Bhushan B. Nanotribology and Nanomechanics: An Introduction

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1204 Bharat Bhushan

22.1.2 Introduction to NEMS

NEMS are produced by nanomachining in a typical top-down approach (from

large to small) and bottom-up approach (from small to large), largely relying on

nanochemistry (see e.g., [39–45]). The NEMS ﬁeld, in addition to fabrication of

nanosystems, has providedimpetus to the developmentof experimentaland compu-

tation tools. Examples of NEMS include microcantileverswith integratedsharp nan-

otipsfor STMand atomicforce microscopy(AFM) [46,47],quantumcorralsformed

using STM by placing atoms one by one [48], AFM cantilever arrays (Millipede)

fordata storage[49], STM andAFM tips for nanolithography,dip-pen nanolithogra-

phy for printing molecules, nanowires, carbon nanotubes, quantum wires (QWRs),

quantum boxes (QBs), quantum transistors [9], nanotube-based sensors [7,50], bio-

logical (DNA) motors, molecular gears made by attaching benzene molecules to the

outer walls of carbon nanotubes [8], devices incorporating nm-thick ﬁlms [e.g., in

giant-magnetoresistive (GMR) read/write magnetic heads and magnetic media for

magnetic rigid disk and magnetic tape drives], nanopatterned magnetic rigid disks,

and nanoparticles(e.g., nanoparticles in magnetictape substrates and nanomagnetic

particles in magnetic tape coatings) [34,51]. More than 2 billion read/write mag-

netic heads were shipped for magnetic disk and tape drives in 2004.

Nanoelectronics can be used to build computer memory using individual mol-

ecules or nanotubes to store bits of information [52], molecular switches, molecular

or nanotube transistors, nanotube ﬂat-panel displays, nanotube integrated circuits,

fast logic gates, switches, nanoscopic lasers, and nanotubes as electrodes in fuel

cells.

22.1.3 BioMEMS/BioNEMS

BioMEMS/BioNEMS are increasingly used in commercial and defense applica-

tions (see e.g., [53–60]). They are used for chemical and biochemical analyses

(biosensors) in medical diagnostics [e.g., DNA, ribonucleic acid (RNA), proteins,

cells, blood pressure and assays, and toxin identiﬁcation] [60, 61], tissue engi-

neering [62–64], and implantable pharmaceutical drug delivery [65–67]. Biosen-

sors, also referred to as biochips, deal with liquids and gases. There are two

types. A large variety of biosensors are based on micro/nanoﬂuidics [60,68–70].

Micro/nanoﬂuidic devices oﬀer the ability to work with smaller reagent volumes

and shorter reaction times, and perform multiple types of analysis at once. The

second type of biosensors include micro/nanoarrays, which perform one type of

analysis thousands of times [71–74].

A chip, called a lab-on-a-CD, with micro/nanoﬂuidic technology embedded on

the disk can test thousands of biological samples rapidly and automatically [68]).

An entire laboratory can be integrated onto a single chip, called a lab-on-a-chip[60,

69, 70]. Silicon-based disposable blood-pressure sensor chips were introduced in

the early 1990sby GE NovaSensorfor blood-pressuremonitoring (about 25 million

units in 2004). A blood-sugar monitor, referred to as GlucoWatch, was introduced

in 2002. It automatically checks blood sugar every 10minutes by detecting glucose

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1205

through the skin, without having to draw blood. If glucose is out of the acceptable

range, it sounds an alarm so the diabetic can address the problem quickly. A variety

ofbiosensors,manyusingplasticsubstrates,are manufacturedbyvariouscompanies

including ACLARA, Agilent Technologies, Calipertech, and I-STAT.

The second type of biochips – micro/nanoarrays – are a tool used in biotech-

nology research to analyze DNA or proteins to diagnose diseases or discover new

drugs. Also called DNA arrays, they can identify thousand of genes simultane-

ously [56,71]. They include a microarray of silicon nanowires, roughly a few nm in

size, to selectively bind and detect even a single biological molecule such as DNA

or a protein by using nanoelectronics to detect the slight electrical charge caused by

such binding, or a microarray of carbon nanotubes to detect glucose electrically.

After the tragedy of Sept. 11, 2001, concern over biological and chemical war-

fare has led to the developmentof handheld units with bio- and chemical sensorsfor

the detection of biological germs, chemical ornerve agents,and mustard agents,and

chemical precursors to protect subways, airports, water supplies, and the population

at large [75].

BioMEMS/BioNEMS are also being developed for minimal-invasive surgery

including endoscopic surgery, laser angioplasty, and microscopic surgery. Implant-

able artiﬁcial organs can also be produced. Other applications include implantable

drug-deliverydevices– e.g., micro/nanoparticleswith drugmolecules encapsulated

in functionalizedshells for a site-speciﬁc targeting applications, and silicon capsules

with a nanoporous membrane ﬁlled with drugs for long-term delivery [65,76–78]

– nanodevices for sequencing single molecules of DNA in the Human Genome

Project [60], cellular growth using carbon nanotubes for spinal-cord repair, nano-

tubes for nanostructured materials for various applications such as spinal fusion

devices, organ growth, and the growth of artiﬁcial tissues using nanoﬁbers.

22.1.4 Tribological Issues in MEMS/NEMS and BioMEMS/BioNEMS

Tribological issues are important in MEMS/NEMS and BioMEMS/BioNEMS re-

quiring intended and/orunintended relative motion. In these devices, various forces

associated with the device scale down with the size. When the length of the ma-

chine decreases from 1mm to 1µm, the area decreases by a factor of a million and

the volume decreases by a factor of a billion. As a result, surface forces such as

adhesion, friction, meniscus forces, viscous drag forces and surface tension that are

proportional to area, become a thousand times larger than the forces proportional

to the volume, such as inertial and electromagnetic forces. In addition to the con-

sequences of a large surface-to-volume ratio, since these devices are designed for

small tolerances, physical contact becomes more likely, which makes them parti-

cularly vulnerable to adhesion between adjacent components. Slight particulate or

chemical contamination present at the interface can be detrimental. Since the start-

up forces and torques involved in operation that are available to overcome retard-

ing forces are small, the increase in resistive forces such as adhesion and friction

become a serious tribological concern that limits the durability and reliability of

1206 Bharat Bhushan

MEMS/NEMS [13]. A large lateral force required to initiate relative motion be-

tween two surfaces, large static friction, is referred to as stiction, which has been

studied extensively in tribology of magnetic storage systems [34, 46, 47, 79–82].

The source of stiction is generally liquid-mediated adhesion with a source of liq-

uid being process ﬂuid or capillary condensation of water vapor from the environ-

ment. Adhesion, friction/stiction (static friction), wear, and surface contamination

aﬀect MEMS/NEMS and BioMEMS/BioNEMS performance and, in some cases,

can even prevent devices from working. Some examples of devices which experi-

ence tribological problems follow.

MEMS

Figure 22.2a shows examples of several microcomponents that can encounter the

aforementionedtribological problems. The polysilicon electrostatic micromotor has

12 stators and a four-polerotor and is produced by surface micromachining.The ro-

tor diameter is 120µm and the air gap between the rotor and stator is 2µm [83]. It is

capable ofcontinuousrotation up to speedsof 100,000revolutionsperminute(RPM).

The intermittent contacts at the rotor–stator interface and physical contact at the

rotor–hub ﬂange interface result in wear issues, and high stiction between the con-

tacting surfaces limits the repeatability of operation or may even prevent opera-

tion altogether. Next, a bulk micromachined silicon stator/rotor pair is shown with

bladed rotor and nozzle guide vanes on the stator with dimensions of less than

a mm [84,85]. These are being developed for high-temperature micro-gas turbine

engine with rotor diameters of 4–6 mm and operating speed of up to 1 million

RPM (with a sliding velocity in excess of 500m/s, comparable to velocities of

large turbines operating at high velocities) to achieve high speciﬁc power, up to

a total of about 10W. Erosion of blades and vanes, and the design of microbear-

ings required to operate at extremely high speeds used in the turbines are some

of the concerns. Ultra-short high-speed micro hydrostatic gas journal bearings with

a length-to-diameter(L/D) ratio of less than 0.1 are beingdevelopedfor operationat

surface speeds on the order of 500m/s, which oﬀer unique design challenges [86].

In Fig. 22.2a is an SEM micrograph of a surface-micromachinedpolysilicon six-

gear chain from Sandia National Laboratory. (For more examples of an early ver-

sion, see Mehregany et al., [87].) As an example of non-silicon components, a mil-

ligear system produced using the LIGA process (a German acronym for Lithogra-

phie Galvanoformung Abformung) for a DC brushless permanent-magnetmillimo-

tor (diameter = 1.9mm, length = 5.5mm with an integrated milligear box [88–90])

is also shown. The gears are made of metal (electroplated Ni–Fe) but can also be

made from injected polymer materials [e.g., polyoxy-methylene (POM)] using the

LIGA process. Even though the torque transmitted at the gear teeth is small, on the

order of a fraction of a nN/m, because of the small dimensions of gear teeth, the

bending stresses are large where the teeth mesh. Tooth breakage and wear at the

contact of gear teeth is a concern.

Figure 22.2b shows a polysilicon, multiple-microgear speed-reduction unit and

its components after laboratory wear tests conducted for 600,000 cycles at 1.8%

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1207

Electrostatic micromoter [83] Microturbine bladed rotor and

nozzle guide vanes on the stator [84]

Six gear chain (www.sandia.gov)

Ni-Fe Wolfrom-type gear system

by LIGA [88]

2 mm

100μm

10μm

1μm

20μm

Multiple

microgear

speed reduction

unit [91]

Pinhole

Clip

Hub

Gap

50μm

Fig. 22.2a,b. Examples of MEMS devices and components that experience tribological

problems: (a) several microcomponents, and (b) a polysilicon, multiple-microgear speed-

reduction unit after laboratory wear testing for 600,000 cycles at 1.8% relative humidity

1208 Bharat Bhushan

RH [91]. These units have been developed for electrostatically driven microactuator

(microengine) developed at Sandia National Laboratory for operation in the kHz

frequency range [92]. Wear of various components is clearly observed in the ﬁgure.

Humidity was shown to be a strong factor in the wear of rubbing surfaces. In order

to improve the wear characteristics of rubbing surfaces, 20-nm-thick tungsten (W)

coating deposited at 450

◦

C using the chemical vapor deposition (CVD) technique

was used[93].Tungsten-coatedmicroenginestested forreliability showedimproved

wear characteristics with longer lifetimes than polysilicon microengines. However,

these coatings have poor yield. Instead, vapor-depositedself-assembled monolayers

of ﬂuorinated (dimethylamino) silane are used [94]. They can be deposited with

high yield, although durability is not as good.

Figure 22.3 shows a micromachined ﬂow modulator; several micromachined

ﬂowchannelsare integratedin series with electrostaticallyactuated microvalves[95].

The ﬂow channels lead to a central gas outlet hole drilled in the glass substrate. Gas

enters the device through a bulk-micromachined gas inlet hole in the silicon cap.

Silicon

cap

Gas

inlet

Beam Flow

channel

Pressure

sensor

Gas

oulet

Sense

plate

Gas

oulet

Metal pull-down

plate

Slider

Spring

Suspension

Electrostatic

actuator (nickel)

SuspensionSilicon

substrate

Fixed

Suspended

Fig. 22.3a,b. Examples of

MEMS devices that experi-

ence tribological problems:

(a) Low pressure ﬂow mod-

ulator with electrostatically

actuated microvalves [95]

(b) Electroplated-nickel ro-

tary microactuator for mag-

netic disc drives [37]

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1209

The gas, after passing through an open microvalve, ﬂows parallel to the glass sub-

strate through ﬂow channels and exits the device through an outlet. The normally

open valve structure consists of a freestanding double-end-clamped beam, which is

positioned beneath the gas inlet oriﬁce. When electrostatically deﬂected upwards,

the beam seals against the inlet oriﬁce and the valve is closed. In these microvalves

used for ﬂow control, the mating valve surfaces should be smooth enough to seal

while maintaining a minimum roughness to ensure low adhesion [79–81,96].

A second MEMS device, shown in Fig. 22.3, is an electrostatically driven

rotary microactuator for a magnetic disk drive, surface-micromachined by a mul-

tilayer electroplating method [37]. This high-bandwidth servo-controlled microac-

tuator, located between a slider and a suspension is being developed for ultrahigh-

track-density applications, serves as the ﬁne-position and high-bandwidth control

element of a two-stage, coarse/ﬁne servo system when coupled with a conventional

actuator [36,37]. A slider is placed on top of the central block of a microactuator,

which gives rotational motion to the slider. The bottom of the silicon substrate is

attached to the suspension. The radial ﬂexure beams in the central block give the

rotational freedom of motion to the suspended mass (slider), and the electrostatic

actuator drives the suspended mass. Actuation is accomplished via interdigitated,

cantilevered electrode ﬁngers, which are alternatingly attached to the central body

of the moving part and to the stationary substrate to form pairs. A voltage applied

across these electrodes results in an electrostatic force, which rotates the central

block. The inter-electrode gap width is about 2 µm. Any unintended contacts be-

tween the moving and stationary electroplated-nickel electrodes may result in wear

and stiction.

Commercially available MEMS devices also exhibit tribological problems. Fig-

ure 22.4 shows an integrated capacitive-type silicon accelerometer fabricated using

surface micromachining by Analog Devices, with dimensions of a couple of mil-

limeters, which is used for deploymentof airbags in automobiles, and more recently

forvariousother consumerelectronicsmarkets[21,97].The central suspendedbeam

mass (about0.7µg) is supportedon the fourcorners byspringstructures.The central

beam has interdigitated cantilevered electrode ﬁngers (about 125µm long and 3µm

thick) on all four sides that alternate with those of the stationary electrode ﬁngers

as shown, with a gap of about 1.3µm. Lateral motion of the central beam causes

a change in the capacitance between these electrodes, which is used to measure the

acceleration. Here stiction between the adjacent electrodes as well as stiction of the

beam structure with the underlying substrate are detrimental to the operation of the

sensor [21,97]. Wear during unintended contacts of these polysilicon ﬁngers is also

a problem.A molecularlythick diphenylsiloxane lubricantﬁlm with high resistance

to temperature and oxidation applied by a vapor deposition process is used on the

electrodes to reduce stiction and wear [98].For deposition, a small amount of liquid

is dispensed into each package before it is sealed. As the package is heated in the

furnace, the liquid evaporates and coats the sensor surface. As sensors are required

to sense low-g accelerations, they need to be more compliant and stiction becomes

an even bigger concern.

1210 Bharat Bhushan

Sensing

diaphram

Protective polymer gel

Die-attach polymer adhesive

Print plane

Nozzle layer

Refill region Bubble

Barrier layer

To intimate

electronics

Heater

Si heater substrate

Ink

To ink supply

Applied pressure

Supporting

springs

Suspended

mass

Stationary

plates

Suspended

mass

Stationary

plates

a) b)

Fig. 22.4a–c. Examples of MEMS devices having commercial use that experience tribolog-

ical problems. (a) Capacitive type silicon accelerometer for automotive sensory applica-

tions [97] (b) Piezoresistive type pressure sensor [101] (c) Thermal inkjet printhead [25]

Figure 22.4 also shows a cross-sectional view of a typical piezoresistive-type

pressure sensor, which is used for various applications including manifold absolute

pressure (MAP), and tire-pressure measurements, and disposable blood-pressure

measurements. The sensing material is a diaphragm formed on a silicon substrate,

which bends with applied pressure [99]. The deformation causes a change in the

band structure of the piezoresistors that are placed on the diaphragm, leading to

a change in the resistivity of the material. The MAP sensors are subjected to dras-

tic conditions - extreme temperatures, vibrations, sensing ﬂuid, and thermal shock.

Fluid under extreme conditions could cause corrosive wear. Fluid cavitation could

cause erosive wear. The protective gel encapsulent generally used can react with

the sensing ﬂuid and result in swelling or dissolution of the gel. Silicon cannot de-

form plastically, therefore any pressure spikes leading to deformation past its elastic

limit will result in fracture and crack propagation. Pressure spikes could also cause

the diaphragm to delaminate from the support substrate. Finally, cyclic loading of

diaphragm during use can lead to fatigue and wear of silicon diaphragm or delami-

nation.

The bottom schematic in Fig. 22.4 shows a cross-sectional view of a thermal

printhead chip (on the order 10–50 cm

in volume) used in inkjet printers [25].

They consist of a supply of ink and an array of elements with microscopic heating

resistors on a substrate mated to a matching arrayof ink-injection oriﬁces or nozzles

(about 70µm in diameter) [23,24,26]. In each element, a small chamber is heated

by the resistor, where a brief electrical impulse vaporizes part of the ink and creates

a tiny bubble. The heaters operate at several kHz, and are therefore capable of high-

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1211

speed printing. As the bubble expands, some of the ink is pushed out of the nozzle

onto the paper. When the bubble pops, a vacuum is created and this causes more

ink from the cartridge to move into the printhead. Clogged ink ports are the major

failure mode. There are also various tribological concerns [23]. The surface of the

printhead where the ink is shot out towards the paper can become scratched and

damaged as a result of countless trips back and forth across the pages, which are

somewhat rough. As a result of repeated heating and cooling, the heated resistors

expand and contract. Over time, these elements will experience fatigue and may

eventually fail. Bubble formation in the ink reservoir can lead to cavitation erosion

of the chamber,which occurs whenbubblesformed in the ﬂuidbecome unstableand

implode against the surface of the solid and apply impact energy on that surface.

Fluid ﬂow through nozzles may cause erosion and ink particles may also cause

abrasive wear. Corrosion of the ink reservoir surfaces can also occur as a result of

exposure of the ink to high temperatures as well as due to ink pH. The substrate

of the chip consists of silicon with a thermal barrier layer followed by thin ﬁlm of

resistive material and then conducting material. The conductor and resister layers

are generally protected by an overcoat layer of a plasma-enhanced chemical vapor

deposition (PECVD) α-SiC : H layer, which is 200–500nm thick [100].

Figure 22.5 shows two digital micromirror device (DMD) pixels used in digi-

tal light processing (DLP) technology for digital projection displays in computer

projectors, high-deﬁnition television (HDTV) sets, and movie projectors [27–29].

The entire array (chip set) consists of a large number of rotatable aluminium alloy

micromirrors (digital light switches) which are fabricated on top of a complemen-

tary metal–oxide–semiconductor(CMOS) static random-access memory integrated

circuit. The surface-micromachined array consists of half of a million to more than

two million of these independently controlled reﬂective, micromirrors (mirror size

on the order of 12µm square and 13µ m pitch) which ﬂip backward and forward at

a frequency on the order of 5000–7000 times a second, as a result of electrostatic

attraction between the micromirror structure and the underlying electrodes. For the

binary operation,micromirror/yokestructure mountedon torsional hingesis rotated

±10

◦

(with respect to the horizontal plane), and is limited by a mechanical stop.

Contact between the cantilevered spring tips at the end of the yoke (four present on

each yoke) with the underlying stationary landing sites is required for true digital

(binary) operation. Stiction and wear during contact between the aluminium alloy

spring tips and landing sites, hinge memory (metal creep at high operating tempera-

tures), hinge fatigue, shock and vibration failure, and sensitivity to particles in the

chip package and operating environment are some of the important issues aﬀecting

the reliable operation of a micromirror device [102–104]. Self-assembled monolay-

ers of a fatty acid – perﬂuorodecanoic acid (PFDA) – applied by a vapor deposition

process is used on the surfaces of the tip and landing sites to reduce stiction and

wear [105,106].However, these ﬁlms are susceptibleto moisture, and to keep mois-

ture out and create a background pressure of PFDA, hermetic chip packages are

used. The spring tip is used in order to use the stored spring energy to pop up the tip

during pull-oﬀ. A lifetime estimate of over one hundred thousand operating hours

1212 Bharat Bhushan

Side view

Highly resistive substrate

Off-state

“large” C

Highly resistive substrate

On-state

“small” C

Top view

GND

RF out

RF in

Flexible

metal bridge

Signal

line

Dielectric

GND

Out

Mirror

Part

Electro-

static

Part

Electrostatic

force

Torsion torque

CMOS

substrate

Mirror –10 deg

Mirror +10 deg

Hinge

Yoke

Landing site

Spring tip

Hinge Yoke

Tip

Landing site

Out

Digital micromirror device for displays (Hornbeck [52.33])

Digital micromirror

device for displays

(Hornbeck [52.33])

Mirror-based optical microswitch (Suzuki, 2002)RF Microswitch (Courtesy IMEC, Belgium)

Fig. 22.5. Examples of MOEMS and RF-MEMS devices having commercial use that experi-

ence tribological problems

with no degradation in image quality is the norm. At a mirror modulationfrequency

of 7kHz, each micromirror element needs to switch about 2.5 trillion cycles.

Figure 22.5 also shows a schematic of an electrostatically actuated capacitive-

type RF microswitch for switching of RF signals at microwave and low frequen-

cies [107]. It is a membrane type and consists of a ﬂexible metal (Al) bridge that

spans the RF transmission line in the center of a coplanar waveguide. When the

bridge is up, the capacitance between the bridge and RF transmission line is small

and the RF signal passes without much loss. When a DC voltage is applied between

the RF transmission line and the bridge, the latter is pulled down until it touches

a dielectric isolation layer. The large capacitance thus created shorts the RF sig-

nal to the ground. The failure modes include creep in the metal bridge, fatigue of

the bridge, charging and degradation of the dielectric insulator, and stiction of the

bridge to the insulator [30,107]. The stiction occurs due to capillary condensation

of water vapor from the environment, van der Waals forces, and/or charging ef-

fects. If the restoring force in the bridge of the switch is not large enough to pull

the bridge up again after the actuation voltage has been removed, the device fails

due to stiction. Humidity-induced stiction can be avoided by hermetically sealing

22 Characterization of MEMS/NEMS and BioMEMS/BioNEMS 1213

the microswitch. Some roughness of the surfaces reduces the probability of stiction.

Selected actuation waveforms can be used to minimize charging eﬀects.

The bottom schematic of Fig. 22.5 shows an electrostatically actuated mirror-

based optical microswitch or attenuator [30]. It is acantilever type and uses a hinged

mirror which rotates to reﬂect light from one (in) ﬁber to another (out) ﬁber. It can

either change light intensity or can be used as an on/oﬀ switch when the deﬂection

angle of the reﬂective mirror is adjusted. A voltage is applied which creates an

electrostatic force that pulls the mirror down until electrical contact is made. The

primary source of failure arises from the rubbing present in the hinge, leading to

wear issues. Failure in the hinge can occur either by mechanical drift due to wear

or complete fracture. Stiction is a major concern after the mirror is kept in contact

with the electrode underneath [30]. The dynamic impact of repeated contacts may

lead to subsurface fatigue [108]. Bumps are placed on the mirror surface facing the

electrode underneath in order to minimize the contact area and stiction. Lubricants

are also used to reduce stiction.

NEMS

Figure 22.6 shows an AFM-probe-based nanoscale data-storage system for ultra-

high-density recording, which experiences tribological problems [49]. The system

uses arrays of 1024 silicon microcantilevers (“Millipede”) for thermomechanical

recording and playback on a polymer [polymethyl methacrylate (PMMA)] medium

about 40nm thick with a harder Si substrate. The cantilevers consist of integrated

tip heaters with tips of nanoscale dimensions. (Sharp tips themselves are also exam-

ple of NEMS.) Thermomechanical recording is a combination of applying a local

force to the polymer layer and softening it by local heating. The tip, heated to about

400

◦

C, is brought into contact with the polymer for recording. Reading is done

using the heater cantilever, originally used for recording, as a thermal read-back

sensor by exploiting its temperature-dependent resistance. The principle of thermal

sensing is based on the fact that the thermal conductivitybetween the heater and the

storage substrate changes according to the spacing between them. When the spacing

between the heater and sample is reduced as the tip moves into a bit, the heater’s

temperature and hence its resistance will decrease. Thus, changes in temperature of

the continuously heated resistor are monitored while the cantilever is scanned over

data bits, providing a means of detecting the bits. Erasing for subsequent rewriting

is carried out by thermal reﬂow of the storageﬁeld by heating the medium to 150

◦

for a few seconds. The smoothness of the reﬂown medium allows multiple rewriting

of the same storage ﬁeld. Bit sizes in the range 10–50 nm have been achieved by us-

ing a 32×32 (1024) array write/read chip (3 mm×3mm). It has been reported that

tip wear occurs due to contact between the tip and the Si substrate during writing.

Tip wear is considered a major concern for device reliability.

In magnetic data storage, magnetic recording is accomplished by relative mo-

tion between the magnetic head slider and a magnetic rigid disk [34]. Magnetic

rigid disks and heads used today for magnetic data storage consist of one- to a few-

nm-thick nanostructured ﬁlms. Figure 22.7a shows the sectional view of a conven-