Bhushan B. Nanotribology and Nanomechanics: An Introduction

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23 Mechanical Properties of Micromachined Structures 1315

Residual Stresses in Polysilicon

The residual stresses of LPCVD polysilicon have been thoroughly characterized us-

ingboth thewafercurvaturetechnique,discussedin Sect.23.1.1,and themicrostrain

gauges, discussed in Sect. 23.2.1. The results from both techniques give consistent

values. Figure 23.17 summarizes the residual stress measurements as a function of

deposition temperature taken from ﬁve diﬀerent investigations at ﬁve diﬀerent lab-

oratories [31]. All ﬁve sets of data show the same trend. The stresses change from

compressive at the lowest deposition temperatures to tensile at intermediate temp-

eratures and back to compressive at the highest temperatures. The exact transition

temperatures vary somewhat between the diﬀerent investigations, probably due to

diﬀerences in the deposition conditions: the silane or dichlorosilane pressure, the

gas ﬂow rate, the geometry of the deposition system, and the temperature unifor-

mity. However, in each data set the transitions are easily discernible. The origin of

these residual stress changes lies with the microstructure of the LPCVD polysilicon

ﬁlms.

As with all deposited ﬁlms, the microstructure of the LPCVD polysilicon ﬁlm is

dependent on the deposition conditions. In general, the ﬁlms are amorphous at the

lowest growth temperatures (lower than ∼ 570

◦

C), display ﬁne (∼0.1µm diameter)

grains at intermediate temperatures (∼ 570

◦

Cto∼ 610

◦

C), and contain columnar

(110)-textured grains with a thin ﬁne-grained nucleation layer at the substrate in-

terface at higher temperatures (∼ 610

◦

Cto∼ 700

◦

C) [31]. The ﬁne-grained mi-

crostructure results from the homogeneous nucleation and growth of silicon grains

within an as-deposited amorphoussilicon ﬁlm. In this regime, the deposition rate is

just slightly faster than the crystallization rate. The as-deposited ﬁlms will be crys-

talline near the substrate interface and amorphous at the free surface. (The amor-

phous fraction can be quickly crystallized by annealing above 610

◦

C.) The colum-

nar microstructure seen at higher growth temperatures results from the formation of

Residual stress (MPa)

Deposition temperature (°C)

550

600

400

200

–200

–400

–600

600 700650

Tensile

Compressive

Fig. 23.17. Results for resid-

ual stress of LPCVD poly-

silicon ﬁlms taken from ﬁve

diﬀerent investigations [31].

Data from the same investga-

tion are connected by a line

1316 Harold Kahn

crystalline silicon ﬁlms as-deposited, with growth being fastest in the 110 direc-

tions.

The origin of the tensile stress in the ﬁne-grainedpolysilicon arises from the vol-

ume decrease that accompanies the crystallization of the as-deposited amorphous

material. The origins of the compressive stresses in the amorphous and columnar

ﬁlms are less well understood. One proposed explanation for compressive stress

generation during thin ﬁlm growth postulates that an increase in the surface chem-

ical potential is caused by the deposition of atoms from the vapor; the increase in

surface chemical potential induces atoms to ﬂow into newly formed grain bound-

aries, creating a compressive stress in the ﬁlm [32].

Stress gradients are alsotypical ofLPCVD polysiliconﬁlms. The partially amor-

phous ﬁlms contain large stress gradients since they are essentially bilayers of com-

pressiveamorphoussilicon on top of tensile ﬁne-grainedpolysilicon.The fully crys-

talline ﬁlms also exhibit stress gradients. The columnar compressive ﬁlms are most

highly stressed at the ﬁlm–substrate interface, with the compressive stresses de-

creasing as the ﬁlm thickness increases; the ﬁne-grained ﬁlms are less tensile at

the ﬁlm–substrate interface, with the tensile stresses increasing as the ﬁlm thick-

ness increases [31]. Both stress gradients are associated with microstructural varia-

tions. For the columnar ﬁlms, the initial nucleation layer corresponds to a very high

compressive stress, which decreases as the columnar morphology develops. For the

ﬁne-grained ﬁlms, the region near the ﬁlm-substrate interface has a slightly smaller

average grain size, due to heterogeneousnucleation at the interface. This region dis-

plays a slightly lower tensile stress than the rest of the ﬁlm, since the increased grain

boundary area reduces the local density.

Young’s Modulus of Polysilicon

The Young’s modulus of polysilicon ﬁlms has been measured using all of the tech-

niques discussed in Sect. 23.2.2. A good review of the experimental results taken

from bulge testing, tensile testing, beam bending and lateral resonators are con-

tained in [33]. All of the reported results are in reasonable agreement, varying from

130 to175GPa, thoughmanyvaluesare reportedwith arelativelyhighexperimental

scatter. The main origin of the error in these results is the uncertainties involving the

geometries of the small specimens used to make the measurements. For example,

from (23.13), the Young’s modulus determined by the lateral resonators depends on

the cube of the tether beam width, typically about 2 µm. In general, the beam width

and other dimensions can be measured via scanning electron microscopy to within

about 0.1µm; however, the width of the beam is not perfectly constant along the

entire length or even throughout the thickness of the beam. These uncertainties in

geometry lead to uncertainties in modulus.

In addition, the various experimental measurements lie close to the Voigt and

Reuss bounds for Young’s modulus calculated using the elastic stiﬀnesses and com-

pliances for single-crystal silicon [33]. This strongly implies that Young’s moduli

of micro- and nanomachined polysilicon structures will be the same as for bulk

samples made from polysilicon. This is not unexpected, since Young’s modulus is

23 Mechanical Properties of Micromachined Structures 1317

a material property. It is related to interatomic interactions and should have no de-

pendence on the geometry of the sample. It should be noted that polysilicon can

display a preferred crystallographic orientation depending on the deposition con-

ditions, and that this could aﬀect the Young’s modulus of the material, since the

Young’s modulus of silicon is not isotropic. However, the anisotropy is fairly small

for cubic silicon.

A more recent investigation that utilized electrostatically actuated cantilevers

and interferometricdeﬂectiondetectionyielded a Young’s modulusof164 GPa [20].

They found the grains in their polysilicon ﬁlms to be randomly oriented, and calcu-

lated the Voigt and Reuss bounds to be 163.4–164.4GPa. This appears to be a very

reliable value for randomly oriented polysilicon.

Fracture Toughness and Strength of Polysilicon

Using the device shown in Fig. 23.13a and the specimen shown in Fig. 23.13d, the

fracturetoughness, K

, of polysilicon has been shown to be 1.0±0.1MPam

1/2

[34].

Several diﬀerent polysilicon microstructures were tested, including ﬁne-grained,

columnar and multilayered. Amorphous silicon was also investigated. All of the

microstructures displayed the same K

. This indicates that, like Young’s modulus,

fracture toughness is a material property,independent of the material microstructure

or the geometry of the sample.

A tensile test, such as that shown in Fig. 23.7 but using a sample with sharp

indentation-induced pre-cracks, yields a K

of 0.86MPam

1/2

[35]. The passive,

residual stress loaded beams with sharp pre-cracks shown in Fig. 23.6 gave a K

0.81MPam

1/2

[13].

Given that K

is a material property for polysilicon, the measured fracture

strength σ

crit

is related to K

= cσ

crit

(πa)

1/2

, (23.14)

where a is the crack-initiating ﬂaw size, and c is a constant of order unity. The

value for c will depend on the exact size, shape and orientation of the ﬂaw; for

a semicircular ﬂaw, c is equalto 0.71 [36]. Therefore,any diﬀerences in the reported

fracture strength of polysilicon will be the result of changes in a.

A good review of the experimental results available in the literature for polysi-

licon strength is contained in [37]. The tensile strength data vary from about 0.5 to

5 GPa. Like many brittle materials, the measured strength of polysilicon is found to

obey Weibull statistics. This implies that the polysilicon samples contain a random

distribution of ﬂaws of various sizes, and that the failure of any particular specimen

will occur at the largest ﬂaw that experiencesthe highest stress. One consequenceof

this behavior is that, since larger specimens have a greater probability of containing

larger ﬂaws, they will exhibit decreased strengths. More speciﬁcally, it was found

that the most important geometrical parameter is the surface area of the sidewalls

of a polysilicon specimen [37]. The sidewalls, as opposed to the top and bottom

surfaces, are those surfaces created by etching the polysilicon ﬁlm. This is not sur-

prising since LPCVD polysilicon ﬁlms contain essentially no ﬂaws within the bulk,

and the top and bottom surfaces are typically very smooth.

1318 Harold Kahn

As a result,the etching techniquesused to createthe structures willhavea strong

impact on the fracture strength of the material. For single-crystal silicon specimens

it was found that the choice of etchant could change the observed tensile strength

by a factor of two [38]. In addition, the bend strength of amorphous silicon was

measured to be twice that of polysilicon for specimens processed identically [34].

It was found that the reactive ion etching used to fabricate the specimens produced

much rougher sidewalls on the polysilicon than on the amorphous silicon.

The tensile strength of single crystal silicon has also been measuredusing a tech-

nique similar to that shown in Fig. 23.8. Sharp notches were introduced into the

beams using a focused ion beam, and the apparent fracture toughnesswas measured

for a variety of planes parallel to the notch front, along which the crack propagated.

For the {110} notch plane, the fracture toughness was about 1 MPam

1/2

, and for the

{100} notch plane it was about 2MPam

1/2

[39].

Fatigue of Polysilicon

Fatigue failure involves fracture after a number of load cycles, when each individual

load is not suﬃcient by itself to generate catastrophic cracking in the material. For

ductile materials, such as metals, fatigue occurs due to accumulated damage at the

site of maximum stress and involves local plasticity. As a brittle material, polysili-

con would not be expected to be susceptible to cyclic fatigue. However, fatigue has

been observed for polysilicontensile samples [35], polysilicon bend specimens with

notches [27,40], and polysilicon bend specimens with sharp cracks [41]. The exact

origins of the fatigue behavior are still subject to debate, but some aspects of the

experimental data are that the fatigue lifetime does not depend on the loading fre-

quency [35], the fatigue behavior is aﬀected by the ambient [13,41], and the fatigue

depends on the ratio of compressive to tensile stresses seen in the load cycle [13].

Friction of Polysilicon

The friction of polysilicon structures has been measured using the techniques de-

scribed in Sect. 23.2.2. The measured coeﬃcient of friction was found to vary

from 4.9 [29] to 7.8 [30].

The static and dynamic friction of polysilicon coated with monolayer lubri-

cants has been measured with a device similar to that shown in Fig. 23.15, but

using a scratch-drive actuator instead of a comb-drive [42]. The dynamic friction

at 0.2m/s was approximately 80% of the static friction value; the static friction at

zero applied load was due to an adhesive force of 0.95nN/µm

23.3.2 Mechanical Properties of Other Materials

As discussed above,of all the materials used for MEMS and NEMS, polysilicon has

generated the most interest as well as the most research in mechanical properties

characterization. However, measurements have been taken on other materials, and

these are summarized in this section.

23 Mechanical Properties of Micromachined Structures 1319

As discussed in Sect. 23.2.2, one advantage of the externally loaded tension

test, as shown in Fig. 23.7, is that essentially any material can be tested using this

technique. As such, tensile strengths have been measured to be 0.6 to 1.9GPafor

SiO

[43] and 0.7 to 1.1GPa for titanium [44]. The yield strength for electrode-

posited nickel was found to vary from 370 to 900MPa, depending on the annealing

temperature [16]. In addition, the yield strength was strongly aﬀected by the current

density during the electrodeposition process. Both the annealing and current density

eﬀects were correlated to changes in the microstructure of the material. Young’s

moduli were determined to be 100 GPa for titanium [44] and 215 GPa for electrode-

posited nickel [16].

The tensile strength, Young’s modulus, and Poisson’s ratio of silicon nitride

were measured to be 5.9GPa, 0.23 and 257GPa, respectively [45], and the same

properties of amorphous diamond-like carbon were found to be 7.3GPa,0.17 and

759GPa, respectively [46].

The technique of bending cantilever beams, shown in Fig. 23.8, can also be

performed on a variety of materials. The yield strength and Young’s modulus of

gold were found to vary from 260MPa and 57 GPa, respectively [19], to 300MPa

and 120GPa, respectively [47], using this method. The same properties in Al were

measured to be 150MPa and 80GPa, respectively [47], and in silicon nitride to be

6.9GPa and 260GPa, respectively [48]. Using a technique similar to that shown

in Fig. 23.8, except that a doubly-clamped beam was used instead of a cantilever

beam, the fracture toughness of ultrananocrystalline diamond was measured to be

4.5MPam

1/2

[49]. Resonating cantilever beams revealed a Young’s modulus for

gold of 47 GPa [50], and Young’s moduli of 1.8GPa and 14.4GPa for silica and

alumina aerogel thin ﬁlms, respectively [51].

Another technique that can be used with a number of materials is the membrane

deﬂection method, shown in Fig. 23.10. Silicon nitride measured with this tech-

nique revealed a Young’s modulus of 258 [45] to 325GPa and a burst strength of

7.1GPa [52]. A polyimide membrane gave a residual stress of 32 MPa, a Young’s

modulus of 3.0 GPa, and an ultimate strain of about four percent [21]. Membranes

were also fabricated from polycrystalline SiC ﬁlms with two diﬀerent grain struc-

tures [53]. The ﬁlm with (110)-texture columnar grains had a residual stress of

434MPa and a Young’s modulus of 349GPa. The ﬁlm with equiaxed (110)- and

(111)-textured grains had a residual stress of 446 MPa and a Young’s modulus of

456GPa.

Other devices that are used to measure mechanical properties require more

complicated micromachining, namely patterning, etching and release, in order to

operate. These devices are more diﬃcult to fabricate with materials that are not

commonly used as MEMS structural materials. However, the following examples

demonstrate work in this area. The structure shown in Fig. 23.5b was fabricated

fromSi

and revealeda apparentfracturetoughnessof 1.8MPam

1/2

[12].The de-

vices shown in Fig. 23.6 revealed a fracture toughness of SiC of 3.1MPam

1/2

[54].

Lateral resonators of the type shown in Fig. 23.11 were processed using polycrys-

talline SiC, and the Young’s modulus was determined to be 426GPa [55]. The de-

1320 Harold Kahn

vice shown in Fig. 23.12 was fabricated from polycrystalline germanium, and used

to measure a bend strength of 1.5GPa for unannealed Ge and 2.2GPa for annealed

Ge [56]. The same device was also fabricated from SiC and revealeda bend strength

of 23GPa [57]. Devices similar to that shown in Fig. 23.13 revealed the tensile

strength of silicon nitride to be 6.4GPa [52], and the Young’s modulus and yield

strength of aluminum to be 74.6GPa and 330MPa, respectively [58].

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Structural, Nanomechanical, and Nanotribological

Characterization of Human Hair Using Atomic Force

Microscopy and Nanoindentation

Bharat Bhushan · Carmen LaTorre

Summary. Human hair is a nanocomposite biological ﬁber. Maintaining the health, feel,

shine, color, softness, and overall aesthetics of the hair is highly desired. Hair care prod-

ucts such as shampoos and conditioners, along with damaging processes such as chemical

dyeing and permanent wave treatments, aﬀect the maintenance and grooming process and

are important to study because they alter many hair properties. Nanoscale characterization

of the cellular structure, mechanical properties, and morphological, frictional, and adhesive

properties (tribological properties) of hair are essential to evaluate and develop better cos-

metic products, and to advance the understanding of biological and cosmetic science. The

atomic/friction force microscope (AFM/FFM) and nanoindenter have become important tools

for studying the micro/nanoscale properties of human hair. In this chapter, we present a com-

prehensive review of structural, mechanical, and tribological properties of various hair and

skin as a function of ethnicity, damage, conditioning treatment, and various environments.

Various cellular structure of human hair and ﬁne sublamellar structures of the cuticle are

identiﬁed and studied. Nanomechanical properties such as hardness, elastic modulus, tensile

deformation, creep, and scratch resistance are discussed. Nanotribological properties such as

roughness, friction, and adhesion are presented, as well as investigations of conditioner dis-

tribution, thickness, and binding interactions. To study the electrostatic charge build up on

hair, surface potential studies are also presented.

24.1 Introduction

Everybody wants beautiful, healthy hair and skin. For most people, grooming and

maintenance of hair and skin is a daily process. The demand for products that im-

provethe look and feel of thesesurfaces has created a huge industryfor hair and skin

care. Beauty care technology has advanced the cleaning, protection, and restoration

of desirable hair properties by altering the hair surface. For many years, especially

in the second half of the twentieth century, scientists have focused on the physi-

cal and chemical properties of hair to consistently develop products which alter the

health, feel, shine, color, softness, and overall aesthetics of the hair. Hair care prod-

ucts such as shampoos and conditioners aid the maintenance and grooming process.

Shampoos clean the hair and skin oils, and conditioners repair hair damage and