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

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Bhushan B. and Venkatesan, S. (1993c), “Friction and Wear Studies of Silicon in Sliding Contact with

Thin-Film Magnetic Rigid Disks,” J. Mater. Res. 8, 1611–1628.

Bhushan, B., and Koinkar, V.N. (1994a), “Tribological Studies of Silicon for Magnetic Recording Appli-

cations,” J. Appl. Phys. 75, 5741–5746.

Bhushan, B. and Koinkar, V.N. (1994b), “Nanoindentation Hardness Measurements Using Atomic Force

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Bhushan B., Koinkar, V.N., and Ruan, J. (1994c), “Microtribology of Magnetic Media,” Proc. Inst. Mech.

Eng. Part J: J. Eng. Tribol. 208, 17–29.

FIGURE 14.61 Friction force as a function of number of cycles using Si

tip at a normal force of 300 nN for

unlubricated and lubricated samples in ambient environment. Arrows in the ﬁgure indicate signiﬁcant changes in

the friction force because of removal of surface or lubricant ﬁlm. (From Koinkar, V.N. and Bhushan, B., 1996, J. Vac.

Sci. Technol. A 14, 2378–2391. With permission.)

FIGURE 14.62 Wear depth as a function of normal force using diamond tip for unlubricated and lubricated samples

after one cycle. (From Koinkar, V.N. and Bhushan, B., 1996, J. Vac. Sci. Technol. A 14, 2378–2391. With permission.)

Bhushan, B., Koinkar, V.N., and Ruan, J. (1994d), “Microtribological Studies by Using Atomic Force and

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Part II — Application to Magnetic Media,” ASME J. Tribol. 116, 389–396.

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FIGURE 14.63 Wear maps for unlubricated and lubricated samples after microwear using diamond tip. Normal

force used and wear depths are listed in the ﬁgure. (From Koinkar, V.N. and Bhushan, B., 1996, J. Vac. Sci. Technol. A

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Video Tapes,”

Wear 180, 9–16.

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Hard Amorphous Carbon Coatings as Thin as 5 nm for Magnetic Disks,” Surf. Coat. Technol. 76–77,

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Tip and Thin-Film Magnetic Rigid Disks by Friction Force Microscopy,” Adv. Info. Storage Syst. 6,

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Polysilicon Films for MEMS Devices,” Sensors Actuators A 57, 91–102.

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Surfaces Using Atomic Force/Friction Force Microscopy,” J. Vac. Sci. Technol. A 14, 2378–2391.

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Measurements,” J. Appl. Phys. 81, 2472–2479.

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Protective Coatings for Thin-Film Magnetic Disks and Heads,” Proc. Inst. Mech. Eng. Part J: J. Eng.

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Nanotechnology 2, 103–106.

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Contact Mechanics of Surfaces,” ASME J. Tribol. 112, 205–216.

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Rev. Lett. 68, 3323–3326.

Mate, C.M. (1993a), “Nanotribology of Lubricated and Unlubricated Carbon Overcoats on Magnetic

Disks Studied by Friction Force Microscopy,” Surf. Coat. Technol. 62, 373–379.

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Ericson, E.; et. al “Mechanical Properties of Materials in Microstructure...”

Handbook of Micro/Nanotribology.

Ed. Bharat Bhushan

Boca Raton: CRC Press LLC, 1999

Mechanical Properties

of Materials

in Microstructure

Technology

Fredric Ericson and Jan-Åke Schweitz

15.1 Introduction

15.2 Cohesion and Crystal Structures

System Energy and Interatomic Binding • Lattice Structures

and Structural Defects

15.3 Elasticity Properties

Isotropic Elasticity • Anisotropic Elasticity

15.4 Internal Stresses

Thermal Film Stress • Intrinsic Film Stress • Substrate and

Interface Stresses

15.5 Plasticity and Thermomechanical Properties

Elastic–Ductile Response • Time-Dependent Effects

15.6 Fracture Properties

Fracture Limit and Fracture Toughness • Some Fracture

Data • Fracture Initiation • Weibull Statistics • Fatigue

15.7 Adhesive Properties and Inﬂuence of Coatings

Adhesion • Inﬂuence of Coatings

15.8 Testing

General Test Structures and Testing Methods • Elasticity

Testing by Static Techniques • Elasticity Testing by Dynamic

Techniques • Testing of Other Properties

15.9 Modeling and Error Analysis

Single-Layer Beam • Two-Layer Beam • Resonant Beam •

Micro vs. Bulk Results

15.10 Summary and Conclusions

References

15.1 Introduction

Mechanical properties are of critical importance to any material that is used for transmission of forces

or moments, or just for sustaining loads. The gradual introduction of microcomponents in practical

applications within microstructure technology (MST) has instigated an increasing demand for insight

into the fundamental factors that determine the mechanical integrity of such elements, for instance, their

long-term reliability or how to choose proper safety limits in design and use. The mechanical integrity

of a microsystem is not only of importance in mechanical applications. It is not unusual that mechanical

(or thermomechanical) integrity is a prerequisite for reliable performance of microsystems with primarily

nonmechanical functions, e.g., electric, optic, or thermal.

Do we have enough knowledge about mechanical properties to determine the long-time reliability of

a micromechanical component or to choose proper safety limits? In general, the answer to this question

is negative. Are the properties of bulk materials applicable to microsystems? Again, we do not know for

certain in every case; we cannot even be absolutely sure that bulk data on the fundamental elastic constants

are valid for a micromachined element. Furthermore, the materials used in semiconductor technology

are usually well characterized from an electronic viewpoint, but from a mechanical viewpoint they are

in many cases more or less uncharted. In some cases we do not even have access to bulk data. This leads

to the conclusion that much more work is required on the systematic exploration of the mechanical

properties of microsized elements, as well as on the inﬂuence of the manufacturing processes on these

properties.

This chapter aims to deﬁne some basic concepts concerning mechanical properties, and to relate these

concepts to experimental procedures and to some practial design aspects. For many properties we give

numerical examples, if they exist, mostly concerning silicon and related materials. Sometimes compari-

sons of these materials with other types of materials are made. Silicon-based micromechanics is predom-

inant today. In the future, mechanically high-performing materials like SiC may be frequently used in

micromachined structures in high-temperature applications, for instance. For this reason, a number of

thermomechanical phenomena are brieﬂy deﬁned and discussed in this chapter.

15.2 Cohesion and Crystal Structures

15.2.1 System Energy and Interatomic Binding

Mechanical properties such as elasticity, plasticity, fracture strength, adhesion, internal stresses, etc.,

depend on the fundamental mechanisms of cohesion between atoms. Basically, the atoms in a solid

material are held together by electrostatic attraction between charges of opposite signs. Magnetic forces

are of minor importance to the cohesion. The potential energy of interatomic binding consists of terms

of classical electrostatic interaction as well as terms of electrostatic quantum interaction (exchange

effects). At equilibrium, the attractive potential energy U

is balanced by the repulsive kinetic energy

in a state of minimum system energy

(15.1)

see Figure 15.1. Neglecting boundary effects, the balance between potential and kinetic energy at equi-

librium is given by the virial theorem:

(15.2)

where

is positive (repulsive) and

is negative (attractive). In Figure 15.1 the parameter

represents

some measure that is proportional to the average interatomic distance, for instance, the lattice parameter.

If the state of equilibrium is shifted by external forces, compressive or tensile, the value of

will decrease

or increase, and the system will move along the curve of Figure 15.1 away from the state of minimum

system energy. The virial theorem is then modiﬁed into

ooo

UT=+,

20TU

+=,

(15.3)

where

= –

∂

is the force striving to restore equilibrium at minimum energy. For small deviations

from equilibrium,

is a harmonic function of

in most materials, and the restoring force

is a linear

function of the change in

. This is one way of expressing

Hooke’s law

of elasticity:

(15.4)

where

is the applied stress (force per area unit),

is the resulting strain

∆

, and

Young’s modulus

of the material. Hence, Young’s modulus (= linear modulus of elasticity) is proportional to the second

derivative of the system energy

with respect to the lattice parameter

at equilibrium (

Depending on the electron structure of the constituent atoms, the mechanism of cohesion can vary

from weak dipole interaction (van der Waals interaction) to strong covalent binding. In silicon the latter

type is predominant, but some materials of interest for micromachining also exhibit ionic binding or

metallic binding. In III-V semiconductors, for instance, the cohesion is of a mixed covalent and ionic

nature, and in tungsten metallic binding is predominant.

Ionic binding

is found in chemical compounds such as common salt, NaCl. One or more electrons are

transferred from one type of atom to the other, whereby electrostatic attraction between ions of opposite

electric charge occurs.

Metallic binding

occurs in metallic elements or compounds. In this case the loosely bound valence

electrons are disconnected from the atoms, and form a quasi-free electron gas, the conduction electron

gas. These electrons are at liberty to move between the ion cores and to a large extent also through them.

The high mobility of these electrons gives rise to the good electric conductivity found in most metals.

Hence, the positive ions are immersed in a sea of negative conduction electrons, which act as a ﬂuid

cement holding the ions together.

Covalent binding

is found in some elemental solids (e.g., silicon) as well as in very complicated

molecular structures (e.g., polymers). The cohesive mechanism is complex, but in a very simpliﬁed picture

it can be described in terms of negative-valence electrons preferring to locate themselves in the regions

between a positive ion and its nearest neighbors, by which an electrostatic coupling occurs. This type of

binding is usually strong and “directional”; i.e., the interatomic bonds are formed at speciﬁc angles,

resulting in well-deﬁned molecular or crystalline structures.

The strength of the interatomic bonds is decisive for the stiffness and the brittleness of the crystal.

Strong and directional covalent bonds give silicon high stiffness and strength. In GaAs the bonds are of

a mixed covalent and ionic type, making this material less stiff and more fragile than Si. Also the melting

points (Table 15.1) are affected by the bond strength.

FIGURE 15.1

Crystal system energy

vs. lattice

spacing parameter

2TU a

+=−

∂

σε= E ,