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

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shows that nanohardness of silicon is higher that its bulk hardness. Figure 7.12 shows the plot of hardness

and Young’s modulus of elasticity as a function of residual depth. Note that hardness increases with a

decrease in the residual depth. Similar results on single-crystal silicon have been reported by Pethica et al.

(1983) and Page et al.

(1992) based on nanoindentation data obtained using commercial nanoindentors,

and by Bhushan and Koinkar (1994d) based on AFM data. Gane and Cox (1970) reported similar results

on gold based on microindenter data. This increase in hardness with a decrease in indentation depth can

be rationalized on the basis that, as the volume of deformed material increases, there is a higher probability

of encountering material defects (Bhushan and Koinkar, 1995d). The increase in hardness also could be

due to surface-localized cold work resulting form polishing.

The nano/picoindentation system has been used to study the creep and strain rate effects of ceramics.

Most materials, including ceramics and even diamond, are known to creep at temperatures well below

half their melting points, even at room temperature. Indentation creep and strain rate sensitivity exper-

iments were conducted on single-crystal silicon. Figure 7.13 shows the load–displacement curves for

various peak loads held at 180 s. To demonstrate the creep effects, the load–displacement curves for a

500-µN peak load held at 0 and 30 s are also shown as an inset. Note that signiﬁcant creep occurs at

room temperature. Nanoindenter experiments conducted by Li et al. (1991) exhibited signiﬁcant creep

only at high temperatures (greater than or equal to 0.25 times the melting point of silicon). The mech-

anism of dislocation glide plasticity is believed to dominate the indentation creep process. To study strain

rate sensitivity of silicon, experiments were conducted at two different (constant) rates of loading

(Figure 7.14). Note that a change in the loading rate of a factor of about ﬁve results in a change in the

load–displacement data. Strain rate sensitivity to single-crystal aluminum (111) has been reported by

LaFontaine et al. (1990).

Hardness of 5-nm- to 100-nm-thick DLC (a–c:H) ﬁlms have been measured by Kulkarni and Bhushan

(1997) and Koinkar and Bhushan (1997a). Figure 7.15a shows the load–displacement plots of silicon

(100) and various 20-nm coatings at 100-µN peak load. Peak indentation depth for silicon (100) at

100-µN load is 8.7 nm and those for sputtered, ion beam and cathodic arc carbon coatings are 7.8, 8.2,

and 6.4 nm, respectively. The residual depth is less than 1 nm for cathodic arc carbon coating at this

load. From the comparison of these coatings just on the basis of load–displacement data, cathodic arc

carbon exhibits the least displacement at the peak load. Representative load–displacement plots for

FIGURE 7.8

Example of nanofabrication. The letters “OHIO” (which stands for the state of Ohio) were generated

by scratching a Si(111) surface using a diamond tip at a normal load of 50 µN and writing speed of 0.2 µm/s.

(Bhushan, 1995b).

100-nm-thick carbon coatings at peak indentation load of 500 µN are shown in Figure 7.15b. Note again

that the cathodic arc carbon specimen exhibits the lowest indentation depth, about 20 nm, at the peak

load as compared with other coatings.

Figure 7.16a shows the plot of hardness as a function of residual depth for silicon(100) and various

carbon coating. The indentation loads used in each case ranged from 100 to 2000 µN. The cathodic arc

carbon coating exhibits the highest hardness of about 24.9 GPa, whereas the sputtered and ion beam

carbon coatings exhibit hardness values of 17.2 and 15.2 GPa, respectively. The hardness of silicon(100)

is 13.2 GPa. The elastic modulus as a function of residual depth is plotted in Figure 7.16b. The cathodic

arc carbon coating exhibits a decrease in the elastic modulus with increasing residual depth, while the

elastic moduli for the other carbon coatings remain almost constant.

In general, hardness and the elastic modulus of coatings are strongly inﬂuenced by their crystalline

structure, stoichiometry, and growth characteristics, which usually depend on the deposition parameters.

Mechanical properties of a–C:H coatings have been known to change over a wide range with

bonding ratio and amount of hydrogen. Hydrogen is believed to play an important role in the bonding

conﬁguration of carbon atoms by helping to stabilize tetrahedral coordination of carbon atoms.

FIGURE 7.9

(a) Trim and (b) spiral patterns generated by scratching a Si(100) surface using a diamond tip at a

normal load of 15 µN and writing speed of 0.5 µm/s.

7.6 Closure

AFM with suitable diamond tips has been used successfully to measure microscratching/microwear and

nano/picoindentation behavior of solid surfaces and thin ﬁlms. AFM has also been used for nanofabri-

cation/nanomachining purposes. Scratch and wear properties of single-crystal silicon have been mea-

sured. Scratch and wear depths increase with an increase of normal load. Wear rate for single-crystal

silicon is found to be negligible below 20 µN, is much higher at higher loads, and increases almost linearly

with load. Elastic deformation at low loads is responsible for negligible wear. The mechanism of material

removal on the microscale is studied. At the loads used in the study, material is removed by the plowing

mode in a brittle manner without much plastic deformation. Most of the wear debris is loose. Evolution

of the wear of thin DLC coatings has also been studied using AFM. Wear is found to be initiated at

nanoscratches. AFM has also been demonstrated to be useful for nanofabrication. AFM has been modiﬁed

to obtain load–displacement curves and for measurement of nanoindentation hardness and Young’s

modulus of elasticity, with depth of indentation as low as 1 nm. Hardness of ceramics on nanoscales is

found to be higher than that on the microscale. Ceramics exhibit signiﬁcant plasticity and creep on the

nanoscale.

Scratching and indentation on nanoscales are the powerful ways to screen for adhesion and resistance

to deformation of ultrathin ﬁlms. These studies are also directly applicable to interfacial phenomena of

MEMS devices.

(a)

FIGURE 7.10

(b)

FIGURE 7.10

(a) Load–displacement curves at various peak loads for Si(100). Arrows indicate the discontinuities

in the displacement; (b) AFM gray scale images of the indentations made at these peak loads. (Kulkarni, A. V. and

Bhushan, B. (1997),

J. Mater. Res.,

12, 2707–2714. With permission.)

FIGURE 7.11

Load–displacement curves during repeated loading–unloading cycles for Si(100) (Bhushan, B. et al.

(1996),

Philos. Mag.,

74, 1117–1128. With permission.)

TABLE 7.1

Comparison of Nanohardness and Young’s

Modulus of Elasticity of Single-Crystal Silicon (100) as a

Function of Normal Load

Normal

Load

(µN)

Residual

Depth

(nm)

Contact

Depth

(nm)

Hardness

(GPa)

Young’s

Modulus of

Elasticity

500 2.8 17.4 13.0 160

700 7.0 25.4 12.7 141

1000 8.5 32.2 13.2 143

1200 9.5 37.0 13.4 141

2000 15.0 55.3 13.1 141

Bulk values of hardness and Young’s modulus of elasticity

are 9 to 10 and 130 GPa, respectively.

FIGURE 7.12

Indentation hardness as a function of residual indentation depth for Si(100). (Bhushan, B. et al.

(1996),

Philos. Mag.,

74, 1117–1128. With permission.)

FIGURE 7.13

Creep behavior of single-crystal silicon. (Bhushan, B. et al. (1996),

Philos. Mag.,

74, 1117–1128. With

permission.)

FIGURE 7.14

Strain rate sensitivity of single-crystal silicon. (Bhushan, B. et al. (1996),

Philos. Mag.,

74, 1117–1128.

With permission.)

FIGURE 7.15

Load–displacement curves for (a) Si(100) and various 20-nm-thick DLC coatings at peak indentation

load of 100 µN and (b) for Si(100) and 100-nm-thick DLC coatings at peak indentation load of 500 µN. Arrow

indicates the discontinuity in the displacement. (Kulkarni, A. V. and Bhushan, B. (1997),

J. Mater. Res.

12, 2707–2714.

With permission.)

(a)

(b)

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