parameters were directly used as predictors, and the tribological properties as dependent variables, thefilm density is increased. In the same way the hardness is increased when stresses are increased. The hydrogen coeYcients of determination were low, which is the same phenomenon observed in the correlation analysis.content, however, had no correlation with the other properties mentioned. These are similar trends as Considering the eVect of basic film properties on the tribological behaviour, the increase in hardness was theobserved also in Table 2 and described above. According to the correlation analyses, the bias voltage only factor which clearly decreased the wear of the a-C:H film against both counterpart materials. The bestis the dominant parameter for determining the basic properties of the a-C:H films, whilst the pressure is more model was created when the film wear against steel was the dependent variable and the natural logarithm of therelated to the growth rate and thus to the eYciency of the deposition process. No direct correlation between film hardness and the hydrogen content were used as the predictors. In this case the coeYcient of determina-the process parameters, bias voltage and pressure, and the tribological properties was observed according to the tion was 0.62, which means that the model explains 62% of the variation of the dependent variable (coatingcorrelation analysis. The most probable reason for the lack of direct correlations is that the correlation wear). For the wear of the steel pin, the predictors were the natural logarithm of the film hardness and the filmanalysis is sensitive mainly to a linear relationship of parameters and thus cannot explain the tribological thickness, the coeYcient of determination being 0.47. When the counterpart material was alumina, the bestperformance with process parameters. The measured hardness of the film was found to be the variable mostly predictor for the coating wear was the natural logarithm of the film hardness. The coeYcient of determinationrelated to wear resistance, increased hardness being connected to lower wear of the film and to some extent was in this case 0.44. When the alumina ball was sliding against a-C:H film, the model for the friction coeYcientalso to the lower wear of the counterpart. The high hardness was combined with high density and intrinsic was also found when hydrogen content was used as a predictor. The coeYcient of determination for the fric-stresses of the film, which were controlled by the depos- ition temperature and bias voltage. tion coeYcient was 0.57 with the quadratic model. Both the F-test and t-test results showed the applicability of these models to be fairly good, as shown in Table 3. The3.2. The regression analysis t-test absolute values should be 2 or greater in order to show the significance of the predictor.As a second step, the regression analysis was used to fit the models to the data. The linear, logarithmic, The regression analysis gave similar results to the 156 H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 Table 3 The model summary of the regression analysis results. R=correlation of the model, R square=coeYcient of determination Dependent variable Predictors R R square t-test values Significance of of the predictors the predictors Film wear against steel ln(hardness) 0.786 0.619 â2.756 0.022 hydrogen content 1.964 0.81 Wear of steel pin ln(hardness) 0.698 0.475 â2.531 0.032 thickness 1.889 0.091 Film wear against alumina ln(hardness) 0.667 0.444 â2.828 0.018 Friction coeYcient against alumina hydrogen content 0.756 0.572 2.496 0.034 correlation analyses, since the high hardness correlated the steel pin wear is given in Fig. 5 with the coeYcient of determination 0.77. In the correlation and regressionwith the low film wear against both the steel and alumina pins, as well as with the low steel pin wear. analyses, no direct correlation between the tribological properties and deposition parameters was found. With modelling, direct relationships were detected, as can be3.3. The response surface models observed from the coating wear and counterpart wear plots. The lower values of wear appeared with lowIn order to verify the results further, the Statistica and Modde programs were used in order to create the pressure, in the range 0.7â2.5 Pa, and intermediate bias voltage, around â550 V. This showed the possibilitiesresponse surface models. The computer programs pro- vided the models, the estimates of the models as well as of the three-dimensional modelling approach, since it could provide relationships and trends that could notthe three-dimensional response surface plots. The depen- dence of tribological properties on the deposition param- be detected with an ordinary two-dimensional pro- cedure. For the friction coeYcient the response surfaceeters, pressure and bias voltage, was studied first. For the wear of the a-C:H film against the steel pin, the showed a minimum value in about the middle of the plot, with pressure around 5.5 Pa and a bias voltage ofmodel and the response surface plot are represented in Fig. 4. The coeYcient of determination was in this case about â550 V (Fig. 6). In this case the coeYcient of determination was 0.73. All these values can be consid-0.60 after statistically insignificant variables were removed from the model. The response surface plot for ered rather reliable, since they explain from 60 to 77% Fig. 4. The response surface plot and the model for the coating wear (COAT_ST ) against steel ball. The bias voltage (V ) and deposition pressure (Pa) were used as variables. 157H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 Fig. 5. The response surface plot and the model for the steel pin wear (PIN_ST) against a-C:H film. The bias voltage (V ) and deposition Fig. 6. The response surface plot and the model for the friction coeY- pressure (Pa) were used as variables. cient (COF_ST) when the steel pin was sliding against a-C:H film. The bias voltage (V ) and deposition pressure (Pa) were used as variables. of the scatter of the dependent variable and the signifi- cance of the dependent variables was confirmed with nation of high pressureâlow bias, however, showed a diVerent trend. The response surfaces plots and modelsthe t-test. However, for the alumina ball sliding against a-C:H films no models, with a suYciently high coeYcient for the density and the intrinsic stresses are given in Figs. 9 and 10. For these models the coeYcient ofof determination, could be formed. As a next step, the response of the basic mechanical determination was as high as 0.90 and 0.92, respectively. The low pressure can be related to high density andproperties to the tribological performance was studied. When the film hardness and hydrogen content were the high stresses, which is in agreement with the above- mentioned values for low coating wear.predicting values, the minimum wear was observed when the hardness was high and the hydrogen content low When considering the models for the basic properties, hardness, density and intrinsic stresses, it is necessary to(Fig. 7). The coeYcient of determination was in this case 0.68, which can also be considered reliable. study the diVerent models and response surface plots simultaneously and to compare critically the informationFinally the deposition parameters, pressure and bias, were used to explain the basic properties of the a-C:H obtained. For both hardness and density, the response surface plots give high values for the low pressure region.films. Since in the correlation analyses the hardness was found to correlate with the coating wear, as well as the However, there is also an indication of high hardness and density when high pressure and low bias are used.density, and intrinsic stresses were found to correlate with the hardness, models were created for these basic There is no confirmation of this trend in other models, and, therefore, this particular combination cannot bemechanical properties. The model and response surface plot for the hardness can be seen in Fig. 8, which shows considered significant. The other way to verify the results is on the physical basis, by considering the physicalhigh hardness for low pressure with medium or high bias voltage and also for high pressure with low bias. phenomena related to diVerent deposition conditions. In several publications it has been reported that the ionThe model had a high coeYcient of determination, namely 0.91. In this model, the deposition pressure also energy of the growing species (CH+4 or CH+3 ), when methane is used, has an optimum value of about 100âhad an eVect on the hardness, even though in the correlation analysis the pressure had no significant rele- 200 eV [23]. If the ion energy is lower or higher, a film with lower hardness and density is grown [24]. For thevance. The first mentioned low pressureâmedium bias combination was about the same as detected earlier to first approximation the bias voltage could be directly related to the ion energy. The deposition gas pressure,provide minimum wear of the coating. The latter combi- 158 H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 Fig. 7. The response surface plot and the model for the coating wear (COAT_ST ) against the steel ball. The film hardness and hydrogen content (H_CONT) were used as variables. Fig. 9. The response surface plot and the model for the film density.Fig. 8. The response surface plot and the model for the film hardness. The bias voltage (V ) and deposition pressure (Pa) were used asThe bias voltage (V ) and deposition pressure (Pa) were used as variables.variables. 159H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 process. In this study, diVerent analyses gave generally similar trends. The correlation and regression analyses showed correlations between diVerent variables and indicated trends in the data. It is a simple and fast way to detect typical trends. Response surface modelling can be used further for more precise and comprehensive information. However, the models and analyses should be treated critically and it is necessary to test the significance and reliability of the analyses. It is also important to understand both the deposition process and the basics of the statistical analysis and modelling in order to gain the full benefit of the experimental design and modelling. 4. Conclusions Experimental design could be used to minimize the number of depositions and tests needed for studying the process parameter eVects on the coating properties. The statistical analysis and modelling yielded useful informa- tion and showed the significance of the trends observed. Even the simple correlation and regression analysis provided information on the trends and correlations.Fig. 10. The response surface plot and the model for the intrinsic stresses of the film. The bias voltage (V ) and deposition pressure (Pa) However, more precise and relevant information could were used as variables. be acquired by using more complicated models, such as response surface modelling. Therefore, experimental design, statistical analysis and modelling are recom- however, has a more complicated eVect on the ion mean mended to be used in coating optimization work. free path, ion energy, ion concentration and ionization The increased film hardness was found to correlate (ion/neutral ratio etc.). Therefore, at low pressure and with the decreased wear of the a-C:H film and to some low bias voltage (about 200 V ), the hardest films are extent also with the decreased wear of the counterpart. expected to grow. On the other hand, at high pressure With the aid of the response surface models, trends the films are expected to be more polymeric, softer films. from the process parameters to tribological properties The high measured hardness values of the films deposited were found. The best wear resistance for the a-C:H films at high pressure in this study could be an artefact of the was found with low pressure (0.7â2.5 Pa) and intermedi- elastic nature of the polymeric films, which gives high ate bias voltage (â550 V ) values. values of hardness due to the elastic recovery of the film. When combining all the information from the response surface models, it can be concluded that the most favourable deposition conditions for wear-resistant Acknowledgements a-C:H films would be low pressure, 0.7â2.5 Pa, and intermediate bias voltage, around â550 V. If the friction The authors wish to express their gratitude to Raimo Haakana for carrying out the statistical analysis of thecoeYcient was considered independently, higher pres- sure, around 5.5 Pa, with intermediate bias voltage could data and being a great help in the interpretation of the analysis results. The financial support for the work wasbe used for the low friction behaviour according to these models. received from the Technology Development Centre of Finland (TEKES).Zou et al. have investigated the eVects of deposition parameters with the same type of deposition equipment. Similar trends to those they found could also be seen in the results of this study. However, it could be observed References that, when experimental design was used and two param- eters were changed simultaneously, more information [1] S. Aisenberg, R. Chabot, J. Appl. Phys. 42 (1971) 2953â2958. could be gained from a lower number of experiments. [2] S. Aisenberg, R.W. Chabot, J. Vac. Sci. Technol. 10 (1973) 104. Therefore, experimental design and statistical analysis [3] E.G. Spencer, P.H. Schmidt, D.C. Joy, F.J. Sansalone, Appl. Phys. Lett. 29 (1976) 118.can be recommended for optimization of the coating 160 H. Ronkainen et al. / Surface and Coatings Technology 122 (1999) 150â160 [4] K. Enke, H. Dimigen, H. 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