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Tribology International Vol. 29. No. 4, pp. 345-356, 1996 Copyright @ 1996 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 0301-679X/96/$15.00 +O.OLl

Optimum film thickness of thin metallic coatings on silicon substrates for low load stiding applications

Dong-Seob Jang*+ and Dae Eun Kim*

The frictional behaviour of thin metallic films on silicon substrates sliding against 52100 steel balls is presented. The motivation of this work is to identify an optimum film thickness that will result in low friction under relatively low loads for various metallic films. Dry sliding friction experiments on silicon substrates with soft metallic coatings (silver, copper, tin and zinc) of various thickness (I-2000 nm) were conducted using a reciprocating pin-on-flat type apparatus under a controlled environment. A thermal vapour deposition technique was used to produce pure and smooth coatings. The morphology of the films was examined using an atomic force microscope, a non-contact optical profilometer and a scanning electron microscope. Following the sliding tests, the sliding tracks were examined by various surface characterization techniques and tools. The results indicate that the frictional characteristics of silicon are improved by coating the surface with a thin metallic film, and furthermore, an optimum film thickness can be identified for silver, copper and zinc coatings. In most cases ploughing marks could be found on the film which suggests that plastic deformation of the film is the dominant mode by which frictional energy dissipation occurred. Based on this observation, the frictional behaviour of thin metallic coatings under low loads is discussed and friction coefficients are correlated with an energy based friction model. Copyright @ 1996 Elsevier Science Ltd

Keywords: friction, wear, thin metallic films, hard substrate, thermal vapour deposition, optimum film thickness

Introduction It has long been recognized that soft coatings improve the tribological properties of sliding systems under certain sliding conditions. However, the fundamental

mechanisms behind such behaviour have not been clearly explained. One basic problem is that friction interactions are not clearly understood yet. Even though much research has been conducted on the subject of identifying the basic friction mechanism, the conflicting theories of friction are continuously

+Currently at Samsung Electra-Mechanics Co., Suwon, Korea *Department of Mechanical Engineering, The Ohio State University, 206 West 18th Avenue, Columb~, OH 43210, USA *Department of Mechanical Engineering, Yonsei University, Seoul, Korea

and vigorously debated. The view shared by many researchers and engineers is that friction depends directly on adhesion phenomena. The adhesion theory suggests that similar materials will result in high friction

Tribology International Volume 29 Number 4 1996 345

Optimum film thickness: D.-S. Jang and D.E. Kim

due to chemical compatibility. On the other hand, there are views which emphasize mechanical interactions at the sliding interface as being the dominant cause of friction. In this school of thought, surface roughness, wear particle geometry and the shapes of asperities are emphasized. This controversy is partly due to the system-dependent nature of friction and wear phenomena.

Bowden and Tabor2 first developed a theory of friction of thin solid films based on the adhesion theory of friction. They concluded that the effectiveness of thin solid films in reducing friction results from the low shear strength of the film material and the high yield strength of the hard substrate. Their proposition was modified by incorporating the pressure dependence of the shear strength of thin solid films3*4. A Hertzian contact model for thin solid films, which has been used to explain the decrease in friction coefficient with increasing load, is derived from this postulatior?. Even though the adhesion model is widely accepted for explaining the frictional behaviour of thin soft films, this model is inadequate for explaining or predicting most frictional phenomena, particularly in certain conditions where the adhesion is not expected to play a significant role as in unclean environments.

Many researchers have presented convincing evidence that plastic deformation is commonly involved in most sliding experiments, even for brittle materials such as silicon and certain ceramics under very low loads7T8. The explanation for such behaviour is that asperity contacts at the sliding interface experience high local stresses that exceed the flow stress of the material. The consequence is that frictional energy dissipation can be attributed to plastic deformation of the material at and near the sliding interface. Based on this observation, Heilmann and Rigney9,10 have developed an energy-based friction model which depends on certain mechanical parameters and microstructural features of the materials, where the principal contribution to sliding friction is the near-surface plastic deformation. In this work, this model has been applied to model the frictional behaviour of coated systems.

Other studies indicate that elastic contact is possible under certain conditions, namely, with smooth surfaces and high hardness, low modulus material@. Indeed, a highly desirable sliding condition would be to restrain all the interfacial interactions to elastic behaviour, so that wear would be zero and frictional energy dissipation would be minimal. However, despite many researchers belief that elastic contact sliding is possible, it is highly unlikely that such an ideal sliding condition can be achievedl*. To achieve minimum friction, therefore, is to confine plastic deformation to a very small volume near the contact region. In addition, the material undergoing plastic deformation needs to be weak or soft to allow minimal energy dissipation during asperity interaction. A composite of a very thin metallic film with low yield strength coated on a substrate with high hardness may be exploited for this purpose.

Film thickness has been recognized as a variable of the frictional behaviour of thin solid films since Bowden and Tabor* illustrated the general nature of the

phenomenon. Their work also indicates that there is an optimum film thickness where a minimum friction coefficient can be obtained. Similar results have been obtained with different combinations of materials, coating techniques and testing conditions13-15. On the other hand, certain experimental results do not show a clear minimum friction coefficient as a function of film thicknesPT1. Even though some information is available in the literature, the effects of the film thickness on the frictional behaviour of solid films have not been clearly identified. In particular, very little information is available on the frictional behaviour of ultra-thin (l-100 nm) films under relatively low loads.

The present study investigates the optimum film thickness to achieve low friction in soft coating systems for low load sliding applications. In addition, the friction mechanism for thin soft coating systems under low loads is suggested. Ultimately, such knowledge may be used for sliding applications in micro-electro- mechanical systems (MEMS) and other micro devices.

Experimental procedures

Scope

In the present study dry friction sliding tests were conducted with bare silicon and silicon substrate coated with silver, copper, tin or zinc film. These specimens were slid against 52100 steel balls using a reciprocating pin-on-flat type apparatus. The coating materials were selected based on their relatively low strength properties. They also have received much attention as thin film solid lubricants. The sliding speed was kept low in order to minimize the effects of thermal interactions at the sliding interface. In addition, the environment was purged with nitrogen gas to minimize chemical changes of the surfaces during the sliding tests. All experiments were conducted at room tem- perature with a relative humidity of 30-40% inside the chamber. A thermal evaporation technique, which can produce highly pure films with smooth surfaces, was used to coat the metallic films. After deposition the morphology of the films was examined using an atomic force microscope (AFM), a non-contact surface profilometer and a scanning electron microscope (SEM). Following the sliding tests, the specimens were examined using various surface characterization tools such as the SEM, energy dispersive spectroscopy (EDS), a non-contact surface profilometer, and an optical microscope.

Apparatus

The custom-built tribotester shown in Fig 1 was used to conduct the experiments. This apparatus is capable of providing either reciprocating or rotary motion between the two surfaces and monitoring the friction coefficient in real time for normal loads ranging from 0.05 to 5 gf. The pin is attached to a spring loaded arm. The back end of the arm is driven with a closed- loop micro-actuator and a motion controller which controls the vertical motion of the pin with a resolution of 0.1 pm. This corresponds to a normal load of 0.003

346 Tribology international Volume 29 Number 4 1996


Strain Ga& (For normal load)

(For friction force)

\ \ Sample Holder

Rotary Stage

Iu Linear Stage

Microactuator

Stage Controller 1 Amplifier

Fig I Schematic of the experimental apparatus

gf. Two sets of full bridge semiconductor strain gauges (gain factor = 155) are attached to flexible cantilever arms of appropriate stiffness for the normal load and friction force measurements. The strain gauge outputs are fed into an A/D converter board in the microcom- puter as well as a chart recorder through two single- channel signal conditioning amplifiers. The friction force and the variations of the applied normal load are continuously monitored and recorded during the experiments. The tribotester is mounted inside a Plexiglass chamber which allows for the control of the environmental conditions. The entire setup is placed on a vibration isolation table to reduce the effects of mechanical vibration.

Materials and preparation of coatings

Single crystal (111) n-type silicon wafers were used as substrates. The hardness was 850 HV (25 g, dwell time: 10 s) or 8.33 GPa. Pure silver (99.999 w/o), copper (99.999 w/o), tin (99.9999 w/o) and zinc (99.9999 w/o) were coated on the silicon wafers using a thermal evaporation technique. The material properties of these metals are listed in Table 1. The base pressure of the vacuum chamber was 0.5 mPa

for the deposition. The fihn thichness was controlled using a thickness monitor during the coating process and was verifkd by observing the edge of the Hm on the substrate with a non-contact surface -meter.

2.5x RM5: 26.4nm PROFILE WVLEN: 649.8nm

0.05 9.85 1.65 2.44 3.24 4.04

Illstance on surface, mllllmeters

Fig 2 Film thickness measurement using a non-contact surface profilometer for the 6.5 nm thick silver coating

Tribology international Volume 29 Number 4 1996 347


Table 1 Material properties of silver, copper, tin and zinc

Material Youngs Hardness= moduIus23 (GPa) (HV/MPa)

Yield strengthz0-23 IMPa)

Silver 78 741725 290 0.92 Copper 120 105/1030 344 1.10 Tin 44 6.6164.7 20.7 0.57 Zinc 91 321314 110 0.79

Measured with cold rolled metal flats using the microhardness tester (25 g, dwell time: 10 s) after polishing

The controlled film thickness values were 1, 10, 100 and 1000 nm and measured thickness values were 2, 7, 6.5 and 680 nm for silver, and 2, 7, 38 and 690 nm for copper, respectively. A sample of the thickness data obtained with the non-contact surface profilometer for silver (65 nm) is shown in Fig 2. For tin, 13, 92, and 1080 nm thick coatings were prepared. For zinc, the controlled film thickness values were 10, 100, 1000 and 2000 nm. The morphology of zinc coatings was highly discontinuous as shown in SEM micrographs (Fig 3). For zinc coatings, the film thickness value may be insufficient to describe the state of zinc deposits due to the discontinuous morphology. Thus, the term average film thickness is used to represent the amount of zinc deposit on the silicon substrate. The state of the zinc coatings can be clarified with SEM micrographs showing the density and grain size of the zinc deposits.

Most zinc grains on the silicon surface have a hexagonal shape, which is indicative of the hexagonal close- packed (HCP) structure of zinc crystals. Furthermore, as the deposition amount increases, the size and density of grains also increase. Despite the discontinuous nature of the zinc coating, it was decided to investigate its frictional properties for comparison with continuous films.

The surface roughness of the coated and bare silicon specimens was measured with a non-contact surface profilometer. The obtained values were 4-5 nm rms for bare silicon and 3-5 nm rms for silver, copper and tin coated specimens. Surface profiles of the bare and silver coated (7 nm) silicon specimens are shown in Fig 4. The values of the surface roughness of zinc coatings were 2-5 nm rms for 10 and 100 nm thick

Fig 3 SEM micrographs of zinc coatings (a) t = 10 nm; (b) t = 100 nm; (c) t = 1000 nm; (d) t = 2000 nm

348 Tribology International Volume 29 Number 4 1996

-14 ial! Ll. 13.0nm

rJ..tanc. LMlCro~~ L.-14.anm

WYKC

WYKC

Fig 4 Non-contact surface projilometer surface profiles for (a) bare silicon, (b) silver coated (7 nm) silicon

coatings, and 1.50-200 nm rms for 1000 and 2000 nm thick coatings.

Pure bulk metals were also tested for their frictional behaviour. Flat metal specimens were ground with 600 grit Sic abrasive paper in water and then polished by 15, 6 and 1 pm diamond pastes with oil. Finally, the flat specimens were polished using 0.05 pm ralumina to obtain a smooth surface finish. The measured values of the surface roughness of bulk metal flats were in the range of 30-60 nm. After polishing with alumina the specimens were cleaned with trichloroethylene and rinsed with methanol using an ultrasonic cleaner.

Sliding and adhesion tests

Dry sliding tests were conducted with the reciprocating tribotester using bare and coated silicon as well as bulk metal specimens as the flat, and 52100 balls as the pin. The diameter of each steel ball was 3.2 mm and its hardness was 890 HV (25 g, dwell time: 10 s). The measured surface roughness value of the steel ball was about 10 nm rms. The steel balls were cleaned with trichloroethylene and rinsed with methanol using an ultrasonic cleaner. 0.1 and 1 gf normal loads were


used in the experiments. The sliding speed was 1 mm/s and the stroke was set to 7 mm. The friction forces and the variations in the applied normal load were recorded for 100 cycles. The friction force was recorded from the output of the strain gauges attached to the vertical flexible cantilever arm. All friction coefficients presented in this study represent the mean values of friction coefficients of three or four tests.

Before and after the sliding test, the adhesive force in the normal direction was measured by monitoring the vertical force needed to separate the pin from the slider after contacting the two with predetermined normal forces. The adhesion coefficient, which is defined as the ratio of the adhesive force to the applied normal force, was calculated. For all specimens tested, the mean values of the adhesion coefficient were less than 0.01. Particularly, for the coated specimens, there was no detectable adhesive force before and after the sliding tests.

Characterization of the specimens

The wear tracks of the specimens and worn areas of the pins were observed using a Nomarski optical microscope and an SEM. The SEM was equipped with an EDS facility which can detect elements heavier than boron. It was used to check for material transfer between the pin and the slider. The surface topography of the wear tracks of the coated specimens was analysed using a non-contact surface profilometer.

Results and discussion

The experimental friction coefficient data with respect to the film thickness are presented for the first and 100th cycle. As sliding proceeds, the film thickness on the sliding track changes since the film material undergoes permanent deformation. Thus, the film thickness value is valid only at the first cycle. Data are also given for the 100th cycle to compare the effectiveness of the deposition material over a given sliding distance.

Silver films on silicon substrates

The variation of friction coefficient with film thickness for silver coated silicon is shown in Fig 5. (Error bars, here and in later figures, represent the range of friction coefficient about mean values of friction coefficients of three or four sliding tests.) The left end of the figure indicates the friction coefficient for bare silicon and the right end shows the value for bulk silver. For both 0.1 and 1 gf loads, initial friction coefficients for bare silicon were relatively high. For the 0.1 gf load, the friction coefficients for bare silicon increased from 0.41 to 0.66 in 100 cycles. On the other hand, the friction coefficients for the coated substrates maintained relatively low values during the tests. In particular, for a 7 nm thick coating, the friction coefficients were reduced significantly. For 65 and 680 nm thick coatings, initial friction coefficients were very close to those of the bulk silver. It seems that the 65 and 680 nm thick coatings behaved like bulk silver under the loads tested. As sliding proceeded, the



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friction coefficients of all coated specimens gradually increased under the 0.1 gf load while the values of friction coefficients remained constant under the 1 gf load. Higher friction coefficients observed for the 0.1 gf load are indicative of the load dependent nature of the soft metallic coating which has been also observed in a different load ranget3+18. For a 2 nm thick coating, the initial friction coefficient was high compared to those for other coatings. The AFM micrograph (Fig 6) shows that the surface of the 2 nm

8 20.0

Fig 6 AFA4 micrograph of a 2 nm thick silver coating

thick coating is not uniform, which is presumed to be responsible for the high friction.

Microscopic examination of the surfaces showed many grooves in the sliding tracks of the coated and bulk flats (Fig 7). It seems clear that severe plastic deformation of the coating took place during sliding action. Some differences in wear track features with the 7 nm thick coating and other thicker coatings or bulk silver were observed. In contrast to the definite grooves on the sliding tracks of the 65 and 680 nm thick coatings, and bulk silver, the sliding tracks of the 7 nm thick coating were relatively smooth. In addition, the topography of the wear tracks (Fig 8) showed that the depth of the wear track (~3 nm) of the 7 nm thick coating was much smaller than those of the 65 and 680 nm thick coatings, and bulk silver. This indicates that the friction and wear can be controlled by an appropriate choice of coating thickness. SEM micrographs and EDS analysis of the steel ball indicated that no detectable silver was transferred to the ball. This observation, in addition to the measured adhesion coefficients, suggest that adhesion did not play a significant role in these tests.

Copper films on silicon substrates

The friction coefficients of silicon could be reduced significantly with copper coatings. Figure 9 shows the friction coefficient values with respect to film thickness for copper coated silicon. The optimum film thickness observed is also 7 nm for both normal loads. The initial friction coefficient with a 2 nm thick coating was low as with other coatings. The AFM examination showed the 2 nm thick copper coated surface is relatively smooth and uniform unlike the 2 nm thick silver coating. This suggests that the film morphology is one of the important factors for controlling friction of thin coating systems.

Bulk copper resulted in lower friction coefficients than most copper coatings. The low friction of bulk copper is assumed to be due to relatively high hardness (= 1.03 GPa) which resulted from work-hardening of the surface layer during mechanical polishing19. The hardness observed for cold rolled copper is about 780 MPa which is very close to that for cold rolled silverzO. Following the friction test, the bulk copper specimen was annealed at 220C for one hour in flowing hydrogen and tested again. The hardness of the annealed copper was 48 HV (25 g, dwell time: 10 s) or 470 MPa. There was no difference in the surface roughness before and after annealing. How- ever, it should be mentioned that annealing may cause a change in the content of the oxide in the copper which in turn may affect the frictional behaviour. The friction coefficients of the annealed copper were almost two times higher than those of the bulk copper. Microscopic examination of the worn areas showed characteristics similar to those of silver coatings.

Tin films on silicon substrates

Figure 10 shows the variation of friction coefficient with respect to film thickness for tin coated silicon. For the 1 gf load, higher friction coefficients were



Fig 7 SEM micrograph and Nomarski optical micrographs of the wear tracks on silicon coated with silver after sliding for 100 cycles against 52100 steel at 1 gf load: (a) t = 7 nm (SEM micrograph); (b) t = 65 nm; (c) - t = 680 nm; (d) bulk silier

-_

observed for all coated specimens compared to the values obtained for bare silicon at both the first and 100th cycle. Nomarski microscopy showed that tin coatings were easily worn out in a few sliding cycles. It seems that the higher friction coefficients are caused by tin wear particles generated during sliding. The easy wearing of the tin coating is probably related to the weak adhesion of a tin film to the substrate owing to the low surface energy of tin (Table l), and the morphology of the tin coating. Unlike the silver and copper coatings, tin coatings consisted of small granules (Fig 11). For the 0.1 gf load, the 1100 nm thick coating shows lower friction coefficients than the values observed for bare silicon, but higher values than those of bulk tin. The minimum friction coefficient of the tin coating was observed with a 92 nm thick coating under a 0.1 gf load after 100 cycles. Though the initial friction coefficient with the 92 nm thick coating was relatively high, as sliding proceeded, the friction coefficient decreased to the value of 0.28 and then remained constant. Such low friction force behaviour is attributed to the transferred film to the pin. The SEM (Fig 12) and X-ray mapping analysis showed that small agglomerates of tin grains formed on the pin sliding against the 92 nm thick coating. The conditions responsible for tin transfer were not identified. However, it is speculated that these conditions involve film thickness, film morphology, and applied normal load. For the 1 gf load, the friction coefficients

for bulk tin rapidly increased to 0.9 after a few sliding cycles. The SEM micrograph (Fig 13) showed many cylindrical wear debris and rough grooves on the wear track. It seems that severe ploughing or microcutting by hard asperities of the steel ball took place. The existence of an optimum film thickness is not obvious for the tin coating under 0.1 and 1 gf loads. However, for the 0.1 gf load, the 1100 nm thick coating seems to be beneficial for short sliding cycles while the 92 nm thick coating is better for longer sliding cycles.

Zinc films on silicon substrates

The dependence of the friction coefficient on average film thickness for zinc coated silicon is shown in Fig 14. The minimum friction coefficient was achieved with the 10 nm thick coating despite the highly non- uniform morphology of the film (Fig 3). For the 1 gf load, all the coated specimens maintained lower friction coefficients than the values obtained for bare silicon and bulk zinc throughout the test. On the other hand, for the 0.1 gf load, as sliding proceeded, the friction for the coated specimen increased rapidly. After sliding for 100 cycles, most of the film was removed from the substrate. For the 1 gf load, small agglomerates of zinc grains formed on the pin (Fig 15) while such agglomerates could not be found on the pin for the 0.1 gf load. It seems that the formation of small agglomerates on the pin is necessary to maintain low



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friction in the case of zinc coated silicon. In addition, it was noticeable that the size of grains agglomerated on the pin increased compared to the grains on the coated surface before the test (Fig 3) and most zinc grains on the pin were distorted from the perfect hexagon shape observed prior to the sliding test. This

Fig 10 Friction coeficient vs. film thickness for silicon coated with tin (a) at j%st cycle (b) at 100th cycle



Fig 11 SEM micrograph of a 92 nm thick tin coating

indicated that the zinc grains were plastically deformed during the sliding action. Definite ploughing marks were also observed on the surface of the zinc agglomer- ate. Even though zinc coatings exhibit discontinuous morphology, the frictional behaviour shows characteristics similar to those of continuous films such as silver. It is believed that such behaviour is observed because the discontinuous zinc deposit gets smeared and transferred to the pin as sliding proceeds, thus creating the effect of a continuous film. As with bulk tin, bulk zinc showed relatively high friction after a few sliding cycles at the 1 gf load. The high friction is attributed to severe plastic deformation as shown in the SEM micrograph (Fig 16).

General discussion

Results of the present study show that the frictional characteristics of silicon can be improved by coating the surfaces with thin metallic films for low load sliding applications. If the film thickness is optimized, the friction may be significantly reduced. For silver, copper and zinc coatings, the optimum film thickness, where the friction coefficient is minimum, can be clearly identified. The optimum film thickness for tin coatings is not clear. Similar results have been reported for tin

Fig 13 SEM micrograph of the wear track on bulk tin after sliding for 100 cycles against 52100 steel at 1 gf load

coatings on 52100 steel at low loadsih. The examination of the morphology of silver and copper coatings shows that as long as the surface of the film is smooth and uniform, the optimum thickness can be achieved with ultra thin coatings. On the other hand, despite the highly discontinuous and non-uniform surface morphology, zinc coatings exhibit low frictional behaviour probably due to the agglomeration of zinc grains transferred to the pin, For tin and zinc coatings, the films were completely worn out after 100 cycles of sliding. The easy wearing is assumed to be due to the weak adhesion strength between the film and substrate which may result from the low surface energy of film material and the limitation of thermal evaporation coating technique. Compared with silver and copper, the surface energies of tin and zinc are relatively low (Table 1). Microscopic examination of worn specimens and the low values of the adhesion coefficient suggest that plastic deformation of the film due to ploughing is the dominant mechanism of friction for thin soft coatings under low loads. There was no indication of any damage to the silicon substrate in these experiments except for the case of bare silicon.

Fig 12 (a) SEM micrograph of the 52100 steel ball after sliding for 100 cycles against a 92 nm thick tin coating at 0.1 gf load; (b) higher magnification of the region indicated by an arrow in Fig 13(a)



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Various mechanisms have been proposed to explain frictional behaviour in dry sliding. These include ploughing, asperity deformation, and adhesion. It is generally agreed that friction is due to the combination of these mechanisms. This limits the effectiveness of friction analysis in terms of a single model. Models based on only one mechanism have not yielded successful results because of the history-dependent nature of frictional phenomena. Based on the observations in the present study, an energy-based friction

Fig 16 SEM micrograph of the wear track on bulk zinc after sliding for 100 cycles against 52100 steel at 1 gf load

model developed by Heilmann and RigneylO may be appropriate for correlating the friction coefficient of thin soft coatings. The contributions of ploughing and asperity deformation on the friction force may be predicted using the energy-based mode121*22. For a thin soft coating on a hard substrate, as long as there is no direct contact between the asperities and the substrate, the minimum friction coefficient is expressed aslo:

(1)

where pL is the friction coefficient of the bulk layer material, r,,, , 7i,, are the ultimate shear stresses of the substrate and bulk layer material, respectively, 7, is the average surface shear stress of the layer and F(x) is a monotonic function expressed as:

)Q) = 1 _ 2 b(l+X)--Xl ln(-X2) (2)

Then, the experimental values of the friction coefficient in the case where the coatings are effective can be

Fig 15 SEM micrographs of the 52100 steel balls after sliding for 100 cycles against: (a) a 10 nm thick zinc coating at 1 gf load; (b) a 1000 nm thick zinc coating at 1 gf load



Table 2 Comparison of experimental and theoretical values of the minimum friction coefficient

Material Normal load (gf) --.~.-~. ___ PL

p (experimental) p (theoretical)

Silver 1 0.25 0.21 0.18 0.1 0.28 0.23 0.20

Copper 1 0.40 0.22 0.29 0.1 0.43 0.20 0.31

Tin 1 N/A N/A N/A 0.1 0.38 0.29 0.27

Zinc 1 0.33 0.18 0.24 0.1 0.36 0.19 0.26

correlated with the theoretical value obtained from the energy-based friction model. In the following correlation, the ultimate shear stress, T,,,~~, is equated to the material shear strength which is obtained from the yield strength values in Table 1 and the minimum friction coefficient is calculated using Eq. (1) with et&,, = 0.9999. Table 2 shows a comparison of the experimental and theoretical values of the minimum friction coefficient.

For the correlation of the minimum friction coefficient of the copper coating, the yield strength and the friction coefficient of the annealed copper were used. The yield strength observed for annealed copper is about 209 MPaz3. For the tin coating, the friction coefficient at the 100th cycle is used in the correlation since the 92 nm thick tin coating is effective only after some of the film material is transferred to the pin. As shown in Table 2, the minimum friction coefficients can be predicted using the energy-based friction model for silver and tin coatings. On the other hand, the theoretical values of the friction coefficient are higher than the experimental values for copper and zinc coatings. In part, such a discrepancy may be caused by the differences in the material properties and microstructures of the bulk and film material. In addition, the relatively thin film can allow the silicon substrate to influence the mechanical properties of the film. Despite such discrepancy, the theoretical values of the friction coefficient are quite reasonable compared to the experimental values. Even though it is difficult to obtain the exact prediction for the friction coefficient using the energy-based friction model, the model may be applied to predict the frictional behaviour with thin soft coatings within reasonable limits.

Conclusions

In the present study, the frictional behaviour and optimum film thickness of the thin soft metallic coating for low load sliding applications have been investigated. The results of the experimental work show that the frictional behaviour of the thin soft coating under relatively low loads depends on the film thickness, normal load and coating material. Furthermore, the morphology of the film as well as the tendency of the film material to transfer to the pin also affected the frictional behaviour of the thin soft coating. It has also shown that the values of the optimum film

thickness are about 7 nm for the silver and copper coating, and about 10 nm for the zinc coating under the 0.1 and 1 gf loads. For the tin coating, an optimum film thickness could not be clearly identified. It was interesting to note that despite discontinuous film morphology, zinc coating showed behaviour that was comparable to those of continuous films. In particular, the effectiveness of the zinc coating seems to be determined by the accumulation of transferred film material on the pin.

Microscopic observations of the specimens indicate that plastic deformation due to ploughing is the main cause of friction with thin soft metallic coatings. The energy-based friction model developed by Heilmann and Rigney may be used to predict the friction coefficient with thin soft metallic coatings for low load contact sliding applications.

Acknowledgements

The authors would like to thank Professor D. Rigney at the Ohio State University, Materials Science and Engineering Department, for his helpful comments. We would also like to thank Professor B. Bhushan at the Ohio State University, Mechanical Engineering Department, for use of the AFM and a non-contact surface profilometer. This study was partly supported by the Center for Materials Research in the Ohio State University.

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Briscoe B.J., Scmton B. and Willis F.R. The shear strength of thin lubricant films. Proc. Roy. Sot. Lond. 1973, A333, 99-114

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