Bhushan B. Nanotribology and Nanomechanics: An Introduction

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13 Computer Simulations of Nanometer-Scale Indentation and Friction 737

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Mechanical Properties of Nanostructures

Bharat Bhushan

Summary. Structural integrity is of paramount importance in all devices. Load applied dur-

ing the use of devices can result in component failure. Cracks can develop and propagate

under tensile stresses, leading to failure. Knowledge of the mechanical properties of nano-

structures is necessary for designing realistic MEMS/NEMS and BioMEMS/BioNEMS de-

vices. Elastic and inelastic properties are needed to predict deformation from an applied load

in the elastic and inelastic regimes, respectively. The strength property is needed to predict

the allowable operating limit. Some of the properties of interest are hardness, elastic modulus,

bending strength, fracture toughness and fatigue strength. Many of the mechanical properties

are scale dependent therefore these should be measured at relevant scales. Atomic force mi-

croscopy and nanoindenters can be used satisfactorily to evaluate the mechanical properties

of micro/nanoscale structures.

Commonly used materials in MEMS/NEMS are single-crystal silicon and silicon-based

materials, e.g., SiO

and polysilicon ﬁlms deposited by low-pressure chemical vapor depo-

sition. An early study showed silicon to be a mechanically resilient material in addition to

its favorable electronic properties. Single-crystal SiC deposited on large-area silicon sub-

strates is used for high-temperature micro/nanosensors and actuators. Amorphous alloys can

be formed on both metal and silicon substrates by sputtering and plating techniques, provid-

ing more ﬂexibility in surface-integration. Electroless deposited Ni–P amorphous thin ﬁlms

have been used to construct microdevices, especially using the so-called LIGA techniques.

Micro/nanodevices need conductors to provide power, as well as electrical/magnetic signals

to make them functional. Electroplated gold ﬁlms have found wide applications in electronic

devices because of their ability to make thin ﬁlms and process simply.

Polymers, such as poly (methyl methacrylate) (PMMA) and poly (dimethylsiloxane)

(PDMS) are commonly used in BioMEMS/BioNEMS, such as micro/nanoﬂuidic devices,

because of ease of manufacturing and reduced cost. The use of polymers also oﬀers a wide

range of material properties to allow tailoring of biological interactions for improved bio-

compatibility.

This chapter presents a review of mechanical property measurements on the micro/nano-

scale of various materials of interest and stress and deformation analyses of nanostructures.

742 Bharat Bhushan

14.1 Introduction

Microelectromechanical systems (MEMS) refer to microscopic devices that have

a characteristic length of less than 1 mm but more than 100nm (1µm), and nano-

electromechanical systems (NEMS) refer to nanoscopic devices that have a charac-

teristic length of less than 100nm (or 1µm). These are referred to as an intelligent

miniaturizedsystem comprisingsensing, processing, and/or actuating functions and

combine electrical and mechanical components. The acronym MEMS originated in

the U.S.A. The term commonly used in Europe is microsystem technology (MST)

and in Japan is micromachines. Another term generally used is micro/nanodevices.

MEMS/NEMS terms are also now used in a broad sense and include electrical, me-

chanical, optical, biological, and/or ﬂuidic functions. To put the dimensions in per-

spective, individual atoms are typically fraction of a nanometer in diameter, DNA

molecules are about 2.5nm wide, biological cells are in the range of thousands of

nm in diameter, and human hair is about 75µm in diameter. The mass of a micro-

machined silicon structure can be as low as 1nN and NEMS can be built with mass

as low as 10

−20

N with cross sections of about 10nm. In comparison, the mass of

a drop of water is about 10µN and the mass of an eyelash is about 100nN.

A wide variety of MEMS, including Si-based devices, chemical and biological

sensorsand actuators, and miniaturenon-silicon structures(e.g., devicesmade from

plastics or ceramics) have been fabricated with dimensions in the range of a couple

to a few thousand microns (see e.g., [1–13]). A variety of NEMS have also been

produced (see e.g., [14–19]). MEMS/NEMS technology and fabrication processes

have found a variety of applications in biology and biomedicine, leading to the es-

tablishment of an entirely new ﬁeld known as BioMEMS/BioNEMS [20–28]. The

ability to use micro/nanofabrication processes to develop precision devices that can

interface with biological environments at the cellular and molecular level has led to

advances in the ﬁelds of biosensor technology [27,29–32], drug delivery [33–35],

and tissue engineering [36–38]. The miniaturization of ﬂuidic systems using mi-

cro/nanofabricationtechniqueshas led to newand more eﬃcientdevicesfor medical

diagnosticsand biochemicalanalysis [39]. Largest“killer” industrial applications of

MEMS include accelerometers (over a billion dollars a year in 2004), pressure sen-

sors for manifold absolute pressure sensing for engines (more than 30 million units

in 2004), and tire pressure measurements, inkjet printer heads (more than 500 mil-

lion units in 2004), and digital micromirror devices (about $700 million revenues

in 2004). BIOMEMS and BIONEMS are increasingly used in commercial appli-

cations. Largest applications of BIOMEMS include silicon-based disposable blood

pressure sensor chips for blood pressure monitoring (more than 25 million units in

2004), and a variety of biosensors.

Structuralintegrity is of paramount importance in all devices. Load applied dur-

ing the use of devices can result into component failure. Cracks can develop and

propagateunder tensilestresses leading tofailure [31,40].Friction/stiction and wear

limit the lifetimes and compromise the performance and reliability of the devices

involving relative motion [4, 5,41]. Most MEMS/NEMS applications demand ex-

treme reliability. Stress and deformation analyses are carried out for an optimal de-

14 Mechanical Properties of Nanostructures 743

sign. MEMS/NEMS designers require mechanical properties on the nanoscale. Me-

chanical properties include elastic, inelastic (plastic, fracture or viscoelastic), and

strength. Elastic and inelastic properties are needed to predict deformation from an

applied load in the elastic and inelastic regimes, respectively. The strength property

is needed to predict the allowable operating limit. Some of the properties of inter-

est are hardness, elastic modulus, creep, bending strength (fracture stress), fracture

toughness, and fatigue strength. Micro/nanostructures have some surface topogra-

phy and local scratches dependent upon the manufacturing process. Surface rough-

ness and local scratches may compromise the reliability of the devices and their

eﬀect needs to be studied.

Most mechanical properties are scale dependent [5,40,42]. Several researchers

have measured mechanical properties of silicon and silicon-based milli- to mi-

croscale structures including tensile tests and bending tests [43–52], resonant struc-

ture tests for measurement of elastic properties [53], fracture toughness tests [44,

46,54–58], and fatigue tests [56,59,60].Most recently, few researchers have meas-

ured mechanical properties of nanoscale structures using atomic force microscopy

(AFM) [61,62] and nanoindentation [63–65]. For stress and deformation analyses

of simple geometries and boundary condition, analytical models can be used. For

analysis of complex geometries, numerical models are needed. Conventional ﬁnite

element method (FEM) can be used down to few tens of nanometer scale although

its applicability is questionable at nanoscale. FEM has been used for simulation and

prediction of residual stresses and strains induced in MEMS devices during fabrica-

tion [66], to perform fault analysis in order to study MEMS faulty behavior [67], to

compute mechanical strain resulting from doping of silicon [68], analyze microme-

chanical experimental data [46,69,70],and nanomechanicalexperimentaldata [62].

FEM analysis of nanostructures has been carried out to analyze the eﬀect of types

of surface roughness and scratches on stresses in nanostructures [71,72].

Commonly used materials for MEMS/NEMS are single-crystal silicon and

silicon-based materials (e.g., SiO

and polysilicon ﬁlms deposited by low pres-

sure chemical vapor deposition (LPCVD) process) [5]. An early study showed sili-

con to be a mechanically resilient material in addition to its favorable electronic

properties [73]. Single-crystal 3C-SiC (cubic or β-SiC) ﬁlms, deposited by atmo-

spheric pressure chemical vapor deposition (APCVD) process on large-area silicon

substrates are produced for high-temperature micro/nanosensor and actuator appli-

cations [74–76]. Amorphous alloys can be formed on both metal and silicon sub-

strates by sputtering and plating techniques, providing more ﬂexibilities in surface-

integration. Electroless deposited Ni

−

P amorphous thin ﬁlms have been used to

construct microdevices, especially using the so-called LIGA techniques [5,64].Mi-

cro/nanodevices need conductors to provide power as well as electrical/magnetic

signals to make them functional. Electroplated gold ﬁlms have found wide applica-

tions in electronic devices because of their ability to make thin ﬁlms and process

simplicity [64].

As the ﬁeld of MEMS/NEMS has progressed, alternative materials, especially

polymers have established an important role in the advancement of the tech-

744 Bharat Bhushan

nology. This trend has been driven by the reduced cost associated with poly-

mer materials. Polymer microfabrication processes, including the micromolding

and hot embossing techniques [77], can be orders of magnitude less expensive

than traditional silicon photolithography processes. The use of polymers in the

BioMEMS/BioNEMS ﬁeld has additional functional advantages, as polymers of-

fer a wide range of material properties to allow tailoring of biological interac-

tions for improved biocompatibility. Polymer BioMEMS structures involving mi-

crobeams have been designed to measure cellular forces [65]. Polymer materials

most commonly used for biomedical applications include poly(methyl methacry-

late) (PMMA), and poly(dimethylsiloxane) (PDMS) [77,78]. Another material of

interest due to ease of fabrication is poly(propyl methacrylate) (PPMA), which has

lower glass transition temperature (T

)(35−43

◦

C) [79] than PMMA (104−106

◦

[80,81], which permits low temperature thermal processing.

This chapter presents a review of mechanical property measurements on nano-

scale of various materials of interest and stress and deformation analyses of nano-

structures.

14.2 Experimental Techniques for Measurement

of Mechanical Properties of Nanostructures

14.2.1 Indentation and Scratch Tests Using Micro/Nanoindenters

A nanoindenter is commonly used to measure hardness, elastic modulus, and frac-

ture toughness, and to perform micro/nanoscratch studies to get a measure of

scratch/wear resistance of materials [5,82].

Hardness and Elastic Modulus

The nanoindenter monitors and records the dynamic load and displacement of the

three-sidedpyramidaldiamond(Berkovich)indenter duringindentationwith a force

resolution of about 75 nN and displacement resolution of about 0.1nm. Hardness

and elastic modulus are calculated from the load-displacement data [5, 82]. The

peak indentation load depends on mechanical properties of the specimen; a harder

material requires higher load for a reasonable indentation depth.

Fracture Toughness

The indentation technique for fracture toughness measurement of brittle samples,

on the microscale, is based on the measurement of the lengths of median-radial

cracks produced by indentation.A Vickers indenter (a four-sideddiamond pyramid)

is used in a microhardness tester. A load on the order of 0.5N is typically used in

making the Vickers indentations. The indentation impressions are examined using

an optical microscope with Nomarski interference contrast to measure the length of

median-radial cracks, c. The fracture toughness (K

) is calculated by the following

14 Mechanical Properties of Nanostructures 745

relation [83],

= α









, (14.1)

where α is an empirical constant depending on the geometry of the indenter, E and

H are hardness and elastic moduli, and P is the peak indentation load. For Vickers

indenters, α has been empirically found based on experimental data and is equal to

0.016 [5]. Both E and H values are obtained from the nanoindentation data. The

crack length is measured from the center of the indent to the end of crack using an

optical microscope.For one indent,all crack lengths are measured. The crack length

c is obtained from the average values of several indents.

Indentation Creep

For indentation creep test of polymer samples, the test is performed using a contin-

uous stiﬀness measurements (CSM) technique [82]. In a study by Wei et al. [65],

the indentation load was typically 30µN and the loading rate was 3 µN/s. The tip

was held typically for 600 s after the indentation load reached 30 µN. To measure

the mean stress and contact stiﬀness, during the hold segment the indenter was os-

cillated at a peak-to-peak load amplitude of 1.2 µN and a frequency of 45Hz.

Scratch Resistance

In micro/nanoscratch studies, in a nanoindenter, a conical diamond indenter having

a tip radius of about 1µm and an included angle of 60

◦

, is drawn over the sample

surface, and the load is ramped up until substantial damage occurs [5,82]. The co-

eﬃcient of friction is monitored during scratching. In order to obtain scratch depths

during scratching,the surface proﬁle of the sample surface is ﬁrst obtained by trans-

lating the sample at a low load of about 0.2 mN, which is insuﬃcient to damage

a hard sample surface. The 500 µm long scratches are made by translating the sam-

ple while ramping the loads on the conical tip over diﬀerent loads dependent upon

the material hardness. The actual depth during scratching is obtained by subtract-

ing the initial proﬁle from the scratch depth measured during scratching. In order to

measure the scratch depth after the scratch, the scratched surface is proﬁled at a low

load of 0.2mN and is subtracted from the actual surface proﬁle before scratching.

14.2.2 Bending Tests of Nanostructures Using an AFM

Quasi-static bending tests of ﬁxed nanobeam arrays are carried out using an AFM

[62, 84]. A three-sided pyramidal diamond tip (with a radius of about 200nm)

mounted on a rectangular stainless steel cantilever is used for the bending tests. The

beam stiﬀness is selected based on the desired load range. The stiﬀness of the can-

tilever beams for application of normal load up to 100µN is about 150–200N/m.

The wafer with nanobeam array is ﬁxed onto a ﬂat sample chuck using double-

stick tape [62]. For the bending test, the tip is brought over the nanobeam array with

746 Bharat Bhushan

Piezo

tube

scanner

Diamond tip/

steel cantilever

Photodetector

Laser-

diode

Nanobeam sample

Sample stage

AFM

piezo

Piezo

tube

scanner

beam

= D

piezo

– D

tip

beam

= F

tip

= stiffness of cantilever u D

tip

= sensitivity u

AFM

beam

Fig. 14.1. Schematic showing

the details of a nanoscale

bending test using an AFM.

The AFM tip is brought to

the center of the nanobeam

and the piezo is extended

over a known distance. By

measuring the tip displace-

ment, a load displacement

curve of the nanobeam can be

obtained [62]

the help of the sample stage of the AFM and a built-in high magniﬁcation optical

microscope Fig. 14.1. For the ﬁne positioning of the tip over a chosen beam, the

array is scanned in contact mode at a contact load of about 2 to 4 µN, which results

in a negligible damage to the sample. After scanning, the tip is located at one end of

a chosen beam. To position the tip at the center of the beam span, the tip is moved to

the other end of the beam by giving the X-piezo an oﬀset voltage. The value of this

oﬀset is determined afterseveral such attempts have been made in order to minimize

eﬀects of piezo drift. Half of this oﬀset is then applied to the X-piezo after the tip is

positionedat one endof the beam,which usuallyresults inthe tipbeing movedto the

center ofthe span. Once thetip is positionedoverthe center of the beam span, the tip

is heldstationary withoutscanning and theZ-piezo is extendedbya known distance,

typically about 2.5µm, at a rate of 10nm/s, as shown in Fig. 14.1. During this time,

the vertical deﬂection signal (dV

AFM

), which is proportional to the deﬂection of the

cantilever (D

tip

), is monitored. The displacement of the piezo is equal to the sum of

the displacements of the cantilever and the nanobeam. Hence the displacement of

the nanobeam (D

beam

) under the point of load can be determined as

beam

= D

piezo

−D

tip

. (14.2)

The load (F

beam

) on the nanobeam is the same as the load on the tip/cantilever(F

tip

)

and is given by

beam

= F

tip

= D

tip

×k , (14.3)