Bhushan B. Nanotribology and Nanomechanics: An Introduction

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1254 Bharat Bhushan

20μm

Nelumbo nucifera (lotus)

Colocasia esculenta

20μm

Fig. 22.35. SEM micrographs

of two hydrophobic leaves,

Nelumbo nucifera (lotus) and

Colocasia esculenta

Liquid

Air

Solid

Smooth surface

Air

Effect of roughness

Solid

Fig. 22.36. Droplet of liquid

in contact with a smooth solid

surface (contact angle θ

)and

rough solid surface (contact

angle θ) [173]

where A

is the ﬂat solid–liquid contact area (or a projectionof the solid–liquid area

onto the horizontal plane). R

is a roughness factor deﬁned as

. (22.3)

Equation (22.3) shows that, if the liquid wets a surface (cosθ

> 0), it will also wet

the roughsurface with a contact angle θ<θ

, and for nonwettingliquids (cosθ

< 0),

the contact angle with a rough surface will be greater than that with the ﬂat surface,

θ<θ

. The dependence of the contact angle on the roughness factor is resented

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1255

120

150

180

= 150

1.5 2

= 120

= 90

= 60

= 30

Fig. 22.37. Contact angle for

rough surface (θ) as a func-

tion of the roughness factor

) for various contact an-

gles for a smooth surface

(θ

) [173]

in Fig. 22.37for diﬀerent valuesof θ

, based on (22.2). It shouldbe notedthat (22.2)

is valid only for moderate roughness, when R

cosθ

< 1 [173].

For higher roughness, air pockets (composite solid–liquid–air interface) will be

formed in the cavities of the surface [175]. In the case of partial contact, the contact

angle is given by

cosθ = R

cosθ

− f

, (22.4)

where f

and f

are fractional solid–liquid and liquid–air contact areas. The ho-

mogeneous and composite interfaces are two metastable states of the system. In re-

ality, some cavities will be ﬁlled with liquid, and others with air, and the value of the

contact angle is between the values predicted by Eqs. (22.2) and (22.4). If the dis-

tance is large between the asperities or if the slope changes slowly, the liquid–air in-

terface can easily be destabilized due to imperfectness of the proﬁle shape or due to

dynamic eﬀects, such as surface waves Fig. 22.38. Nosonovsky and Bhushan [176]

proposed a stochastic model, which relates the contact angle to roughness and takes

into account the possibility of destabilization of the composite interface due to im-

perfectness of the shape of the liquid–air interface, caused by eﬀects such as capil-

lary waves.

In addition to the surface roughness, sharp edges of asperities may aﬀect wet-

ting, because they result in pinning of the solid–liquid–air contact line and resist

liquid ﬂow. Nosonovsky and Bhushan [173] considered the eﬀect of the surface

roughness and sharp edges and found the optimum roughness distribution for non-

wetting. They formulated ﬁve requirements for roughness-induced superhydropho-

bic surfaces. First, asperities must have a high aspect ratio to provide a high surface

area. Second, sharp edges should be avoided, to prevent pinning of the triple line.

Third, asperities should be tightly packed to minimize the distance between them

and avoid destabilization of the composite interface. Fourth, asperities should be

small compared to typical droplet size (on the order of few hundred microns or

larger). And ﬁfth, in the case of hydrophilic surfaces, a hydrophobic ﬁlm must be

applied in order to have initial θ>90

◦

. These recommendations can be utilized for

1256 Bharat Bhushan

Liquid

Solid

Air

Liquid

Solid

Air

Fig. 22.38. (a) Formation

of a composite solid–liquid–

air interface for sawtooth

and smooth proﬁles, and

(b) destabilization of the

composite interface for the

sawtooth and smooth pro-

ﬁles due to dynamic eﬀects.

The dynamic contact angle

>θ

corresponds to an ad-

vancing liquid–air interface,

whereas θ

<θ

corresponds

to a receding interface [176]

Hemispherically topped

cylindrical asperities

Hemispherically topped

pyramidal asperities

Fig. 22.39. Optimized rough-

ness distribution – hemispher-

ically topped cylindrical as-

perities and pyramidal asper-

ities with square foundation

and rounded tops. The square

base gives a higher packing

density but introduces unde-

sirable sharp edges [173]

producingsuperhydrophobicsurfaces. Remarkably,all theseconditions are satisﬁed

by biologicalwater-repellentsurfaces,such as some leaves:they have tightly packed

hemispherically topped papillae with high (on the order of unity) aspect ratios and

a wax coating [173]. Figure 22.39 shows two recommended geometries which use

either hemispherically topped asperities with a hexagonal packing pattern or pyra-

midal asperities with a rounded top. These geometries can be used for producing

superhydrophobicsurfaces.

22.5.2 Experimental Validation

To validate the model of contact angle as a function of surface roughness, Burton

and Bhushan [177] measured contact angles and adhesive forces on hydrophilic

and hydrophobic polymer ﬁlms with smooth surfaces and with discrete asperities.

PMMA was chosen because it is a polymer often used in BioMEMS/BioNEMS

devices. Three types of surface structures were measured: ﬁlm, low-aspect-ratio as-

perities (LAR, 1:1 height-to-diameter ratio) and high-aspect-ratio asperities (HAR,

3:1 height-to-diameter ratio). Roughness (σ) and peak-to-valley distance (P–V) for

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1257

PMMA ﬁlm was measured using an AFM with values σ = 0.98nm and P−−V =

7.3 nm. The diameter of the asperities near the top is approximately 100nm and the

pitch of the asperities (distance between each asperity) is approximately 500nm.

Figure 22.40a showsSEM images of the two types of patterned structures, LAR and

HAR, on a PMMA surface. According to the model presented earlier, by introduc-

ing roughness to a ﬂat surface, the hydrophobicity will either increase or decrease

depending on the initial contact angle on a ﬂat surface. The material chosen was

initially hydrophilic, so to obtain a sample that is hydrophobic, a self-assembled

monolayer (SAM) was deposited on the sample surfaces. The samples chosen for

the SAM deposition were the ﬂat ﬁlm and the HAR for each polymer. The SAM per-

ﬂuorodecyltriethoxysilane (PFDTES) was deposited on the polymer surface using

a vapor-phase deposition technique. PFDTES was chosen because of the hydropho-

bic nature of the surface. It should be noted that the bumps should be as close as

possible to provide a high surface area. In order to beneﬁt from an increase in con-

tact angle and decrease in contact area with an increase in surface roughness, the

pitch of the bumps should be smaller than the water droplet and the size of the

contacting body.

To study the eﬀect of scale dependence, the adhesive force between the four

AFM tips with ﬂat and patterned polymer ﬁlms was examined. This allowed for

complete characterization of the adhesive force of the patterned surfaces with vary-

PMMA sample surface microfabricated with asperities

20nm

3.8μm

15μm

200nm

PIMMA low aspect ratio (LAR)

PIMMA high aspect ratio (HAR)

1μm

Fig. 22.40. (a)SEMmi-

crographs of the patterned

polymer surfaces. Both LAR

and HAR are shown at two

magniﬁcations to see both

the asperity shape and the

asperity pattern on the sur-

face. (b) Cartoon showing the

eﬀect of diﬀerent radii on the

patterned surface. Small radii

can ﬁt between asperities,

while large radii rest on top

of the asperities

1258 Bharat Bhushan

ing tip radii. Figure 22.40b is a cartoon showing the eﬀect of the diﬀerent radii on

the patterned surface. For small radii, such as the 20nm and 50 nm tips used in this

experiment, the tip can easily ﬁt between the asperities and therefore, there is less

eﬀect from the asperities. The 3.8-µm- and 15-µm-radii tips will primarily sit on

the asperities and will not come into contact with the ﬂat polymer, thus reducing

the real area of contact. Experiments in varying relative humidities show the depen-

dence of hydrophobicityfor a givensurfaceroughness on adhesionand friction. Dry

and wet friction and adhesion can vary dramatically because the dominant mechan-

ism makes a transition from the real area of contact to meniscus forces. Therefore,

the eﬀect of relative humidity was also studied by performing measurements at 5,

50, and 80% relative humidity (RH). For these experiments, a tip of radius 15µm

was used to measure both adhesion and coeﬃcient of friction for both the ﬁlm and

patterned polymer surfaces along with the surfaces with the PFDTES coating. Both

LAR and HAR were studied to determine the eﬀect of a taller asperity on adhesion.

Contact Angle Measurements

Figure 22.41 shows the static contact angle for various samples. These values cor-

relate well with the model describing roughness with hydrophobicity. The contact

angle decreased with increased roughnessfor the hydrophilicPMMA ﬁlm. For a hy-

drophobic surface, the model predicts an increase of contact angle with roughness,

which is what happens when PMMA HAR is coated with PFDTES.

Adhesion Studies and Scale Dependence

Scale-dependent eﬀects of adhesion are present because the tip–surface interface

changes with size. Meniscus force will change by varying either the tip radius, the

hydrophobicity of the sample or the number of contact and near-contacting points.

Figure 22.42a shows the dependence of tip radius and hydrophobicity on adhesive

Contact angle (deg)

PMMA

film

PMMA

LAR

PMMA

HAR

PFDTES

on PMMA

film

PFDTES

on PMMA

HAR

100

120

Fig. 22.41. Bar chart showing

the contact angles for diﬀer-

ent materials and for diﬀerent

roughnesses [177]

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1259

force for PMMA and PFDTES coated on PMMA. By changing the radius of the

tip, the contact angle of the sample, and adding asperities to the sample surface, the

adhesive force will change due to the change in the meniscus force and the real area

of contact.

Figure 22.42a shows the adhesive force on a linear scale for the diﬀerent sur-

faces with varying tip radius. The ﬁrst bar chart in Fig. 22.42a has PMMA ﬁlm

for the ﬁrst bar while the second bar is for PFDTES coated on PMMA ﬁlm and

shows the eﬀect of tip radius and hydrophobicity on the adhesive force. For an in-

crease in radius, the adhesive force increases for each material, and decreases for

PFDTES on PMMA ﬁlm compared to PMMA ﬁlm. With larger radius, the real area

of contact and number of meniscus bridges increase and the adhesion is increased.

The hydrophobicityof PFDTES on PMMA ﬁlm reduces meniscus forces, which in

turn reduces the adhesion on the PMMA ﬁlm. The dominant mechanism for the hy-

drophobic ﬁlm is the real area of contact and not the meniscus force, whereas with

PMMA ﬁlm there is a combination of real area of contact and meniscus forces.

The second bar chart in Fig. 22.42a shows the results for PMMA HAR and

PFDTES coated on PMMA HAR. These samples show the same trends as the ﬁlm

Adhesive force (nN)

20 nm

PMMA film

PFDTES on PMMA film

PMMA film and PFDTES on PMMA film and PMMA HAR and PFDTES on PMMA HAR (22°C, 50% RH)

15 μm50 nm 3.8 μm

Tip radius

100

200

300

Adhesive force (nN)

20 nm

PMMA HAR

PFDTES on PMMA HAR

15 μm50 nm 3.8 μm

Tip radius

100

200

300

Adhesive force (nN)

5% RH

PMMA film

PMMA LAR

PMMA HAR

Three PMMA surfaces and a PFDTES coating on two PMMA surfaces (tip radius = 15 μm)

500

Adhesive force (nN)

PFDTES on PMMA film

PFDTES on PMMA HAR

50% RH 80% RH

375

250

125

500

375

250

125

5% RH 50% RH 80% RH

Fig. 22.42. (a) Scale-dependent adhesive force for PMMA ﬁlm versus PFDTES on PMMA

ﬁlm and PMMA HAR versus PFDTES on PMMA HAR (top), and (b)theeﬀect of relative

humidity on the adhesive force for PMMA ﬁlm, LAR and HAR and for PFDTES on PMMA

ﬁlm and HAR [177]

1260 Bharat Bhushan

samples, but the increase in adhesion is not as dramatic. This is because of the de-

crease in real area of contact for each radiusfrom a ﬂat ﬁlm. Again, meniscus forces

do not play a large role in adhesion for PFDTES on PMMA HAR, and the increase

in adhesion is due to the real area of contact. With PMMA HAR, a combination of

both meniscus forces and real area of contact contribute to the adhesion.

Eﬀect of Relative Humidity on Adhesive Force

The results from varying surface roughness, hydrophobicity and relative humidity

are summarizedin Fig. 22.42b.Experimentswere also run on PMMAﬁlm and HAR

with a PFDTES coating and are shown in Fig. 22.42b. Film HAR and LAR were

used to see the change in adhesion for each type of surface structure. Only ﬁlm and

HAR were used for Fig. 22.42b to show the diﬀerence in the two extremes of the

surfaces.For these experiments,only the 15µm tip was used to study the eﬀectfrom

the asperities on the patterned surfaces.

For the adhesive force values, there is a decrease from PMMA ﬁlm to LAR to

HAR for the three humidities. The decrease between LAR and HAR is very small,

which means that the contact area is about the same for a single-point measurement.

There is, however, a large decrease in adhesive force from ﬁlm to LAR and HAR.

For a ﬂat ﬁlm, meniscus bridges are the dominant factor in the adhesion, but for

a patterned sample the dominant factor is still the contact area and not the formation

of menisci. At 5% RH the only factor in the adhesion is the area of contact and not

the formation of menisci. The data shows that there is a smaller diﬀerence at 5% in

adhesion compared to the diﬀerence at 80% RH.

Results for PFDTES coating on PMMA ﬁlm and HAR are also shown in

Fig. 22.42b. The adhesion values are much lower than those for PMMA and PMMA

HAR and that is primarily due to the lack of meniscus bridge formation because of

the hydrophobiccontact angle of PFDTES. There is a decrease in adhesion between

PFDTES ﬁlm and PFDTES HAR, which is directly related to the area of contact

diﬀerence between a ﬁlm and HAR. Looking at the data across the three humidi-

ties, there is not much change in the values. Since the surfaces are hydrophobic,

meniscus bridges are not the determining factor in the material adhesion.

In summary, increasing roughness on a hydrophilic surface decreases the con-

tact angle, whereasincreasing roughnesson a hydrophobicsurface increasescontact

angle. For a ﬂat ﬁlm, with increasing tip radius, the adhesive force increases due to

increased real area of contact between the tip and the ﬂat sample and meniscus force

contributions. Introducing a pattern on a ﬂat polymer surface will reduce adhesion

because of the reduction of the real area of contact between the tip and the sample

surface if the tip is larger than the size of the asperities. In addition, introducing

a pattern on a hydrophobic surface increases the contact angle and decreases the

number of menisci, which then decreases the adhesive force. Adhesion increases

with increasing RH for every sample and decreases from ﬁlm to LAR to HAR.

When PFDTES is coated on the PMMA samples, the adhesion decreases but fol-

lows the same trend as the bare polymer. These trends are due to the formation of

more menisci at higher relative humidities. In addition, with an increase in relative

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1261

humidity, the increase in adhesive force for PMMA ﬁlm is more dramatic than for

the patterned samples due to larger menisci formations for a ﬁlm sample.

22.6 Component-Level Studies

22.6.1 Surface Roughness Studies of Micromotor Components

Most of the friction forces resisting motion in the micromotor are concentrated

near the rotor–hub interface where continuous physical contact occurs. The surface

roughness of the surfaces usually has a strong inﬂuence on the friction character-

istics on the micro/nanoscale. A catalog of roughness measurements on various

components of a MEMS device does not exist in the literature. Using an AFM,

measurements on variouscomponent surfaces, for the ﬁrst time, were made by Sun-

dararajan and Bhushan [178]. Table 22.6 shows various surface roughness param-

eters obtained from 5 ×5 µm scans of the various component surfaces of several

unlubricated micromotors using the AFM in tapping mode. A surface with a Gaus-

sian height distribution should have a skewness of zero and kurtosis of three. Al-

though the rotor and stator top surfaces exhibit comparable roughness parameters,

the underside of the rotors exhibits lower root mean square (RMS) roughness and

peak-to-valley distance values. More importantly, the rotor underside shows nega-

tive skewness and lower kurtosis than the topsides, both of which are conducive to

high real area of contact and hence high friction [79,81]. The rotor underside also

exhibits a higher coeﬃcient of microscale friction than the rotor topside and stator,

as shown in Table 22.6. Figure 22.43 shows representative surface-height maps of

the varioussurfaces ofa micromotormeasured using theAFM in tapping mode.The

Table 22.6. Surface roughness parameters and microscale coeﬃcient of friction for various

micromotor component surfaces measured using an AFM. Mean and ±1σ values are given

RMS

roughness

(nm)

Peak-to-

valley

distance

(nm)

Skewness

Kurtosis

KCoeﬃcient

of microscale

friction

(µ)

Rotor

topside

21±0.6 225±23

1.4±0.30

6.1±1.70.07±0.02

Rotor

underside

14±2.480±11 −1.0±0.22 3.5±0.50 0.11±0.03

Stator

topside

19±1 246±21

1.4±0.50

6.6±1.50.08±0.01

Measured from a tapping-mode AFM scan of size 5 µm×5 µm using a standard Si tip

scanning at 5 µm/s in a direction orthogonal to the long axis of the cantilever.

Measured using an AFM in contact mode at 5 µm×5 µm scan size using a standard

tip scanning at 10 µm/s in a direction parallel to the long axis of the cantilever.

1262 Bharat Bhushan

σ =20 nm, P–V=190 nm σ =19 nm, P–V=156 nm

Substrate

Rotor underside

σ = 13 nm, P–V= 95 nm σ = 11 nm, P–V=100 nm

σ = 14 nm, P–V= 75 nm

σ = 13 nm, P–V= 80 nm

100

05μm

Rotor

Stator

05μm

Rotor underside

Fig. 22.43. Representative AFM surface-height images obtained in tapping mode (5 µ m ×

5 µm scan size) of various component surfaces of a micromotor. RMS roughness and peak-to-

valley values of the surfaces are given. The underside of the rotor exhibits drastically diﬀerent

topography from the topside [178]

rotor underside exhibits a diﬀerent topography from the outer edge to the middle

and inner edge. At the outer edges, the topography shows smaller circular asperi-

ties, similar to the topside. The middle and inner regions show deep pits with ﬁne

edges that may have been created by the etchants used for etching of the sacriﬁcial

layer. It is known that etching can aﬀect the roughness of surfaces in surface micro-

machining. The residence time of the etchant near the inner region is high, which is

responsible for larger pits. Figure 22.44 shows the roughness of the surface directly

beneath the rotors (the base polysilicon layer). There appears to be a diﬀerence in

the roughness between the portion of this surface that was initially underneath the

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1263

20μm

5 μm5

σ = 25 nm, P–V= 184 nm

σ = 8.5 nm, P–V= 59 nm

100 nm

Fig. 22.44. Surface-height

images of polysilicon regions

directly below the rotor.

Region A is away from the

rotor while region B was

initially covered by the rotor

prior to the release etch of the

rotor. During this step, slight

movement of the rotor caused

region B to be exposed [178]

rotor (region B) during fabrication and the portion that was away from the rotor and

hence always exposed (region A). The former region shows a lower roughness than

the latter region. This suggests that the surfaces at the rotor–hub interface that come

into contact at the end of the fabrication process exhibit large real areas of contact,

which result in high friction.

22.6.2 Adhesion Measurements of Microstructures

Surface forceapparatus (SFA) and AFMs are used to measure adhesionon micro- to

nanoscales between two surfaces. In the SFA, adhesion of liquid ﬁlms sandwiched

between two curved and smooth surfaces is measured. In an AFM, as discussed

earlier, adhesion between a sharp tip and the surface of interest is measured. The

propensity for adhesion between two surfaces can be evaluated by studying the

tendency of microstructures with well-deﬁned contact areas, covering a wide of

suspension compliances, to stick to the underlying substrate. The test structures

which have been used include cantilever beam array (CBA) technique with diﬀer-

ent lengths [179–182] and stand-oﬀ multiple dimples mounted on microstructures

with a range of compliances, standing above a substrate [183]. The CBA technique,

more commonly used, utilizes an array of micromachined polysilicon beams (for Si

MEMS applications), on the mesoscopic length scale, anchored to the substrate at

one end and with diﬀerent lengths parallel to the surface. It relies on peeling and

detachment of cantileverbeams. Changes in the free energy or reversible work done