Bhushan B. Handbook of Micro/Nano Tribology, Second Edition

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a level of 2 · 10

–3

will cause an increase of

max

by a factor of 10, whereas doping with B to the same

level will lower the strain rate by a factor of 0.5 (Milvidskij et al., 1966).

Aging means that the mechanical properties of a material are changed by thermal, thermochemical,

or thermomechanical processes during a period of time. If a semiconductor is thermally aged at elevated

temperature in some process step, the Cottrell atmospheres around the dislocations may dissolve and

the yield limit will be correspondingly lowered. On return to lower temperature, the Cottrell atmospheres

Table 15.6 Microhardness Values Obtained by Vickers

Indentation at 50g Load (polarity effect neglected)

Indentation orientation

(GPa) 1 2

Si(111) 10.8 ± 1.3 [

–

110] [11

–

Si(100) 11.2 ± 1.0 [011] [0

–

11]

Si(110) 11.3 ± 1.1 [001] [1

–

10]

Ge(111) 9.2 ± 0.5 Undeﬁned

GaAs(100) 6.9 ± 0.3 [011] [0

–

11]

GaAs(100)(doped) 6.9 ± 0.1 Undeﬁned

GaAs(111) 7.0 ± 0.2 [

–

110] [11

–

InP(100) 4.3 ± 0.2 [011] [0

–

11]

InAs(polycrystalline) 3.5 ± 0.1 Undeﬁned

Orientations 1 and 2 are the two diagonals of the indentation mark.

Data from Ericson, F. et al., 1988, Mater. Sci. Eng. A 105/106, 131.

With permission.

FIGURE 15.6 Creep curves for silicon (Reppich et al.,

1964). (a) Varying applied stress at 900°C, and (b) varying

temperature at 5 MPa applied stress. (Adapted from Rep-

pich, B. et al., Acta Met. 12, 1283.)

will not always reestablish themselves, but the impurities instead prefer to form small, particle-like

precipitates, resulting in a maintained low yield limit, see Figure 15.5. Also, during plastic deformation

these precipitates may act as sources for generation of new dislocations, hence affecting the strain

hardening behavior of the material. For these reasons, the thermal history of a semiconductor material

is of great importance to its plasticity behavior.

Strain aging is a thermomechanical effect causing recovery of a plasticized material after unloading,

and a raised yield limit with yield drop upon reloading. Figure 15.7 shows examples of the strain aging

behavior of CZ-Si and FZ-Si at 800°C (Yasutake et al., 1982b). Other thermomechanical phenomena are

thermal chock and thermal fatigue. These effects are discussed in the Section 15.6.

As was previously mentioned, plastic deformation of a micromachined construction element usually

is detrimental to the structure, and is therefore avoided by a proper choice of materials, ample dimen-

sioning, or simply by avoiding overloads. On the other hand, micromachined structures offer one of the

few existing means of investigating the plasticity and the thermomechanical behavior of thin ﬁlms (Smith

et al., 1991; Kristensen et al., 1991a,b; Ericson et al., 1991).

15.6 Fracture Properties

15.6.1 Fracture Limit and Fracture Toughness

First of all, it is important to clarify the fact that the fracture limit is not a materials property, but essentially

a design property. This implies that the “intrinsic” strength properties of a material, for instance, expressed

FIGURE 15.7 Strain aging behavior at 800°C of (a)

Czochralski-grown Si and (b) ﬂoat-zone-grown Si.

(From Yasutake et al., 1982b.)

in terms of the interatomic bond strength, are of less importance to the overall strength of a component

than pure design factors such as geometric shape, surface roughness, how the load is applied, etc.

Obviously, the intrinsic strength is not completely without importance, and is sometimes used to deﬁne

an upper, theoretical strength limit, the so-called theoretical fracture limit, commonly given by

(15.30)

E is the Young’s modulus, γ is the surface energy, and a

is the distance between atomic planes parallel

to the crack plane. In a generalized representation, the γ value in Equation 15.30 should be the fracture

surface energy, i.e., one half of a cleavage energy including the broken bond energies as well as the energy

of the dynamic elastic stress ﬁeld around the propagating crack (this energy is eventually dissipated as

heat) and energy dissipated or stored by plastic deformation or other irreversible processes during

cracking. Usually σ

is of an order of E/10 or E/5, but the practical fracture limit often is several orders

of magnitude lower due to design factors.

Hence, the practical fracture limit, although important in design, is not a useful measure of the general

fracture strength of a material. A more useful concept is the fracture toughness ( = the critical stress

intensity factor) K

, which is considered to be a true, or nearly true, materials constant. For instance,

for a body containing a stress-concentrating sharp crack of length c perpendicular to the applied load,

is related to the effective fracture limit σ

of the body by:

(15.31)

Y is a dimensionless factor which equals 1.12 for a surface crack and 1/ for an interior crack. Both Y

and σ

are geometry dependent, but according to practical experience they are related in such a manner

that K

of Equation 15.31 becomes independent of crack geometry. Expressions similar to Equation 15.31

exist also for stress-concentrating geometries other than sharp cracks. The subscript “I” refers to fracture

of mode I type, i.e., tensile cracking perpendicularly to the applied load. Modes II and III are cracking

during longitudinal or transverse shearing, i.e., shearing in the crack propagation direction or transversely

to it, respectively. In brittle materials, modes II and III rarely occur.

Similarly to σ

of Equation 15.30, K

can be related to the surface energy and the Young’s modulus.

For plane strain, we have

(15.32)

and, for plane stress,

(15.33)

Combining Equations 15.30 and 15.33, we obtain a formal and simple relationship between the theoretical

fracture limit and the fracture toughness:

(15.34)

σγ

()

KYc

ccI

=πσ.

=−

()

[]

γν,

[]

γ .

coIth

=σ 2.

15.6.2 Some Fracture Data

In single-crystalline materials fracture data are anisotropic. In Table 15.7 fracture data for differently

oriented cleavage planes in Si are listed (Johansson et al., 1989). These data are interrelated by

Equations 15.33 and 15.34. It is seen that (111) is the low-energy cleavage plane, in agreement with

common experience. In practice, cleavage is sometimes observed also in (110) planes in Si, whereas

cleavage along (100) is difﬁcult to achieve. In GaAs the preferential cleavage planes are of (110) type

(Blakemore, 1982). Averaged (isotropic) fracture toughness data for a number of semiconductors have

been determined by indentation and solid particle erosion techniques (Ericson et al., 1988). Fracture

data from erosion experiments are listed in Table 15.8. In this case, the γ values have been calculated by

means of Equation 15.32.

Measured fracture stresses for single-crystalline Si microbeams can be very high: 6.1 GPa on the average

was found in one investigation (Ericson and Schweitz, 1990). For comparison, an extremely high-strength

steel has a fracture limit of ~1 GPa. Introduction of a thermal oxide ﬁlm 0.53 µm thick (which consumed

the top 0.23 µm of the Si surface) was found to raise the fracture strength to 7.2 GPa; subsequent removal

of the oxide by HF treatment lowered the strength marginally to 6.6 GPa, i.e., still 10% higher than the

original strength. This behavior is explained by the fact that all submicron damage present in the original

silicon surface was incorporated in the oxide ﬁlm. Possibly some of the damage was “healed” in the oxide

by the formation of oxygen bridges, which could explain the increased fracture limit of the oxidized

beam. But more important is that the elastic modulus of SiO

is much lower than for Si, and the stress

concentrations at the surface damage were correspondingly reduced. Subsequent removal of the oxide

by HF treatment also removed the original surface defects. The high fracture limit after removal indicates

that the resulting Si surface was less imperfect than the original surface. Tensile tests performed on surface

micromachined polysilicon structures show a widespread in the presented data. Greek et al. (1997)

presented measured fracture strength values of 566 and 768 MPa for two different polysilicon ﬁlms, while

Tsuchiya et al. (1997) presented values in the range of 2.0 to 2.7 GPa. The large difference between the

two investigations is mainly due to differences in techniques used to etch out the test specimens. The

TABLE 15.7 Fracture Data for Different Cleavage Planes in Si (Johansson

et al.,1989)

Fracture Plane E (GPa) a

(Å) K

(MPa m

1/2

) σ

(GPa) γ (Jm

–2

)

{100} 130 1.36 0.95 58 3.52

{110} 171 1.92 0.90 46 2.38

{111} 190 3.14 0.82 33 1.80

The K

values are taken from Chen et al. (1980).

TABLE 15.8 K

Values and γ Values Deduced

from Erosion Results

Specimen E (GPa) ν K

(MPa m

1/2

) γ (Jm

–2

)

Si 163 0.22 0.94 2.58

Ge 132 0.21 0.60 1.30

GaAs 116 0.24 0.44 0.79

InP 89 0.29 0.36 0.67

InAs 76 0.28 0.32 0.62

The E and ν values are for polycrystalline specimens.

Data from Ericson, F. et al., 1988, Mater. Sci. Eng.

A105/106, 131.

reactive ion-etching process in the case of Greek et al. (1997) introduced more severe surface defects on

their test specimens. Walker et al.

(1990) exposed thin polysilicon membranes to HF solutions of various

concentrations, and found opposite behavior; the fracture limits were drastically reduced. This result

might be because no surface defects were removed (since no oxidization was performed); on the contrary,

new defects might have been introduced by HF attacks on the grain boundaries.

The fracture strength of carefully bulk-micromachined GaAs has been found by Hjort et al. (1994) to

be 2.7 GPa, which is about one half of the Si value, but certainly high enough to satisfy most demands

on mechanical strength (several times higher than steel). The general notion that GaAs is extremely

fragile as compared to Si stems from the fact that wafers or components of GaAs often contain more

serious surface damage. This is a problem that is possible to overcome by a careful processing and gentle

handling of the specimens.

15.6.3 Fracture Initiation

Knowing the fracture toughness K

, and having experimentally determined the effective fracture limit

of the body in question, Equation 15.31 opens the possibility of a postfailure evaluation of the size c

of the defect which initiated the fracture. In brittle materials like micromachined silicon, fracture is

almost always initiated at some surface defect, and sharp, vertical cracks in the surface are the most

detrimental type of defects in this respect. Although we usually do not know the exact geometry of the

initiating surface ﬂaw, Equation 15.31 (with Y equal to 1.12) yields the c value of a defect which is

equivalent to the real defect from a fracture viewpoint, but with an assumed, known geometry.

For microbeams, bulk micromachined by conventional KOH etching in a (001) Si wafer, the initiating

defect size typically is of the order c ~ 10 nm (Johansson et al., 1988a, 1989; Ericson and Schweitz, 1990).

In beams oriented along an 〈110〉 direction, the initiating ﬂaws have been found to be twice as large as

in beams oriented along 〈100〉 type directions. The effective fracture limit was found to be correspondingly

lower in 〈110〉 beams than in 〈100〉 beams (~4 and ~6 GPa, respectively) (Johansson et al., 1989). These

results are consistent with the observation that (110)-cleavage is energetically more favorable than (100)-

cleavage (see Table 15.7), implying that the unintentional submicron cracks which initiate fracture might

be more extended in (110) planes. In the ﬁnal fracture process, on the other hand, “clean” fracture along

crystallographic planes only occurs for low-strength beams, i.e., beams containing a serious crack-

initiating defect. High-strength beams usually exhibit strongly irregular and “hackled” fracture surfaces.

This is in agreement with the theory of crack propagation, stating that low-velocity cracking (caused by

a low fracture limit) results in a smooth fracture surface — a so-called fracture mirror — whereas high-

velocity cracking results in hackled fractures. Hence, simple fractographic observations may yield some

qualitative information on the magnitude of the initiating defect.

15.6.4 Weibull Statistics

It is obvious from the discussion above that the size and shape distributions of the surface defects are of

crucial importance to the strength properties of a brittle component, and that a probabilistic approach

is called for. The most popular statistical theory of brittle fracture is due to Weibull (1939, 1951), and is

based on a weakest link argument.

The Weibull probability distribution function,

(15.35)

gives the probability of failure of a body which is exposed to a stress distribution σ

(x,y,z). The stressed

volume of the body is V, the stress σ

is a lower limit which is usually equal to zero in brittle materials,

xyz

=− −

()

−

























∫

exp

σσ

is a parameter related to the average fracture stress, and m is the Weibull modulus, which is a measure

of the statistical scatter displayed by the fracture events. A low m value indicates a large scatter, whereas

a high m value means low scatter. The Weibull modulus is an important measure of the engineering

reliability of a material used in design. For simple analysis, the stress distribution within a structure can

be expressed as

(15.36)

where σ

is the maximum applied stress and g is a function that depends on the geometry of the structure

and the load distribution. The fracture probabilities are calculated as

(15.37)

where n is the total number of fracture tests and i is the index of the fracture stress result in an array

where the values are written in ascending order.

A plot presenting the fracture probability as a function of applied stress for tensile tests on polysilicon

ﬁlm structures (Greek et al., 1997) is shown in Figure 15.8. The solid curve in Figure 15.8 is ﬁtted by the

chi-square method to the measured data, and the Weibull modulus, m, as well as σ

are derived from

this ﬁt. The expected mean fracture strength of the tests can be calculated from

(15.38)

where Γ(z) is the gamma function and h is given by

(15.39)

FIGURE 15.8 A plot showing the fracture probability as a function of the fracture stress from tensile tests of

micromachined polysilicon beams. The Weibull modulus m, σ

, as well as the expected mean fracture strength can

be determined from the ﬁtted curve. (Data from Greek, S. et al., 1997, Thin Solid Films, 292, 247–254.

σσ

xyz g,,

()

−













Γ ,

hgdV

∫

The expected mean fracture strength can also be deduced from the ﬁtted curve, see Figure 15.8, for P

0.5, and it is not equal to the arithmetical mean value. A Weibull modulus of 7 and an expected mean

fracture strength of 768 MPa was deduced from the tensile test experiments shown in Figure 15.8.

Use of probabilistic design allows a trade-off in material selection between high strength and low

scatter. An application requiring 0.99 reliability could be satisﬁed by, for example, a material with an

effective strength of 120 MPa and an m of 8, or a material with a strength of 94 MPa and an m of 10, or

a material with a strength of only 61 MPa and an m of 16. The advantage of probabilistic design is that

these trade-offs are possible and can be integrated into the design analysis. This ﬂexibility is not available

in empirical and deterministic approaches. One drawback of the Weibull method is that a large number

of tests (usually 100 or more) is required in order to determine the Weibull parameters with a reasonable

degree of statistical conﬁdence. Examples of typical Weibull moduli for different ceramic specimens are

given in Table 15.9.

15.6.5 Fatigue

Static fatigue is a slow fracture process that is given many names in the literature: delayed fracture, slow

crack growth, subcritical crack growth, secondary crack growth, or stress rupture. These names fairly well

describe the phenomenon: at some constant load (below the nominal fracture limit of the body) stress

concentrations at local defects in the material may cause an insidious crack growth. When the crack

reaches a certain critical size, the effective cross-sectional area of the specimen has been sufﬁciently

reduced as to make the specimen reach its nominal fracture limit, and a disastrous residual failure occurs.

This phenomenon is well known in many ceramic materials, e.g., glass and SiO

, and is partly considered

to be due to stress corrosion at the crack tip. Static fatigue of Si has been reported, but this result has been

disputed by others.

Dynamic fatigue is a fracture process caused by progressive crack growth during cyclic or intermittent

loading. Similarly to static fatigue, the crack growth is initiated at some local point of weakness (usually

in the surface) at a stress level which clearly falls below the nominal static fracture limit of the component.

The crack will grow a small distance with every load cycle, and sometimes cause a characteristic pattern

(so-called striations) in the fracture surface. When the effective cross section has been sufﬁciently reduced,

a sudden, residual rupture will occur. The dynamic fatigue behavior of a material can be determined in

a series of tests on identical specimens, where the amplitude of an applied, periodic load is systematically

varied, and the corresponding lifetimes of the specimens are measured. Such load-vs.-lifetime plots are

named Wöhler diagrams. Dynamic fatigue is a statistic phenomenon, and the theory is based on prob-

abilistic arguments. In extensive fatigue tests, failure probability distributions can be determined and

included in the diagram. Such Wöhler diagrams of PSN type (Probability of failure, Stress level, Number

of cycles) are sometimes used to adjust the load amplitude to a desired probability of failure during a

given lifetime. Dynamic fatigue is a fairly common phenomenon in metallic materials, where it is

attributed to dislocation slip in intersecting slip systems and to cross-slip. In brittle ceramic materials,

these mechanisms seldom operate at normal working temperatures, and consequently dynamic fatigue

is rare in this type of material. It has never been reported for silicon, and is unlikely to occur in this

material except perhaps under extreme thermal or environmental conditions.

TABLE 15.9 Typical Weibull Moduli m

of Different Ceramic Specimens

Material m

Glass 2–3

China 8

Silicon wafer 10

(reaction sintered) 10

SiC (pressure sintered) 18

(isotropic pressure sintered) 25–40

Thermal fatigue is a special case of dynamic fatigue where the load cycling is caused by temperature

changes and an associated variation in the thermal stress. The fatigue process is accelerated by the periodic

temperature peaks, which causes thermal destabilization of the material, activates corrosion processes,

speeds up diffusion processes, etc. Contrary to “normal” dynamic fatigue, which usually is of a high-

cycle character, thermal fatigue often is of low-cycle character. Thermal chock is a well-known problem

in brittle materials used for high-temperature applications. A rapid temperature change gives rise to a

steep thermal gradient in the body, which fractures under the inﬂuence of the high local thermostress

generated. Silicon and other conventional semiconductors are normally used in low-temperature appli-

cations and in chemically protected environments, and there is little reason to worry about thermal

fatigue or thermal chock under these conditions. In the near future, however, materials like Si

and

SiC will be frequently used in micromachined structures for high-temperature applications, and phe-

nomena such as thermal fatigue and thermal chock will have to be taken into consideration.

15.7 Adhesive Properties and Inﬂuence of Coatings

15.7.1 Adhesion

Adhesion is the single most important mechanical property of a ﬁlm–substrate composite because

without it the composite could not exist. It is of interest not only in the context of thin-ﬁlm adhesion

(Mittal, 1978; Valli, 1986), but equally so in all types of bonded or sealed structures (Johansson et al.,

1988b,c). In MST, ﬂaking is a frequently observed problem such as in silicon nitride ﬁlms on silicon

substrates. Similarly, the limited strength of bonded structures produced by, for example, ﬁeld-assisted

bonding (anodic bonding) or Si direct bonding (fusion bonding) has been a problem to many workers.

Sometimes a deposited ﬁlm will ﬂake or spall off spontaneously as a result of strong internal stresses in

the system. In other cases ﬂaking is the result of external bending moments. In yet other cases neither

internal nor external causes seem to be able to detach the ﬁlm; it just sticks to the substrate for good.

Sometimes a careful pretreatment of the surface combined with an equally careful optimization of the

deposition parameters is sufﬁcient to produce a well-adhered ﬁlm.

Bad “mating” properties often are due to contaminants or oxides in the surfaces to be bonded, or to

factors like crystalline misﬁt and thermal or elastic mismatch. Also the fundamental chemical afﬁnity

between the two materials, i.e., their mutual attraction or repulsion when it comes to forming interatomic

bonds, is of importance. The latter factor, however, is not as important as one might assume at ﬁrst sight,

as will be further discussed below.

Reports of micromechanical adhesion tests are scarce in the literature, due partly to experimental

difﬁculties and evaluation problems. However, since adhesion testing frequently turns up as an issue in

discussions concerning layered structures, it is useful to highlight a few aspects of theory and practice.

Note that unintentional sticking or stiction, due to electrostatic, van der Waals, or other weak interaction,

is a different problem which is not included in this context.

Adhesive strength is commonly associated with the work required to break up the interface into two

free surfaces, and therefore it is sometimes deﬁned as the sum of the two free surface energies. This is

an improper deﬁnition, however, since it excludes the chemical afﬁnity. Disregarding all types of oxides

and interfacial contaminants, a better deﬁnition is

(15.40)

which expresses the adhesive strength γ

adh

between materials A and B as a negative energy per unit area.

This deﬁnition comprises one large, negative (attractive) term involving the two free surface energies γ

and γ

, and another smaller term accounting for the chemical afﬁnity γ

chem

between A and B. The latter

term can be either negative (attractive) or positive (repulsive) and, hence, tends to strengthen or weaken

γκγγγ

AB A B AB

adh s s chem

=− +

()

+ ,

the interfacial bond. In the theory of alloy formation, chemical afﬁnity is commonly expressed in terms

of the heat of solution of A in B. The factor κ included in the ﬁrst term accounts for the atomic misﬁt

at the interface. For no atomic misﬁt κ equals unity; otherwise it is less than unity. For example, in a

large-angle grain boundary κ is about 0.85 (Öberg et al., 1985). Since this way of deﬁning adhesive

strength is based on the work required to separate the two materials, the surface energies γ

and γ

are

fracture surface energies which were previously deﬁned in Equation 15.30.

The observation that the last term of Equation 15.40 is nearly always much smaller than the ﬁrst term

illustrates the interesting fact that a well-adjusted deposition or bonding process can produce strong

adhesion even when the chemical afﬁnity between the two materials is positive (repulsive).

Commonly in adhesion or bond-strength tests, a high-quality bond does not fracture in the interface

but instead fractures nearby. The cracking usually occurs in the weaker of the two constituent materials,

close to the interface, and runs parallel to it (Johansson et al., 1988b). A customary interpretation of this

behavior is that the interface is “stronger than the weaker of the two materials.” However, this is usually

a misconception. Closer investigation of the fracture surface normally reveals that the cracking has indeed

initiated at a ﬂaw somewhere in the interface, and then has rather abruptly veered into one of the two

bulk materials and, at some small distance from the interface, turned again to run parallel to it. This

behavior does not reﬂect the high strength of the interface, but rather the asymmetric stress that develops

during interfacial cracking between dissimilar materials.

15.7.2 Inﬂuence of Coatings

When discussing adhesive strength, interfacial cracking or delamination comes naturally into the argu-

ment. However, even in composites that do not delaminate under an applied load the fracture properties

of the coatings are of interest from two different aspects: the fracture strength of the ﬁlms themselves

and their inﬂuence on the fracture strength of the substrate or composite. In this context we concentrate

on transverse fracture, i.e., crack propagation in planes more or less orthogonal to the interface between

ﬁlm and substrate.

Surface coatings may have drastic effects on the strength of a component (Johansson et al., 1989). For

instance, a hard brittle surface layer can reduce the fracture strength of an Si microbeam by as much as

a factor of 10, whereas a ductile surface layer instead may increase the fracture strength. These effects

depend on where in the layer–substrate composite fracture is initiated. An early cracking of a brittle

surface layer may generate signiﬁcant stress concentrations in the silicon substrate at the interface, and

hence cause premature failure of the component. A ductile surface layer, on the other hand, may reduce

the stress concentrations at microdefects in the silicon surface, and hence tend to postpone failure to

higher loads. In Table 15.10 the effect of a number of surface layers on the fracture strength of Si beams

TABLE 15.10 Reinforcement Factors f for Various

Coatings on Si Cantilever Beams Oriented along

〈110〉 and 〈100〉, Respectively Johansson et al. (1989)

Thickness Si<110> Si<100>

Coating (µm) ff

SiO

0.53 1.1 0.8

Al 0.41 — 1.0

Al 0.60 1.3 1.0

Ti 0.40 0.4 0.2

Ti 0.84 0.9 0.5

TiN 0.40 0.2 0.1

TiN 0.82 0.2 0.1

f > 1 implies strengthening, f < 1 implies weakening.

Data from Johansson, S. et al., 1989, J. Appl. Phys. 65,

122.

is illustrated in terms of a reinforcement factor f, which is larger than unity for strengthening and lower

than unity for weakening (Johansson et al., 1989). From this table it is seen that magnetron-sputtered

TiN can have a disastrous effect on the strength of the beams, whereas Al deposited by the same method

has shown a somewhat strengthening effect in one case. It should be pointed out, however, that the effect

of an Al coating is temperature dependent. High deposition or annealing temperatures may cause

diffusion of Al into the Si substrate — so-called spiking — which is detrimental to the strength. This

effect can be avoided by special measures.

Various types of crack initiation in layer composites are discussed by Johansson et al. (1989) in terms

of the fracture toughness concept. Fracture toughnesses are not easily determined for thin coatings. There

are, however, two interesting reports on a fracture toughness measurement on a released polysilicon ﬁlm

(Fan et al.,1990a; Kahn et al., 1996). In the experiment of Fan et al. (1990a) the test load was provided

by the internal stress of the system itself and in the other case by an external probe.

15.8 Testing

15.8.1 General Test Structures and Testing Methods

In micromechanical property characterization the most common specimen structures are free-standing

cantilever beams, bridges, or membranes. They are either a single-layer type, bulk or surface microma-

chined, or a two-layer type. In the latter case a thin substrate structure, e.g., a cantilever beam of silicon,

may have been produced by bulk or surface micromachining prior to the deposition of the ﬁlm. Alter-

natively, the ﬁlm can ﬁrst be deposited on the whole wafer, and the two-layer test structure fabricated

by surface micromachining or combined surface and bulk micromachining.

Evaluation of elasticity properties, internal stresses, fracture properties, and, to some extent, plasticity

properties by measurements on micromachined structures is performed by three main methods: (1) static

deﬂection, i.e., a micromachined layer is deﬂected out-of-plane by external or internal forces, (2) static

tension or compression, i.e., the structure is longitudinally strained in its plane, and (3) dynamic testing,

usually of resonant structures, i.e., different modes of vibration are somehow excited in the structure.

Since the mechanical properties are of major concern within the ﬁeld of MST, most measurements

using micromachined structures have been made on materials used for MST, primarily silicon. However,

investigations on polymers, metals, and ceramic materials have also been performed, and the present

subsection aims to review these. We start with static or quasi-static measuring techniques, then proceed

to dynamic testing.

15.8.2 Elasticity Testing by Static Techniques

Several different techniques for measuring elastic properties of micromachined structures have been

devised, for example, bending experiments on cantilever beams. Such experiments require high-resolu-

tion micromechanical test equipment capable of simultaneous measurement of applied force and beam

deﬂection on microsized specimens. Equipment capable of this is the Nanoindenter (Doerner et al., 1987;

Weihs et al., 1988, 1989; Hong et al., 1989; Vinci and Braveman, 1991; ) with a load resolution of 0.25 µN

and a displacement resolution of 0.2 nm.

Using the Nanoindenter on single-layer beams, E values in reasonable agreement with literature data

have been measured for Si, thermal and low-temperature SiO

, and for Au (Weihs et al., 1988, 1989).

The same technique has also been used to determine E values of nitride ﬁlms in SiN

/SiO

two-layer

beams (Hong et al., 1989).

As will be further discussed below, from an error analysis viewpoint the best way to measure elastic

moduli is by direct tensile testing. Several investigations have been carried out in this ﬁeld during the

last years. The most difﬁcult part during a tensile test on a microscale is to measure the true strain in

the test specimen. A solution to that problem was presented by Sharpe et al. (1997) where thin gold lines

were deposited in a square shape onto surface-micromachined polysilicon test specimens. By using an