Bhushan B. Nanotribology and Nanomechanics: An Introduction

Подождите немного. Документ загружается.

4 Noncontact Atomic Force Microscopy and Related Topics 151

dependence, between the dangling bond pointing out of the silicon dimer structure

on the Si(100)-(2×1) reconstructed surface and the dangling bond pointing out of

the apex of the silicon tip; a dimer structure is obtained with a larger separation than

between silicones on the surface.

The bright spots in Fig. 4.13 seem to be located at hydrogen atom sites on the

Si(100)-(2× 1):H monohydride surface, because the distance between the bright

spots forming the dimer structure (3.5±0.1Å) approximately agrees with the dis-

tance between the hydrogens, i.e., 3.52Å. Thus, the noncontact AFM atomically

resolved the individual hydrogen atoms on the topmost layer. On this surface, the

dangling bond is terminated by a hydrogen atom, and the hydrogen atom on the

topmost layer does not have chemical reactivity. Therefore, the interaction between

the hydrogen atom on the topmost layer and the apex of the silicon tip does not con-

tribute to the chemical bonding interaction with strong direction dependence as on

the silicon surface, and the bright spots in the noncontact AFM image correspondto

the hydrogen atom sites on the topmost layer.

4.3.3 Metal Deposited Si Surface

In this section, we will introduce the comparative study of force interactions be-

tween a Si tip and a metal-deposited Si surface, and between a metal adsorbed Si

tip and a metal-deposited Si surface [51,52]. As for the metal-deposited Si surface,

Si(111)-(

√

3×

√

3)-Ag (hereafter referred to as

√

3-Ag) surface was used.

For the

√

3-Ag surface, the honeycomb-chained trimer (HCT) model has been

accepted as the appropriate model. As shown in Fig. 4.5, this structure contains a Si

trimer in the second layer, 0.75Å below the Ag trimer in the topmost layer. The

topmost Ag atoms and lower Si atoms form covalent bonds. The interatomic dis-

tances between the nearest-neighbor Ag atoms forming the Ag trimer and between

the lower Si atoms forming the Si trimer are 3.43Å and 2.31 Å, respectively. The

apexes of the Si trimers and Ag trimers face the [11

2] direction and the direction

tilted a little to the [

112] direction, respectively.

In Fig. 4.15, we show the noncontact AFM images measured using a normal

Si tip at a frequency shift of (a) −37Hz, (b) −43 Hz and (c) −51 Hz, respectively.

These frequency shifts correspond to tip–sample distances of about 0–3Å. We de-

ﬁned the zero position of the tip–sample distance, i.e., the contact point, as the

point at which the vibration amplitude began to decrease. The rhombus indicates

the

√

3×

√

3 unit cell. When the tip approachedthe surface, the contrast of the non-

contact AFM images become strong and the pattern changed remarkably. That is,

by approachingthe tip toward the sample surface, the hexagonal pattern, the trefoil-

like pattern composed of three dark lines, and the triangle pattern can be observed

sequentially. In Fig. 4.15a, the distance between the bright spots is 3.9 ±0.2Å. In

Fig. 4.15c, the distance between the bright spots is 3.0±0.2Å, and the direction of

the apex of all the triangles composed of three bright spots is [11

2].

In Fig. 4.16, we show the noncontact AFM images measured by using Ag-

absorbed tip at a frequency shift of (a) −4.4Hz, (b) −6.9Hz and (c) −9.4Hz,

respectively. The tip–sample distances Z are roughly estimated to be Z = 1.9Å,

152 Franz J. Giessibl et al.

Top view

Side view

[112]

2.31 Å

6.65 Å

3.43 Å

0.75 Å

Fig. 4.14. HCT model for the structure of the Si(111)-(

√

3×

√

3)–Ag surface. Black closed

circle, gray closed circle, open circle,andclosed circle with horizontal line indicate Ag atom

at the topmost layer, Si atom at the second layer, Si atom at the third layer, and Si atom at

the fourth layer, respectively. The rhombus indicates the

√

3×

√

3 unit cell. The thick, large,

solid triangle indicates an Ag trimer. The thin, small, solid triangle indicates a Si trimer

0.6Åand≈ 0 Å (in the noncontact region), respectively. When the tip approached

the surface, the pattern of the noncontact AFM images did not change, although the

contrast become clearer. A triangle pattern can be observed. The distance between

the brightspots is3.5±0.2Å. The direction ofthe apex of all thetriangles composed

of three bright spots is tilted a little from the [

112] direction.

Thus, noncontact AFM images measured on Si(111)-(

√

3 ×

√

3)-Ag surface

showed two types of distance dependence in the image patterns depending on the

atom species on the apex of the tip.

4 Noncontact Atomic Force Microscopy and Related Topics 153

a) b) c)

[112]

~3.0 Å

[112]

~3.9 Å

Fig. 4.15. Noncontact AFM images obtained at frequency shifts of (a) −37 Hz, (b) −43 Hz,

and (c) −51 Hz on a Si(111)-(

√

3×

√

3)–Ag surface. This distance dependence was obtained

with a Si tip. The scan area is 38Å×34 Å. A rhombus indicates the

√

3×

√

3 unit cell

By using the normal Si tip with a dangling bond, in Fig. 4.15a, the measured

distance between the bright spot of 3.9 ±0.2Å agrees with the distance of 3.84Å

between the centers of the Ag trimers in the HCT model within the experimental

error. Furthermore, the hexagonal pattern composed of six bright spots also agrees

with the honeycombstructure ofthe Ag trimer in HCT model. So the most appropri-

ate site corresponding to the bright spots in Fig. 4.15a is the site of the center of Ag

trimers. In Fig. 4.15c, the measured distance of 3.0±0.2Å between the bright spots

forming the triangle pattern agrees with neither the distance between the Si trimer

of 2.31Å nor the distance between the Ag trimer of 3.43Å in the HCT model, while

the direction of the apex of the triangles composed of three bright spots agrees with

the [11

2] direction of the apex of the Si trimer in the HCT model. So the most ap-

propriate site corresponding to the bright spots in Fig. 4.15c is the intermediate site

between the Si atoms and Ag atoms. On the other hand, by using the Ag-adsorbed

tip, the measured distance between the bright spots of 3.5±0.2Å in Fig. 4.16 agrees

with the distance of 3.43Å between the nearest-neighborAg atoms forming the Ag

trimer in the topmost layer in the HCT model within the experimental error. Further-

more, the direction of the apex of the triangles composed of three bright spots also

~3.5Å

a) b) c)

[112]

Fig. 4.16. Noncontact AFM images obtained at frequency shifts of (a) −4.4Hz,(b) −6.9Hz,

and (c) −9.4 Hz on a Si(111)-(

√

3×

√

3)-Ag surface. This distance dependence was obtained

with the Ag-adsorbed tip. The scan area is 38 Å×34 Å

154 Franz J. Giessibl et al.

agrees with the direction of the apex of the Ag trimer, i.e., tilted [112], in the HCT

model. So, the most appropriate site corresponding to the bright spots in Fig. 4.16

is the site of individual Ag atoms forming the Ag trimer in the topmost layer.

It should be noted that, by using the noncontact AFM with a Ag-adsorbed tip,

for the ﬁrst time, the individual Ag atom on the

√

3-Ag surface could be resolved

in real space, although by using the noncontact AFM with an Si tip, it could not

be resolved. So far, the

√

3-Ag surface has been observed by a scanning tunneling

microscope (STM) with atomic resolution. However, the STM can also measure the

local chargedensity of statesnear the Fermilevelon the surface.From ﬁrst-principle

calculations, it was proven that unoccupied surface states are densely distributed

around the center of the Ag trimer. As a result, bright contrast is obtained at the

center of the Ag trimer with the STM.

Finally,we considerthe originof theatomic-resolutionimaging ofthe individual

Ag atoms on the

√

3-Ag surface. Here, we discuss the diﬀerence between the force

interactions when using the Si tip and the Ag-adsorbed tip. As shown in Fig. 4.17a,

when using the Si tip, there is a dangling bond pointing out of the topmost Si atom

on the apex of the Si tip. As a result, the force interaction is dominated by phys-

ical bonding interactions, such as the Coulomb force, far from the surface and by

chemical bonding interaction very close to the surface. Namely, if a reactive Si tip

with a dangling bond approaches a surface, at distances far from the surface the

Coulomb force acts between the electron localized on the dangling bond pointing

out of the topmost Si atom on the apex of the tip, and the positive charge distributed

around the center of the Ag trimer. At distances very close to the surface, the chem-

ical bonding interaction will occur due to the onset of orbital hybridizationbetween

the dangling bond pointing out of the topmost Si atom on the apex of the Si tip and

Dangling

bond

Adsorbed

Ag atom

Si tip

Fig. 4.17. Schematic illustra-

tion of (a) the Si atom with

dangling bond and (b)the

Ag-adsorbed tip above the

−

Ag covalent bond on

a Si(111)-(

√

3 ×

√

3)-Ag

surface

4 Noncontact Atomic Force Microscopy and Related Topics 155

aSi

−

Ag covalent bond on the surface. Hence, the individual Ag atoms will not be

resolved and the image pattern will change depending on the tip–sample distance.

On the other hand, as shown in Fig. 4.17b, by using the Ag-adsorbed tip, the dan-

gling bond localized out of topmost Si atom on the apex of the Si tip is terminated

by the adsorbed Ag atom. As a result, even at very close tip–sample distances, the

force interaction is dominated by physical bonding interactions such as the vdW

force. Namely, if the Ag-adsorbed tip approaches the surface, the vdW force acts

between the Ag atom on the apex of the tip and the Ag or Si atom on the surface.

Ag atoms in the topmost layer of the

√

3-Ag surface are located higher than the Si

atoms in the lower layer. Hence, the individual Ag atoms (or their nearly true topog-

raphy) will be resolved, and the image pattern will not change even at very small

tip–sample distances. It should be emphasized that there is a possibility to identify

or recognize atomic species on a sample surface using noncontact AFM if we can

control the atomic species at the tip apex.

4.4 Applications to Insulators

Insulators such as alkali halides, ﬂuorides, and metal oxides are key materials in

many applications, including optics, microelectronics, catalysis, and so on. Surface

properties are important in these technologies, but they are usually poorly under-

stood. This is due to their low conductivity, which makes it diﬃcult to investigate

them using electron- and ion-based measurement techniques such as low-energy

electrondiﬀraction,ion-scatteringspectroscopy,and scanningtunnelingmicroscopy

(STM). Surface imaging by noncontact atomic force microscopy (NC-AFM) does

not require a sample surface with a high conductivity because NC-AFM detects

a force between the tip on the cantilever and the surface of the sample. Since the

ﬁrst report of atomically resolved NC-AFM on a Si(111)-(7×7) surface [33], sev-

eral groups have succeeded in obtaining “true” atomic resolution images of insula-

tors, including defects, and it has been shown that NC-AFM is a powerful new tool

for atomic-scale surface investigation of insulators.

In this section we will describe typical results of atomically resolved NC-AFM

imaging of insulators such as alkali halides, ﬂuorides and metal oxides. For the al-

kali halides and ﬂuorides, we will focus on contrast formation, which is the most

important issue for interpreting atomically resolved images of binary compounds

on the basis of experimental and theoretical results. For the metal oxides, typical

examples of atomically resolved imaging will be exhibited and the diﬀerence be-

tween the STM and NC-AFM images will be demonstrated. Also, theoretical stud-

ies on the interaction between realistic Si tips and representative oxide surfaces will

be shown. Finally, we will describe an antiferromagnetic NiO(001) surface imaged

with a ferromagentic tip to explore the possibility of detecting short-range magnetic

interactions using the NC-AFM.

156 Franz J. Giessibl et al.

4.4.1 Alkali Halides, Fluorides and Metal Oxides

The surfaces of alkali halides were the ﬁrst insulating materials to be imaged by

NC-AFM with “true” atomic resolution [53]. To date, there have been reports on

atomically resolved images of (001) cleaved surfaces for single-crystal NaF, RbBr,

LiF, KI, NaCl, [54], KBr [55] and thin ﬁlms of NaCl(001) on Cu(111) [56]. In this

section we describe the contrast formation of alkali halides surfaces on the basis of

experimental and theoretical results.

Alkali Halides

In experiments on alkali halides, the symmetry of the observed topographic im-

ages indicates that the protrusions exhibit only one type of ions, either the positive

or negatively charged ions. This leads to the conclusion that the atomic contrast

is dominantly caused by electrostatic interactions between a charged atom at the

apex of the tip and the surface ions, i.e. long-range forces between the macroscopic

tip and the sample, such as the van der Waals force, are modulated by an alter-

nating short-range electrostatic interaction with the surface ions. Theoretical work

employing the atomistic simulation technique has revealed the mechanism for con-

trast formation on an ionic surface [57]. A signiﬁcant part of the contrast is due to

the displacement of ions in the force ﬁeld, not only enhancing the atomic corruga-

tions, but also contributing to the electrostatic potential by forming dipoles at the

surface. The experimentally observed atomic corrugation height is determined by

the interplay of the long- and short-range forces. In the case of NaCl, it has been ex-

perimentally demonstrated that a blunter tip produces a lager corrugation when the

tip–sample distance is shorter [54]. This result shows that the increased long-range

forces induced by a blunter tip allow for more stable imaging closer to the surface.

The stronger electrostatic short-range interaction and lager ion displacement pro-

duce a more pronounced atomic corrugation. At steps and kinks on an NaCl thin

ﬁlm on Cu(111), the corrugation amplitude of atoms with low coordination number

has been observed to increase by a factor of up to two more than that of atomically

ﬂat terraces [56]. The low coordination number of the ions results in an enhance-

ment of the electrostatic potential over the site and an increase in the displacement

induced by the interaction with the tip.

Theoretical study predicts that the image contrast depends on the chemical

species at the apex of the tip. Bennewitz et al. [56] have performed the calcula-

tions using an MgO tip terminated by oxygen and an Mg ion. The magnitude of

the atomic contrast for the Mg-terminated tip shows a slight increase in comparison

with an oxygen-terminated tip. The atomic contrast with the oxygen-terminated tip

is dominated by the attractive electrostatic interaction between the oxygen on the tip

apex and the Na ion, but the Mg-terminated tip attractively interacts with the Cl ion.

In other words, these results demonstrated that the species of the ion imaged as the

bright protrusions depends on the polarity of the tip apex.

These theoretical results emphasized the importanceof the atomic species at the

tip apex for the alkali halide (001) surface, while it is not straightforward to deﬁne

4 Noncontact Atomic Force Microscopy and Related Topics 157

the nature of the tip apex experimentally because of the high symmetry of the sur-

face structure. However, there are a few experiments exploring the possibilities to

determine the polarity of the tip apex. Bennewitz et al. [58] studied imaging of sur-

faces of a mixed alkali halide crystal, which was designed to observe the chemically

inhomogeneoussurface. The mixed crystal is composed of 60% KCl and 40% KBr,

with the Cl and Br ions interfused randomly in the crystal. The image of the cleaved

KCl

0.6

0.4

(001) surface indicates that only one type of ion is imaged as protru-

sions, as if it were a purealkali halide crystal. However, the amplitude of the atomic

corrugation varies strongly between the positionsof the ions imaged as depressions.

This variation in the corrugations corresponds to the constituents of the crystal, i.e.

the Cl and Br ions, and it is concludedthat the tip apex is negativelycharged. More-

over, the deep depressionscan be assigned to Br ions by comparing the numberwith

the relative density of anions. The diﬀerence between Cl and Br anions with diﬀer-

ent masses is enhanced in the damping signal measured simultaneously with the

topographic image [59]. The damping is recorded as an increase in the excitation

amplitude necessary to maintain the oscillation amplitude of the cantilever in the

constant-amplitude mode [56]. Although the dissipation phenomena on an atomic

scale are a subject under discussion, any dissipative interaction must generally in-

duce energy losses in the cantilever oscillation [60,61]. The measurement of energy

dissipation has the potential to enable chemical discrimination on an atomic scale.

Recently, a new procedure for species recognition on a alkali halide surface was

proposed [62]. This method is based on a comparison between theoretical results

and the site-speciﬁc measurement of frequency versus distance. The diﬀerences in

the force curves measured at the typical sites, such as protrusion, depression, and

their bridge position, are compared to the corresponding diﬀerences obtained from

atomistic simulation. The polarity of the tip apex can be determined, leading to the

identiﬁcation of the surface species. This method is applicable to highly symmetric

surfaces and is useful for determining the sign of the tip polarity.

Fluorides

Fluorides are important materials for the progress of an atomic-scale-resolutionNC-

AFM imaging of insulators. There are reports in the literature of surface images for

single-crystal BaF

,SrF

[63], CaF

[64–66] and a CaF bilayer on Si(111) [67].

Surfaces of ﬂuorite-type crystals are prepared by cleaving along the (111) planes.

Their structure is more complex than the structure of alkali halides, which have

a rock-salt structure. The complexity is of great interest for atomic-resolution imag-

ing using NC-AFM and also for theoretical predictions of the interpretation of the

atomic-scale contrast information.

The ﬁrst atomically resolved images of a CaF

(111) surface were obtained in

topographic mode [65], and the surface ions mostly appear as spherical caps. Barth

et al. [68] have found that the CaF

(111) surface images obtained by using the

constant-height mode, in which the frequency shift is recorded with a very low loop

gain, can be categorized into two contrast patterns. In the ﬁrst of these the ions

appear as triangles and in the second they have the appearance of circles, similar

158 Franz J. Giessibl et al.

to the contrast obtained in a topographic image. Theoretical studies demonstrated

that these two diﬀerent contrast patterns could be explained as a result of imag-

ing with tips of diﬀerent polarity [68–70]. When imaging with a positively charged

(cation-terminated) tip, the triangular pattern appears. In this case, the contrast is

dominated by the strong short-range electrostatic attraction between the positive tip

and the negative F ions. The cross section along the [121] direction of the trian-

gular image shows two maxima: one is a larger peak over the F(I) ions located in

the topmost layer and the other is a smaller peak at the position of the F(III) ions

in the third layer. The minima appear at the position of the Ca ions in the second

layer. When imaging with a negatively charged (anion-terminated)tip, the spherical

image contrast appears and the main periodicity is created by the Ca ions between

the topmost and the third F ion layers. In the cross section along the [121] direction,

the large maxima correspond to the Ca sites because of the strong attraction of the

negative tip and the minima appear at the sites of maximum repulsion over the F(I)

ions. At a position between two F ions, there are smaller maxima. This reﬂects the

weaker repulsion over the F(III) ion sites compared to the protruding F(I) ion sites

and a slower decay in the contrast on one side of the Ca ions.

The triangularpattern obtainedwith a positively charged tip appearsat relatively

large tip–sample distance, as shown in Fig. 4.18a. The cross section along the [121]

direction,experimentresultsand theoretical studies bothdemonstratethe large-peak

andsmall-shouldercharacteristicfor thetriangularpatternimage (Fig.4.18d).When

the tip approaches the surface more closely, the triangular pattern of the experi-

mental images is more vivid (Fig. 4.18b), as predicted in the theoretical works. As

the tip approaches, the amplitude of the shoulder increases until it is equal to that

of the main peak, and this feature gives rise to the honeycomb pattern image, as

shown in Fig. 4.18c. Moreover, theoretical results predict that the image contrast

changes again when the tip apex is in close proximity to surface. Recently, Giessibl

et al. [71] achieved atomic imaging in the repulsive region and proved experimen-

tally the predicted change of the image contrast. As described here, there is good

correspondence in the distance dependency of the image obtained by experimental

and theoretical investigations.

From detailed theoretical analysis of the electrostatic potential [72], it was sug-

gested that the change in displacement of the ions due to the proximity of the tip

plays an importantrole in the formation of the image contrast. Such a drastic change

in image contrast, depending on both the polarity of the terminated tip atom and on

the tip–sample distance, is inherent to the ﬂuoride (111) surface, and this image-

contrast feature cannot be seen on the (001) surface of alkali halides with a simple

crystal structure.

The results of careful experiments show another feature: that the cross sections

taken along the three equivalent [121] directions do not yield identical results [68].

It is thought that this can be attributed to the asymmetry of the nanocluster at the

tip apex, which leads to diﬀerent interactions in the equivalent directions. A bet-

ter understanding of the asymmetric image contrast may require more complicated

modeling of the tip structure. In fact, it should be mentioned that perfect tips on an

4 Noncontact Atomic Force Microscopy and Related Topics 159

Detuning (Hz)

Distance (nm)

0.0 0.5 1.0 1.5 2.0

Fig. 4.18. (a)–(c)CaF

(111) surface images obtained by using the constant-height mode.

From (a)to(c) the frequency shift was lowered. The white lines represent the positions of

the cross section. (d)–(f) The cross section extracted from the Fourier-ﬁltered images of (a)–

(c). The white and black arrows represent the scanning direction. The images and the cross

sections are from [68]

atomic scale can occasionally be obtained. These tips do yield identical results in

forwardand backwardscanning, and cross sections in thethree equivalentdirections

taken with this tip are almost identical [74].

The ﬂuoride (111) surface is an excellent standard surface for calibrating tips on

an atomic scale. The polarity of the tip-terminated atom can be determined from the

image contrast pattern (spherical or triangular pattern). The irregularities in the tip

structurecan be detected,since the surface structure is highly symmetric. Therefore,

once such a tip has been prepared, it can be used as a calibrated tip for imaging

unknown surfaces.

The polarity and shape of the tip apex play an important role in interpreting NC-

AFM images of alkali halide and ﬂuorides surfaces. It is expected that the achieve-

160 Franz J. Giessibl et al.

ment of good correlation between experimental and theoretical studies will help to

advance surface imaging of insulators by NC-AFM.

Metal Oxides

Most of the metal oxides that have attracted strong interest for their technological

importance are insulating. Therefore, in the case of atomically resolved imaging of

metal oxide surfaces by STM, eﬀorts to increase the conductivity of the sample are

needed, such as, the introduction of anions or cations defects, doping with other

atoms and surface observationsduring heating of the sample. However,in principle,

NC-AFM provides the possibility of observing nonconductivemetal oxides without

these eﬀorts. In cases where the conductivity of the metal oxides is high enough for

a tunneling current to ﬂow, it should be noted that most surface images obtained by

NC-AFM and STM are not identical.

Since the ﬁrst report of atomically resolved images on a TiO

(110) surface with

oxygen pointdefects [75], they havealso been reported on rutile TiO

(100)[76–78],

anataseTiO

(001)thinﬁlmonSrTiO

(100)[79]andonLaAO

(001)[80],SnO

(110)

[81],NiO(001)[82,83],SrTiO

(100)[84],CeO

(111)[85]andMoO

(010)[86]sur-

faces. Also, Barth et al. have succeeded in obtaining atomically resolved NC-AFM

imagesof acleanα

−

(0001)surface[73]andofaUHVcleavedMgO(001)[87]

surface, which are impossible to investigate using STM. In this section we describe

typical results of the imaging of metal oxides by NC-AFM.

The α

−

(0001) surface exists in several ordered phases that can reversibly

be transformed into each other by thermal treatments and oxygen exposure. It is

known that the high-temperature phase has a large (

√

31×

√

31)R±9

◦

unit cell.

However, the details of the atomic structure of this surface have not been revealed,

and two models have been proposed. Barth et al. [73] have directly observed this

reconstructed α

−

(0001) surface by NC-AFM. They conﬁrmed that the dom-

inant contrast of the low-magniﬁcation image corresponds to a rhombic grid repre-

senting a unit cell of (

√

31×

√

31)R+ 9

◦

, as shown in Fig. 4.19a. Also, more de-

tails of the atomic structures were determined from the higher-magniﬁcation image

(Fig. 4.19b), which was taken at a reduced tip–sample distance. In this atomically

resolved image, it was revealed that each side of the rhombus is intersected by ten

atomic rows, and that a hexagonal arrangement of atoms exists in the center of the

rhombi (Fig. 4.19c). This feature agrees with the proposed surface structure that

predicts order in the center of the hexagonal surface domains and disorder at the

domain boundaries. Their result is an excellent demonstration of the capabilities of

the NC-AFM for the atomic-scale surface investigation of insulators.

The atomic structure of the SrTiO

(100)-(

√

5x×

√

5)R26.6

◦

surface, as well as

that of Al

(0001)can be determined on the basis of the results of NC-AFM imag-

ing [84]. SrTiO

is one of the perovskite oxides, and its (100) surface exhibits the

many diﬀerentkinds of reconstructedstructures.In the case of the (

√

5×

√

5)R26.6

◦

reconstruction, the oxygen vacancy–Ti

–oxygen model (where the terminated sur-

face is TiO

and the observed spots are related to oxygen vacancies) was proposed

from the results of STM imaging. As shown in Fig. 4.20, Kubo et al. [84] have