Bhushan B. Nanotribology and Nanomechanics: An Introduction

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130 Jason H. Hafner

0.1 to 1 nA. As in AFM, a piezo-scanner rasters the sample under the tip, and the

Z-position is adjusted to hold the tunneling current constant. The Z-position data

represents the “topography”, or in this case the surface, of constant electron den-

sity. As with other SPMs, the tip properties and performance greatly depend on the

experiment being carried out. Although it is nearly impossible to prepare a tip with

a known atomic structure, a number of factors are known to aﬀect tip performance,

and several preparation methods have been developed that produce good tips.

The nature of the sample being investigated and the scanning environment will

aﬀect the choice of the tip material and how the tip is fabricated. Factors to consider

are mechanicalproperties – a hardmaterial that will resist damageduring tip-sample

contact is desired. Chemical properties shouldalso be considered – formationof ox-

ides, or other insulatingcontaminants willaﬀecttip performance.Tungstenis acom-

mon tip material because it is very hard and will resist damage, but its use is limited

to ultrahigh vacuum (UHV) conditions, since it readily oxidizes. For imaging un-

der ambient conditions an inert tip material such as platinum or gold is preferred.

Platinum is typically alloyed with iridium to increase its stiﬀness.

3.3.1 Mechanically Cut STM Tips

STM tips can be fabricated by simple mechanical procedures such as grinding or

cutting metal wires. Such tips are not formed with highly reproducible shapes and

have a large openingangle and a large radiusof curvaturein the range of 0.1to1µm

(see Fig. 3.18a). They are not useful for imaging samples with surface roughness

above a few nanometers. However, on atomically ﬂat samples, mechanically cut

tips can achieve atomic resolution due to the nature of the tunneling signal, which

drops exponentially with tip-sample separation. Since mechanically cut tips contain

many small asperities on the larger tip structure, atomic resolution is easily achieved

as long as one atom of the tip is just a few angstroms lower than all of the others.

0.5 μm

50 μm

Fig. 3.18. A mechanically cut STM tip (left) and an electrochemically etched STMtip (right),

from [35]

3 Probes in Scanning Microscopies 131

3.3.2 Electrochemically Etched STM Tips

For samples with more than a few nanometersof surface roughness,the tip structure

in the nanometer-size range becomes an issue. Electrochemical etching can provide

tips with reproducible and desirable shapes and sizes (Fig. 3.18), although the exact

atomic structure of the tip apex is still not well controlled. The parameters of elec-

trochemicaletching depend greatly on the tip material and the desired tip shape. The

following is an entirely general description. A ﬁne metal wire (0.1–1 mm diameter)

of the tip material is immersed in an appropriate electrochemical etchant solution.

A voltage bias of 1–10V is applied between the tip and a counterelectrode such

that the tip is etched. Due to the enhanced etch rate at the electrolyte-air interface,

a neck is formed in the wire. This neck is eventually etched thin enough so that it

cannot support the weight of the part of the wire suspended in the solution, and it

breaks to form a sharp tip. The widely varying parameters and methods will be not

be covered in detail here, but many recipes are found in the literature for common

tip materials [36–39].

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Noncontact Atomic Force Microscopy

and Related Topics

Franz J. Giessibl, Yasuhiro Sugawara, Seizo Morita, Hirotaka Hosoi,

Kazuhisa Sueoka, Koichi Mukasa, Akira Sasahara, and Hiroshi Onishi

Summary. Scanning probe microscopy (SPM) methods such as scanning tunneling mi-

croscopy (STM) and noncontact atomic force microscopy (NC-AFM) are the basic technolo-

gies for nanotechnology and also for future bottom-up processes. In Sect. 4.2, the principles

of AFM such as its operating modes and the NC-AFM frequency-modulation method are

fully explained. Then, in Sect. 4.3, applications of NC-AFM to semiconductors, which make

clear its potential interms of spatial resolution andfunction, are introduced. Next, in Sect. 4.4,

applications of NC-AFM to insulators such as alkali halides, ﬂuorides and transition-metal

oxides are introduced. Lastly, in Sect. 4.5, applications of NC-AFM to molecules such as car-

boxylate (RCOO

−

) with R=H, CH

,C(CH

)

and CF

are introduced. Thus, NC-AFM can

observe atoms and molecules on various kinds of surfaces such as semiconductors, insulators

and metal oxides with atomic or molecular resolution. These sections are essential to under-

stand the state of the art and future possibilities for NC-AFM, which is the second generation

of atom/molecule technology.

4.1 Introduction

The scanning tunneling microscope (STM) is an atomic tool based on an electric

method that measures the tunneling current between a conductive tip and a conduc-

tive surface. It can electrically observe individual atoms/molecules. It can charac-

terize or analyze the electronic nature around surface atoms/molecules. In addition,

it can manipulate individual atoms/molecules. Hence, the STM is the ﬁrst genera-

tion of atom/molecule technology. On the other hand, the atomic force microscopy

(AFM) is a unique atomic tool based on a mechanical method that can even deal

with insulator surfaces. Since the inventionof noncontact AFM (NC-AFM) in 1995,

the NC-AFM and NC-AFM-based methods have rapidly developed into powerful

surface tools on the atomic/molecular scales, because NC-AFM has the following

characteristics: (1) it has true atomic resolution, (2) it can measure atomic force

(so-called atomic force spectroscopy), (3) it can observe even insulators, and (4) it

can measure mechanical responses such as elastic deformation. Thus, NC-AFM is

the second generation of atom/molecule technology. Scanning probe microscopy

136 Franz J. Giessibl et al.

(SPM) such as STM and NC-AFM is the basic technology for nanotechnology and

also for future bottom-up processes.

In Sect. 4.2, the principles of NC-AFM will be fully introduced. Then, in

Sect. 4.3, applicationsto semiconductorswill be presented. Next,in Sect. 4.4, appli-

cations to insulators will be described. And, in Sect. 4.5, applications to molecules

will be introduced. These sections are essential to understanding the state of the art

and future possibilities for NC-AFM.

4.2 Atomic Force Microscopy (AFM)

The atomic force microscope (AFM), invented by Binnig [1] and introduced in

1986 by Binnig, Quate and Gerber [2] is an oﬀspring of the scanning tunneling

microscope (STM) [3]. The STM is covered in several books and review articles,

e.g. [4–9]. Early in the developmentof STM it became evident that relatively strong

forces act betweena tip in close proximityto a sample. It wasfound that these forces

could be put to good use in the atomic force microscope (AFM). Detailed informa-

tion about the noncontact AFM can be found in [10–12].

4.2.1 Imaging Signal in AFM

Figure 4.1 shows a sharp tip close to a sample. The potential energy between the

tip and the sample V

causes a z component of the tip–sample force F

= −∂V

/∂z.

Dependingon the mode of operation,the AFM uses F

, or some entity derivedfrom

, as the imaging signal.

Unlike the tunneling current, which has a very strong distance dependence, F

has long- and short-range contributions. We can classify the contributions by their

range and strength. In vacuum, there are van-der-Waals, electrostatic and magnetic

forces with a long range (up to 100 nm) and short-range chemical forces (fractions

of nm).

The van-der-Waals interaction is caused by ﬂuctuations in the electric dipole

moment of atoms and their mutual polarization. For a spherical tip with radius R

Tip

Sample

Fig. 4.1. Schematic view of an AFM tip close to a sample

4 Noncontact Atomic Force Microscopy and Related Topics 137

next to a ﬂat surface (z is the distance between the plane connecting the centers of

the surface atoms and the center of the closest tip atom) the van-der-Waals potential

is given by [13]:

vdW

= −

. (4.1)

The Hamaker constant A

depends on the type of materials (atomic polarizability

and density) of the tip and sample and is of the order of 1eV for most solids [13].

When the tip and sample are both conductive and have an electrostatic potential

diﬀerence U  0, electrostatic forces are important. For a spherical tip with radius

R, the force is given by [14]:

electrostatic

= −

πε

. (4.2)

Chemical forces are more complicated. Empirical model potentials for chemical

bonds are the Morse potential (see e.g. [13]).

Morse

= −E

bond



−κ(z−σ)

− e

−2κ(z−σ)



(4.3)

and the Lennard–Jones potential [13]:

Lennard–Jones

= −E

bond



−



(4.4)

These potentials describe a chemical bond with bonding energy E

bond

and equilib-

rium distance σ. The Morse potential has an additional parameter: a decay length κ.

4.2.2 Experimental Measurement and Noise

Forces between the tip and sample are typically measured by recording the deﬂec-

tion of a cantilever beam that has a tip mounted on its end (see Fig. 4.2). Today’s

microfabricated silicon cantilevers were ﬁrst created in the group of Quate [15–17]

and at IBM [18].

The cantilever is characterized by its spring constant k, eigenfrequency f

and

quality factor Q.

For a rectangular cantilever with dimensions w, t and L (see Fig. 4.2), the spring

constant k is given by [6]:

k =

(4.5)

where E

is the Young’s modulus. The eigenfrequency f

is given by [6]:

= 0.162



(4.6)

138 Franz J. Giessibl et al.

[

110]

[001]

Fig. 4.2. Top view and side view of a microfabricated silicon cantilever (schematic)

where ρ is the mass density of the cantilever material. The Q-factor depends on the

damping mechanisms present in the cantilever. For micromachined cantilevers op-

erated in air, Q is typically a few hundred,while Q can reach hundreds of thousands

in vacuum.

In the ﬁrstAFM, the deﬂection of the cantilever was measured with an STM; the

back side of the cantilever was metalized, and a tunneling tip was broughtclose to it

to measure the deﬂection [2]. Today’s designs use optical (interferometer, beam-

bounce) or electrical methods (piezoresistive, piezoelectric) to measure the can-

tilever deﬂection. A discussion of the various techniques can be found in [19], de-

scriptionsof piezoresistive detection schemes are found in [17,20] and piezoelectric

methods are explained in [21–24].

The quality of the cantileverdeﬂection measurement can be expressed in a sche-

matic plot of the deﬂection noise density versus frequency as in Fig. 4.3.

The noise density has a 1/ f dependence for low frequency and merges into

a constant noise density (white noise) above the 1/ f corner frequency.

4.2.3 Static AFM Operating Mode

In the static mode of operation, the force translates into a deﬂection q



= F

/k of

the cantilever, yielding images as maps of z(x, y, F

= const.). The noise level of

the force measurement is then given by the cantilever’s spring constant k times

the noise level of the deﬂection measurement. In this respect, a small value for k

increases force sensitivity. On the other hand, instabilities are more likely to oc-

cur with soft cantilevers (see Sect. 4.2.1). Because the deﬂection of the cantilever

should be signiﬁcantly larger than the deformation of the tip and sample, the can-

tilever should be much softer than the bonds between the bulk atoms in the tip and

sample. Interatomic force constants in solids are in the range 10–100N/m; in bio-

logical samples, they can be as small as 0.1N/m. Thus, typical values for k in the

static mode are 0.01–5N/m.

4 Noncontact Atomic Force Microscopy and Related Topics 139

1,000

100

0.1

0.1 1 100 10,000

f (Hz)

Spectral noise density of cantilever deflection (pm/Hz

0,5

)

1/f noise

1/f corner at f = f

with noise n

Fig. 4.3. Schematic view of 1/ f noise apparent in force detectors. Static AFMs operate in

a frequency range from 0.01 Hz to a few hundred Hz, while dynamic AFMs operate at fre-

quencies around 10 kHz to a few hundred kHz. The noise of the cantilever deﬂection sensor

is characterized by the 1/ f corner frequency f

and the constant deﬂection noise density n



for the frequency range where white noise dominates

Even though it has been demonstrated that atomic resolution is possible with

static AFM, the method can only be applied in certain cases. The detrimental eﬀects

of 1/ f-noise can be limited by working at low temperatures [25], where the coeﬃ-

cients of thermal expansion are very small or by building the AFM using a material

with a low thermal-expansion coeﬃcient [26]. The long-range attractive forces have

to be canceled by immersing the tip and sample in a liquid [26] or by partly com-

pensating the attractive force by pulling at the cantilever after jump-to-contact has

occurred [27]. Jarvis et al. have canceled the long-range attractive force with an

electromagnetic force applied to the cantilever [28]. Even with these restrictions,

static AFM does not produce atomic resolution on reactive surfaces like silicon, as

the chemical bonding of the AFM tip and sample poses an unsurmountable prob-

lem [29,30].

4.2.4 Dynamic AFM Operating Mode

In the dynamic operation modes, the cantilever is deliberately vibrated. There

are two basic methods of dynamic operation: amplitude-modulation (AM) and

frequency-modulation (FM) operation. In AM-AFM [31], the actuator is driven by

a ﬁxed amplitude A

drive

at a ﬁxed frequency f

drive

where f

drive

is close to f

.When

the tip approaches the sample, elastic and inelastic interactions cause a change

in both the amplitude and the phase (relative to the driving signal) of the can-

tilever. These changes are used as the feedback signal. While the AM mode was

initially used in a noncontant mode, it was later implemented very successfully at

a closer distance range in ambient conditions involving repulsive tip–sample inter-

actions.

140 Franz J. Giessibl et al.

The change in amplitude in AM mode does not occur instantaneously with

a change in the tip–sample interaction, but on a timescale of τ

≈ 2Q/ f

and the

AM mode is slow with high-Q cantilevers. However, the use of high Q-factors re-

duces noise. Albrecht et al. found a way to combine the beneﬁts of high Q and high

speed by introducing the frequency-modulation(FM) mode [32], where the change

in the eigenfrequency settles on a timescale of τ

≈ 1/ f

Using the FM mode, the resolution was improved dramatically and ﬁnally

atomic resolution [33, 34] was obtained by reducing the tip–sample distance and

working in vacuum. For atomic studies in vacuum, the FM mode (see Sect. 4.2.6) is

now the preferred AFM technique. However, atomic resolution in vacuum can also

be obtained with the AM mode, as demonstrated by Erlandsson et al. [35].

4.2.5 The Four Additional Challenges Faced by AFM

Some of the inherent AFM challenges are apparent by comparing the tunneling

current and tip–sample force as a function of distance (Fig. 4.4).

The tunneling current is a monotonic function of the tip–sample distance and

has a very sharp distance dependence. In contrast, the tip–sample force has long-

and short-range components and is not monotonic.

Jump-to-Contact and Other Instabilities

If the tip is mounted on a soft cantilever, the initially attractive tip–sample forces

can cause a sudden jump-to-contact when approaching the tip to the sample. This

–1

–2

–3

–4

0 5 10 15 20

z (Å)

(z) (nN) I

(z) (nA)

Short-range force (Morse potential)

Long-range (vdW) force

Total force

Tunneling current

Fig. 4.4. Plot of the tunneling current I

and force F

(typical values) as a function of the

distance z between the front atom and surface atom layer