Bhushan B. Nanotribology and Nanomechanics: An Introduction

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344 Bharat Bhushan

Surface height (nm)

010

250

–250

Friction force (V)

010

0.35

–0.35

Friction force (V)

0.35

–0.35

Friction force (V)

010

0.35

–0.35

Scan distance (μm)

High

friction

Low

friction

Low

friction

High

friction

T-R

Fig. 8.21. (b) two dimen-

sional proﬁles of surface

height and friction forces

across a silicon grid pit.

Friction force data in trace

and retrace directions, and

subtracted force data are pre-

sented

with particles having a preferred orientation. The directionality eﬀect in friction on

a macroscale is observed in some magnetic tapes. In a macroscale test, a 12.7-mm-

wide polymeric magnetic tape was wrapped over an aluminum drum and slid in

a reciprocating motion with a normal load of 0.5N and a sliding speed of about

60mm/s [3]. The coeﬃcient of friction as a function of sliding distance in either di-

rection is shown in Fig. 8.23. We note that the coeﬃcient of friction on a macroscale

for this tape is diﬀerent in diﬀerent directions. Directionality in friction is some-

8 Nanotribology, Nanomechanics and Materials Characterization 345

Friction force (V)

010

0.35

–0.35

Surface slope

–2

010010

Surface height (nm)

250

–250

Scan distance (μm) Scan distance (μm)Scan distance (μm)

0 5.00

μm

0 5.00

μm

0 5.00

μm

Low

friction

High

friction

Low

friction

High

friction

Trace Retrace

–Retrace

Surface

height

Trace Retrace

Surface

slope

Friction

force

–Retrace

Fig. 8.22. (a) Greyscale images of surface heights, surface slopes and friction forces for

scans across a gold-coated ruling, and (b) two-dimensional proﬁles of surface heights, surface

slopes and friction forces for scans across the silicon grid pit. Arrows indicate the tip sliding

direction [80]

times observed on the macroscale; on the microscale this is the norm [4, 15]. On

the macroscale, the eﬀect of surface asperities is normally averaged out over a large

number of contacting asperities.

346 Bharat Bhushan

Forward

Coefficient of friction

Number of drum passes

0 125

0.4

0.3

0.2

0.1

25 50 75 100

Fig. 8.23. Coeﬃcient of macroscale friction as a function of drum passes for a polymeric

magnetic tape sliding over an aluminum drum in a reciprocating mode in both directions.

Normal load = 0.5 N over 12.7-mm-wide tape, sliding speed = 60 mm/s [65]

8.3.4 Surface-Roughness-Independent Microscale Friction

As just reported, friction contrast in conventional friction measurements is based on

interactions that are dependent upon interfacial material properties superimposed

with roughness-induced lateral forces, and the cantilever twist is dependent on the

sliding direction because of the local surface slope. Hence it is diﬃcult to separate

friction-induced from roughness-induced cantilever twist in the image. To obtain

roughness-independentfriction, lateral or torsional modulation techniques are used

in which the tip is oscillated in-plane with a small amplitude at a constant normal

load, and changes in the shape and magnitude of the cantilever resonance are used

as a measure of the friction force [31–36,82]. These techniques also allow measure-

ments over a very small region (a few nm to a few µm).

Scherer et al. [32] and Reinstaedtler et al. [33, 34] used the lateral mode for

friction measurements (Fig. 8.10b). Bhushan and Kasai [36] used the TR mode

for these measurements (Fig. 8.11). Before engagement, the cantilever is driven into

torsional motion of the cantilever/tipassembly with a given normal vibration ampli-

tude (the vibration amplitude in free air). After engagement,the vibration amplitude

decreases due to the interaction between the tip and the sample, the vibration fre-

quency increases and a phase shift occurs. During scanning, the normal load is kept

constant, and the vibration amplitude of the cantilever is measured at the contact

frequency.

As mentionedearlier,the shift inthe contact resonance frequencyin both the lat-

eral and the TR modes is a measure of the contact stiﬀness, as shown schematically

in Fig. 8.24. At excitation voltage above a certain value, as a result of micro-slip at

the interface, a ﬂattening of the resonance frequency spectra occurs (Fig. 8.22). At

the lowest excitation voltage, the AFM tip sticks to the sample surface and follows

the motion like an elastic contact with viscous damping, and the resonance curve

is Lorentzian with a well-deﬁned maximum. The excitation voltage should be high

enough to initiate micro-slip. The maximum torsional amplitude at a given reso-

nance frequencyis a function of friction force and sample stiﬀness, so the technique

8 Nanotribology, Nanomechanics and Materials Characterization 347

TR amplitude (V)

TR amplitude versus frequency

TR amplitude (V)

Frequency (kHz)

Material with two stiffness regions

with no slip

Material with uniform stiffness

with slip (plateau)

Excitation

voltage

Fig. 8.24. Schematic show-

ing frequency proﬁles of the

TR amplitude for materials

with two phases and a sin-

gle phase. The maximum

TR amplitude at the contact

resonance frequency of the

resonance curve with a ﬂat-

tened top, resulting from slip,

can be used for friction force

measurement

is not valid for inhomogeneoussamples. If the torsional stiﬀness of the cantilever is

very high compared to the sample stiﬀness, the technique should work.

Reinstaedtler et al. [33] performed lateral-mode experiments on bare Si and Si

lubricated with 5-nm-thick chemically bonded perﬂuoropolyether (Z-DOL) lubri-

cant ﬁlm. Figure 8.25a shows the amplitude of the cantilever torsional vibration as

a function of frequency on a bare silicon sample. The frequency sweep was ad-

justed such that a contact resonance frequency was covered. The diﬀerent curves

correspond to diﬀerent excitation voltages applied to the shear-wave transducer. At

low amplitudes, the shape of the resonance curve is Lorentzian. Above a critical

excitation amplitude of the transducer (excitation voltage = 4V corresponding to

≈ 0.2 nm lateral surface amplitude, as measured by interferometry), the resonance

curve ﬂattens out and the frequency span of the ﬂattened part increases further with

the excitation amplitude. Here, the static force applied was 47nN and the adhesion

force was 15 nN. The resonance behavior of the tip–cantilever system in contact

with the lubricated silicon sample (Fig. 8.25b) was similar to that of the bare sili-

con sample. By increasing the static load, the critical amplitude for the appearance

of the ﬂattening increases. The deviations from the Lorentzian resonance curve be-

348 Bharat Bhushan

Torsional amplitude θ (arb. units)

Frequency (kHz)

230 250

240

θ (arb. units)

Frequency (kHz)

210 250

230

θ (arb. units)

Frequency (kHz)

210 250

230

Excitation

voltage (V)

0.5

23 nN

70 nN

95 nN

Si+

5 nm

Z-DOL

c) Effect of lubricant filmb) Effect of load

Fig. 8.25. Torsional vibration

amplitude of the cantilever

as a function of excitation

frequency. (a) Measurement

on bare silicon. The diﬀer-

ent curves correspond to

increasing excitation voltages

applied to the transducer and,

hence, increasing surface

amplitudes. (b) Measure-

ment on silicon lubricated

with a 5-nm-thick Z-DOL

layer. Curves for three dif-

ferent static loads are shown.

The transducer was excited

with an amplitude of 5 V.

load of 70 nN and an exci-

tation amplitude of 7 V. The

two curves correspond to bare

silicon and lubricated silicon,

respectively [33]

came visible at static loads lower than 95nN. As shown in Fig. 8.25c, the resonance

curve obtained at the same normal load of 70 nN and at the same excitation volt-

age (7 V) is more ﬂattened on the lubricated sample than on the bare silicon, which

led us to conclude that the critical amplitude is lower on the lubricated sample than

on the bare sample. These experiments clearly demonstrate that torsional vibration

of an AFM cantilever at ultrasonic frequencies leads to stick–slip phenomena and

sliding friction. Above a critical vibration amplitude, sliding friction sets in.

Bhushan and Kasai [36] performed friction measurements on a silicon ruler and

demonstrated that friction data in the TR mode is essentially independent of surface

roughnessand slidingdirection.Figure 8.26ashowssurfaceheight and frictionforce

maps on a silicon ruler obtained using the TR mode and contact-mode techniques.

A comparison is made between the TR mode and contact-modefriction force maps.

For easy comparison, the line scan proﬁles near the central area are shown on top of

the greyscalemaps. The verticalscales of the frictionforce proﬁlesin the two graphs

areselected to coverthe samerange of frictionforce sothat directcomparisoncan be

made, i.e., 0.25V in full scale for the TR mode corresponds to 0.5V for the contact

modein these measurements.As expected,for the tracescan, small downwardpeaks

in theTR modemap andlargeupwardand downwardpeaks inthe contactmode map

are observed. The positions of these peaks coincide with those of the surface slope;

8 Nanotribology, Nanomechanics and Materials Characterization 349

Fig. 8.26. (a) A comparison

between the TR-mode friction

and contact-mode friction

maps together withline scans,

on the silicon ruler. The TR-

mode surface height and

contact-mode surface height

images are also shown

350 Bharat Bhushan

μm

3.0

1.5

0 1.5 3.0

Surface height (nm)

Scan distance (μm)

0.0

3.0

–60

TR amplitude (V)

1.05

0.80

TR amplitude (V)

0.13

0.00

–0.13

TR amplitude (V)

1.05

0.80

Surface height (nm)

–60

Friction force (V)

0.25

0.00

–0.25

Friction force (V)

0.50

0.25

0.00

Friction force (V)

0.25

0.00

–0.25

Scan distance (μm)

0.0

3.0

Silicon ruler

TR mode friction force

TR amplitude = 0.3 nm

Normal load = 100 nN

Contact mode friction force

Normal load = 50 nN

Trace

Retrace Retrace

Trace

Trace – Retrace Trace – Retrace

Trace + Retrace Trace + Retrace

Fig. 8.26. (b) A comparison of the line scans of the TR-mode friction and contact-mode

friction on a selected pitch of the silicon ruler [36]

therefore, the peaks in the friction signals are attributed to a topography-induced

eﬀect. For the retrace scan, the peak pattern for the TR mode stays similar, but for

the contact mode, the pattern becomes reversed.

The subtraction image for the TR mode shows almost ﬂat contrast, since the

trace and retrace friction data proﬁles are almost identical. For the contact mode,

the subtraction image shows that the topography-induced contribution still exists.

As stated earlier, the addition image of the TR mode and the addition image of

the contact mode enhance the topography-induced eﬀect, which is observed in the

ﬁgure.

A closer look at the silicon ruler images at one pitch was taken, and the associ-

ated images are shown in Fig. 8.26b.The surface height proﬁles in the TR mode and

contact mode are somewhat diﬀerent. The TR mode shows sharper edges than those

in the contact mode. The ratios of the change in amplitude at the steps to the change

in the mean amplitude in the TR mode and in the contact mode are a measure of to-

pography eﬀects. The ratio in the contact mode (≈ 85%) is about seven times larger

than that of the TR mode (≈ 12%).

8 Nanotribology, Nanomechanics and Materials Characterization 351

8.3.5 Velocity Dependence on Micro/Nanoscale Friction

AFM/FFM experiments are generally conducted at relative velocities as high as

about 200µm/s. To simulate applications, it is of interest to conduct friction exper-

iments at higher velocities. Furthermore, high-velocity experiments (up to 1 m/s)

would be useful to study the dependence of friction and wear on velocity. One ap-

proach has been to mount samples on a shear-wave transducer (ultrasonic trans-

ducer) and then drive it at very high frequencies (in the MHz range) as reported

earlier, see Fig. 8.10 [31–35,82,83]. The coeﬃcient of friction is estimated based

on the contact resonance frequency and requires the solution of the characteristic

equations for the tip vibrating in contact with the sample surface. The approach is

complex and depends on various assumptions.

An alternative approach is to utilize piezo stages with a large amplitude

(≈100µm) and a relatively low resonance frequency (a few kHz) and measure

the friction force directly using the FFM signal without any analysis, with the

assumptions used in the previous approaches using shear-wave transducers. The

commercial AFM set-up modiﬁed with this approach yields sliding velocities up

to 10mm/s [37]. In the modiﬁed set-up, the single-axis piezo stage is oriented such

that the scanning axis is perpendicular to the long axis of the AFM cantilever(which

correspondsto the 90

◦

scan-anglemode of thecommercialAFM; see Fig.8.27).The

displacement is monitored using an integrated capacitive feedback sensor, located

diametrically opposite to the piezo crystal, as shown in Fig. 8.27. The capacitive

change, corresponding to the stage displacement, gives a measure of the amount of

displacement and can be used as feedback to the piezo controller for better guid-

ing and tracking accuracy during scanning. The closed-loop position control of

the piezoelectric-driven stages using capacitive feedback sensors provides linear-

ity of motion better than 0.01% with nanometer resolution and a stable drift-free

motion [37].

Integrated

capacitive

sensor (target

& probe)

Flexure

design

Piezo crystal

Stage motion

i/p

Constructional details of piezo stage

Fig. 8.27. Schematic of cross-sectional view showing construction details of the piezo stage.

The integrated capacitive sensors are used as feedback sensors to drive the piezo. The piezo

stage is mounted on the standard motorized AFM base and operated using independent am-

pliﬁer and controller units driven by a frequency generator (not shown in the schematic) [37]

352 Bharat Bhushan

Friction force (nN)

Velocity (μm/s)

200

150

100

Adhesive force (nN)

Friction force (nN)

Velocity (μm/s)

200

150

100

Adhesive force (nN)

F ~ lnV

Asperity

deformation

dominates

F ~ f(V)

Tribo-

chemical

reaction

Meniscus

force dominates

Si (100) with native SiO

Atomic stick-slip

dominates

F ~ lnV

DLC (10 nm FCA)

Phase transformation

of DLC at the tip'

sample interface

Fig. 8.28. Eﬀect of velocity

on friction force at a normal

load of 70 nN and adhesive

force over a wide range of

velocities between 1 µm/s

and 10 mm/s measured over

a25µm scan size on Si(100)

and DLC samples. The dom-

inant friction mechanisms

acting at diﬀerent velocities

are marked on the ﬁgure [84]

Figure 8.28 shows the friction force and adhesive force dependence on sliding

velocity for single-crystal silicon, Si(100), and diamond-like carbon (DLC) with

10-nm thickness deposited using the ﬁltered cathode arc (FCA) deposition tech-

nique [84–87]. The friction force and adhesive force are seen to vary with a change

in velocity and both materials exhibita reversal in friction behaviorat certaincritical

sliding velocities. These reversals correspond to deﬁnitive transitions between dif-

ferent dominant friction mechanisms. For Si(100), which is hydrophilic, meniscus

forces are dominant. The initial decrease in friction force with velocity corresponds

to diminishing meniscus contributions. Beyond a certain critical velocity the resi-

dence time of the tip is not suﬃcient to form meniscus bridges at the sliding inter-

face and the meniscus force contributionto the friction force drops out. At moderate

velocities, tribochemicalreactions at the tip–sample interface, in which a low-shear-

strength Si(OH)

layer is formed [42,88], also reduce friction. At high sliding ve-

locities, deformation of asperities resulting from the high-velocity impacts becomes

dominant and governs the friction behavior (see Fig. 8.29a). For DLC, being par-

tially hydrophobic, meniscus forces are not dominant. The increase in friction force

with velocity arises from atomic-scale stick–slip. Based on a thermally-activated

Eyring model incorporated by Bouhacina et al. [89], the potential barrier divided

by absolute temperature required for making jumps during stick–slip follows the

8 Nanotribology, Nanomechanics and Materials Characterization 353

Friction

force

Scan length

Low sliding

velocity

High sliding

velocity

Atomic scale

stick-slip

Meniscus force

contribution

Deformation

Impact wear

debris

Zone of plastic

deformation

Meniscus bridges

Individual

atoms

Dominant for hydrophilic and

partially hydrophobic surfaces

Atomic

stick-slip

Micro/nanoscale

stick-slip

Tribochemical

reactions

Plastic

deformations

Meniscus

bridges

Viscous

fluid film

shearing

Asperity

impacts

Localized melting/

phase transformations/

coating removal

Atomic stick-slip

contribution

Meniscus

contribution

Viscous

fluid film

shearing

contribution

Asperity

deformation

contribution

πN

•

Analytical expression for micro/nanoscale friction

Dominant friction mechanisms with increasing velocity

F = c ln

+ φ

adh

W – φ

aτ

+ (l – a) kWV

7/3

Fig. 8.29. (a) Schematic il-

lustrating various dominant

regimes of friction force at

diﬀerent relative sliding ve-

locities from atomic scale

stick–slip at low velocities

to meniscus force contribu-

tion at mid velocities and

deformation-related energy

dissipation at high velocities,

and (b) comprehensive ana-

lytical expression for velocity

dependence of nanoscale

friction with the dominant

friction mechanisms [85]

logarithm of the velocity, and is responsible for the logarithmic dependence on ve-

locity shown by friction force. Further work by Gnecco et al. [90] showed that this

increase continues up to a certain sliding velocity and then levels oﬀ.Athighve-

locities, the large frictional-energy dissipation results in a phase transformation of

DLC to a graphite-like phase which is responsible for low friction.

For Si(100), the adhesive force is constant initially but then starts to increase

beyond a certain velocity. The increase in the adhesive force for Si(100) is believed

to be the result of a tribochemicalreaction. This layer gets replenishedcontinuously

during sliding and results in a higher adhesive force between the tip and sample

surface. For DLC, the adhesive force starts to increase beyond a critical velocity

and is believed to be the result of phase transformation of DLC to a graphitic phase

at the tip–sample interface [87,92,93].

For the development of a comprehensive friction model that encompasses vari-

ous friction mechanisms and accounts for the velocity dependence of each mecha-

nism, it is necessary to take into consideration the atomic-scale stick–slip, the adhe-

sive contributions arising from meniscus forces and the deformation of asperities at

the sliding interface resulting from high-velocity impacts [85]. Figure 8.29b gives