Bhushan B. Nanotribology and Nanomechanics: An Introduction

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Nanomechanical Properties of Solid Surfaces

andThinFilms

Adrian B. Mann

Summary. Instrumentation for the testing of mechanical properties on the submicron scale

has developed enormously in recent years. This has enabled the mechanical behavior of sur-

faces, thin ﬁlms, and coatings to be studied with unprecedented accuracy. In this chapter,

the various techniques available for studying nanomechanical properties are reviewed with

particular emphasis on nanoindentation. The standard methods for analyzing the raw data

obtained using these techniques are described, along with the main sources of error. These

include residual stresses, environmental eﬀects, elastic anisotropy, and substrate eﬀects. The

methods that have been developed for extracting thin-ﬁlm mechanical properties from the

often convoluted mix of ﬁlm and substrate properties measured by nanoindentation are dis-

cussed. Interpreting the data is frequently diﬃcult, as residual stresses can modify the contact

geometry and, hence, invalidate the standard analysis routines. Work hardening in the de-

formed region can also result in variations in mechanical behavior with indentation depth.

A further unavoidable complication stems from the ratio of ﬁlm to substrate mechanical

properties and the depth of indentation in comparison to ﬁlm thickness. Even very shallow

indentations may be inﬂuenced by substrate properties if the ﬁlm is hard and very elastic but

the substrate is compliant. Under these circumstances nonstandard methods of analysis must

be used. For multilayered systems many diﬀerent mechanisms aﬀect the nanomechanical be-

havior, including Orowan strengthening, Hall–Petch behavior, image force eﬀects, coherency

and thermal stresses, and composition modulation.

The application of nanoindentation to the study of phase transformations in semicon-

ductors, fracture in brittle materials, and mechanical properties in biological materials are

described. Recent developments such as the testing of viscoelasticity using nanoindentation

methods are likely to be particularly important in future studies of polymers and biologi-

cal materials. The importance of using a range of complementary methods such as electron

microscopy, in situ AFMmaging, acoustic monitoring, and electrical contact measurements

is emphasized. These are especially important on the nanoscale because so many diﬀerent

physical and chemical processes can aﬀect the measured mechanical properties.

12.1 Introduction

When two bodies come into contact their surfaces experience the ﬁrst and usually

largest mechanical loads. Hence, characterizing and understanding the mechanical

608 Adrian B. Mann

properties of surfaces is of paramount importance in a wide range of engineering

applications. Obvious examples of where surface mechanical properties are impor-

tant are in wear-resistant coatings on reciprocating surfaces and hard coatings for

machine tool bits. This chapter details the current methods for measuring the me-

chanical properties of surfaces and highlights some of the key experimental results

that have been obtained.

The experimental technique that is highlighted in this chapter is nanoindenta-

tion. This is for the simple reason that it is now recognized as the preferred method

for testing thin ﬁlm and surface mechanical properties. Despite this recognition,

there are still many pitfalls for the unwary researcher when performing nanoin-

dentation tests. The commercial instruments that are currently available all have

attractive, user-friendly software, which makes the performance and analysis of

nanoindentation tests easy. Hidden within the software, however, are a myriad of

assumptions regarding the tests that are being performed and the material that is

being examined. Unless the researcher is aware of these, there is a real danger that

the results obtainedwill say more about the analysis routines than they do about the

material being tested.

12.2 Instrumentation

The instruments used to examine nanomechanical properties of surfaces and thin

ﬁlms can be split into those based on point probes and those complimentary meth-

ods that can be used separately or in conjunction with point probes. The compli-

mentary methods include a wide variety of techniques ranging from optical tests

such as micro-Raman spectroscopy to high-energy diﬀraction studies using X-rays,

neutrons, or electrons to mechanical tests such as bulge or blister testing.

Point-probe methods have developed from two historically diﬀerent method-

ologies, namely, scanning probe microscopy [1] and microindentation [2]. The two

converge at a length scale between 10–1000nm. Point-probe mechanical tests in

this range are often referred to as nanoindentation.

12.2.1 AFM and Scanning Probe Microscopy

Atomic force microscopy (AFM) and other scanning probe microscopies are cov-

ered in detail elsewhere in this volume, but it is worth brieﬂy highlighting the main

features in order to demonstrate the similarities to nanoindentation. There are now

amyriadofdiﬀerent variantson thebasic scanningprobemicroscope.All usepiezo-

electric stacks to move either a probe tip or the sample with subnanometer precision

in the lateral and vertical planes. The probe itself can be as simple as a tungsten

wire electrochemically polished to give a single atom at the tip, or as complex as

an AFM tip that is bio-active with, for instance, antigens attached. A range of scan-

ning probes have been developed with the intention of measuring speciﬁc physical

properties such as magnetism and heat capacity.

12 Nanomechanical Properties of Solid Surfaces and Thin Films 609

4-quadrant

detector

Laser diode

Cantilever and tip

Fig. 12.1. Diagram of a com-

mercial AFM. The AFM tip

is mounted on a compliant

cantilever, and a laser light

is reﬂected oﬀ the back of

the cantilever onto a position-

sensitive detector (4-quadrant

detector). Any movements

of the cantilever beam cause

a deﬂection of the laser light

that the detector senses. The

sample is moved using piezo-

electric stack, and forces

are calculated from the can-

tilever’s stiﬀness and the

measured deﬂection

To measure mechanical properties with an AFM, the standard conﬁguration is

a hard probe tip (such as silicon nitride or diamond) mounted on a cantilever (see

Fig. 12.1). The elastic deﬂection of the cantilever is monitored either directly or

via a feedback mechanism to measure the forces acting on the probe. In general,

the forces experienced by the probe tip split into attractive or repulsive forces. As

the tip approaches the surface, it experiences intermolecular forces that are attrac-

tive, althoughthey can be repulsiveunder certain circumstances[3]. Once in contact

with the surface the tip usually experiences a combination of attractive intermolec-

ular forces and repulsive elastic forces. Two schools of thought exist regarding the

attractive forces when the tip is in contact with the surface.The ﬁrst is oftenreferred

to as the DMT or Bradley model. It holds that attractive forces only act outside the

region of contact [4–7]. The second theory, usually called the JKR model, assumes

that all the forces experienced by the tip, whether attractive or repulsive, act in the

region of contact [8]. Most real nanoscale contacts lie somewhere between these

two theoretical extremes.

12.2.2 Nanoindentation

The fundamental diﬀerence between AFM and nanoindentation is that during a na-

noindentation experiment an external load is applied to the indenter tip. This load

enables the tip to be pushed into the sample, creating a nanoscale impression on the

surface, otherwise referred to as a nanoindentation or nanoindent.

Conventionalindentation or microindentationtests involve pushing a hard tip of

knowngeometry into the sample surface using a ﬁxed peak load. The area of inden-

tation that is created is then measured, and the mechanical properties of the sample,

in particular its hardness, is calculated from the peak load and the indentation area.

610 Adrian B. Mann

Varioustypes of indentationtestingare used inmeasuring hardness,includingRock-

well, Vickers, and Knoop tests. The geometries and deﬁnitions of hardness used in

these tests are shown by Fig. 12.2.

When indentations are performed on the nanoscale there is a basic problem in

measuring the size of the indents. Standard optical techniques cannot easily be used

to image anything smaller than a micron, while electron microscopy is simply im-

practicaldue to the timeinvolvedin ﬁndingand imagingsmall indents.To overcome

these diﬃculties, nanoindentation methods have been developed that continuously

record the load, displacement, time, and contact stiﬀness throughout the indenta-

tion process. This type of continuously recording indentation testing was originally

developed in the former Soviet Union [9–13] as an extension of microindentation

Ball sizes:

1/2''

1/4''

1/8''

1/16''

Rockwell hardness

10 kgf minor load

Vickers hardness

10 kgf minor load60 kgf, 100 kgf, 150 kgf

Major loads:

= Load (kgf)/Impression area (mm

)

Load (kgf)

Bottom

view

Side view

Knoop hardness

KHN = 14,229 u Load (gf) / Length

(μm)

Load (kgf)

136q

Length (μm)

Side views

Bottom view

130q

172q 30’

Fig. 12.2. (a) The standard Rockwell hardness test involves pushing a ball into the sample

with a minor load, recording the depth, d

, then applying a major load and recording the

depth, d

, then returning to the lower load and recording the depth, d

. Using the depths, the

hardness is calculated. (b) Vickers hardness testing uses a four-sided pyramid pushed into the

sample with a known load. The area of the resulting indentation is measured optically and

the hardness calculated as the load is divided by area. (c) Knoop indentation uses the same

deﬁnition of hardness as the Vickers test, load divided by area, but the indenter geometry has

one long diagonal and one short diagonal

12 Nanomechanical Properties of Solid Surfaces and Thin Films 611

tests. It was applied to nanoscale indentation testing in the early 1980s [14, 15],

hence, giving rise to the ﬁeld of nanoindentation testing.

In general, nanoindentation instruments include a loading system that may be

electrostatic, electromagnetic, or mechanical, along with a displacement measuring

system that may be capacitive or optical. Schematics of several commercial nanoin-

dentation instruments are shown in Fig. 12.3a–c.

Among the many advantages of nanoindentationover conventionalmicroinden-

tation testing is the ability to measure the elastic, as well as the plastic properties of

the test sample. The elastic modulus is obtained from the contact stiﬀness (S )using

the following equation that appears to be valid for all elastic contacts [16,17]:

S =

√

A . (12.1)

Loading coil

Capacitive

displacement

plates

Support

springs

Permanent

magnet

Sample

Loading coil

and magnets

Indenter shaft

“Frictionless” pivots

Diamond indenter tip

Diamond

indenter tip

Displacement

and loading

plates

Diamond indenter

Capacitive Plates

Sample

Fig. 12.3. Schematics of three

commercial nanoindentation

devices made by (a)MTS

Nanoinstruments, Oak Ridge,

Tennessee, (b) Hysitron Inc.,

Minneapolis, Minnesota, (c)

Micro Materials Limited,

Wrexham, UK. Instruments

and use electromagnetic

loading, while uses electro-

static loads

612 Adrian B. Mann

A is the contact area and E

is the reduced modulus of the tip and sample as given

by:



1−ν





1−ν



, (12.2)

where E

, ν

and E

, ν

are the elastic modulus and Poissons ratio of the tip and

sample, respectively.

12.2.3 Adaptations of Nanoindentation

Several adaptations to the basic nanoindentation setup have been used to obtain ad-

ditional information about the processes that occur during nanoindentation testing,

for example, in situ measurements of acoustic emissions and contact resistance. En-

vironmental control has also been used to examine the eﬀects of temperature and

surface chemistry on the mechanical behavior of nanocontacts. In general, it is fair

to say that the more informationthat can be obtained and the greaterthe control over

the experimental parameters the easier it will be to understand the nanoindentation

results. Load-displacement curves provide a lot of information, but they are only

part of the story.

During nanoindentation testing discontinuities are frequently seen in the load–

displacement curve. These are often called “pop-ins” or “pop-outs”, depending on

their direction. These sudden changes in the indenter displacement, at a constant

load (see Fig. 12.4), can be caused by a wide range of events, including fracture,

delamination, dislocation multiplication, or nucleation and phase transformations.

To help distinguish between the various sources of discontinuities, acoustic trans-

ducers have been placed either in contactwith the sample or immediately behind the

indenter tip. For example, the results of nanoindentation tests that monitor acoustic

emissions have shown that the phase transformations seen in silicon during nanoin-

dentation are not the sudden events that they would appear to be from the load–

displacement curve. There is no acoustic emission associated with the pop-out seen

in the unloading curve of silicon [18]. An acoustic emission would be expected if

Load

“pop-in”

“pop-out”

Displacement

Fig. 12.4. Sketch of a load/displacement curve

showing a pop-in and a pop-out

12 Nanomechanical Properties of Solid Surfaces and Thin Films 613

Small hole

Indenter shank

Tungsten wire

(Low stiffness)

Resistance meter

VC tip

Ohmic contact

Fig. 12.5. Schematic of the

basic setup for making con-

tact resistance measurements

during nanoindentation test-

ing

there were a very rapid phase transformation causing a sudden change in volume.

Fracture and delamination of ﬁlms, however, give very strong acoustic signals [19],

but the exact form of the signal appears to be more closely related to the sample

geometry than to the event [20].

Additional information about the nature of the deformed region under the

nanoindentation can be obtained by performing in situ measurements of contact re-

sistance. The basic setup for this type of testing is shown in Fig. 12.5. An electrically

conductive tip is needed to study contact resistance. Consequently, a conventional

diamond tip is of limited use. Elastic, hard, and metallically conductive materials

such as vanadium carbide can be used as substitutes for diamond [21,22], or a thin

conductive ﬁlm (e.g., Ag) can be deposited on the diamond’s surface (such a ﬁlm

is easily transferred to the indented surface so great care must be taken if multiple

indents are performed). Measurements of contact resistance have been most useful

for examining phase transformations in semiconductors [21,22] and the dielectric

breakdown of oxide ﬁlms under mechanical loading [23].

One factor that is all too frequently neglected during nanoindentation testing is

the eﬀect of the experimental environment. Two obvious ways in which the envi-

ronment can aﬀect the results of nanoindentation tests are increases in temperature,

which give elevated creep rates, and condensation of water vapor, which modiﬁes

the tip-sample interactions. Both of these environmental eﬀects have been shown

to signiﬁcantly aﬀect the measured mechanical properties and the modes of defor-

mation that occur during nanoindentation [24–27]. Other environmental eﬀects, for

instance, those due to photoplasticity or hydrogen ion absorption, are also possible,

but they are generally less troublesome than temperature ﬂuctuations and variations

in atmospheric humidity.

12.2.4 Complimentary Techniques

Nanoindentationtesting is probablythe most important techniquefor characterizing

the mechanical properties of thin ﬁlms and surfaces, but there are many alternative

or additional techniques that can be used. One of the most important alternative

614 Adrian B. Mann

Michelson

interferometer

Pressure sensor

Sample geometry

(viewed from below)

Outlet

Syringe

Fig. 12.6. Schematic of the

basic setup for bulge testing.

The sample is prepared so

that it is a thin membrane,

and then a pressure is applied

to the back of the membrane

to make it bulge upwards.

The height of the bulge is

measured using an interfer-

ometer

methods for measuring the mechanical properties of thin ﬁlms uses bulge or blister

testing [28]. Bulge tests are performed on thin ﬁlms mounted on supporting sub-

strates. A small area of the substrate is removed to give a window of unsupported

ﬁlm. A pressure is then applied to one side of the window causing it to bulge. By

measuring the height of the bulge, the stress-strain curve and the residual stress are

obtained. The basic conﬁguration for bulge testing is shown in Fig. 12.6.

12.2.5 Bulge Tests

The original bulge tests used circular windows because they are easier to ana-

lyze mathematically, but now square and rectangular windows have become com-

mon [29]. These geometries tend to be easier to fabricate. Unfortunately, there are

several sources of errors in bulge testing that can potentially lead to large errors in

the measured mechanical properties. These errors at one time led to the belief that

multilayerﬁlms can showa “supermodulus”eﬀect, wherethe elastic modulusof the

multilayer is several times that of its constituent layers [30]. It is now accepted that

any enhancement to the elastic modulus in multilayer ﬁlms is small, on the order of

15% [31].The main sourcesof error stem fromcompressivestresses in the ﬁlm(ten-

sile stress is not a problem), small variations in the dimensions of the window, and

uncertainty in the exact height of the bulge. Despite these diﬃculties, one advantage

of bulge testing over nanoindentationtesting is that the stress state is biaxial, so that

only properties in the plane of the ﬁlm are measured. In contrast, nanoindentation

testing measures a combination of in-plane and out-of-planeproperties.

12.2.6 Acoustic Methods

Acoustic and ultrasonic techniques have been used for many years to study the elas-

tic properties of materials. Essentially, these techniques take advantage of the fact

12 Nanomechanical Properties of Solid Surfaces and Thin Films 615

that the velocity of sound in a material is dependent on the inter-atomic or inter-

molecular forces in the material. These, of course, are directly related to the mate-

rial’s elastic constants. In fact, any nonlinearity of inter-atomic forces enables slight

variations in acoustic signals to be used as a measure of residual stress.

An acoustic method ideally suited to studying surfaces is scanning acoustic mi-

croscopy (SAM) [32]. There are also several other techniques that have been used

to study surface ﬁlms and multilayers, but we will ﬁrst consider SAM in detail. In

a SAM, a lens made of sapphire is used to bring acoustic waves to focus via a cou-

pling ﬂuid on the surface. A small piezoelectric transducer at the top of the lens

generates the acoustic signal. The same transducer can be used to detect the signal

when the SAM is used in reﬂection mode. The use of a transducer as both gener-

ator and detector, a common imaging mode, necessitates the use of a pulsed rather

than a continuous acoustic signal. Continuous waves can be used if phase changes

are used to build up the image. The transducer lens generates two types of acoustic

waves in the material: longitudinal and shear. The ability of a solid to sustain both

types of wave (liquids can only sustain longitudinal waves) gives rise to a third type

of acoustic wave called a Rayleigh, or surface, wave. These waves are generated as

a result of superposition of the shear and longitudinal waves with a common phase

velocity. The stresses and displacements associated with a Rayleigh wave are only

of signiﬁcance to a depth of ≈ 0.6 Rayleigh wavelengths below the solid surface.

Hence, using SAM to examine Rayleigh waves in a material is a true surface char-

acterization technique.

Using a SAM in reﬂection mode gives an image where the contrast is directly

related to the Rayleigh wave velocity, which is in turn a function of the material’s

elastic constants.The resolution of the image depends on the frequencyof the trans-

ducer used, i.e., for a 2GHz signal a resolution better than 1µm is achievable. The

contrast in the image results from the interference of two diﬀerent waves in the cou-

pling ﬂuid. Rayleigh waves that are excited in the surface “leak” into the coupling

ﬂuid and interfere with the acoustic signal that is directly reﬂected back from the

surface. It is usually assumed that the properties of the coupling ﬂuid are well char-

acterized. The interference of the two waves gives a characteristic V(z)curve,as

illustrated by Fig. 12.7, where z is the separation between the lens and the surface.

Analyzing the periodicity of the V(z) curves provides information on the Rayleigh

wave velocity. As with other acoustic waves, the Rayleigh velocity is related to the

elastic constants of the material. When using the SAM for a material’s characteri-

zation, the lens is usually held in a ﬁxed position on the surface. By using a lens

designed speciﬁcally to give a line-focus beam, rather than the standard spherical

lens, it is possible to use SAM to look at anisotropy in the wave velocity [33] and

hence in elastic properties by producing waves with a speciﬁc direction.

One advantage of using SAM in conjunction with nanoindentationto character-

ize a surfaceis that the measurements obtainedwith the two methods have a slightly

diﬀerent dependence on the test material’s elastic properties, E

and ν

(the elastic

modulus and Poisson’s ratio). As a result, it is possible to use SAM and nanoinden-